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rspa_1907_0047

0950-1207

On the two modes of condensation of water vapour on glass surfaces, and their analogy with James Thomson\#x2019;s curve of transition from gas to liquid

383

390

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Professor Fred. T. Trouton, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0047

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0047

10.1098/rspa.1907.0047

Thermodynamics

Fluid Dynamics

Thermodynamics

383 On the Two Modes of Condensation of Water Vapour on GlassSurfaces , and their Analogy James Thomson 's Curve of Transition from Gas to Liquid . By Professor Fred . T. Trouton , F.R.S. ( Received May 1 , \#151 ; Read June 6 , 1907 . ) Experiments were made , using glass wool as the substance on which the-condensation of water vapour was observed , in continuation of work published last year in the ' Proceedings of the Royal Society '* on the condensation of water vapour by wool and cotton . The apparatus used is similar to that previously employed except for an alteration to enable the material under examination to be raised in temperature for the purpose of drying . The general arrangement is shown in fig. 1 . The cylindrical bulb holds . Toll pump Fig. 1 . the material , and can be surrounded with a vessel of hot oil in order to dry it the more thoroughly . The branch tube on the left leads to the drying * ' Roy . Soc. Proc. , ' A , vol. 77 , 1906 . 384 Prof. Trouton . Two Modes of Condensation of [ May 1 , tube and air pump . On the right is the arrangement for supplying known .feeds of water freed from air . The volume of the feed is that of the fine bore tube lying between the two taps . Next it is the gauge for reading the vapour pressure . The glass wool used in these experiments was placed in the bulb seen on the left in the figure , and was dried in vacuo at 160 ' C. for about 70 hours by means of phosphorus pentoxide . The experiment after that consisted in feeding in water from time to time , and in observing the depression produced in the pressure gauge . The amount of water supplied at each feed was sufficient to saturate the bulb about four times over in the absence of the glass wool . The character of the curve connecting the pressure with the amount of water held by the glass wool was altogether different from that obtained wTith wool or cotton . The pressure increases with the quantity of water absorbed much more rapidly at first than with either of those substances ; but on reaching a certain critical value the further additions of water reduce the pressure . After that the pressure begins to again increase , with increase of water absorbed , finally passing to saturation in a similar manner to that with wool or cotton . In making these experiments , several days were allowed to intervene between successive feeds of wTater , as it was found that some time was required for equilibrium to be set up . In one series of experiments as long as 10 days was given between the feeds , but practically after three days no further change was observed to take place . This was the period allowed in all subsequent experiments . The following table ( p. 385 ) shows the results obtained in one series of experiments . The observations in Table I are shown plotted in fig. 2 . It will be seen that at about 0*6 cm . , or , roughly , at about one-half saturation , a rapid absorption sets in , suggesting a state of supersaturation . The final and initial parts of the curve lie well on the continuous one which has been drawn in as a dotted line . It will be also noticed that , after the breaking down of the stage of supersaturation , a small rise occurs in the actual observation . This has been ignored in drawing the curve , as in amount the variation is almost comparable with the errors of observation ; but , on the other hand , similar rises were obtained in the other experiments , suggesting that there may be minute alternations in the pressure following the first breaking down of the state of supersaturation . It is obvious from these observations that it could be arranged for a glass surface , holding a certain amount of water , to have a less vapour pressuie 1907 . ] Water Vapour on Glass , etc. Table I. Weight per square centimetre in arbitrary units . Pressure in centimetres . Weight per square centimetre in arbitrary units . Pressure in centimetres . Weight per square centimetre in arbitrary units . Pressure in centimetres . i 0-548 14 i 1 -102 27 1 -206 2 0-656 15 1 -1.29 29 1 -182 3 0-629 16 1 -126 31 1 -217 4 0-637 17 1 -131 33 1 -210 5 0-614 18 1 -136 34 1 -215 6 0-617 19 1 -140 35 1 -221 7 0-772 20 1*141 37 1 -202 8 0-961 21 1 -159 39 1-220 9 1 -024 22 1 -167 40 1 -221 10 1 -073 23 1 -158 41 1 -228 11 1-089 24 1 -180 43 1 -243 12 1 -095 25 1 -174 44 1-219 13 1 -093 26 1 -186 45 1 -225 The observed pressures have been reduced to a common temperature of 15 ' 0 . by means of the law of isoneres ( see 'Roy . Soc. Proc. , ' A , vol. 77 , 1906 , p. 292 ) . Fig. 2 . than a drier surface , and we are led to the remarkable conclusion that it is quite possible for a relatively wet surface to act as a drying agent to a surface drier than itself . Two other series of experiments were made , but were only carried as far as the point showing the diminution in pressure on the addition of further moisture . These experiments are shown plotted in figs. 3 and 4 . The supersaturation effect , bringing about this curious diminution in VOL. lxxix.\#151 ; a. 2 D 386 Prof. Trouton . Two Modes of Condensation of [ May 1 , pressure after a certain point is reached would seem to depend on processes taking place when a gas condenses on a solid , similar in character to those necessary to enable a gas to follow James Thomson 's curve of condensation of Fig. 3 . Fig. 4 . vapour to liquid . The isothermal on the pressure-volume curve was conceived by him as passing in a continuous manner from . the state of gas to that of liquid ( fig. 5 ) . Curves of this kind are given by any of the numerous characteristic gas-equations . Fig. 5 . That this mode of passage between these states is not one commonly followed is , perhaps , not surprising when we remember that the gas must be enclosed in an envelope in order to be compressed along an isothermal , and 1907 . ] Water Vapour on Glass Surfaces , etc. is , on reaching the point a , consequently in contact with material in virtually the liquid state , already deposited on the walls of the containing vessel through surface condensation or absorption at an earlier stage . In presence of this liquid the material passes over directly into the liquid form instead of traversing the continuous path . To expect the continuous process to take place , under these circumstances , is thus not unlike attempting to obtain a supersaturated solution in presence of a crystal of the dissolved salt . For a substance to follow freely the transition curve*from gas to liquid , the absence of other kinds of matter , even of an envelope , is essential . Such a condensation is conceivable when the material condenses under its own mutual gravitation in a place apart from all other attracting matter . We now turn to the corresponding case of a vapour becoming deposited on a surface of a solid through the mutual attraction between the particles of the solid and of the gas or , shortly , by " adsorption . " The law of force\#151 ; Laplace 's law , F = o-i\lt ; r2/ ( r)\#151 ; is probably the same for this case as for where the forces are between the particles of the gas itself , only the " densities " \lt ; rx and cr2 of the two attracting substances being different . Thus , we might expect a similar course of events to take place wffien under these forces condensation on a surface occurs , to that which takes place in the case of a gas following James Thomson 's curve . If this were so , the character of the curve ( fig. 2 ) experimentally found for the condensation or adsorption of water vapour on glass becomes explicable . When the pressure of the vapour in contact with a surface quite free from moisture gradually increases , the material at first condenses in a form which , for convenience , may be called the a form . The pressure goes up to a certain maximum value , after which it falls , owing to the material passing into the / 3 or liquid form along a James Thomson curve . After this , on addition of sufficient material , the pressure can be increased up to saturation . The question suggests itself : is there a case of adsorption of a vapour by a surface corresponding to the case of direct passage into the liquid from the gaseous state without going through the intermediate stage of the transition curve ? That is to say , if there were any of the material in the / 3 or liquid state , would direct conversion into that state take place in a manner analogous to the usual direct path of condensation on a gas liquefying ? The necessary condition\#151 ; the presence of material in the / 3 state\#151 ; for this form of condensation , was found to be obtained by drying the glass wool with phosphorus pentoxide at ordinary temperatures for a time only just sufficient to reduce the pressure of the vapour to zero. . The results obtained with the material so dried are given in Table II , and are shown plotted in fig. 6 . It will be seen that the curve , unlike the 388 Prof. Trouton . Two Modes of Condensation of [ May 1 , previous curve , begins by being concave to the pressure co-ordinate and is thus similar in this respect to those obtained with wool and cotton . Table II . Weight per square centi- Pressure in Weight per square centi- Pressure . metre in arbitrary units . * centimetres . metre in arbitrary units . m centimetres . 0-3 0 -0075 7-5 0-909 0-5 0 -010 8-3 0-989 1 -3 0-020 9-5 1-060 2-0 0-216 10 -7 1-165 3-0 0-480 12 -2 1 -243 3-8 0-583 12 -9 1-249 5 -0 0-698 13 -8 1 -271 6*0 0-688 14-8 1 -330 6-8 0-837 These pressures were reduced to a common temperature of 20 ' C. Observations were continued on to saturation , but are not given , as presenting nothing of interest . 9 io n 12 13 14 15 Fig. 6 . It is to be noticed that in this case , though the glass begins by being " wet " relatively to the glass in the previous case , yet a fresh quantity of water produces only a small increase in the pressure compared to what it produces when the glass is very dry . The presence , then , of condensed vapour , or liquid , gives a nucleus , so to speak , for further condensations , or affords an example for condensation which 1907 . ] Water Vapour on Glass etc. is absent in the case where more complete drying is effected . This would seem to require us to suppose that there are two modes in which the molecules of water in condensing can arrange themselves on the surface of the glass . Two other curves are given , fig. 7 and fig. 8 , where the drying was at ordinary temperature but was continued for a longer period . In all these a slight indication of supersaturation will be noticed at about the same pressure as for the dry case . This may be due to a mixed effect brought about by a small quantity of the material being really dry , so that there is a small amount of absorption thus reducing the pressure . Feeds i z 3 4 5 Fig. 7 . Feeds 1 Fig. 8 . The phenomenon described throws light on a curious observation which , no doubt , all have noticed who have worked much with phosphorus-pentoxide drying tubes . The absorption of vapour is seen to be apparently confined to certain parts of the tube , and there the pentoxide may actually liquefy , while at other points it remains apparently dry . The explanation is that the wetter portion may absorb moisture without the pressure going up sensibly , while the relatively dry material can only absorb if the pressure goes up . In fact , a wet portion might be used to dry a drier portion . A simple experiment to illustrate the effect can be easily made with two portions of phosphorus pentoxide in this way . Two small porcelain dishes are taken : one of these is dried by heating it red hot , while the other is left as it is with the usual condensed moisture from the atmosphere on it . Pentoxide is placed on both and they are then put under a bell-jar . In a short time signs of condensation in the form of small liquid globules will appear round the edge of the pentoxide on the undried dish along the line of contact with it , also , perhaps , at a few points of dust over the surface of both portions of pentoxide . As the drying proceeds , it will be seen to be almost entirely effected by the portion in the undried dish , the other , except for a few globules on the surface , remaining unwet . In fact , if there is the proper quantity of moisture present in the bell-jar , the one will run liquid 390 Two Modes of Condensation of Water , etc. while the other remains dry , except for the few specks mentioned . The action is , no doubt , due to the pentoxide in the first instance obtaining moisture from the porcelain surface which was left undried and thus forming a material to which moisture can be added , without the vapour pressure going rapidly up ; whereas in the case of the dry salt , the pressure has first to reach a maximum or critical value before free absorption can take place . We may expect similar effects to take place in the case of other vapours or gases , that is to say , for two modes of condensation of a gas on solid surfaces to be possible , or , shortly , for the surface density not to be a single valued function of the pressure . The variation in the pressure which is liable to take place in vacuum discharge tubes may , in part at least , be due to this phenomenon . Thus , with a given amount of gas in the tube , we would have the possibility of two stable modes of condensation , each with its own proper pressure . When the condensation is in the a state , the pressure is necessarily higher than when in the / 3 state , as less is on the glass . The running of the tube , we may suppose , forces gas to take up the / 3 state , which increases the proportion on the glass with a corresponding diminution in the pressure , while by means of external heating the a state may be restored with a rise in pressure . The possibility for two layers of condensed vapour of different surface densities to be in equilibrium with the same vapour probably arises through molecular association in the ft state and , in consequence , the tendency for molecules to escape into the space above the condensed layer being somehow lessened thereby ; but it is not easy to say if this relative lessening in the f3 state as compared with the a state is to be attributed to an increased molecular force between the particles of the glass and those of the associated molecules in the / 3 state or to the molecules in the a state being at a greater distance from those of the glass due to a looser molecular piling of the condensed surface layer . Several important points suggest themselves in connection with the question of the two possible states in which vapour can condense on solid surfaces . It would be of interest , for instance , to be able to compare the conducting power for electricity of the surface layers on glass at the same vapour pressure , according as they are in the a or / 3 state ; also to ascertain what function of temperature the critical pressure is . Experiments for these purposes are now being undertaken . I take this opportunity for acknowledging my obligation to my assistant Mr. Burgess , for the accuracy and care with which he has made the observations necessary for this work .

rspa_1907_0048

0950-1207

The mechanical effects of canal rays.

391

395

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

A. A. Campbell Swinton|Sir William Crookes, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0048

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0048

10.1098/rspa.1907.0048

Optics

Electricity

Optics

391 + Aj The Mechanical Effects of Canal Rays . By A. A. Campbell Swinton . ( Communicated by Sir AVilliam Crookes , F.R.S. Received May 16 , \#151 ; Read June 6 , 1907 . ) This investigation was undertaken in order to discover whether the so-called canal rays ( Canalstrahlen ) discovered by Goldstein , which , at suitable pressures , visibly stream through the apertures in a perforated cathode , backward away from the anode , share with cathode rays the property discovered , as regards the latter , by Sir William Crookes many years ago , of producing a sufficient mechanical pressure to cause small and light mica mill-wheels to rotate . Several tubes were constructed and experimented with , and all showed that canal rays do cause mica mill-wheels to rotate quite rapidly . Fig. 1 is the form of tube with which this was most conclusively demonstrated . Ai is the anode , the lower end of which is tipped with a glass plate , so as to preclude the transmission of cathode rays vertically downwards in the event of this electrode acquiring at any moment a negative charge due to oscillations in the electric discharge . A2 is a supplemental anode , added since the paper was communicated , and referred to in the addendum . C is the perforated cathode of aluminium , which is compound , consisting of Oi of the cathode proper , perforated with six apertures . C2 is a similar plate correspondingly perforated , and C3 a third plate or shutter of aluminium also correspondingly perforated , loosely pivoted on a central pin between Ci and C2 , and furnished with an armature D of soft iron , so that by means of a magnet it can be slightly rotated so as to open or close simultaneously all the six apertures A plan view of the shutter and armature is shown in Fig. 2 . It was found advisable to make Ci , C3 , and especially C2 of thick plate , so as to avoid thermal effects . Mr. A. A. C. Swinton . Fig. 2 . ------------ [ May 16 , E is the mill-wheel of the screw propeller form , with mica vanes set at an oblique angle to the axis , mounted on a pivot F. The complete mill-wheel weighs about 0T9 gramme . The experiments were conducted with the tube connected to a vacuum pump , so that the pressure could be regulated as desired . An induction coil was employed to produce the electrical discharge , a spark-gap being usually inserted in the circuit , with a view to obtaining currents only in one direction . Eapid rotation of the mill-wheel , in the direction that would indicate that the canal rays consist of particles travelling away from the cathode , was easily obtained in all cases , the best results being got with medium vacua , when the canal rays were highly luminous . That the effect was due to the action of the canal rays , was tested in several ways . Firstly , the shutter C3 was rotated until all the apertures were closed . Under these conditions no rotation could be obtained , whereas when the apertures were open the mill-wheel was found to commence rotation the moment the current was turned on . Again , the current was reversed and A made cathode in order to observe whether cathode rays from A might not be the cause of the rotation . This was found not to be the case . The upper part of the tube was also placed in a strong magnetic field , so as to deflect on to the walls of the tube any cathode rays reflected from the upper end of the tube , which , it was thought , might cause the rotation . As the motion was in no ways affected by the deflection of these reflected rays , it was obvious that the effect was not due to them . It seems , therefore , clear that the rotation of the mill-wheel is caused by the canal rays impinging on the vanes of the former , though it appeared very probable that the effect was a secondary one , due to the rays making the vanes hotter on one side than on the other , with a consequent radiometer action , as is put forward by Professor J. J. Thomson , * as the true explanation of the rotation of mill-wheels under cathode ray .bombardment . This question of difference of temperatures on the two sides of the vanes of the mica mill-wheel was therefore investigated in a special tube , in which a small piece of mica furnished with two thermo-junctions of Constantan-copper , one on each side of the mica , arranged so as to oppose their E.M.F. 's , and connected to a mirror galvanometer , was placed behind the aperture in a perforated cathode , so as to be impinged upon by canal rays . Experiments * \#163 ; Conduction of Electricity through Gases , ' by J. J. Thomson , Second Edition , 1906 , p. 629 . The Mechanical Effects of Canal Rays . 1907 . ] with this apparatus showed that the side of the mica vane struck by the canal rays was very much hotter than the other side , the difference in temperatures amounting to as much as 200 ' F. when the pressure was suitable . It was also found that a maximum difference of temperature was obtained at those pressures which gave a maximum luminosity in the canal rays , which , as already mentioned , is the condition where the most rapid motion is imparted to the mill-wheel . It thus appears that canal rays produce very similar mechanical effects as cathode rays , and in this connection the writer would draw attention to the experiment shown by Sir William Crookes , in 1891 , * and the results obtained by the writer in 1898 , f which show that mica mill-wheels , while rotating in one direction under the impact of cathode rays , revolve in the opposite direction if so placed in the tube so as to be just outside the cathode stream . The canal rays are supposed to be streams of positively electrified particles which , travelling towards the cathode , pass through the apertures in the latter , and emerge on the other side . These mill-wheels would appear to demonstrate the motion of these particles , both when they are approaching the cathode , and after they have passed through the latter . The writer is indebted to the assistance of Mr. J. C. M. Stanton and Mr. B. C. Pierce in carrying out the experiments . [ Addendum , June 6 , 1907.\#151 ; Since the above paper was communicated , further investigations have . been conducted by the writer , all of which confirm the fact that canal rays do produce marked mechanical effects . In the tube illustrated in fig. 3 , A is the anode and C the aluminium cathode , with a single perforation which allows the canal rays to impinge on the mica vanes of the mill-wheel E , which is of the water-wheel type having vanes with their surfaces in radial planes parallel with the axis . This arrangement was found to be very effective , the mill-wheel rotating rapidly at suitable vacua in the direction indicated by the arrow , which is that which one would expect from canal ray bombardment . An exactly similar tube , but fitted with a mill-wheel entirely constructed of aluminium , the vanes being of foil about 0'0127 mm. in thickness , gave exactly similar results , except that it appeared to require rather more power to make it work . The tube illustrated in figs. 1 and 2 was also fitted with an additional * Electricity in transitu from Plenum to Vacuum , " 'Journal of the Institution of Electrical Engineers , ' vol. 20 , No. 91 , p. 25 . + 'Phil . Mag. , ' October , 1898 . The Mechanical Effects of Canal Rays . anode A2 . When this was employed in substitution for Ai , the millwheel was obviously subjected to the influence both of cathode rays proceeding from the cathode C , and also to the influence of canal rays streaming towards the cathode in the opposite direction . With this tube , with a mill-wheel with mica vanes , the cathode rays apparently had the more powerful effect , as both when the apertures in the cathode were open and also when they were closed the mill-wheel rotated invariably in the direction that corresponds with the motion being due to the ^ cathode rays . Another tube made according to figs. 1 and 2 , but with the upper surfaces of the mica vanes of its mill-wheel coated with chloride of lithium , a salt which gives red fluorescence under canal ray bombardment , and blue fluorescence when the bombardment is by cathode rays , was also used . With this tube , when Ai was anode , with the apertures in the cathode open , the wheel revolved and fluoresced red under the influence of the canal rays , while with A2 as anode , the wheel turned in the same direction , but fluoresced blue under the bombardment of the cathode rays . A further tube , constructed exactly as that illustrated in figs. 1 and 2 , but with the mill-wheel and its vanes entirely constructed of aluminium foil about 00127 mm. in thickness and weighing altogether about 002 gramme , gave in one case different results . Using Ai as anode , the rotation of the mill-wheel , when the apertures were open , was the same as that of the mill-wheel with mica vanes , being in the direction that would indicate that the effect was due to the canal rays ; but when A2 was made anode , the aluminium mill-wheel , instead of rotating as did the wheel with mica vanes in the direction that would correspond with the effect being due to cathode ray bombardment , was found to rotate with remarkable energy in the reverse direction , as would be caused by the canal rays proceeding towards the cathode . This was the case equally whether the apertures in the cathode were open or shut , the inference being that the force acting on the wheel due to positive particles approaching the cathode was in this case much greater than the force in the opposite direction due to the cathode ray corpuscles leaving the cathode . + A The Distribution of Blue and Violet Light in the Corona . 395 In order to elucidate this divergence in the effect produced under as nearly as practicable similar circumstances upon mica mill-wheels on the one hand , and aluminium wheels on the other , further research seems necessary , but it would appear very probable that the heat insulating properties of mica , which would enable the two sides of a vane of this material to remain at widely different temperatures , and the high conductivity of aluminium for heat , which would not allow of such temperature differences , have an important bearing on this question . ] The Distribution of Blue and Violet Light the Corona on August 30 , 1905 , as derived from Photographs taken at Kalaa-es-Senam , Tunisia . By Dr. L. Becker , Professor of Astronomy , University of Glasgow . ( Communicated by the Joint Permanent Eclipse Committee . Received November 27 , 1906 , \#151 ; Read June 6 , 1907 . ) ( Abstract . ) Nine photographs of the corona are available for discussion . They were all taken with the same instrument on the same plate ( the two halves of a whole plate placed end to end ) and developed in the same tray . A strong developer was used so as to produce as much contrast as possible . The plate had been exposed and moved onwards 1 or 2 inches after each exposure by an automatic device governed by a pendulum clock which closed and opened two electric circuits at specified intervals . The operator merely started the pendulum of the clock at the beginning of totality and the photographs were taken without further interference on his part . There are five exposures of 085 second , and one each of 9 , 3 , 89 , 21 , and 46 seconds duration . Owing to damage done in transit to the mechanism which propels the plate , the 3 seconds ' exposure is partly superposed on the images belonging to those of 9 seconds and 89 seconds , with the result that only the sum of the exposures belonging to these two photographs is accurately known . This failure has somewhat complicated the reduction of the . plates . During the first four exposures of 0'85 second the aperture of the lens was reduced respectively to 0'05 , 0'09 , 0'2 , 0'4 , of its area by screens , each of which had 13 equal openings distributed over the area of the lens . The effect due to diffraction produced by the screens is investigated in the

rspa_1907_0049

0950-1207

The distribution of blue and violet light in the corona on August 30, 1905, as derived from photographs taken at Kalaa-es-Senam, Tunisia.

395

396

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Dr. L. Becker

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0049

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0049

10.1098/rspa.1907.0049

Optics

Astronomy

Optics

The Distribution of Blue and Violet Light in the Corona . 395 In order to elucidate this divergence in the effect produced under as nearly as practicable similar circumstances upon mica mill-wheels on the one hand , and aluminium wheels on the other , further research seems necessary , but it would appear very probable that the heat insulating properties of mica , which would enable the two sides of a vane of this material to remain at widely different temperatures , and the high conductivity of aluminium for heat , which would not allow of such temperature differences , have an important bearing on this question . ] The Distribution of Blue and Violet Light the Corona on August 30 , 1905 , as derived from Photographs taken at Kalaa-es-Senam , Tunisia . By Dr. L. Becker , Professor of Astronomy , University of Glasgow . ( Communicated by the Joint Permanent Eclipse Committee . Received November 27 , 1906 , \#151 ; Read June 6 , 1907 . ) ( Abstract . ) Nine photographs of the corona are available for discussion . They were all taken with the same instrument on the same plate ( the two halves of a whole plate placed end to end ) and developed in the same tray . A strong developer was used so as to produce as much contrast as possible . The plate had been exposed and moved onwards 1 or 2 inches after each exposure by an automatic device governed by a pendulum clock which closed and opened two electric circuits at specified intervals . The operator merely started the pendulum of the clock at the beginning of totality and the photographs were taken without further interference on his part . There are five exposures of 085 second , and one each of 9 , 3 , 89 , 21 , and 46 seconds duration . Owing to damage done in transit to the mechanism which propels the plate , the 3 seconds ' exposure is partly superposed on the images belonging to those of 9 seconds and 89 seconds , with the result that only the sum of the exposures belonging to these two photographs is accurately known . This failure has somewhat complicated the reduction of the . plates . During the first four exposures of 0'85 second the aperture of the lens was reduced respectively to 0'05 , 0'09 , 0'2 , 0'4 , of its area by screens , each of which had 13 equal openings distributed over the area of the lens . The effect due to diffraction produced by the screens is investigated in the 396 The Distribution of Blue and Violet Light in the Corona . paper . The observations made on the photographs and utilised in this paper , consist in the selection of points on the several corona-images at which the photographic film shows the same degree of blackness , and in the measurement of their distance from the lunar disc . For instance , the first five photographs show the same degree of blackness at distances from the sun 's limb of 0-063 , 0096 , 0T39 , 0T87 , 0263 , respectively ( unity =10-3 solar diameter ) . The measurements were actually made on positives which showed the corona as a transparent ring round the lunar disc , arid not one but 24 points of an equal-blackness curve were measured . For the first five photographs the intensities of the corona at points where there is equal blackness are inversely as the areas of the exposed portions of the lens , while for the photographs taken at full aperture the intensity is a function of the duration of exposure , which function was determined from experiments . A complication arises from the fact that the intensity of the* light diffusely reflected by the sky and various parts of the instrument is of the order of the intensity of the outlying coronal radiations . The observations thus give for a series of pairs of points whose distances from the moon 's or sun 's limb are known , the ratio of the intensities of light , and the problem is to represent the intensity as a function of the distance of the point from the sun 's limb . The calculation was carried out only for the average distance of an equal-blackness ( i.e. , intensity ) curve , and the result is that the intensity of the corona decreases inversely as the fourth power of the average distance of the curve from a circle which is concentric with the sun 's disc and whose diameter is about three-quarters of the solar diameter . The formula does not hold good in each of the 24 radial directions . I have further attempted to refer the intensity to that of a certain region on the moon , utilising photographs of the moon which were taken at the Observatory after my return from the eclipse expedition . The object of the final sections of the paper is to show that such photographs as used here , if taken on ordinary plates and plates sensitised for red and yellow rays , would be well suited for settling the debated question whether or not the luminosity of the corona is actually caused by particles heated to luminescence by solar radiation .

rspa_1907_0050

0950-1207

Investigation of the law of burning of modified cordite.

397

398

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Major J. H. Mansell|Sir A. Noble, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0050

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0050

10.1098/rspa.1907.0050

Thermodynamics

Fluid Dynamics

Thermodynamics

397 Investigation of the Law of Burning of Modified Cordite . By Major J. H. Mansell , Eoyal Artillery . ( Communicated by Sir A. Noble , F.R.S. Received November 29 , 1906 , \#151 ; Read February 14 , 1907 . ) ( Abstract . ) Some years ago Vieille first propounded the law of combustion by parallel surfaces for smokeless propellants . This law has generally been accepted as correct . Investigators have assumed that the relation is expressed by an equation of the form S = aPn , where S is the skin burnt in a given time under the average pressure P , a and nbeing constants for the given explosive . The constants a and n have been obtained by a system of trial and error , testing the results obtained by calculation against the actual results obtained in a gun . In the gun the space behind the projectile is treated as a closed vessel . As the projectile moves down the bore the size of this vessel increases , and the increase in a given time under a given pressure depends on what allowance is made for loss of effective pressure due to friction . The assumptions made as to frictional loss , combined with a hitherto unsuspected variation due to the form of the propellant , have led to wide differences in the values of a and n put forward . In my experiments I used a closed vessel of constant capacity , the description and method of use of which are described in the complete paper . The records obtained by this closed vessel enabled me to obtain , ( 1 ) the pressure density relation of M.D. cordite , and ( 2 ) the time rise of pressure at different densities of loading . The first experiments were made with M.D. cordite in the cord form . From the time rise of pressure I was able to calculate what cordite had been burnt in a given time under the average pressure over that interval which was given me on the curve . The relation found to exist is expressed by an equation of the form S = aP + C , where a varies with the initial temperature of the cordite . The constant C is thought to mean that below a pressure of about 0 ; 1 ton on the square inch true explosion does not take place , and combustion by parallel surfaces over the whole charge is not going on . During this time the cordite is lit and burning slowly up to the point where true explosion begins . 398 Investigation of the Law of Burning of Modified Cordite . Time-rises of pressure calculated from this formula show very close agreement with those actually obtained with cords . Experiments were then made with the propellant in the tubular form . The time rise of pressure was found not to agree with that given by calculation , using the above formula . The rise at the beginning is much more rapid than would be expected from theory . A comparison of the actual and theoretical curves and observation of certain phenomena connected with the burning of tubes in the air led to the belief that there is excess pressure inside the tube even when burning explosively . Calculations were therefore made to determine the amount of this excess internal pressure on the assumption that the fundamental law , as found for cords , must still be true . The result of these calculations is the advancement of the theory that in the burning of tubes there is a two-phase condition : ( 1 ) when excess internal pressure exists , and ( 2 ) when it disappears . The . amount of excess pressure depends on the size of the internal hole and length of the tube . Calculating on this principle , the theoretical time-rise shows agreement with the actual . By this theory one is also enabled to understand ballistic and other phenomena connected with the burning of tubes which are incapable of explanation on the assumption of a relation of the form S = \#171 ; Pn . Experiments were then made with the propellant in the double tubular form , and the influence of excess internal pressure is shown to be more marked than with the tubular . It is this form-influence on the time-rise which in part accounts for the great variation in formulas put forward by various investigators . The results of this investigation have been applied to the practical case of the gun . Having adopted certain frictional laws , the application with cords , with which we have most experience , has been found to hold over a wide range of varying conditions of loading and calibre .

rspa_1907_0051

0950-1207

On the dynamical theory of gratings.

399

416

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Lord Rayleigh, O. M., Pres. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0051

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0051

10.1098/rspa.1907.0051

Fluid Dynamics

Formulae

Fluid Dynamics

]\gt ; the of By LORD AYLEIGH , O.M. , Received June ll , \mdash ; Read June 27 , 1907 . ) In the usual theory of gratings , upon the lines laid } by , the various parts of the primary wave-front , after oing influences , whether affecting the phase or the amplitude , are conceived to pursue their course as if they still formed the fronts of waves of area . This supposition , justifiable as an approximation when the rating interval is , tends to fail altogether wheu the interval is reduced so as to be comparable with the wave-length . A simple example will ) explain the nature of the failure . Considel a grating of perfectly material whose alternate parts are flat and parallel and equally wide , but so disposed as to form a crroove of depth equal to a quarter , and upon this let be incident perpendicularly . Upon Fresnel 's principles the centrall.egularly reflected FIG. 1 . must vanish , being constituted by the combination of equal and opposite vibrations . If the grating interval be enough , this conclusion is approximately correct and could be verified by experiment . now suppose that the rating interval is reduced until it is less than the wavelength of the light . The conclusion is now entirely wide of the marl Under the circumstances supposed there are no lateral spectra and the of the incident energy is necessarily thrown into the regular reflection , which is accordingly total instead of evanescent . A closer consideratio shows that the recesses in this case act as resonators in a manner not covered by Fresnel 's ations , and illustrates the need of a theory strictly dynamical . The present investigation , of which the interest is mainly optical , may be regarded as an extension of that given in ' Theory of Soun plane waves were supposed to be incident perpendicularly upon a ularly corrugated surface , whose form was limited a certain condition symmetry . Moreover , attention was there principally fixed upon the case where the of the corrugations was long in comparison with that * Second edition , S ) . VOL LXXIX.\mdash ; A. 2 Lord Rayleigh . [ June 11 , of the waves themselves , so that in the optical application there would be a large number of spectra . It is proposed now to dispense with these restrictions . On the other hand , it will be supposed that the depth of the corrugations is small in comparison with the length ( ) of the waves . The equation of the reflecting surface may be taken to be , where is a periodic function of , whose mean value is zero , and which is independent of . By Fourier 's theorem we may write . ( 1 ) the wave-length of the corrugation being . Formerly the terms were omitted and attention was concentrated upon the case where was alone sensible . The omission of the terms makes the grating symmetrical , so that at perpendicular incidence the spectra on the two sides are similar . It is known that this condition is often , and indeed advantageously , departed from in practice . FIG. 2 . The vibrations incident at obliquity , POZ , fig. 2 , are represented by ( 2 ) where , and is the velocity of propagation in the upper medium . Here satisfies in all cases the same general differential equation , but its significance must depend upon the character of the waves . In the application , to which for the present we may confine our attention , is the 1907 . ] On the Theory of velocity-potential . In optics it is convenient to change the precise interpretation according to circumstances , as we shall see later . The waves regularly reflected along OQ are represented by , ( 3 ) in which is ( possibly complex ) coefficient to be determined . In all the expressions with which we have to deal the time occurs only in the factor , running through . For brevity this factor may be omitted . In like manner the waves regularly refracted along OB into the lower medium have the expression , ( 4 ) being the angle of refraction ; and , by the law of refraction , . ( 5 ) In addition to the incident and regularly reflected and refracted waves , we have to consider those corresponding to the various spectra . For the reflected spectra of the nth order we have ( 5 ) where , by the elementary theory of these spectra , , or . ( 6 ) We shall choose the upper sign for and the lower for . In virtue of ( 6 ) the complete expression for in the upper medium takes the form , ( 7 ) where has in succession the values 1 , 2 , 3 , etc. Similarly , in the lower medium the spectra of the order are represented by , ( 8 ) where . ( 9 ) Accordingly , for the complete expression of , we have with use of , . ( 10 ) must now introduce boundary con ditions to be satisfied at the transition between the two media when . It may be convenient to commence with a very simple case determined by the condition that The.whole of the incident energy is then thrown back , and is distributed between the regularly reflected waves and the various reflected spectra . 40.2 Lord Rayleigh . [ Juns 11 , We proceed by approximation depending on the smallness of . Expanding the exponentials on the right side of ( 7 ) , we get . ( 11 ) In this equation the value of is to be substituted from ( 1 ) , and then in accordance with Fourier 's theorem the coefficients of the various exponential terms , such as , are to be separately equated to zero . As the first approximation , we get from the constant term ( independent of , ( 12 ) and from the terms in . ( 13 ) Thus , as was to be expected , are of the first order in , and if we stop at the second order inclusive , ( 11 ) may be written ( 14 ) For the second approximation to we get . ( 15 ) By means of ( 13 ) and ( 15 ) we may verify the principle that the energies of the incident , and of all the reflected vibrations taken together , are equal . The energy corresponding to unit of wave-front of the incident waves may be supposed to be unity , and for the other waves etc. But what we have to consider are not equal areas of wave-front , but areas to the me extent of reflecting surface , i.e. , areas of wave-front proportional to , etc. Hence , , ( 16 ) with which the special approximate values already given are in harmony . In the formation of ( 16 ) only real values of are to be included . If , no real values exist , i.e. , there are no lateral spectra . The regular reflection is then total , and this without limitation upon the magnitude of the . The question is further considered in 'Theory of Sound , ' S In pursuing a second approximation for the coefficients of the lateral spectra , we will suppose for the sake of brevity that the terms in ( 1 ) are omitted . From the term involving in ( 14 ) , we get with use of ( 13 ) , 1907 . ] On the \ldquo ; , ( 17 ) in which the first ( descending ) series is to terminate when the suffix in is equal to unity . The value of may be derived from ( 17 ) by interchange of and in remaining unchanged . As a particular case of ( 17 ) , we have , for the spectra of the first order , . ( 18 ) , ( 19 ) the descending series in ( 17 ) disappearing altogether . If the incidence is normal , , and thus become identical and assume specially simple forms . Referling to ( 7 ) , see that in this case , ( 20 ) in which , to the second order , . ( 21 ) . ( 22 ) If we suppose that in ( 1 ) only and are sensible , we have , ( 24 ) , ( 25 ) , ( 26 ) while , etc. , vanish to the second order of small quantities inclusive . here is no especial difficulty in carrying the approximations further . As Lord Rayleigh . [ June 11 , an example , we may suppose that is alone sensible in ( 1 ) , so that we may write , ( 27 ) and also that the incidence is perpendicular . For brevity we will denote or by . The boundary condition becomes by ( 7 ) in this case , , ( 28 ) in which ( kc ) ( kc ) ( kc ) ( 29 ) ( ) ( ) . ( 30 ) with similar expressions for , etc. By Fourier 's theorem the terms independent of , in , etc. , must vanish separately . The gives ( 31 ) The term in gives The term in gives . ( 33 ) The term in gives . ( 34 ) We see from these that is of the second order in , that is of the first order , of the second order , of the third order , and so on . Expanding the Bessel 's functions , we find , to the second order inclusive , as in ( 23 ) , ( 24 ) , ( 25 ) , ( 26 ) , , etc. , vanishing . To the third order inclusive ( 34 ) now gives . ( 36 ) From ( 33 ) to the same order }havs still for and from ( 32 ) . ( 38 ) 1907 . ] On the Dynamical Theory of These are complete to the third order of inclusive . To this order , etc. , vanish . So far as the third order of inclusive , remains as in ; but it is worth while here to retain the terms of the fourth order . We find from ( 31)\mdash ; . ( 39 ) It is to be noted that are not independent . By ( 6 ! , with , ( 40 ) so that and By use of ( 41 ) it may be verified to the fourth order that when are real , so that the spectra of the second order are actually formed , expressing the conservation of vibratory energy . When is real , but not , we may write , where is positive . In this case ; and in virtue of ( 41 ) to the fourth order , Again , if are both imaginary , equal , say , , we have from ( 39 ) with separation of real and imaginary parts , terms , so that , to the fourth order , , ( 44 ) expressing thaC the regular reflection is now total . In the acoustical interpretation for a gaseous medium represents the velocity-potential , and the boundary condition is that of constant pressure . In the electrical and optical interpretation the waves are incident from air , or other dielectric medium , upon a perfectly conducting and , therefore , perfectly reflecting corrugated substance . Here represents the electromotive intensity parallel to , that is parallel to the lines of the rating , the boundary condition being the evanescence of Q. 1 , 406 Lord Rayleigh . [ June ] We now pass on to the boundary condition next in order of simplicity , ordains that , where is drawn normally at the surface of separation . Since the surfaces , constant , are to be perpendicular , the condition expressed in rectangular co-ordinates is , ( 45 ) being given by 7 ) and by ( 1 ) . For the purposes of the first approximation , we require in only the part independent of the 's and , since . is already of the first order Thus at the surface Also , correct to the first order , - Thus ( 45 ) gives . ( 46 ) From the term independent ' we see that , as was to be expected , . ( 47 ) Also , ( 48 ) . ( 49 ) When in ( 48 ) , ( 49 ) , we may put . These equations constitute the complete solution to a first approximation . For the second approximation we must retain the terms of the first order in . Thus from ( 5 ) , , ( 50 ) since to the first ordel inclusive . Also -ik . ( 51 ) On the of ratings . Thus by ( 45 ) the mdary condition is In the small terms we may substitute for their approximate valnes from ( 48 ) , ( 49 ) . In ( 52 ) the coefficients of the various terms in must vanish sepalately . In pursuing the approximation we will write for breyity where and , . ( 54 ) The term independent gives to the secolld approximation . Thus . ( 5o- ) In , as follows from ( 6 ) , and Hence with introduction of the values of from ( 48 ) , ( 49 ) , , ( 56 ) as also be inferred from ( 48 ) , ( 49 ) alone , with the aid of the energy equation\mdash ; From the ternl in in ( 52 ) we get . ( 58 ) Lord Rayleigh . [ June : In ( 58 ) is to assume the values 1 , 2 , 3 , etc. , the descending series terminating when The corresponding equation for may } ) derived from ( 58 ) by changing the sign of , with the understanding that ; . ( 59 ) If the incidence be perpendicular , so that , and if which requires that , the values of and become identical . If , the descending series in ( 58 ) make no contribution . We have ( 60 ) We will now introduce the simplifying suppositions that making , and also that only and are sensible , so that . We will also , as before , denote or by Accordingly ( 60 ) gives , with use of ( 6 ) , ( 48 ) , ( 49 ) , In like manner , we get from ( 08 ) , ( 62 ) , ( 63 ) after which , etc. , vanish to this order of approximation . In any of these equations we may replace by its value from ( 6 ) , that is The boundary condition of this case , i.e. , , is realised acoustically when aerial waves are incident upon an inmlovable corrugated surface . In the interpretation for electrical and luminous waves , the magnetic induction ( b ) paralled to , so that the electric vector is perpendicular to the lines of the grating , the boundary condition at the surface of a perfect reflector being We have thus obtained the solutions for the two principal cases of the incidence of polarised light upon a perfect corrugated reflector . In comparing 1907 . ] On the Theory of the results for the first order of approximation as iven in ( 13 ) for the first case and in ( 48 ) , ( 49 ) for the second , we are at once struck with the fact that in the second case , though not in the first , the intensity of a spectrum may become infinite through the evanescence of or , which occurs when the spectrum is just disappearing from the field of view . But the effect is not limited to the particular spectrum which is on the point of disappearing . Thus in ( 61 ) , giving the spectrum of the first order , becomes infinite as the spectrum of the second order disappears . Regarded from a mathematical point of view , the method of approximation breaks down . The problem has no definite solution , so long as we maintain the suppositions of perfect reflection , of an infinite train of simple waves , and of a grating infinitely extended in the direction perpendicular to its ruling . But under the conditions of experiment , we may at least infer the probability of abnormalities in the brightness of any spectrum at the moment when one of higher order is just disappearing , abnormalities limited , however , to the case where the electric displacement is perpendicular to the ruling . * It may be remarked that when the incident ight is unpolarised , the spectrum about to disappear is polarised in a plane parallel to the ruling . In both the cases of boundary conditions hitherto treated , the circumstances are especially simple in that the aggregate reflection is perfect , the whole of the incident energy being returned into the upper medium . We now pass on to more complicated conditions , which we may interpret as those of two gaseous media of densities and . Equality of pressures at the interface requires that and we have also to satisfy the continuity of normal velocity expressed by or , as in ( 45 ) , and being given by ( 7 ) , ( 10 ) . We must content ourselves with a solution to the first approximation , at least for general incidence . From ( 65 ) , * See a Vote on the Remarkable of Diffraction Spectra described by Professor Wood recently communicated to the ' Philosophical Magazine , ' vol. 14 , p. 60 , 1907 . Lord Rayleigh . Distinguishing the various components in as in ( 53 ) , we find ( 69 ) , ( 70 ) ( 71 ) In forming the second boundary condition ( 67 ) we require in the part independent of Also Thus ( 67 ) takes the form . ( 72 ) From the part independent we get , ( 73 ) and from the parts in , ( 74 ) and a similar equation involving From ( 69 ) , ( 73 ) we find . ( 75 ) 1907 . ] On the of Again , eliminating between ( 70 ) , ) , get , with use of ( 5 ) , denoting the denominators in ( 75 ) . The equations ( 75 ) for the waves regularly reflected and those given ( after Green ) in ' Theory of Sound , ' S . They are to cover the case where the two gaseous media have different constants of compressibility as well as of density . The elocities of wave propagation are connected with these quantities by the relation , see , : : . ( 77 ) In ideal gases the compressibilities are the same , so thaf In this case ( 75 ) gives , ( 79 ) . Fresnel 's expression for the reflection of polarised in a plane ) dicular to that of incidence . In accordance with Brewster 's law the reflection vanishes at the angle of incidence whose tangent is In like mannel the introduction of ( 78 ) into ( 76 ) , after reduction , . ( S0 ) If the wave-length of the corrugations be very identical with , and thus vanishes when , that is at same ( Brewsterian ) angle of incidence for which , as was to be expected . In general , when . ( 81 ) If we suppose that . is somewhat small , we may obtain a second approximation to the value of . Thus , setting in the small ternls , we get Lord Rayleigh . [ June 11 , Here so that . ( 82 ) This determines the angle of incidence at which to a second approximation in the reflected vibration vanishes in the nth spectrum . Since according to ( 82 ) with positive , and , it seemed not impossible that ( 82 ) might be equivalent to , forming a kind of extension of Brewster 's law . It appears , however , from ( 6 ) that , ( 83 ) so that the suggested law is not observed , although the departure from it would be somewhat small in the case of moderately refractive media . For the other spectrum of the nth order we have only to change the sign of in , ( 83 ) . When is not small , we must revert to the original equation ( 81 ) . Even this , it must be remembered , depends upon a first approximation , including only the first powers of the Another special case of interest occurs when , so that in the acoustical application the difference between the two media is one of compressibility only . The introduction of this condition into ( 75 ) gives , ( 84 ) the other Fresnel 's expression . Again , from ( 76 ) , whence ( 85 ) In this case the vibration in the nth spectrum does not vanish at any of incidence . We have now to consider the application of our solutions to electromagnetic vibrations , such as constitute light , the polarisation being in one or principal plane . In the usual electrical notation , being the specific inductive capacities , and the magnetic permeabilities ; while in the acoustical problem , 1907 . ] On the Dynamical Theory of Gratings . The boundary conditions are also of the same general form . For instance , the acoustical conditions may be written ; and in the upper medium where is constant it makes no difference whether we deal with or . Thus if in the case of we identify with , the component of netic force parallel to ? / , the conditions to be satisfied at the surface are the continuity of and of Comparing with the acoustical conditions , we see that replaces , and consequently ( by value of ) replaces . Hence , in the general solution , ( 76 ) , it is only necessary to write in place of . For optical purposes we may usually treat as constant . This corresponds to the special supposition ( 78 ) , so that ( 79 ) , ( 80 ) apply to light for which the netic force is parallel to the lines of the grating , or the electric force perpendicular to the lines , i.e. , in the plane of incidence . From ( 76 ) we may fall back upon ( 48 ) by making , in such a way that , and therefore , remains finite . The other optical application depends upon identifying with , the electromotive intensity parallel to ? / , i.e. , parallel to the lines of the rating . The conditions at the surface are now the continuity of and of Equations ( 75 ) , ( 76 ) become applicable if we replace by . If be invariable , this is the special case of ( 84 ) , ( 85 ) ; so that these equations are applicable to light when the electric vibration is parallel to the lines of the grating , or perpendicular to the plane of incidence . The associated Fresnel 's expression ( 79 ) suffices in each case to remind us of the optical circumstances . In order to pass back from ( 76 ) to ( 13 ) , we are to suppose ( or ) , so that remains finite . Thus , and the only terms to be retained in ( 76 ) are those which include the factor The polarisation of the spectra eflected from glass gratings was noticed by raunhofer : Sehr merkwurdig ist es , dass unter einem gewissen ein Theil eines durch Reflexion entstandenen Spectrums aus vollstandig polarisirter Lichte besteht . Dieser Einfallswinkel ist fur die verschiedenen Spectra sehr verschieden , und selbst noch sehr merklich fur die verschiedenen arben ein und desselben Spectrums . Mit dem Glasgitter ist polarisirt : , , der grune Theil dieses ersten * See ' Phil. Mag vol. 1 p. 81 , 1881 ; 'Scientific Papers , ' vol. 1 , p. 520 . Lord Rayleigh . Spectrums , wean ist ; , oder der grune Theil in dem zweiten auf derselben Seite der Axe enden Spectrum , wenn betragt ; endlich , oder der grune Theil des ersten auf der esetzten Seite der Axe liegenden Spectrums , wenn . Wenn polarisirt ist , sind es die ubrigen Farben dieses Spectl.ums noch In Fraunhofer 's notation is the angle of incidence , here denoted by and in the same measure ( the Paris inch ) as that employed for , so that . If we suppose that the refractive index of the glass was , we get On the other hand : from ( 82 ) we get for , for , and , a fair agreement between the two values of , except in the case of . It appears , howevel , that the of upon which ( 82 ) is founded is too rough a procedure . By trial and error I calculate from ( 81 ) for ; for ; for These agree perhaps as closely as could be expected with the observed values , considering that they are deduced from a theory which neglects the square of the depth of the ruling . The ordinary polarising angle for this index It would be of interest to extend Fraunhofer 's observations ; but the work should be in the hands of one who is in a position to rule gratings himself . On old and deteriorated surfaces polarisation phenomena are liable irregularities . In the hope of throwing upon the remarkable observation of Professor Wood , that a frilled collodion surface shows an enhanced reflection , I have pursued the calculation of the regularly reflected light to the second order in , the depth of the groove , limiting myself , however , to the case of perpendicular incidence and to the supposition that and its- equal * Gilbert 's 'Ann . . Physik , ' vol. 74 , p. 337 ( 1823 ) ; 'Colle ted Writings , ' Munich , 1888 , p. 134 . Physical Optics , ' p. 145 . 1907 . ] On iloe Theory of are alone sensible . Although the results are not I had hoped , it may be worth while to record the principal steps . Retaining only the terms independent of , we get from the first condition ( 65 ) , ( 86 ) and from the second condition ( b7 ) , . ( 87 ) Eliminating , and remembering that we get , ( 88 ) in which we are to substitute the values of from ( 70 ) , ( 74 ) . From this point it is , perhaps , more convenient to take the principal suppositions separately . Let , as in ( 78 ) , : ; we have ' and accordingly , from ( 70 ) , ( 74 ) , ; so that Hence , from ( 88 ) , . ( 89 ) Again , when and from ( 70 ) , ( 74 ) , . ( 90 ) The introduction of these into ( 88 ) gives . ( 91 ) VOL. LXXJX.\mdash ; A. 416 On the Theory of Gratings . The question is whether the numerical value of is increased or diminished by the term in . In ( 89 ) it is easy to recognise that in the standard case of greater than ( air to glass in optics ) the term in is positive . and being supposed real . The effect of the second term is thus to bring the right-hand member nearer to unity than it would otherwise be , and thus to the reflection . Again , in ( 91 ) , the second term is ative , even when , as we may see by introducing the appropriate value of , viz. , . The effect is therefore to subtract something from , which is greater than unity , and thus again to diminish the reflection . If in ( 89 ) , ( 91 ) we neglect the terms in , which will be specially small when the two media do not differ much , the formulae become independent of the angles and . In both cases the effect is the same as if the refractive index , supposed greater than unity , were diminished in the ratio 1-2 . It appears then that the present investigation gives no hint of the enhanced reflection observed in certain cases by Professor Wood .

rspa_1907_0052

0950-1207

On the velocity of rotation of the electric discharge in gases at low pressures in a radial magnetic field.

417

427

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Professor H. A. Wilson, F. R. S.|G. H. Martyn, B. Sc.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0052

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0052

10.1098/rspa.1907.0052

Electricity

Thermodynamics

Electricity

]\gt ; On the Velocity of Rotation of the Electric Discharge in Gases at Low Pressures in gnetic Field . By Professor H. A. WILSON , F.R.S. , and G. H. MARTYN , B.Sc. , Wheatstone Laboratory , King 's College , London . ( Received May 13 , \mdash ; Read June 6 , 1907 . ) The following paper contains an account of a series of experiments on the motion of an electric discharge in a magnetic field perpendicular to the direction of the discharge current . The fact that the discharge moves in a field like a flexible conductor carrying a current was discovered , and De La Rive showed that it could be made to rotate continuously one pole of a magnet placed inside the vacuum tube . The apparatus used in the present experiments was similar in principle to De La Rive 's , but was so that fairly exact measurements of the various quantities concerned could be obtained . Fig. 1 shows a vertical section of the vacuum tnbe and magnet used . The tube consisted of two concentric glass tubes cemented with sealing wax into aluminium discs . The discs had grooves turned in them to fit the glass tubes , and the part of the discs between the tubes projected a few millimetres , so that there was no danger of the discharge passing the sealing wax . Polished platinum rings were fixed on to the aluminium discs between the glass tubes , and these formed the electrodes between which the discharge passed . The ends of the tubes were carefully ground truly perpendicular to their axes , and the two platinum rings were accurately parallel . To keep the electrodes cool , a ring of narrow brass was soldered on to the back of each disc and a stream of water was kept through these whenever a discharge was passed . This ement enabled ] large currents to be used without softening the sealing wax . A narrow copper tube was soldered into one of the discs and communicated with the interior of the vacuum tube through a fine hole . The tube was connected by a mercury sealed joint with a glass tube leading to a bulb pure phosphorus pentoxide , a Topler pump , and a McLeod gauge . The aluminium discs could be connected through an ammeter and resistance to a battery of 800 secondary cells . The magnet used to produce the netic field consisted of a soft iron bar which was etised by meaIlS of two solenoids , one at each end , so as to have one pole in the middle and opposite poles at each end . The bar was fixed along the axis of the vacuum tube as shown , so that the middle of the bar was at the centre of the tube . The bar was 418 Prof Wilson and Mr. Martyn . On the Velocity of [ May 13 , surrounded by a closely fitting thin-walled glass tube , which prevented the aluminium discs coming in contact with it . discharge tube through its axis . T T\mdash ; Glass tubes . A A\mdash ; Annular space through which discharge passed . W W\mdash ; Water cooling tubes , The distribution of the magnetic force around the bar in the region occupied by the vacuum tube was investigated by means of a small compass needle and was found to be sensibly radial . The current through the magnetising solenoids was measured with an accurate ammeter . Before beginning an experiment , the bar was demagnetised by the method of reversals and then the current was slowly increased , with frequent reversals , up to the required value . In this way the effects of permanent magnetism in the bar were eliminated and the magnetic field could be regarded as a definite function of the current . The strength of the magnetic field corresponding to different values of the current was found by means of a coil of 50 turns of wire , which was 1907 . ] Rotation of thoe Electric in Gases , etc. connected to a ballistic galvanometer and placed round the bar magnet in the position usually occupied by the vacuum tube . The deflections of the galvanometer , produced by a series of currents in the , were found , and then the coil was placed in a solenoid a field of known strength , which was then reversed and the galvanometer deflection measured . The coil of 50 turns was wound in two sections in grooves of square crosssection turned on a vood circular cylinder , each groove containing turns . The outside diameter of each section was equal to the outside diameter of annular space between the two glass tubes forming the vacuum tube , and the inside diameters equal to the inside diameter of the annular space . The distance veen the centres of the two sections was equal to the distance between the platinum electrodes . The two sections were first connected together in series , so that a current would pass round them in opposite directions , and the boxwood cylinder was then placed in the position of the vacuum tube on the iron bar and the galvanometer deflections obtained . The two sections were then connected in series , so that a current would pass round them in the same direction , and were placed inside the solenoid so that the axis of the cylinder was parallel to its magnetic field , and the galvanometer deflection due to reversing this field obtained . Let strength of field due to the solenoid when a current of 1 ampere is passed round it . current reversed in the solenoid . radius of the mean area of each section of the coil of 50 tulns . distance between the centres of the two sections . galvanometer . due to reversing C. galvanometer swing due to reversing the magnetisation of the iron bar . field due to iron bar at radius ? : Then Ad and Ad ' where A is a constant . Hence SCrd ' The values of corresponding to a series of currents in the solenoids for magnetising the bar were found in this way . The are the dimensions of the vacuum tube : Inside diameter of outside tube cm . Outside diameter of inside tube , , Distance between electrodes 317 , , 420 Prof. Wilson and Mr. Martyn . On the Velocity of [ May 13 , The radius of the mean area of each section of the coil used to find the strength of the magnetic field was cm . , which is nearly equal to the mean radius , cm . The magnetic field acting on the discharge is inversely proportional to the radius , so that the parts of the discharge furthest from tho axis of the tube are acted on by the field . The fields given in the tables of results are in every case the field at the radius cm . When a was passed through a gas at a few millimetres pressure it usually formed a narrow positive column perpendicular to the surfaces of the electrodes . The negative glow covered the part of the negative electrode opposite to the end of the positive column and extended over a greater or less area ' to the strength of the current . With large currents , the whole of the negative electrode was covered by the negative glow , but even when this was the case the positive column remained quite narrow , usually not more than 1 cm . wide . At low pressures with large currents , the positive column sometimes spread out and extended all round the tube , so that it became impossible to observe the rotation of the discharge when a magnetic field was produced . When the iron bar was magnctised so as to produce a radial netic field through the vacuum tube , the positive column usually to move rapidly round the annular space between the electrodes . The negative went round with the positive column unless it covered the whole surface of the electrode , in which case it was impossible to tell whether it went round or not . The number of revolutions per second was found by observing the discharge through a stroboscopic disc driven by an electric motor . The speed of rotation of the disc was measured with a revolution counter , which was usually kept on for 30 seconds at a time . The disc had several concentric rings of holes bored in it and its speed was adjusted so that the discharge as seen through it appeared to remain at rest in one of the circles of holes . In this way it was usually easy to the number of revolutions per second made by the in terms of the number made by the disc . With a weak onetic field the rotation was sometimes slow enough for the revolutions to be directly counted . At low pressures with fields the speed sometimes was several hundred revolutions per second , and it was rather difficult to be quite sure of the relation between the speed of the disc and the speed of the discharge . In such cases several independent determinations were made , using different speeds for the disc . When the way in which the speed depends on the magnetic field and gas pressure had been , it was possible to calculate roughly what the speed might be expected to be ) a particular case , so that 1907 . ] Rotation of thoe Electric Discharge in , etc. it became easy to find the correct factor required to convert the speed of the disc into the speed of the discharge . When a weak magnetic field was turned on , the discharge sometimes did not start revolving , but appeared to stick at one of the electrodes ( usually the cathode ) and was bent into the shape of a screw round the discharge tube . The screw usually did not make more than a fraction of a turn round the tube . On the field slowly , the discharge suddenly began to rotate , and then , on diminishing the field , would continue rotating with a much smaller field than necessary to start it . When rotating rapidly , the discharge as seen in the stroboscope appeared exactly as it appeared when at rest without any field , and was always perpendicular to the electrodes . An exception to this rule was observed in the case of hydrogen low pressures , when the positive column sometimes became broader when set rotating and sometimes split up into two separate columns diametrically opposite each other , which always coalesced on turning off the field . The rotation of the discharge in air , nitrogen , and hydrogen was examined . The air was passed over solid caustic potash and dried with phosphorus pentoxide . The nitrogen was prepared by the action of pure urea on potassium hypobromite and was passed over caustic potash , calcium chloride , and phosphorus pentoxide ; it appeared to be pure and did not act on the mercury in the pump . The hydrogen was prepared by the action of pure hydrochloric acid on pure zinc , and was passed over caustic potash , calcium chloride , and phosphorus pentoxide . The spectrum of the discharge was observed in each case through a large direct-vision spectroscope and appeared to be that of the gas supposed to be present . The most complete set of results was obtained with nitrogen ; hydrogen was found difficult to work with , except at pressures . The Rotation of the Discharge in Yitrogen . The following table ( page 422 ) gives some of the results obtained , showing the variation of the velocity of rotation with the netic field at several pressures . Prof Wilson and . Martyn . On the Velocity of [ May 13 , Pressure mm. 9.5 13.9 19.0 23.7 31.3 85.9 0.25 0.27 Mean Pressure mm. Pressure mm. Mean Pressure mm. Mean Mean It will be seen that , except at the lowest pressure , the velocity of rotation at each pressure is nearly proportional to the netic field . In the following table , the mean values of are given , and the product of and the pressure:\mdash ; The product is nearly constant , so that the number of revolutions per second ( n ) is given approximately by the equation , where In all the above experiments the currents carried by the discharge were between and ampere . A number of measurements were made to find how the velocity varied with the current . The results obtained can be best exhibited by means of curves . shows a typical curve representing a series of observations at constant pressure and with a constant magnetic field . Rotation of the Electric Discharge in Gases , etc. It will be seen that the velocity of rotation passes a very flat minimum value as the current is varied . The numbers given above on the variation of the velocity with the pressure and the field are for currents lying in the range for which the velocity is nearly independent of the FIG. 2.\mdash ; Magnetic field 41 . Pressure mm. current . The velocity appeared to be nearly proportional to the netic field under any conditions , but when the velocity varied rapidly with the current it was difficult to obtain satisfactory measurements , because of the difficulty of keeping the current exactly constant . 424 Prof. Wilson and Mr. Martyn . On the Velocity of [ May 13 , The Velocity of Rotation in Air and in Hydrogen . SimiIar results were obtained with air to those obtained with nitrogen . The following table contains some of them : It will be seen that is nearly constant , so that , for air , and so does not differ much from in . The rapid variation of with the current observed with nitrogen when the current was small was not observed with air . In the case of hydrogen , the of current and pressure over which it was possible to make observations were ' limited . The following table contains some of the results obtained:\mdash ; Mean Thus , for hydrogen , , and so is about 13 times greater than iu . The velocity seems , therefore , to be inversely as the density of the gas . The numbers given above refer to the number of revolutions per second made by the discharge . For purposes of theoretical calculation it is more convenient to express the results in terms of the velocity of motion of the discharge in centimetres per second . Since the mean radius of the discharge tube was cm . , the revolutions per second must be multiplied by . If denotes the velocity , we have , then , for nitrogen , ; for air , ; and for hydrogen , 1907 . ] of the Electric in , etc. Theory of the Rotation of the Discharge . The quantity observed was the velocity of rotation of the positive column of the discharge . In many of the experiments the negative glow covered the whole surface of the ative electrode and so could not be observed to rotate . Very often the positive column was striated when at rest , and remained so when rotating without any in its appearance as seen through the stroboscopic disc . To simplify the theory , we shall suppose the discharge to be uniform and to be moving perpendicular to itself in a uniform magnetic field of strength H. If denote the current carried by the discharge , then the transverse force per centimetre acting on the discharge is . If we suppose that this force is balanced by the resistance to the motion of the positive and ative ions through the gas , we get , where denotes the transverse velocity of the discharge , and denote the resistances to the motion of one positive and one ative ion respectively when moving with unit velocity , and and denote the numbers of positive and negative ions present per centimetre of the discharge . If X denotes the electric intensity along the disct ) , then , where is the charge on each ion and and are the velocities of the ions due to unit electric intensity . If and denote the velocities of the ions the discharge , then and also and so that and Hence HC . Therefore HX , and , if we assume , we get , or The Hall effect in the positive column in several gases was measured by one of us in and it was shown that if is the transverse electric intensity due to the Hall effect , then , theoretically , , in which was found experimentally to be boiven by the equation where is a constant anrl the pressure in millimetres of mercury . Since the ocit of motion of the discharge is given approximately by the 'Proceedings of the Cambridge Philosophical Society , ' vol. 11 , Parts and 426 Prof. Wilson and Mr. Martyn . On the Velocity of [ May 13 , equation , it follows that the Hall effect should be proportional tc the velocity of motion . We have\mdash ; and , so that and . If X is known , these two equations enable and to be calculated . Unfortunately , there is considerable uncertainty about the value of X. X falls off as the current density is increased ; and the current density in the experiments on the rate of motion of the discharge was considerably greater than iu the experiments on the Hall effect . Further , the measurements of the Hall effect were made at lower pressures than those on the velocity of rotation , and it is probable that the formula is only an approximation to the truth , so that extrapolation is not allowable . We have , , only calculated and for each gas at the pressure intermediate between the lowest pressure at which the velocity was measured and the highest pressure at which the Hall effect was measured , so reducing the extrapolation as much as possible . The following table contains the results of this calculation:\mdash ; If we assume that the velocity of the positive ion varies inversely as the pressure , we get , at 760 mm. , for air , cm . , and for hydrogen , cm . . According to Zeleny , the velocity of the positive ions produced in air at 760 mm. by Rontgen rays is cm . . for air and cm . . for hydrogen . Mr. Aston*has calculated from the results of measurements on the cathode dark space at pressures below mm. , and his results , calculated to mm. , are for air and for hydrogen . It seems probable , therefore , that does not vary much with the pressure . The above results show that is much larger than at low pressures , which probably means that some of the aGive ions are free electrons . If the empirical formulae obtained for the Hall effect and for the velocity of motion are both assumed to apply at pressures below mm. , and and 'Roy . Soc. Proc , vol. 79 , p. 80 . 1907 . ] Rotation of the Electric Discharge in calculated , it is found that is nearly independent of the pressure , while rises rapidly with ninishing pressure . The highest pressure at which the Hall effect in air was measured was mm. , and the lowest pressure at which the velocity of motion measured was mm. , so that for mm. the calculation of and is fairly reliable , but it is certainly not justifiable to use the formula for the velocity of motion below this pressure , or that for the Hall effect above it . In the case of hydrogen , the Hall effect was not measured above 1 mm. . and the velocity not below mm. , so that very much cannot be attached to the values of and calculated for hydrogen at mm. If we assume that is inversely proportional to the pressure at all pressures , then , since ? , we see that is a constant for all the pressures at which the velocity of motion was measured . It appears , therefore , that in air between and 12 mm. , the velocity of the aCive ions in the positive column , i.e. , , does not vary much with the pressure . At low pressures , is small compared to , so that the Hall effect gives approximately equal to , and varies inversely as the pressure . At high pressures , X is probably nearly proportional to the pressure , while is inversely proportional to the pressure , so that is constant . Most of the apparatus used in this investigation was purchased out of a grant of S500 given to the Wheatstone Laboratory at by the Drapers ' Company , to whom , therefore , we wish to our indebtedness .

rspa_1907_0053

0950-1207

On a standard of mutual inductance.

428

435

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Albert Campbell, B. A.|Dr. R. T. Glazebrook, F. R. S.

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10.1098/rspa.1907.0053

Tables

Electricity

Tables

]\gt ; On Standard of Mutual Inductance . By ALBERT CAMPBELL , B.A. ( Communicated by Dr. R. T. Glazebrook , F.R.S. Received June 5 , \mdash ; Read June 27 , 1907 . ) ( From the National Physical Laboratory . ) CONTEN TS . PAGE S1 . Introductory 428 S 2 . Practical Conditions in the Problem 428 S 3 . Variation of with Dimensions and Positions of Coils 429 S4 . Practical Case of Two Helixes and Circle 432 S 5 . Actual Construction of Standard 435 S1 . Introductory.\mdash ; In many electrical measurements , such as those of capacity and , as well as in the netic testing of iron , an accurately known standard of mutual inductance is of great . It is sometimes convenient to derive such a standard from the standard unib of resistance , and this may be done in several ways , for example , by the wellknown method of the ballistic galvanometer ; or by Carey Foster 's method the mutual inductions may be tested against a condenser whose capacity has been found in terms of resistance and frequency by Maxwell 's commutator method ; or it may be obtained directly in similar terms by the help of an unknown inductance by the Hughes-Rayleigh method . In the National Physical Laboratory I have used both of these latter methods ( with the help of a vibration galvanometer ) to obtain a working standard of mutual inductance . * But this procedure is somewhat seeing that the unit of resistance has been itself commonly determined by the aid of mutual inductances calculated from the dimension of the coils or other conductors used ; thus for the highest accuracy it is desirable to revert to a standard whose value can be determined solely from the geometrical dimensions . Accordingly , some eighteen months , I took in hand the investigation of a suitable design for such a standard , and I proceed describe the result at which I arrived . S2 . Practical Conditions.\mdash ; The most important conditions governing the design were that the standard must be\mdash ; ( a ) accurately calculable from the geometrical dimensions ; ( b ) as permanent as possible ; and 'Phys . Soc May , 1907 . On of ( c ) of a value sufficiently large to give high sensitivity when used in comparison methods , such as those mentioned above . In addition to these , it was desirable to keep the resistances of the parts as low as possible and to avoid ( as far as possible ) the occurrence of eddy currents , and also of capacity effects between the and secondary oircuits . As is so often the case in designs , a compromise had to be effected between the various conditions , and so it was decided to make the value approximately henry . In order to carry out some of the above conditions , it is clearly desirable that the distance from the primary circuit to the secondary should , for all points , be relatively as great as possible . For convenience , let us call the circuit with the smaller number of turns the primary , the secondary having turns , and let be the mutual inductance in millihenries . Since , for a given geometrical disposition of the circuits , is proportional to , a little consideration showed that for millihenries it old be desirable to make of order of 100,000 . Now it seems to be generally recognised that , for a coil whose dimensions have to be accurately measured , the satisfactory construction is of bare wire wound in an accurate screw-cut on a marble cylinder . If the above conditions be kept in mind , it is out of the question , with , to attempt to construct both the primary and secondar ) circuits of single-layer coils . As will be shown later , the solution of the problem consists in making the primary an accurately measured single-layer coil or coils , while the is a many-layered coil , so designed its dimensions position do equire to very accurately . The possibility of such a and the method of carrying it out were found by an examination of the manner in which varies with the dimensions and positions of the primary and secondary coils . I proceed to give some of the more interesting results of examination . S3 . Variation of Dimensions and Positions of the Coils.\mdash ; First , let us consider the simple case of two circular co-axial coils with ible section , assuming for convenience of calculation Let their radii be A and , and let be the distance between their Let , and Then* ( in henlies ) , ( 1 ) . where and are complete elliptic integrals to modulus * Maxwell 's ( Elect. and Mag vol. 2 , S 701 . 430 Mr. A. Campbell . [ June 9- , Since and , it can be shown that . ( 2 ) From equation ( 1 ) , mainly by the help of Lord Rayleigh 's table , in some cases by 's formula and tables , were calculated sets of values of for a fixed value of ( viz. , 10 cm and values of and From these calculations the families of curves shown in figs. 1 and 2 were drawn . Each curve in fig. 1 corresponds to a constant value of , and in FIO . 1 . *Ibid . , 2nd edition . TOky5 S\amp ; ubar ; g , ' Bntsu . Kiji.gaiyo , ' vo12 , No. 17 . 1907 . ] On Standard of Mutual Inducta to a constant value of . It will be noticed that in is always Illaximunl and only when , while in fig. 2 the nlaximum value occurs for a different value of not for each . Thus when only two coils are used , should either be zero or relatively . When is zero , is zero only when or the coils coincide ; when is relatively large , the whole construction has to be very bulky in order to obtain a enough M. the case of two coils is not sufficient for our purpose . If , however , the primary consists of two equal coils arranged with the secondary between them as in fig. 3 , all three coaxial , is a maximmn minimum for axial displacements when If , then , for any desired value of we choose from the proper curve in the value of which gives a maximum , the mutual inductance thus obtained varies only very slightly for small variations of VOL. LXXIX.\mdash ; A. 2 Mr. A. Campbell . [ June 5 , or small axial displacements of the centre coil ; in fact , we have placed the secondary coil in such a position that all round its mean circumference the due to tlu primary coils is zero . FIG. 3 . If be chosen of such a value that the corresponding curve in fig. 2 is reasonably flat at its highest point , then the mutual inductance per turn will be practically constant over the whole section of a secondary coil whose axial and radial depths are both small ; and the secondary may consist of a many-layered coil whose dimensions and position need not be known with any high accuracy . By doing this we throw all the burden of accuracy on the two primary coils which we have assumed to be mere circles . Clearly these must be replaced by single-layer coils of accurately known dimensiOns and relative position , and so we must extend the above investiga- tion to the more complicated case where the ) rimary consists of two coaxial helixes , of equal and finite length , with the secondary coil midway between them as in fig. 4 . Here at the points and ( and all round the mean circumference of the field due to the two primaries should be zero , the component lines of force due to the upper and lower helixes bein , tangential to one another , and in opposite directions as shown . S4 . Helix Cirde.\mdash ; Several cases of the system shown in fig. 4 were investigated by means of the curves of fig. 2 . The mutual inductance between the helix LN and the circle was taken as approximately* , where , and refer to circles at the ends and middle of the helix ; a similar approximation to was also made and a series of curves were * Merrifield 's 'B.A . Report , ' 1880 . 907 . ] On Standard of Inductance . lrawn . The and the curves for the particular dimensions which roved satisfactory are shown in fig. 5 . The relative dimensions ( fig. 4 ) Q. Mr. A. Campbell . [ June 5 , , OH , OK , and OP , this last being the value of for which It will be noticed that , near the value shows very little variation with . ( I should mention that the values for shown in fig. 5 for a single helix and a circle are the same for the two helixes and circle , provided the total number of primary turns be kept constant . ) After the proper relative dimensions had been found by the above method , it was thought desirable to check the results by means of the much more laborious accurate formula of Viriamu Jones . * The formula is applied to the helix LN in fig. 4 by calculating for a helix of height OK , and then for one of height OH , and taking the difference . If , ' and then the Viriamu Jones formula may be reduced to , ( 3 ) where , also . ( 4 ) From ( 3 ) were calculated the values of for , helix to 10 , with , and cm . respectively . The results which are given in the following table entirely corroborate those obtained by the less exact method . Similarly , formula ( 4 ) gave for Table . ries Millihenries Finally the variation in dne to a small axial displacement of the secondary c , oil ( from the mid position ) was estimated . It was found that a displacement of cm . reduced by less than 1 in 10,000 . 'Roy . Soc. Proc p. 192 , December 9 , 1897 . 1907 . ] On Standard of Mutual It will be seen that , with the above proportions , if the radius of the secondary coil is cm . , we may make it a coil of many layers and of appreciable cross-section . If , for example , the cross-section be cm . cm . , then the nlaximum variation from the mean value , over the whole section , of the inductance per turn will be the same within a few parts in 1000 , and thus we can with perfect safety obtain an accurate result by a method of averaging , such as the Purkiss formula used by Lord Rayleigh . * S Actual of standard of the described above is at present being constructed at the National Laboratory . In this the two primary helixes are of bare wire ( turns each ) wound on one nlarble cylinder of 30 cm . diameter , while secondary coil consists of 488 turns in a channel of 1 sq . cm . section with a mean diameter of cm . , the nominal value , therefore , close to 10 millihenries . I may remark that the principle here employed will , without doubt , be of value in ) problems where accurately known mutual inductances are required . In conclusion , I would express thanks to Dr. R. T. Glazebrook for valued and helpful criticism of the design , and to Mr. F. E. Smith for kind advice with regard to the material construction of it . Maxwell 's ' Elect. and Mag vol. 2 , p. 350 , 3rd edition .

rspa_1907_0054

0950-1207

On the origin of the gases evolved by Mineral springs.

436

439

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

The Hon. R. J. Strutt, F. R. S.

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10.1098/rspa.1907.0054

Thermodynamics

Atomic Physics

Thermodynamics

436 On the Origin of the Gases evolved hy Mineral Springs . By the Hon. R J. Strutt , E.RS . ( Received May 31 , \#151 ; Read June 20 , 1907 . ) It has long been known that thermal springs , such as those at Bath , give off considerable quantities of gas , which bubbles up with the water , and consists , for the most part , of nitrogen . Of recent years interest in this subject has been revived by Lord Rayleigh 's observation that helium and argon are present along with nitrogen.* Dewar has used the Bath gas as a practical source of helium , and has observed that it contains a trace of neon ; more recently , Moureuf has exhaustively studied the thermal springs of France , some forty in number , and has found that the same constituents are of quite general occurrence . It appears from his analyses that the Bath gas may fairly be regarded as typical of the gases of almost all other thermal springs , although a much larger percentage of helium is occasionally met with . It has been found that such gases , when fresh , are rich in radium emanation , and that the deposit thrown down by the water on standing contains a notable quantity of radium . It is natural to connect this observation with the discharge of helium by the springs . I was formerly inclined to think j that the facts were most easily explained by supposing that the supplies of helium and radium were derived from the disintegration of uranium lodes at a great depth by the water ; but this view scarcely seems compatible with the universal presence of helium and radium in mineral springs , which has since been brought to light ; for uranium lodes are very rare near the earth 's surface , and there are fatal objections to supposing that metal to be generally more abundant at greater depths . S The unexpectedly large quantities of radium found in common rocks || led me to suspect that perhaps they might after all be able to supply the helium and radium products , as well as the ordinary gases and saline constituents of the spring . With a view to deciding this question , I have examined the gases given off by several varieties of rock , on heating . The subject has attracted some attention from previous experimenters . Thus Ansell and * * * S * ' Roy . Soc. Proc. , ' vol. 59 , p. 198 , Jan. , 1896 . t 'Comptes Rend us , ' 1906 , vol. 142 , pp. 1155\#151 ; 1158 . J ' Roy . Soc. Proc. , ' vol. 73 , 1904 , p. 197 . S ' Roy . Soc. Proc. , ' A , vol. 77 , 1906 , p. 482 . || Loc . cit. On the Origin of the Gases evolved hy Mineral Springs . 437 Dewar , * and afterwards Tilden , f showed that the hydrogen evolved is probably not occluded in the rock , but has its origin in the reaction of metallic iron and water , which are both constituents . They also observed the evolution of carbonic acid , nitrogen , and methane . I do not propose to give minute details of my experimental methods in this paper , since other experiments on the same lines are still in progress and may lead to improvements . The powdered rock was heated in an iron tube , and the evolved gases were extracted with a mercury pump in the ordinary way . After explosion with oxygen and absorption by caustic potash , the inert residue , consisting chiefly of nitrogen , wTas measured . The nitrogen was removed by sparking , and the residue introduced into a vacuum tube for spectroscopic examination . A further separation of the gases was made by means of Sir J. Dewar 's method of absorption with cooled charcoal . In this way helium ( with neon ) could be isolated and pumped off . Argon was absorbed by the charcoal , and could be recovered on warming up . The volumes of the inert gases were measured in the capillary tube of a gas pipette . The results for two normal rocks were as follows:\#151 ; Matopo Granite . Quantity taken , 850 grammes . The inert residue consisted of\#151 ; Nitrogen Argon . . Helium Neon . . 11 c.c. 014 c.c. 0'04 c.c. traces Syenite Rock , Mt . Sorrel , Leicestershire . Quantity taken , 900 grammes . Inert residue\#151 ; Nitrogen Argon ... Helium Neon . . 9 c.c. 0-026 c.c. 0 010 c.c. traces In both these cases the vacuum tube , after removal of argon , gave a brilliant yellowr helium glow . We may compare these analyses with the composition of the Bath gas , as a type of the gases evolved by mineral springs . The total volume of inert gas ( mainly nitrogen ) is taken as 100 . * ' Roy . Soc. Proc. , ' vol. 40 , 1886 , p. 549 . t ' Roy . Soc. Proc. , ' vol. 60 , 1896 , p. 455 . Hon. R. J. Strutt . On the Origin of the [ May 31 , Gas . Argon . Helium . Neon . Bath spring Matopo granite Syenite , Mt . Sorrel per cent. 1 5 1 -27 0-29 per cent. 0-12 0-36 o-ii traces traces traces These figures make it fairly clear that there is a general resemblance between the gases of mineral springs and the gases of rocks , so far as nitrogen and the other inert constituents are concerned . In addition to these constituents , rocks give off hydrogen , carbonic oxide , carbonic acid , and a little methane . The two former are probably secondary products , produced by chemical actions set up on heating . Carbonic acid is represented at the spring by the dissolved carbonates of the mineral water , while methane is present in the evolved gases . I think , therefore , that we may consider that the disintegration and partial solution of ordinary rocks by water at a high temperature accounts for the gaseous , as well as the solid , products delivered by springs such as those at Bath . To collect enough gas from a rock for quantitative examination of the rare gases , repeated operations , requiring considerable labour , were necessary . Gases from the following rocks were merely examined qualitatively\#151 ; augite syenite , from Laurvig , Norway ; greenstone , St. Ives , Cornwall ; olivine euchrite , Isle of Rum ; red sandstone , East Lothian . In each case nitrogen was present , and , on sparking down , the spectra of argon and helium were visible . Neon was not observed , but probably it would have been possible to detect it if more material had been worked up . An exceptional case was found in commercial pumice-stone , which , I believe , comes from the Lipari Islands ; 480 grammes of this gave 3'5 c.c. of nitrogen , which , on sparking down , yielded 0049 c.c. of inert residue\#151 ; 1*4 per cent , of the nitrogen . This inert residue showed the spectra of argon and neon , without helium ; and after absorption in charcoal , neon alone remained . The presence of helium could not be detected with certainty . With regard to the primary origin of the argon and neon contained in rocks , I have no theory to offer . It is natural , however , to associate the helium of rocks with the radium they contain . The relative quantities are quite in accordance with such a view , for the ratio is of the same order as in the strongly radio-active minerals . I hope to discuss this subject in detail in a future paper . I have found at least traces of helium in almost all of a considerable collection of ores and other minerals ; but hitherto only one case has been found\#151 ; in certain beryls\#151 ; where there seems to be sufficient reason Gases evolved by Mineral Springs . 1907 . ] to look for any other cause than traces of the radio-active elements to explain its presence . The evidence , so far obtained , is not favourable to the view that the ionising radiation from ordinary substances is accompanied by production of helium . Assuming that helium in rocks has been generated situ by radio-active change , it becomes of interest to enquire whether any connection can be traced between the quantity of helium and the time which has elapsed since solidification of the rock . With a view to answering this question , various modern lavas from Vesuvius of the eruptions of 1809 , 1822 , and 1906 were examined . Helium was detected in each case , accompanied , as usual , by argon . I had not enough material to determine the helium quantitatively , but it did not seem to be conspicuously less than usual . Probably the gases are unable to escape to more than a slight extent from a compact mass of melted lava . The experiments recorded in this note are not regarded as in any way exhaustive . It has been thought well , howrever , to publish them , without waiting for the completion of the further enquiry which has been referred to , since they seem to throw light on a geological problem of independent interest .

rspa_1907_0055

0950-1207

Preliminary note on a new method of measuring directly the double-refraction in strained glass.

440

442

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

L. N. G. Filon, M. A., D. Sc.|Professor F. T. Trouton, F. R. S.

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10.1098/rspa.1907.0055

Atomic Physics

Optics

Atomic Physics

]\gt ; Preliminary Note on a New Method of suring directly the Double-refraction in Strained Glass . By L. N. G. FILON , , D.Sc . , Fellow and of Universily College , London . ( Communicated by Professor F. T. Trouton , F.R.S. Received May 31 , \mdash ; Read June 20 , 1907 . ) In seneral the methods employed for observing the double-refraction in strained glass depend on the use of crossed Nic , ols , and are similar in principle to those used for observing the colours of crystalline plates . So as the between the two indices of refraction is concerned , a method described by the author*allows of continuous observation of the double-refraction throughout the spectrum . But with to the absolute change in the refractive index of either of the two polarised rays , into which light passing through the strained glass is broken up , the only method hitherto known for detelmining it is the one employed by Kerr and by . This requires the use of homogeneous light , and of some form or other of interferometer . Very difficult and delicate adjustments are necessary , and , moreover , the method is not suited to observations extending continuously throughout the spectrum . The following method is free from these objections , and depends upon an effect which appears interesting in itself . Consider a horizontal beam of parallel homogeneous light incident normally upon bhe face AD of a rectangular glass slab of which ABCD represents the cross-section . The slab is under flexure in a vertical plane perpendicular to the direction of the incident light . Let -optical coefficient for the ray polarised in the plane of the cross-section , and for light of the given . Then if bending Camb . Phil. Soc. Proceedings , ' vol. 12 , p. 55 , et seq. , and ' Roy . Soc. , vol 79 , pp. 200\mdash ; 202 . 'Phil . Mag October , 1888 . 'Ann . . Phys 1902 . New Method oj Measuring directly action . 441 moment , moment of inertia of the cross-section about the " " neutral axis\ldquo ; MN , thickness of slab , the retardation of a ray passing through at a distance from the neutral axis is Thus the points at which the disturbance is in the same phase , instead of lying upon a line perpendicular to MN , lie upon a line inclined to at an Such a slab under flexure will therefore deflect the -front like a It will do the same , only to a different extent , to the wave rised in the perpendicular direction . Thus if we analyse such a beam by means of a , the spectrum lines all appear doubled , the two components being oppositely polarised . If be the of incidence on the the of ction of the wave of length , we have being the number of lines per unit breadth of the . Whence Therefore the shifts of the spectrum line corresponding to wave-length due to the effect of strain on the two oppositely polarised rays , are By measurin these shifts , and therefore can be found . Hence the absolute changes in the two indices of refraction can be calculated , and this not only for one kind of light , but for as many kinds at once as are lines visible in the spectrum under observation . A correction has to be introduced on account of the fact that the Iass slab , owing to lateral expansion under longibudinal pressure and contraction under tension , loses its fular shape and becomes a prism of very small angle . This causes an additional deflection of the wave-front after the glass . This correction may be computed from the elastic constants of the glass , which have then to be determined , or it may be eliminated by slab in a fluid whose refractiye index is equal to that of the glass . Actual experiment with a borosilicate glass , the total thickness traversed being 6 cm . and the diHerence of relative retardation per centimetre about 10 wave-lengths for sodium , showed the doubling most clearly . The grating used was a reflection grating of 14,000 lines to the inch , and 442 Mr. P. D. Innes . On the Vdocity of the [ June 13 , with the magnification employed the lines were widely separated . The definition of the lines was not sensibly impaired by the thickness of glass traversed , and remained good when the load was applied . The maximum load which could be applied with safety separated the two components of either or by an amount approximately equal to the original distance between the sodium lines , so that one component of was coincident with the other component of On the Velociiy of the Cathode ticles emitted by under the Influence of Rontgen Rays , and its on the Theory of Atomic Dismtegration . By P. D. INNES , M.A. , , 1851 Exhibition Scholar of the University of Edinburgh ; College , Cambridge . ( Communicated by Professor J. J. Thomson , F.R.S. Received June 13 , \mdash ; Read June 27 , 1907 . ) The numerous theoretical and experimental investigations during the past few years of J. J. Thomson , Rutherford , Becquerel , and others on the radio-active substances have demonstrated conclusively that the only theory which can satisfactorily account for the phenomena observed is that of atomic disintegration , a process which is apparently going on in several , if not in all , of the elements . This process , however , seems to be entirely spontaneous , to depend only on the special substance under investigation , and to be outside the control of any external influence brought to bear upon it . Immense labour has been expended on experiments involving the utmost variation in the temperature and in the chemical and physical conditions of the elements , but all to no purpose so far as influencing the rate of atomic disintegration is concerned . As far as is known at present , no variation in the output of energy has been detected . There are , it is true , results by Curie and Danne , more recently by Makower , which seem to show an effect of temperature on radium emanation . These results are not , however , confirmed by Bronson in his experiments on the same subject , so that no definite conclusion can yet be reached on this point . Obviously , it would be of immense interest and irnportance , not only from the scientific point of view , but also from the technical and commercial standpoint , if some method could be devised of stimulating or retarding at 'Comptes Bendus , ' vol. 138 , 1904 , p. 748 . 'Roy . Soc. Proc vol. 77 , 1906 , p. 241 . 'Amer . Jour . Sc 1905 , p. 60 , and ' Phil. Mag [ 6 ] , vol. 11 , 1906 , p. 143 .

rspa_1907_0056

0950-1207

On the velocity of the cathode particles emitted by various metals under the influence of R\#xF6;ntgen rays, and its bearing on the theory of atomic disintegration.

442

462

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

P. D. Innes, M. A., B. Sc.|Professor J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0056

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0056

10.1098/rspa.1907.0056

Atomic Physics

Electricity

Atomic Physics

]\gt ; 442 Mr. P. D. Innes . On the Vdocity of the [ June 13 , with the magnification employed the lines were widely separated . The definition of the lines was not sensibly impaired by the thickness of glass traversed , and remained good when the load was applied . The maximum load which could be applied with safety separated the two components of either or by an amount approximately equal to the original distance between the sodium lines , so that one component of was coincident with the other component of On the Velociiy of the Cathode ticles emitted by under the Influence of Rontgen Rays , and its on the Theory of Atomic Dismtegration . By P. D. INNES , M.A. , , 1851 Exhibition Scholar of the University of Edinburgh ; College , Cambridge . ( Communicated by Professor J. J. Thomson , F.R.S. Received June 13 , \mdash ; Read June 27 , 1907 . ) The numerous theoretical and experimental investigations during the past few years of J. J. Thomson , Rutherford , Becquerel , and others on the radio-active substances have demonstrated conclusively that the only theory which can satisfactorily account for the phenomena observed is that of atomic disintegration , a process which is apparently going on in several , if not in all , of the elements . This process , however , seems to be entirely spontaneous , to depend only on the special substance under investigation , and to be outside the control of any external influence brought to bear upon it . Immense labour has been expended on experiments involving the utmost variation in the temperature and in the chemical and physical conditions of the elements , but all to no purpose so far as influencing the rate of atomic disintegration is concerned . As far as is known at present , no variation in the output of energy has been detected . There are , it is true , results by Curie and Danne , more recently by Makower , which seem to show an effect of temperature on radium emanation . These results are not , however , confirmed by Bronson in his experiments on the same subject , so that no definite conclusion can yet be reached on this point . Obviously , it would be of immense interest and irnportance , not only from the scientific point of view , but also from the technical and commercial standpoint , if some method could be devised of stimulating or retarding at 'Comptes Bendus , ' vol. 138 , 1904 , p. 748 . 'Roy . Soc. Proc vol. 77 , 1906 , p. 241 . 'Amer . Jour . Sc 1905 , p. 60 , and ' Phil. Mag [ 6 ] , vol. 11 , 1906 , p. 143 . 1907 . ] Cathode Particles emitted by Various will this output of atomic energy . That there is a great store of energy in the atom seems now beyond question , and if this reservoir could only become available , all our present conditions might be completely revolutionised . Naturally , the only mode of attacking this problem is by what the of this atomic emission of energy is . Now in the case of radium and the other properly so-called radio-active elements , in which the radiated energy is great , of different kinds , and continually being emitted , the question of ating the factors atomic crration is more complicated . There is , ever , a simpler kind of ration , or , at least , of radiating power , and this , too , a kind which can be excited at will , and therefore it was natural to turn one 's attention to it for a solution of the problem . It was early discovered in the history of the rays that , when they impinge on a metallic surface , they rise to ( 1 ) a set of to the original rays , but usually less penetrating , called the secondary rays ; ( 2 ) ively charged particles which can be dellected by an electric or magnetic field . The presence of these particles or cathode rays seems to indicate that here , too , there is a kind of atomic disintegration going on , somewhat similar to that which takes place in the radio-active elements , the cathode particles being corpuscles emitted or extracted from the atoms of the element . Such a conclusion , though very natural is , however , not necessarily true , for it is quite possible to account for them in another way . The modern theories of electrical conduction assume that there is present in conductors a large number of free corpuscles , not intimately bou.nd up in the atomic structure of the element , and it may be these electrons which are extracted or hurled out by the impulse of the impinging Rontgen rays . If such were the case , then there could be no question of tapping the energy of the atom , for there would be no atomic disintegration taking place . There to be a possibility of discriminating between these two hypotheses . Granting , for the moment , that there is disintegration , i.e. , that under the influence of the Rontgen rays a kind of explosion takes place in the atom , then the velocity of the corpuscle will be primarily ) due to the energy of the explosion . We may regard the atom as and storing up the energy of the primary rays . This will go on till certain stage the atom , now possessing the requisite energy or being in the proper condition , hurls out one or more of its corpuscles . Under these circumstances the original velocity of the ejected electron will be independent of the rate of reception of energy from the rays , and will be that due to the explosion alone . The number of corpuscles given out 1S 444 Mr. P. D. Innes . On the Velocity of the [ June 13 , might conceivably , and indeed naturally would , vary , while the velocity might be different in different elements , as a result of difference in internal atomic structure , which would involve the reception of a different amount of energy to different atoms to the exploding stage , and also a different violence of explosion . lf , on the other hand , it was the free corpuscles which were hurled out by the impulse of the impinging rays , then a variation in their velocity of ejection with a varying intensity of the primary rays would naturally follow . It was from this standpoint that Professor J. J. Thomson proposed to me the experiment of which the following give an account . Many experiments have already been performed investigating this secondary radiation , notably by Curie and Sagnac , *Perrin , and Dorn , while Sagnae has published a further paper . S The results of Curie and Sagnac and of Perrin show that these ejected cathode particles are of feeble power , being almost entirely absorbed in 1 mm. of air at atmospheric pressure , while Dorn has measured their velocities , and finds that they are not homogeneous . His values vary from to , depending on the value of adopted . These results , however , cannot be used to solve our problem , as Dorn took no pains to keep his rays of the same intensity or hardness except within very wide limits . Experim After due consideration it was decided that a photographic method offered several advantages over an electrical one , especially in that the results were permanent and could be referred to when desired as a check . while a magnetic field was used to deflect the cathode particles . Obviously , from Sagnac 's results , the experiment had to be carried out in vacuo , and a specially good vacuum was required , otherwise the particles would be scattered in their path and no clear lines would be obtained on the photographic plate . The first method thought of was similar to that used by McKenzie in his determination of the velocity of the rays from polonium i.e. , by placing a screen of zinc sulphide in front of the raphic plate and inside the vacuum ; this , on being struck by the rays , phosphoresced and affected the plate . A great advantage offered by this mode of experiment was that it 'Jour . de Phys [ 4 ] , vol. 1 , 1902 , p. 13 . 'Ann . de Chim . et Phys [ 7 ] , vol. 2 , 1897 , p. 496 . 'Lorentz Jubilee Volume , ' p. 595 , 1900 . 8 'Ann . de Chim . et Phys [ 7 ] , vol. 22 , p. 493 , 1901 . 'Phil . Mag [ 6 ] , vol. 10 , p. 538 , 1905 . 1907 . ] Cathode Particles emitted by Metals . did not entail the renewing of the vacuum every time the apparatus to be opened to insert a fresh plate . It was found , however , that the photographs so obtained were slightly fuzzy at the . Hence it was believed that more accurate measurements could be obtained if the rays were allowed to fall directly on the plate , even the vacuum had to be renewed each exposure . The latter method was , therefore , immediately adopted in preference to that of McKenzie . The tubes used were fitted with an anticathode of stout platinum fixed on to a glass tube containing water , good contact being obtained by means of a wire sealed through this tube . Thus , a heavy current could be used with a minimum of risk to the tube . It may be mentioned that in an experiment such as this , where the rays require to be kept as constant in intensity and hardness as possible , the Rontgen bulbs are a constant source of trouble . The very heavy discharge which was required ( as will ) shown later ) , as well as the hardness of the rays which were frequently used , often broke them . This greatly hindered the of the experiment , one having sometimes to wait several weeks before the bulb again available . vork the bulb , a 12-inch Apps induction coil was used . It might be well to mention here the method of using the bulb which was adopted hout the whole course of the experiments , in order to overcome the difficulty due to inconstancy of the rays . The bulb was allowed to work for one minute , then rest for two minutes or slightly longer , then one minute of work and so on . Such a method undoubtedly renders the work much slower ; for example , it will be seen later that nearly four and a-half hours ' exposure was required in some instances , so that the time required for the taking of one such photograph amounted to three days of continual work . The greater regularity and constancy of rays obtained were , however , considered well worth such an expenditure of time . It might be convenient also to give at this stage the method used of testing the constancy and regularity of the Rontgen rays during the exposures . It is well known that if the rays impinge on a plate of lead , and the resulting ionisation of the air is driven back to the plate struck , alarge leak is obtained . This ionisation is partly that due to the secondary rays and partly to the cathode particles which we are ating , and its total amount alters very much with variation in the intensity or hardness of the tube . The apparatus consisted of a brass box ( fig. 1 ) in the centre of one of which was a circular hole cm . in diameter . inside the box and directly opposite this hole were placed a ring A of copper wire gauze and a circular lead plate mm. thick , each larger in diameter than the hole in $ ? ( It ; Sk ? Al [ puoo Japun ? OS xoq OS 'xoq $ SJ0$Iq xoq I uoqa loe eo ) xoq 1907 . ] Cathodc Particle . An attempt was made roughly to measure the penetration of the rays by means of aluminium plates of different thicknesses and a standard plate of tin . The were placed in fronlt of ] -cyauide screen on which the rays were ( it was noted which alulninium plate ) Yave the same absorption as the standard plate . The finally adopted of estimatin the hardness of the rays lvas the parallel spark gap , spherical brass electrodes of about cm . diameter being used . The esults are }iven with each plate . reliminary experiments with a simple form of apparatus to obtain the of exposure necessary for a photograph showed that it almost impo , sible , unless with very exposure , to get an impression on plate while the -break of the induction coil was used , and as the Wehnelt Electrolytic Interrupter is not suited for constant rays , a turbine interrupter was nsed throughout the experiments . The apparatus found most suitable from preliminary experiment wholly of brass 3 mm. thick , and was designed as ( fig. 2 ) . It consisted of ppel rectangular part 9 cm . broad by 2 cm . thick cm . high . To the bottom of this and in the centre fixed , an angle of a narrower portion of the same thickness . long , but cm . bload . ( The reason for beino t. at an of to the top part will be apparent later from the description of the ngeulen t of the netic field . ) In one side of this lower part , at distance of ) cm . from the bottom , was cut the inlet A ) cm . broad by , for the primary rays . A lead plate , 3 cm . by cm . by 2 stened , insulated , on an ebonite block , which again was fixed on a brass , the ebonite of such a size that it fitted exactly into the the apparatus , and so shaped that when it wa sealed in the lead plate opposite the inlet at an ngle of to the prinlary rays horizontally . the brass and the ebonite block passed a wire hich was soldered the lead leflector , and insulated by passed through brass . This wire permitted the metallic reflector earthed or aised to any thought convenient . I may here mention that this wire was kept earthed during the whole course of the experiments . In two lead plates mm. thick , and of such a size as to fit exactly into the lower palt of the apparatus , were cut slits and . long and 1 mm. broad , at such an to the sides of the plates that fitted into the apparatus the slits were exactly parallel to each other , and vertically beneath the centre of the broad upper part , their edges ' perpendicular to the lon edges of the upper of the ratus , and , a will be VOL. LXXIX.\mdash ; A. 2 Il Mr. P. D. Innes . On the Velocity of the [ June 13 , seen later , parallel to the lines of force in the netic field . The slits were fixed during the experiments with the lead reflector , at a distance of cm . between their middle points , the lower one being 0.2 cm . above the inlet A. The inlet was covered with aluminium foil 0 mm. thick , strengthened by a mesh of aluminium mm. thick placed under it , an air-tight joint obtained by means of -wax . The apparatus was connected to a Topler pump and McLeod ) auge by a tube bent to exclude the light . FIG. 3 . Within the upper part of the apparatus was inserted the raphic plate-holder . The holder was of brass , and fitted exactly , so as to slide smoothly up and down . It could be fixed at any distance above the slits by means of a thin brass rod sing through a hole in the top of the holder . This rod had small holes bored in it at intervals of 1 cm . , so that a thin brass pin could be inserted in any hole , and on this pin the top of the holder rested . Thus the plate could be fixed at any required distance above the slit . The strip of raphic plate inserted was of plate and cm . broad . This size was chosen to avoid exerting pressure on the plates while cutting them into very small parts , it been found from previous experience that such pressure tended to fog sensitive plates considerably . Two thick smoothly planed brass plates 1 cm . thick were taken , and one of them soldered to the top of the apparatus . Holes were bored in these plates and by means of nuts ( all of brass , as they were to be in a field ) they could be pressed firmly ether . Lead wires were drawn , and one was placed inside the nuts between the brass plates , just like a washer . When 1907 . ] Cathode Particles emitted by Various Metals . the nuts were screwed up , it was found that a high vacuum could be readily obtained and maintained a considerable time . A great many different kinds of raphic plates were tried :Ilford Ordinary , Ilford Monarch , Cadett Cldinary , Caclett , Cadett Spectrum , Imperial Ordinary , Seed Orthochromatic , , and Wrattenspectrum plates . These brands of plates range from comparatively slow to very , and it is of interest to note those plates which are most sensitive to ordinary are by no means in the same category when it is a question of particles . Thus the Wainwright plates , which are extremely sensitive , the potassium quite easily , were unsuitable for this work . The most suitable here were Cadett Spectrum , L ) , and Seed Orthochromatic , and it is the last named plates that have been mainly used . of Ficld . At first a horse-shoe electro-magnet was used . This was soon discarded in favour of a magnetic field induced by two coils used in the manner of a Helmholtz galvanometer . With such an arrangement , the field is uniform almost up to the boundary of the coils , can be most readily calculated . In these circumstances , too , the particles were , during the whole of their path , under the influence of a uniform magnetic field , and consequently moved in circle , thus immensely the process of the velocity . The coils were most carefully wound on mahogany grooves , there in each coil 17 turns and 19 turns in all . Their circumfelence was measured by a steel tape after each successive layer , the mean radius calculated from this . Its value was cm . The principal galvanometer constant at the centre to umit current absolute was . These calculated constants were checked by comparing the magnetometric deflection obtained with these coils with the deflection due to another standard coil , the circumstances sixnilal . The reement was found to be very satisfactory . The coils were placed parallel to ) longer edges of the ) part of the apparatus , and so perpendicular to the slits . The induction coil was placed at such a distance that its field was practically ible , while its orientation with reference to the apparatus was such that any field due to it was perpendicular to the netic field of the coils , and had , therefore , no effect on the deviation of the cathode particles . The whole arrangement was placed so that the ) etween the earth 's horizontal ( netic field and that of the coils was . As the ) ' * See Maxwell 's ' Electricity . ' . P. D. Innes . On the Velocity of the [ June 13 , horizontal field has only a value of ) , the effect of this resolved along the direction of the magnetic field will be oible . The choice of Helmholtz coils had this further that the Bontgen could be placed inside these , and so closer to the inlet shortening the length of exposure . If , however , tube is to be placed inside the magnetic coils , it has obviously to be turned so that the path of the discharge inside it is parallel to the lines of magnetic force , otherwise the cathode would be so much deflected by the field that it would not strike the anticathode . Such was actually found to be the case during the experiment . It was for this reason that the lower portion of the apparatus was turned at an of to the upper part , thus allowing the bulb to lie along the lines of force , and permitting the X rays to enter at A. When the field is turned on , the cathode particles emitted from reflector move in a circle . They come off the plate in all dixections , but only those which come off at such an angle that their circular path due to the field can pass through the two slits will be able to reach the photographic plate ( fig. 4 ) . If , as is nearly the case , all directions are the same , in to the number of particles eulitted , we shall get as many capable by a circular path of the photo.raphic plate as we should have if we took a pencil of particles proceeding in any one direction vertically ) , and then deviated them . If is the velocity of particles , and the magnetic field , then , therefore where and are respectively the mass and charge of the electron , bein the radius of the circle traced out by the patl ] . Since , as previously stated , these circular paths pass through the two slits , we have two points whose co-ordinates are given . The third point on the path is given by the photograph and , therefore , by the deflection can fix the circle completely . We can , of course , at once calculate , and we know H. Throughout the work I have taken to be invariable , as I assume the electrons which come under notice here to be similar to the ones usually obtained , an assumption which , as it seems to me , is quite reasonable from the results of many experiments on this quantity . The value taken for ? is Results . The results obtained for the various metals with the different kinds of Rontgen rays are given in the tables . It was found that the photographs were not dense enough to be 1neasurable by a microscope , so another 1907 . ] athode Particles emitted by llethod was adopted . They were projected by an arc lamp ou to a sheet , with a Zeiss 10 mm. scale . One observer sketched in the image to the dictation of another standing farther away ; then the process was rep eated , the observers being interchanged , thus eliminating the error due to the person . The magnification was usually about 22 times . Each plate was then 1neasured with a pair of very fine-pointed diyiders , and the results by the two methods compared . The reement was found to be very satis- factory . The pressure was in all the experiments less than . of mercury measured by the McLeod gauge . The distance ) )veen the middle points the slits was cm . , while the raphic plate was cm . above the upper slit . The current in magnetic coils was amperes in case . Table I.\mdash ; Lead . Prints of the photographs of the aboye plates are here appended . should remark that , as they have been intensified with nranium , and the film is somelvhat broken and , they do not print well . The cutting of the plates , and the due to their being put into the holder , does , of course , tend to injure the film . The negatives themselves are much . easy to measure . All the plates mentioned above are given here in order to fihow where they are alike and they differ . Plates and are types of those taken under exactly similar circumstances ; and are examples of those obtained with different intensity of bulb , got by varying the distance of the bulb . It is to be noted here that the bulb is Slightly harder , the spark gap being cm . instead of . ; ' is one of the photographs got with much harder rays . An exalnination of the results of shows that the varyin ] of the distance of the } bulb from the l.eflector causes practically no change in the velocity of the fastest cathode parCicles emitted , their llean velocity being greatest difference from this less than 2 per cent Mr. P. D. Innes . On the elocity of the [ June 13 , Besides varying the distance of the bulb , means were taken to vary the current passing through it by a variation of the current in the primary of the mduction coil ; this varied from 3 amperes to 9 amperes . No difference of velocity was , however , observed . Then the rate of the mercury interrupter was varied , thus altering the number of interruptions of the current in unit time , but here also no change was observable . We therefore conclude that this fastest velocity is quite independent of the intensity of the rays . ( It has not been thought necessary to give these photographs , as they are similar to the ones already given . ) When , however , we examine plate , an example of the hard ray photographs , we find a fairly large difference in the velocity of the fastest particles , amounting to about 7 per cent. This difference is quite beyond the limit of experimental error , as is shown by the agreement of the other plates . This result is typical of all the plates taken with the hard rays . It is interesting to compare the duration of exposure necessary in the different cases . The farther away the bulb is , the longer is the exposure required , thus showing that the intensity does influence the number of particles given off . An increase in the hardness of the tube has the same effect on the number e1nitted as a decrease of intensity . I may mention that only the minimum number of confirmatory photographs were taken with very hard rays in the case of lead and also of all the other 1907 . ] Cathode Particles emitted by Various metals used , as it was in this condition that the tube most frequently " " sparked through\ldquo ; and became useless . When we turn our attention to the velocities of the slowest particles emitted , we find that there is not such close agreement in the results obtained . This was owing to the line being more indistinct than was the case with that due to the fastest rays , doubtless because fewer of the slow ones are emitted . This is what we should expect , if we take the view ( which seems the only natural one ) , that the cause of the reduced velocity of these particles is that they come from a lower layer in the metal , and hence retarded in their progress to the surface . Besides being retarded , they ] also get scattered , so that only a few of those emitted originally would emerge at the surface . It is interesting to note , however , that the results of the various plates , though not so consistent as those of the fastest particles , are quite within the limit of error made in the measurement of the most deviated of the line in any one plate , and we can therefore say that , so far as experiment , it shows them to be the same . It is quite evident from the atives that the line does not gradually diminish in intensity down to zero , and we therefore conclude that there does seem to be a definite minimum velocity which the particles must possess if they are to emerge . articles with a velocity less than this minimum will get caughl and emaiu inside the metal . Table II.\mdash ; Silver . * 454 Mr. P. D. Innes . On the Velocity of [ June 13 , The details have been given of only a few of the photographs taken with this metal , as to give more would merely recount many of the remarks made regarding those with lead . The velocity , as may be seen from the typical plates and , was again independent of the intensity of the rays or the current passing through the tube and varied only with the hardness , as witness the example plate . The plates taken under similar circumstances again agreed within about 2 per cent. , as also did those obtained with different intensities , while the hard rays gave a velocity of about 10 per cent. greater for the fastest particles . This is more than in the case of lead , but it must be remarked that the bulb was harder with silver than with lead . One very interesting point is that the velocities here got for the fastest particles are lower both with soft and hard rays than they were with lead , and that the differences between those got with soft rays and those with hard rays are much the same if we take into account the fact of the tube bein . slightly harder for plate of silver than for plate of lead . The velocities of the slowest particles are , however , of very nearly the same magnitude as those got with lead , at least there is no such marked variation , and the same remarks apply here as did to the slowest lead particles . The long time of exposure necessary with silver is somewhat surprising in view of the fact that its atomic weight is more than half that of lead . Here , too , it varies with the intensity and hardness of the lays . Photographs were taken with very soft rays impinging on zinc . The following is given as an example of the results obtained:\mdash ; Table III . The print given by this is the accompanying one , and is seen to be rather indistinct , despite the long exposure . The negative is of course better . 1907 . ] Partictes 'mitted by letals . Other photographs with the same hardness and intensity confirmed this result , the differences between tlJe results being of a similar nitude to those existing for lead and silver . The velocity is here also independent of the intensity . It is interesting to llote , lowever , that the velocity of the fastest particles emitted from zinc have a velocity much lower than that obtained for lead or silver , the difference being about 16 per cent. if we compare it with the velocity of the lead particles when the tube was in a similar condition . The atomic weight of zinc is , of course , The bulb having been hardened up , atte1npts were made to get a photograph , but when an exposule of seyeral hotlrs . gave no result it was decided to pass on to other metals , especially as fears were entertained the safety of the tube when running so long in a condition . The slowest particles have a velocity almost the same as those of silver . Table Platiuum . The distance between the slits was in this case cm . , the magnetic lield beiug kept as before . The pl'ints from these negatives are the following ones . A curious third line appears in one of them , but as this does not -ome out in any of the others no explanation can be iven of its presence . The results have of course been confirmed by other , those given Mr. P. D. Innes . On the Velocity of the [ June 13 , here being printed as examples of what was Jbtained . The print of plate apparently shows a deflected line much narrower than that occurring in the other plates . Although this is to some extent the case , as can be seen from the results calculated by measurement of the , yet the print seems greatly to exaggerate the difference . Here it is apparent that the velocity of the fastest particles is independent of the intensity , but does increase with increasing hardness of the . The velocity is less than that of the lead particles , but greater than that of silver . The difference between the results for lead and those for platinum is small , but even if the velocity does depend on the atomic weight , we should not expect a great difference , their atomic weights being so near to one another . Lead has an atomic weight of 207 , while that of platinum is 195 . As ards the slowest particles , an interesting point is that they seem to have much the same velocity as resulted from the other metals , if we remember the greater inaccuracy which is possible in measuring their deflection , due , as explained before , to the somewhat indistinct nature of this edge of the line . Table Gold . For this metal the distance between the slits was cm . with the same magnetic field as before . The prints are the following\mdash ; 1907 . ] rticles emitted by It is apparent from plates and thaf ] the velocity of the particles is independent of the intensity of the rays , while shows how the velocity varies with increasing hardness . The plates confirmed in each case by others taken uuder similar circumstances . It is at once apparent that the velocities obtained with gold are practically identical with those in the case of platinum , which is what we should expect if it depends on the atomic weight . The same remarks apply to the est velocities as did formerly to those of platinum . ussion of them clclsion S It will be of to compare the velocities obtained with those by Dorn , in his earlier work . He found velocities varying from to , on the assumption that , had a value of As the value of here used is , we must reduce his restllts per cent. This would give values of about to . Now it is to be remembered that Dorn did not trouble himself very much about keeping the hardness of his Rontgen tube exactly the same . He himself says that " " generally rays to a parallel spark of 10 cm . to 20 cm . were used , and when the tube became harder than this the experiment was stopped while the tube wss softened It , therefore , be admitted that , since the velocity varies with the hardness , the . of the present results with those of Dorn is satisfactory . A fe weeks , just as this work was completion , a paper was published by Bestelmeyer . * He only used one metal , , platinunl , in his experiments , and he says that the velocity varied with the hardness of the tube but not with the intensity , yet he does not mention what hardness of tube he used in the various exposures . His results , taking to be , which is the same value as I have assumed , from to ; thus they are higher , while those of Dornl were } than the results given by me for the fastest particles emitted . 1}estelmeyer 's results for the slowest particles are practically identical with owll The most remarkable fact which arises out of the results yive in this paper is the complete sense of any of the intensity of the Rontgen rays on the velocity of the cathode particles emitted . have seen , we may vary the current the tube , or the number of interruptions unit of of the current in the of uction coil , and no change is ) in the velocity . ) , the tube ma ) be taken farther away , but still we no change in the velocity . Now if the ' Annalen der Physik . ' 458 Mr. P. D. Innes . On the Velocity the [ June 13 , cathode particles are ejected by the energy of t'ne impinging ntgen rays , it is at once evident that a change is to be expected in the velocity of the emitted particles . Let us take as the simplest case that.of an electron free to move and not held in position by other forces . ( The more complicated case of an electron maintained in equilibrium by attractive and repulsive forces can be treated by supposing*that the effective mass of the electron is increased . ) If X is the force in the pulse , and the breadth of the pulse , while ' and are respectively the change and the mass of the electron , then is the impulse acting on the electron , and we have where velocity of light is the time taken by the eleotromagnetic pulse to pass over the electron and is the resulting electronic velocity . Now it is natural to assume that the effective mass of the electron not vary for atoms of the same element , while that the charge is invariable is proved by a large number of experiments . If , however , we alter the position of the tube , with reference to the metallic reflector emitting the rays , keeping its hardness and intensity the same , then the breadth of the pulse will remain as before , but the force X will vary inversely as the square of the distance of the tube from the metal . It follows , therefore , that the velocity acquired by the electron in this latter case cannot possibly be the same as in the first instance . As was pointed out in the introduction to this paper , a gestion has been put forward that the particles got here are the free electrons occurring in the metal , and that they have been ejected by the electromagnetic energy of the rays . If this were so , we should necessarily expect , as stated already , a dependence of the velocity of ejection on the velocity of the primary rays , and as this is not the case , we have strong evidence for the view that the expulsion of these particles is due to disintegration of the atom , and that the velocity acquired by the electron is that imparted by the energy of this disintegration . This view receives additional confirmation if we take into account the values obtained for the velocities , , a velocity greater than cm . per second was obtained in each case . Now , if this velocity were derived entirely from the energy of the incident rays , it is easy to show by calculation that it could not possibly attain to this value . For if X is the force See$J . J. Thomson 's ' Conduction through Gases , ' 2nd edition , See J. J. Thomson 's ' Conduction through Gases , ' p. 320 . 1907 . ] Cathode Particles by in the pulse , and is the time ) the pulse to ) ttSS over the electron , then approxinlately . the of the incident ] per is has that for the rays examined him a of about cm . , but even if we much further , and assume which must be an upper limit , we should still get the eller(y per unit of the incident pulse to be almost a calorie . This value we at once perceive to be far too great acceptance . It is instructive to note that the velocity of the fastest particles omitted varies from metal to metal , . with decreasing atomic This fact is an additional oument for the disintegration theory , it does , that there is a definite energy of disintegrating possessed by the atoms of an element . Bumstead ilas published a the lesults of which seem to be strongly in accord with the ration theory supported ) . He fin that the Rontgen rays , when equally absorbed by different give rise to different , effects . This is quite in reenlent with the results given in this ) is not to be expected that the explosiun will be equally violent in all elements . If we ssume that the velocity of the fastest emitted pal.ticles is a of the relative energy of disintegration in each metal , then , from the variation of this elocity mentioned above , we should expect to have diffe , rent euergies liberated . Take for comparison the metals lead and zinc , which are the two used by Bumstead . The velocity of the fastest lead icles is per second , and that of fastest zinc particles cm . per second , if the conditions of the primary rays are nearly the same . On the ) mentioned above , regarding the velocity and energy of explosion , we shonld say thab the energy liberated in lead would be about 1 . in zinc . Bumstead found that the energy in lead was that liberated in zinc . It is satisfactory to find that . from results , a greater amount of heat 'Ann . Physik , ' vol. 18 , 1905 , } ) . ) ' Phil. Mag [ 6 ] , vol. ] ] , 1906 , p. 292 . Mr. P. D. Innes . On the Velocity of the [ June 13 , might be expected to be obtained in lead than in zinc , a l.esult obtained before umstead . This gests that there is at least some truth in the assumption mentioned above ; it is only a suggestion , however , as so many other factors come in . Thus the number of particles given off , i.e. , the number of explosions taking place , would naturally have a great influence , and this would , if we take into account the duration of exposure necessary for raphing , reatly increase the relative energy generated in lead . Again , the number of particles coming from a layer too low to be emitted , whose kinetic energy is completely absorbed in the body of the metal , and which never emerge at the surface , is a factor not to be neglected ; this would naturally be greatly dependent on the number of atoms " " exploded\ldquo ; at the various depths by the Rontgen rays , as they penetrated the two metals , a number not necessarily varying directly as the energy of primary rays absorbed in each successive layer ( for , as will be discussed later , every atom of an element does not require the same amount of energy to enable it to disintegrate ) . Hence it is not possible to get , by simple calculation , the relative amounts of the total liberated in the above metals , even if the assumption made earlier were quite true , until further investigation eveals more concerning the influencing factors mentioned above . It is , however , interesting to find thab the results are at least qualitatively in agreement . Barkla*has shown that the penetrating power of the secondary Bontgen rays is independent of the intensity of the primary rays , and this result certainly helps to confirm the theory of atomic disintegration . He remarks that the fact discovered by him , that the secondary rays were never more penetrating than the primary rays , is strongly ainst any idea that atoms are " " exploded implying that if this were so , a very penetrating radiation would be produced . This is not necessarily the case , for the corpuscles may not , in fact probably do not , derive all their velocity from the energy of the disintegration , and the greater and perhaps more penetrating part of the secondary radiation is that due to the acceleration of the corpuscles in the atom . If this were not so , we should expect that the greater the velocity possessed by these corpuscles , the more would be the secondary radiation . This is , , by no means the case , for , as we have seen , this velocity certainly decreases ( though comparatively slowly ) with decreasing atomic weight , whereas Barkla finds that the elements of lower atomic ( e.g. , aluminium ) the most penetratirg secondary radiation . The fact that the velocity of the electron emitted increases with the hardness of the rays does not militate against the disintegration theory . 'Phil . Mag [ 6 ] , vol. 11 , 1906 , p. 812 . 1907 . ] Cathode Particles titted by Professor Thomson has , in his well-known papers on the structure of the atom , shown that a reat many of the known } ) erties of tter and the resulting phenomena can be explained by an atom built up of corpuscles in rings in a sphere of positive electricity . Now , the difference between hard and soft rays being that of different electric force and breadth of pulse , it may be the case that the hard rays are able to displace one or more of the corpuscles situated in an inner . If this , then the repulsive forces of the atom have to act on the corpuscle and so eject it at a boreater rate . The disintegration theory gives an explanation , too , of the decrease in the number given off with decreasing intensity of primary rays , as , the energy imparted by each pulse . smaller , more pulses must pass over an ato1n befol'e it reaches the proper . A similar explanation applies to the decreased emitted with hard rays which are less absorbed . The atoms of an element will , of course , not be all in the same state . Some will be near the exploding stage and others will be a way from it , so that we get some idea of the reason why all atoms are not ionised when struck by rays . Again , the number of atoms in the various elelnents in the different stages of disintegration is not lecessarily the same , so different times of exposure are required . It will be noticed that only the metals of atomic have been investigated and , from the results with zinc , it is appalent that a raphic method cannot be used with success in the case of the metals of low atomic weight . Since Barkla finds a disappearance of ' of the rays at a certain , it seems to be of interest to on to the ation of these metals of low atomic . An electrical method has been deyised which it is hoped will effect the investigation of these velocities . of Rcsnlts and Conclusioms . 1 . The velocity of the electrons emitted by lead , silver , zinc , platinum , and gold under the influence of rays has been measured , both for soft and hard rays . 2 . The values found are as follows , the accuracy being within about per cent. :\mdash ; Soft Rays . Lead to 7 Silver to 7 Zinc 6 to 6 Platinum 61 to 7 ' Gold to Soft Rays . Lead to Silver to 7 Zinc 6 to 6 Platinunl to 7 ) ' Gold 0.1 to Soft Rays . Lead to Silver to 7 Zinc 6 to 6 Platinunl to 7 ) ' Gold 0.1 to Soft Rays . Lead to Silver to 7 Zinc 6 to 6 Platinunl to 7 ) ' Gold 0.1 to Soft Rays . Lead to Silver to 7 Zinc 6 to 6 Platinunl to 7 ) ' Gold 0.1 to Hard Rays . 63 to 8 61 to 8 64 to 8 462 Velocity of ticles emitted by 3 . The velocity of the fastest electrons emitted from each metal is completely independent of the intensity of the primary rays , but increases with the hardness of the tube . 4 . The velocity decreases with the atomic weight , the difference between the speed of the fastest electron with hard rays and that with soft rays being practically the same for the various metals , if the variation in hardness of the rays is the same . 5 . A minimum velocity is necessary to enabJ.e the electron to emerge , and the minimum velocity is nearly the same in the different metals . 6 . number of electrons given off decreases with decreasing intensity of the rays , as well as with increasing hardness . 7 . The number emitted also decreases with decreasing atomic weight and density . 8 . conclusion is drawn from calculation and discussion of other theories , that the most probable theory is that of atomic yration . It is that the velocity of the emitted electron is too reat to be that acquired under the influence of the electric force in the X ray pulse . The other theory of ejeciion is discussed and objections to it pointed out . A possible explanation is iven of the increase of the velocity with hardness of the rays , and this fact is shown not to be inconsistent with the disintegration theory . It is a pleasure to me , in conclusion , to acknowledge the keen interest and ever helpful of Professor J. J. Thomson during the whole of the experiments , and I desire to tender him my most sincere thanks .

rspa_1907_0057

0950-1207

The hard and soft states in ductile metals.

463

480

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

G. T. Beilby, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0057

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0057

10.1098/rspa.1907.0057

Measurement

Electricity

Measurement

463 The Hard and Soft States in Ductile Metals . By Gr . T. Beilby , F.B.S. . ( Received June 20 , \#151 ; Read June 27 , 1907 . ) The Micro-structure of Hard-drawn Gold Wires . In connection with the previous research* attempts were made to break down the crystalline structure of the metal as completely as possible by wire drawing . On etching the surface of wires prepared in this way the structure disclosed appeared to be finely granular , no traces of crystalline grains or of patches of uniform orientation being visible . After the publication of the former paper the wires which had been then used were subjected to a more searching examination . Specimens were ground so as to expose longitudinal sections at various depths and these were etched till the true understructure was disclosed . At low magnifications the structure appeared to consist of parallel strands or fibres which became thinner and either pinched out or drew closer together at the point of fracture . The general character of this structure is shown on fig. 1 , which is a diagrammatic sketch of the fractured end of a hard-drawn gold wire . For the proper resolution of the intimate structure of these strands or Fig. 1 . 464 Mr. G. T. Beilby . [ June 20 , fibres , a lens of fairly high N.A. is necessary , and in the photomicrographs , figs. 2 and 3 , a 4-mrn . objective of 095 N.A. was found most suitable . On fig. 2 the etching has not penetrated very deeply , and portions of the surface are still covered by the remains of the disturbed layer which had been produced by the grinding and polishing ; but on the lighter parts of the photograph the internal structure is plainly disclosed , and it is seen that the strands or fibres are composed of grains which have been drawn out and pinched into long torpedo-like forms . Fig. 4 is a diagrammatic sketch of this type of structure . Fig. 3 shows the effect of etching away still more of the matrix of amorphous metal , and with it the smaller fragments of crystalline grains . In photographing this specimen , as the irregularity of the surface made it impossible to get more than a small part in perfect focus at one time , that adjustment of focus was chosen which gave the best general idea of the arrangement of the comparatively large masses which have survived the severe treatment of wire drawing . The material which has been removed from between these ridges is the more soluble , but also the more mechanically stable , amorphous metal which has acted as a rigid matrix to the deformed grains which are enclosed within it . During the successive stages of stretching it seems probable that within any given portion of the wire the roles of protector and protected may be taken in turn by the substance of adjoining grains . A breakdown of structure occurring in certain grains or lamellse will result in the momentary production of a relatively large quantity of the mobile phase at the rubbing surfaces , so that for this moment the line of least resistance will be through these grains which will , therefore , take the chief part in the adjustment of strain . But the momentary mobility having given place to the rigidity of the hardened state , this will become the line of greatest resistance , and the stress will now fall on the adjoining grains or lamellae , which will in their turn break down and flow and in so doing will play their part in the adjustment of strains . Under an augmenting stress , these alternations will naturally continue till the rigidity of the matrix as a whole becomes so great that it will break rather than yield . The present observations show that this stage is reached while there are still comparatively large masses of crystalline substance . which have been concreted into rigidity by the flow which has occurred at surfaces within the mass . These masses do not consist of uniformly 1907 . ] The Hard and Soft States in Ductile Metals . 465 oriented lamellae , but are a conglomerate made up of deformed lamellae cemented together by flowed metal ( fig. 3 ) . These results confirm the conclusions of the earlier research , that the mechanical stability of the amorphous state gives even to the thinnest films an extraordinary power to protect from further destruction the masses of crystalline phase which they enclose . The persistence of the crystalline phase under the most severe mechanical treatment is well illustrated in the case of gold leaf . In my earlier observations on thin metal films I adopted Faraday 's conclusion , that when a gold leaf is floated on a solution of potassium cyanide , the metal is uniformly reduced in thickness by the action of the solvent . Subsequent observations have satisfied me that this is not the case . The cyanide does not proceed by dissolving away the surface uniformly , but it first attacks the amorphous metal , removing it and penetrating right through the substance of the leaf , so that the attenuated film which remains is a skeleton built up of the minute units of the crystalline phase which have survived the severe ordeal of beating . These units are , of course , much too minute to exhibit any crystalline micro-structure , so that but for their difference in solubility they would have escaped detection . A gold leaf may be compared to a light gauzy fabric which has been stiffened by a coating of gum or starch . As the removal of the gum by solution will restore the fabric to its original openness and pliability , so the removal of the flowed amorphous metal by solution leaves the gold leaf with an open spongy texture . A leaf which has been treated in this way absorbs water like a sponge , and in the wet condition appears to have a thickness much greater than that of the original leaf . When spread on a glass plate and dried it becomes less transparent , owing to the replacement of the water by air , and at the same time the appearance of thickness vanishes . The failure of the drastic operation of gold beating to convert the whole of the metal of so thin a film into the amorphous phase suggests that the complete conversion cannot be effected by any purely mechanical process . Observations on the thickness of the surface layer developed by polishing show that the apparently homogeneous layer to which the liquid-like surface is due is not many molecules in thickness , even though the mechanical disturbance penetrates to a much greater depth . As this subject will be fully discussed in another communication , it is not necessary to refer to it further in the present connection . For the metallurgist and the engineer these observations are of importance , in so far as they show that the hardness which is conferred on ductile metals bj any form of cold working is due to the development of a structure in which the distorted remains of the crystalline units are cemented together by a portion 2 i 2 466 Mr. G. T. Beilby . [ June 20 , of the metal itself which has momentarily flowed around , them , and has then congealed into a harder and more resistant form of the metal . Among alloys , metallurgists are familiar with many cases in which rigidity is conferred by the concreting action of one of the constituents separated during crystallisation , but in the pure metals hardening does not result from the building up of a new crystalline structure , but from the breaking down and flow of the already existing structure . By a single blow with a hammer , a crystal of ductile metal is instantly transformed , so that its mechanical properties are as completely changed as if the metal had been converted into a new compound by alloying . This transformation certainly does not depend on the presence of foreign substances or of mixed constituents , for the property of hardening is not in the least diminished by the most careful purification of the metal . It is quite as marked in the purest specimens as in those which are much less pure . The observations which follow were made with the object of defining more accurately the temperature range over which crystallisation and the striking changes in physical properties which accompany it take place in metals in the hardened state . The specimens used were obtained from the same sources as those used in the earlier researches . The gold had a purity of 9997 , the copper of 9993 , and the silver of 10,000 . The Crystallisation Temperature of Hardened Cold . The crystallisation of various ductile metals has been studied , but the most complete series of observations has been made on gold , partly because it does not oxidise or tarnish on heating , and partly because it is rather less difficult to develop the crystalline structure by etching in gold than in silver or copper . Specimens from the hard-drawn gold wires prepared in the earlier experiments , and having the micro-structure shown in figs. 2 and 3 , were ground and polished and were then heated in an air bath for one hour at temperatures ranging from 195 ' to 335 ' . They were afterwards etched in warm aqua regia in which a good deal of gold had already been dissolved . The microscopic examination of the etched specimens was made by normally reflected light with lenses of 0*65 and 0*95 N.A. These lenses were preferred to the immersion lens of T4 N.A. on account of their greater depth of focus . Depth of focus was specially important , as the etching was conducted so as to bring out the crystalline grains in relief , and not merely as the traces of geometrical figures on a perfectly flat field . This relief was brought more clearly into view by giving to the illuminating beam a slight obliquity , so that there was a considerable play of light and shadow among the different 1907.J The Hard and Soft States in Ductile Metals . crystalline facets . In tracing the changes of structure brought about by heat , attention \vas directed , firstly , to the disappearance of the strained type of structure ( figs. 2 and 3 ) and , secondly , to the appearance of a new crystalline structure ( figs. 5 and 6 ) . Microscopic appearance of the etched specimens :\#151 ; 1 . Heated for 1 hour at 195 ' . Distorted grains unchanged ( tigs . 2 and 3 ) . 2 . \gt ; \gt ; \gt ; \gt ; 215'\#151 ; 219 ' . Distorted grains still unchanged . 3 . 225'\#151 ; 230 ' . " " disappearing . 4 . \gt ; \gt ; \gt ; \gt ; 258'\#151 ; 267 ' . New crystalline masses but no grains . 5 . 278'\#151 ; 284 ' . Well-formed crystalline grains ( fig. 5 ) . 6 . \gt ; 5 320'\#151 ; 330 ' . Fig. 5 shows the structure of No. 5 at a magnification of 700 diameters . The differently oriented grains and lamellae can be distinctly traced on the photograph , but were of course much more plainly seen in the microscope , as the natural advantage of the accommodation of the eye , as well as the power of rapidly focussing the microscope from one plane to another , have to be sacrificed when the image is received directly on the photographic film . Fig. 5.\#151 ; Magnification x 700 . A diagrammatic sketch of this structure is , therefore , given on fig. 6 for comparison with the similar sketch of the distorted structure . This great change of structure has been brought about in the solid metal at a temperature 800 ' below the liquefying point and by a temperature rise of only 50 ' . The disappearance of the distorted structure which set in about 225 ' was clear and unmistakable , as was also the appearance of the definitely oriented Mr. GL T. Beilby . [ June 20 , crystals at 278 ' . The intermediate changes of structure were more difficult to follow , but the impression gained from frequent re-exarpination of the specimens was that regular orientation sets in from many centres simultaneously , the oriented units being small but numerous . As the kinetic energy of the molecules rises with the temperature , the larger of these units impress their own orientation on their smaller neighbours , and thus absorb them . This process of growth is only arrested when the smaller units have all been absorbed and the surfaces of the larger crystal grains are in contact with each other . With each rise of temperature a new state of equilibrium among the grains is quickly established , and no re-adjustment of their various spheres of influence takes place thereafter till the kinetic energy of the molecules is again increased by a further rise of temperature . The exact conditions of crystalline growth at higher temperatures have not been studied , but there are definite indications that growth and re-adjustment of equilibrium may continue at temperatures considerably above 300 ' . The Effects of Heat at Various Temperatures on the Mechanical Stability of Harcl-drawn Wires . The term " mechanical stability " is used here in preference to the more specific terms " hardness " or " rigidity . " It has been shown that wiredrawing can be carried to a point at which a certain condition of mechanical stability is reached , so that the wire will break practically without further extension , if a sufficient stress is applied . The ductile metals show their highest tenacity when they are in this condition , and , owing to the relatively small amount of molecular slipping or displacement which occurs before fracture , it maybe accepted that the rigidity and the tenacity break down practically at the same point . This state of stability , therefore , supplies a definite and convenient starting point from which to measure any reduction in stability which may result from heating the hardened metal at various temperatures . For the purpose of the present research it was decided to measure the alterations in stability , not by the " yield-point " as usually understood , but by the stress required to produce a permanent extension of 1 per cent. The standard extension was fixed at this amount only after considerable experience on the behaviour of hard-drawn and annealed wires had been accumulated in this and previous researches . The results obtained by its use show that while considerable irregularity is found in the earliest beginnings of yielding , yet after a 1-per-cent , extension is reached the strain responds fairly promptly and regularly to changes of stress . The oven in which the hard-drawn wires were heated consisted of a thin 1907 . ] The Hard and Soft States in Ductile Metals . 469 steel tube about 5 mm. in diameter and 1 metre long , through which a current up to 125 amperes could be passed . The current was regulated by a water-cooled resistance , while the temperature of the tube was watched by means of a thermo-electric pyrometer . The uniformity of the temperature along the tube was tested once for all by moving the thermo-couple from end to end and noting the temperature . In this way it was found that , with the exception of a short distance at either end , the temperature was practically uniform throughout . The wires annealed were 500/ 600 mm. long ; they were slipped into a thin glass tube which in turn was slipped into the steel tube so as to occupy its middle portion . I am indebted to Mr. Frederick Soddy for the suggestion of this method , and for fitting up for me the necessary apparatus in which it could be carried out . As the available supply of silver wire of uniform quality was , in the first instance , all required for the E.M.F. tests , the principal series of stability tests were made with gold and copper , but after the conclusion of the E.M.F. observations a few stability tests were made with silver wire . The hard-drawn gold wire had a tenacity of 14*6 tons per square inch ; this corresponded with an actual load of rather over 13 lbs. on the wire . Under this load the wire stretched less than 0*3 per cent. , and then yielded no further . The load of 13 lbs. was then applied to wires which had been heated at 30 ' , 100 ' , and 200 ' , and in no case did the extension exceed 0'3 per cent. , the stability , therefore , was still unimpaired . A wire which had been heated at 225 ' was loaded with 12J lbs. , and stretched 0*7 per cent. From the behaviour of the next wire after heating at 235 ' , it was judged that the 225 ' wire would have stood the full load of 13 lbs. without stretching more than 1 per cent. The 235 ' wire was gradually loaded with 12 lbs. , and only stretched 0*3 per cent. , but on increasing the load to 13 lbs. it broke without any general stretching . The measurement of the broken pieces showed an extension of rather less than 1 per cent. While the last two wires fully conformed to the arbitrary standard of stability , their behaviour indicated that a slight impairment of stability had set in . The 250 ' wire was gradually loaded to 13 lbs. , and stretched exactly 1 per cent. The 260 ' wire showed the first failure to reach the full standard ; it was gradually loaded to 12 lbs. , and stretched 1 per cent. The 270 ' wire broke at 11*6 lbs. , and the measurement of the pieces showed that it had stretched 1 per cent. The 280 ' wire , gradually loaded to 11 lbs. , stretched rather less than 1 per cent. , but when the load was increased to 11^ lbs. it stretched rapidly and broke . The measurement of the pieces showed an extension of 5 per cent. , of which 4 per cent , had occurred under the last 470 Mr. Gr . T. Beilby . [ June 20 , i lb. of load . It is to be noted that this serious reduction of stability occurred at 280 ' , which is the temperature at which well-developed crystalline grains were first visible ( fig. 5 ) . The 300 ' wire stretched 1 per cent , with a load of lbs. , and the 355 ' wire gave a similar extension at 4 lbs. The latter is equal to a stress of 4*55 tons per square inch ; the stability has thus fallen to less than one-third of its original value , the chief part of the reduction having occurred under an increase of 100 ' in the annealing temperature . The tests with copper wires showed the unexpected result that hardened copper begins to lose its stability at a lower temperature than gold , and that the loss proceeds much more quickly thereafter . The full load of 21 lbs. , which was still carried by the wire at 200 ' , had to be reduced to 19 lbs. for the 210 ' wire , though at this point the extension was rather less than 1 per cent. With the 230 ' wire a load of 11 lbs. , or little more than half the original load , produced an extension of IT per cent. A minimum load of 6 lbs. was reached by the 305 ' wire ; thus the stability had fallen to 0*28 of its original value under an increase of less than 100 ' in the annealing-temperature . The stability curves of gold and copper ( figs. 8 and 9 ) are shown in an inverted position for more convenient comparison with.the E.M.F. curve ( fig. 7 ) . Mechanical stability in the foregoing observations refers to that property as it exists in the mass of metal as an aggregate . Up to a certain point the stability diminishes as the crystallisation becomes more complete ; but even in the wires annealed at the higher temperatures the size of the crystalline grains is small when compared with the whole cross-section of the wire . It is probable , therefore , that the stability of even the softest aggregate is much higher than that of the individual crystals . In gold , the aggregate stability fell to 4*55 tons per square inch , but it may safely be assumed that this does not represent the minimum stability of the individual crystalline units . This has an important bearing on the behaviour of metals under alternating stresses . When the theory of hardening by flow was first put forward by me in 1904 , * it was then pointed out that the theory might be applied to the elucidation of the disintegration of metals under alternating-stresses . So far as I am aware , this has never been done , and this application will therefore be shortly developed here . Wherever the effects of alternating stresses on the micro-structure have been carefully observed , as in the researches on iron and steel of Ewing and Humphrey , and of Stanton , it has been found that the cracks which led to the ultimate destruction of the specimens generally passed through ferrite * 4 Phil. Mag./ ' August , 1904 . The Hard and Soft States in Ductile ( f So'* too f 2CO 2So ' doo 55b ' Scafc oi oincicort n/ i/ C**j ft A ) J -O J [ Mt*csu\gt ; - S-tAs*-\lt ; sC'UAjiJO wru^LzsrugexL X ' ^vystals foa^rusm ! X Gijjstajs g.'Lowirity X LacuL 1 T V 6o InU ' mas 'll in j rsi 1 . s7st this* / ttlMPJ . So f V / : too y^ . ho So* / \lt ; *\gt ; ' / So* 200 25b ' too* 35o* Lo\lt ; lcL . r 90 tin \lt ; rruta uvriA^x 2/ $teU JhJy ( / / SO 20 0 2,1 O X So* too* 150 ' 200* zSo ' $00* 3So* Figs. 7 , 8 , 9 . grains or areas . Ferrite grains consist of pure iron in its crystalline or softest state . From the analogy of other ductile metals it may be concluded that the stability of the ferrite grains is much less than that of the aggregates Mr. G. T. Beilby . [ June 20 , in which they occur , so that a stress which would be insufficient to produce permanent strain in the aggregate would , if it could gain access to them , be more than sufficient to break down these crystalline units . It is necessary , therefore , to consider in what way disintegrating stresses can gain access to these elements in the mixed structure . It will be shown in the last section of this paper that while the crystalline phase is more perfectly elastic than the hard phase , yet that the amplitude of the vibrations is greater in the latter state . In a reed vibrator the vibrations of the tongue when it is in the hard state are slower but more ample than when it is in the soft state ; the hard tongue is less elastic , but more springy . In an aggregate composed of the two phases which is subjected to rapidly alternating stresses , the hard elements may for this reason be able , with safety to themselves , to transmit stresses which will unduly strain the soft elements . Consider , now , the part played by the mobile phase through which the crystalline passes into the hardened state . In the opening section , the study of the hardened structure , produced by wire-drawing , showed that this structure owes its hardness and stability to the cementing or concreting effect of the flowed metal , while in an earlier paper it was shown that it is possible to overdraw a wire and thus to reduce its hardness and tenacity . The latter result may be taken to mean that , during the final drawings , the mobile phase was not produced in sufficient quantity to cement together again the surfaces at which slipping had occurred . Something of the same nature must occur at the surfaces of slip caused by alternating stresses . When the stress is reversed , slip will occur in the opposite direction , but not on the identical plane on which it occurred before , for the cementing action of the hard phase will prevent this . Suppose the second slip to occur at a thickness of one lamella from the first , a new layer of hard phase will be formed at the other face of the intervening lamella , and a sheet of crystalline phase will thus be sandwiched between two hard sheets . The next reversal of stress may find the sandwiched lamella so strengthened that it can resist further slipping . But suppose that one result of the formation of the sandwich has been to leave the crystalline lamella under a slight tension normal to the surfaces , then with each reversal of stress there will be further slips , and the thickness of the hard sheets will increase at the expense of the crystalline substance . Eventually , if the process continued , and assuming that the tension also continued , the whole of the crystalline material would be used up in thickening the hard sheets , and an incipient crack would develop between them , which , in the absence of further supplies of the mobile phase , every additional slip would rub into greater distinctness . )07 . ] The Hard and Soft States in Ductile Metals . In fig. 10 , these steps are shown diagrammatically. . / a 3 4 Fig. 10.\#151 ; 1 . Unstrained lamellae in c phase . 2 . Layers of hard phase a formed by slipping . 3 . Layers thickened by further slipping . 4 . c phase all used up and a crack , \amp ; , developing . Thermal E.M.F. betiveen Hardened Wires which have been heated at Various Temperatures . In a former paper* the thermal E.M.F. between silver in its hard and soft states was determined by gradually heating the couple till the maximum deflexion of the galvanometer was reached . The temperature at which this occurred was in the neighbourhood of 250 ' . It was then realised that this method could only be expected to give satisfactory results if the hard wire of the couple retained its hardness unimpaired till a definite transition temperature was reached . The observations themselves showed that this was not the case . In the newer experiments it was , therefore , arranged that the couples should not be heated above the temperature at which the hard wire would retain its permanent hardness unimpaired . Preliminary experiments showed that by heating to 100 ' hard wires could be brought into a stable condition while their hardness was only slightly impaired ; this was , therefore , selected as the upper temperature to which the couples were to be heated for the development of their thermal E.M.F. The soft wires of the couples were prepared by heating hard wires to various temperatures in the electrical oven already referred to . After heating , it was necessary to handle the soft wires with great care , so as to avoid straining them by bending or twisting . The two wires of the couple were slipped through separate glass tubes , and the junction was made by binding the projecting ends together with very fine silver wire . The junctions with the galvanometer leads were kept at 17 ' . The couples were heated to 100 ' by plunging them into a glass tube through which steam was freely blowing at atmospheric temperature ; they were cooled by dipping them in water at 17 ' . The temperature difference for which the E.M.F. was .taken * ' Phil. Mag. , ' loc. cit. 474 Mr. G. T. Beilby . [ June 20 , was thus only 83 ' , and it was , therefore , necessary to employ a galvanometer of great sensitiveness . The instrument used was of the Kelvin type , and its resistance was 5 ohms . It was adjusted so that each scale-division was equivalent to 0*054 microvolts . This degree of sensitiveness , while amply sufficient for silver , was less satisfactory for gold . With the former a maximum deflexion of 500 scale-divisions was reached , while with the latter the maximum was only 38 divisions . For this reason many more observations were made with silver than with gold , and the E.M.F. curve of the former has been more fully developed and studied . A number of hard-drawn silver wires were brought into the stable state by hanging them in a glass tube through which steam was blowing freely . Some of these were reserved as standard hard wires , and the others were heated at various temperatures in the electrical oven . In the principal series of observations wires were heated at 130 ' , 155 ' , 175 ' , 200 ' , 220 ' , 240 ' , 260 ' , 280 ' , 305 ' , 325 ' , and 380 ' . Each of these wires was tested in a couple with the standard hard wire and in addition the heated wires were tested in pairs among themselves . These latter tests were a useful check on the former . An example will show the extent to which the two sets of observations were in agreement and will at the same time indicate the order of accuracy of the observations as a whole . Let the letters a , b , c , etc. , stand for the different couples , then:\#151 ; a. 100'\#151 ; 200 ' heated and cooled between 17 ' and 100 ' gave a deflexion of 65 scale-divisions . b. 200'\#151 ; 220 ' n 11 11 ii 86 c. 100'\#151 ; 220 ' n 11 11 ii 156 ii d. 200'\#151 ; 240 ' n 11 17 ii 215 ii e. 220'\#151 ; 240 ' 11 11 11 ii 125 ii f. 100'\#151 ; 240 ' 11 11 11 ii 280 ii Therefore\#151 ; f measured in one step = 280 scale-divisions . / 11 three steps , a + b + c = 276 " / 11 two steps , a-\- d = 280 " / 11 two steps , c-f e = 281 " Observations were made on the effects of heating hardened wires at temperatures below 100 ' : in these the couples were heated and cooled by plunging them alternately in water at 17 ' and in melting ice . With a couple consisting of silver wires in the hardest and softest states respectively , the maximum deflexion obtained for the temperature difference of 83 ' was 500 scale-divisions , equal to 27 microvolts . This corresponds with an average of 0*09 microvolt per 1 ' over the whole range . For the different sections of the annealing range the E.M.F. per 1 ' was as follows : 1907 . ] The Hard and Soft States in Ductile Metals . 475 From 100 ' to 200 ' , 65 scale-divisions = 0*035 microvolt per 1 ' . 200 ' to 220 ' , 86 " = 0*232 " " 220 ' to 240 ' , 125 " = 0*337 " " 240 ' to 260 ' , 45 " = 0*121 " " In the diagram ( fig. 10 ) the deflexions have been plotted exactly as they were observed , and no attempt has been made to smooth the curve . The rapid increase of E.M.F. over the crystallising range is sufficiently obvious . The branch curve which starts at 0 ' and runs up to 200 ' is the result of E.M.F. measurements with hard wires which had not been brought into the stable condition by a preliminary heating in steam . Considerable irregularity at the lower part of the curve was found among wires which had been drawn at different times . These were traced to secular changes of the same nature as those observed by Muir in his experiments on glass-hard steel . Taken in connection with the other observations , the lower part of the curve suggests that the changes which occur up to 200 ' are largely due to the relief of strains of this nature , but that above this point a fundamentally different change sets in . The gold curve of E.M.F. ( fig. 7 ) confirms generally the conclusions drawn from the other observations . It will be noted that the steepest part of the curve corresponds with the temperature range within which complete crystallisation occurs . Heating Curves of the Hardened Metals . . Kepeated attempts have been made to obtain heating curves for hardened silver so as to show the evolution of heat over the transition range , but so far the results have not been sufficiently definite to justify their reproduction here . The researches of Guertler* on the transformation of the silicates and borates from the vitreous to the crystalline state show this heat evolution in a very striking way ; but these substances , owing no doubt to their high viscosity and low conductivity for heat , lend themselves to this method of investigation in a way which metals with their low viscosity and high conductivity cannot be expected to do . Acoustical Tests of the Changes in Elasticity due to Annealing at Various Temperatures . Feed vibrators were prepared in which the vibrating tongues were made of gold , silver , copper , and iron . These reeds could be fitted on a wind chest and sounded in the usual way by compressed air . The pitch of the notes produced was compared with that of the corresponding notes on a * ' Zeits . Anorg . Chem. , J vol. 40 , No. 2 , p. 268 . 476 Mr. G. T. Beilby . [ Junej20 , harmonium , the beats being counted with the help of a stop watch . The tongues were annealed by placing the vsholc reed in an air bath , for , had the tongue been removed from the reed for each annealing , there would have been no certainty that its pitch had not been altered in the subsequent readjustment . With the metals experimented on , it was found generally Soa\#151 ; cfoifisd , 7%6 Ur\gt ; c 3aa \gt ; 0/ 7r\gt ; / . { ft , " , H 9/ 1/ 1 / / or ) / 0 1 0 ' So0 WO ' / to ' 2oo ' 2So* 3 oo ' 3\amp ; ) J\gt ; nn / c \#163 ; in\#153 ; v)'f .J u \#163 ; a T'yrifh^ f'ustrS . / o r 1 Ann * Lb 5 Snr\gt ; 3 fOQ- o0 so ' to(f i So0 2.00 ' zso ' 300 3*0* t*0* Figs. 11 , 12 . that the pitch of the hardened tongue was raised from one to two semitones by annealing at the crystallising temperature . The pitch of the vibrators used was in the neighbourhood of G = 195 vibrations per second , so that an interval of a semitone was equivalent to about 10 beats per second or 600 per minute . As the pitch could be taken either from the note above or 1907 . ] The Hard and Soft States in Ductile Metals . 477 from that below the vibrator note , it was not necessary to count beats quicker than 300/ 360 per minute , and this could readily be done with a limit of error not exceeding 2 per cent. A siren was tried instead of tlm harmonium , but for notes of low pitch the latter was found to be superior . A complete vibration curve for silver is given on fig. 11 . . The two stages in the relief of strain which are indicated on the E.M.F. curve are here shown much more distinctly . After rising at the rate of about 1 vibration per 1 ' up to 100 ' , the rate of increase falls to 0*3 vibration and remains at this rate till 250 ' is reached . A fresh increase begins at 250 ' , which develops at 260 ' into the final very rapid rise of eight vibrations per minute per 1 ' over the next 30 ' . At 290 ' the maximum elasticity is reached , and further heating to 320 ' produces no increase in the rate of vibration . This method of measurement lends itself particularly well to the study of secular changes of elasticity in newly strained metal ; for example , in one instance the rate of vibration of a freshly beaten silver tongue which was kept at the room temperature of 16 ' rose 30 beats in three hours . The amplitude of the vibrations of tongues of gold and silver in the crystalline state is very small , owing to the extreme softness of the metal ; indeed , unless a small and very thin tongue is used , the stresses caused by the vibrations are sufficient to cause permanent strain . This was first discovered with a gold vibrator . As the annealing temperature was raised , the rate of vibration increased quite normally up to 250 ' , but at this point the rate suddenly fell back to what it had been at 100 ' . The annealed tongue was so soft that at first it could only be sounded by a very gentle stream of air : after continued blowing , a portion of its former spring was restored , but with it a lower degree of elasticity . In the case of the silver vibrator , the first tongue used showed the same effect ; it was therefore re-hardened by beating it to one-half of its thickness , after which it showed no signs of reverting to the less elastic condition , even after annealing at 320 ' . It is my intention to apply this method in a more extended investigation of the elasticity of metals and alloys at their various critical points . General Conclusions . 1 . A number of new observations have been made on the phenomena which are associated with the hard and soft states in metals . Certain of these have referred particularly to the phenomena as they occur in goldr silver , and copper , being a continuation of a research described in a previous paper on " The Influence of Phase Changes on the Tenacity of the Ductile Metals.5'* In the course of that research attempts were made to push the * 4 Boy . Soc. Proc. , ' A , vol. 76 , p. 462 . 478 Mr. G. T. Beilby . [ June 20 , process of hardening by wire-drawing to its furthest development , the ideal aimed at being the complete conversion of the metal into the hard or amorphous modification . It was then believed that the maximum tenacity would be reached only when the conversion was practically complete . It has not as yet been found possible to produce a homogeneous specimen of metal entirely in the hard state , for mechanical working , however severe , of even the purest specimens , always produces a mixed structure consisting of the hard and soft phases . The rigidity and tenacity of the hardened metal appear to depend quite as much on the type of structure developed as on the actual proportions in which the two phases are present . 2 . As regards the heat treatment of metals in the hardened state , the temperature ranges over which ( 1 ) recrystallisation , ( 2 ) loss of mechanical stability , ( 3 ) development of thermal E.M.F. between wires in the hard and soft states , and ( 4 ) the complete restoration of elasticity in hardened metal occur , are all so well marked , and they coincide with each other so closely , that there can be no doubt that they point to the occurrence of a true change of state in the hardened metal when a certain temperature is reached . The nature of this change of state is shown by the microscope to be a development of the crystalline from the non-crystalline condition . 3 . In annealing by heat , no important softening of the metal or reduction of mechanical stability occurs till the recrystallisation temperature is reached , but at that point there is a sharp drop in the stability curve , which drop continues as the temperature of annealing is raised over a range of about 50 ' . Over this range there is a corresponding growth of the crystalline grains . Above this range the curve flattens rapidly , but there is evidence that the crystals may continue to grow further as the temperature is raised . The mechanical stability diminishes as the crystals grow larger , and it is probable that the true stability of the crystalline phase as it occurs in single crystals is considerably lower than that of any aggregate of crystalline grains . 4 . The thermo-electric observations , especially those on silver , show that the thermal E.M.F. is an exceedingly delicate indicator of a state of strain in hardened wires . The observed E.M.F. is therefore in part due to strains of a temporary character and in part to a physical change of state of a fundamental nature . By using as the hard wire of the thermo-junctions a wire which had already been annealed at 100 ' , these temporary strains were partly eliminated , but the curve obtained still indicated that strains of this type persisted till a temperature of 180 ' to 200 ' is reached . 5 . The secular changes in hardened metal appear to be limited to the gradual relief of strains similar in kind to the contraction strains observed by Muir in the case of glass-hard steel . This relief of strain differs not 1907 . ] The Hard and Soft States in Ductile Metals . 479 only in degree , but also in kind , from the molecular change which occurs when the crystallisation temperature is reached . The first state is unstable even at ordinary temperatures , while the second is stable up to the lower limit of the crystallisation range . In the first state the relief of strain is not accompanied by any change of micro structure , while in the second a very obvious change occurs . With reference to these two kinds of molecular constraint in hardened metal , it is now suggested that in the first state the molecules themselves are strained , while in the second state they are merely restrained by their mutual cohesion from turning into a uniformly oriented condition . 6 . By using an acoustical test for the detection of minute changes of elasticity in the metal tongue of a reed vibrator , elasticity curves have been obtained which show even more clearly than the E.M.F. curves that the relief of strain by heat occurs in two distinct stages and that the rate of change per degree of temperature is much greater in the second than in the first stage . 7 . It is believed that the hardening of metals by chilling from a high temperature is in certain cases due to the development of contraction strains . These strains , if of sufficient magnitude , will lead to the displacement of the molecules from their crystalline orientation at the internal surfaces of grains and lamellae , thus forming a rigid structure of the mixed phases in the same way as mechanically applied stress would do . From this point of view the hardening produced by hammering and that produced by chilling are both due to the same hind of molecular change of structure . The present observations explain for the first time why ductile metals like gold and copper are not hardened when they are chilled from a high temperature . In the case of gold , for example , recrystallisation can occur over the whole range from the solidifying point at 1080 ' down to the minimum crystallising temperature at 220 ' . It is clear , therefore , that the contraction strains which occur at any point over this range will immediately be relieved by recrystallisation . In cooling below 220 ' the contraction is probably too small to give rise to strains of sufficient magnitude to deform the crystals and to produce a hardened condition . From this point of view , a substance with a high crystallising temperature and a high coefficient of expansion is more likely to harden by chilling than one in which these constants are lower . Substances like the silicates and borates , owing no doubt to their high viscosity , have a comparatively high crystallising temperature ; it is , therefore , easy to cool them quickly through the crystallisation range , hence they most naturally pass into the vitreous or amorphous state on cooling . It VOL. lxxix.\#151 ; a. 2 K The Hard and Soft States in Ductile Metals . would be interesting to ascertain to what extent the hardening of the iron alloys by chilling is due to an increase of viscosity brought about by the added substances . 8 . In considering the effects of repeated alternations of stress in metals , it is evident that the endurance of the specimen will be determined not only by the mechanical stability of the aggregate as a whole , but also by the stability of its separate units of structure . In the ductile metals the stability of the crystalline phase is greatly inferior to that of the amorphous phase ; this inferiority may at first be completely disguised in a mixed structure composed of the two phases , though it may ultimately make itself apparent under repeated alternations of stress . The present observations indicate why the superior plasticity of the crystalline phase , instead of being in all cases a source of strength in the mixed structures produced by hardening , may \#166 ; actually be an element of weakness .

rspa_1907_0058

0950-1207

On light elliptically polarised by reflexion, especially near the polarising angle: a comparison with theory.

481

508

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Richard C. Maclaurin, M. A., LL. D.|Professor J. Larmor, Sec. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0058

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0058

10.1098/rspa.1907.0058

Optics

Tables

Optics

]\gt ; On Light Etliptically by Reflexion , especially the Polarising Angle : a with Theory . * By RICHARD C. MACLAURIN , M.A. , LL. D. , late Fellow of St. John 's College , Cambridge , Professor of Mathematics , Wellington , New Zealand . ( Communicated by Professor J. Larmor , Sec. R.S. Beceived January 14 , \mdash ; Read May 23 , 1907 . ) the phenomena of light to be due to periodic displacements in a rotational ether , we shall vestigate the exact character of these displacements in the case of reflection from an isotropic transparent substance . Two wellknown vectors play the principal parts in any such optical discussion\mdash ; the displacement of the medium and its curl , in the electro-magnetic theory the former is proportional to the magnetic force and the latter to the electric " " displacement To give precision to the discussion we shall deal thoughout with the displacement of the medium , there being no difficulty in , in a similar fashion with the Let the displacement in the incident light be of unit amplitude and polarised in a plane making an angle with the plane of incidence . It can be resolved into two components pt in the plane of incidence , and pt perpendicular to this plane . The corresponding components in the reflected beam then given by the formulae and . [ With lefe1ence to an oversight in his paper " " On Metallic Reflexion . Soc. Proc vol. 77 , Jan. , 1906 , which has recently been pointed out privately by Mr. Hasse , Prof. Maclaurin w1ites that he had himselfobserved it immediately on receipt of the printed paper , but that fortunately the blemish does not invalidate any of the results , beyond requiring a slight modification of the argument in one place . At the foot of p. 218 , in quoting the formula from the previous paper , the first factor was left out . When it is inserted , the modulus of is no longer large , and the follow ing modification becomes necessary . We have ( E-1 ) If both the terms ( E\mdash ; 1 ) and ( F-E ) ) are to be retained , we would lequire two complex constants to specify the layer of transition , which the experimental knowledge would hardly be adequate to detelmine When , however , snlall , term will 1ible compwison with and en if is not small , the term ill not usually be more than one tenth of the second , the modulus of the factol in the latter being large . The neglect of the first term may therefore be expected to produce an error of about one-tenth in the estimated co1rection due to the layer of transition for lalge incidences , and practically no elror at all small incidences . This degree of app1oxima- tion tunately remains adequate , in relation to the exactness of the data utilised in the argument . ] VOL. LXXIX . Prof. R. C. Maclaurin . [ Jan. 14 , Here and are given by the sine and formulae of Fresnel , viz.:\mdash ; where and are the angles of incidence and refraction , and the upper or lower sign is chosen so as to make positive throughout . and are the changes of phase produced by reflection . In the case of an abrupt transition from one medium to the other , would be zero throughout , while would be zero or according as were less or greater than Brewster 's angle In the more usual circumstances of a gradual transition and are given very approximately by the formulae : ; and the difference of phase by the formula Here , where is the in air and is the thickness of the transition layer ; and are numbers depending on the law of distribution of the refractive index within the layer , and is the coefficient of ellipticity at Brewster 's The formula for shows that it is proportional to , so that it will diminish to zero as the incidence increases . In nearly all cases tlJat have beeIl examined is less than unity and is a small quantity . Thus will be small and positive hout , the limit zero as the incidence becomes grazing . At direct incidence , where there is no tion between the plane of incidence and that at angles to it , is equal to With the substances that are dealt with specially in this paper , and in nearly all cases where the experimental rminations are well assured , increases with the incidence , slowly everywhere except near 's angle , in the neighbourhood of which its increase is very rapid . In such circumstances is greater than and the crests of the waves are reached sooner than the crests of the waves . Thus , the * See ' Roy . Soc. Proc , vol. 76 , 1905 , pp. 56 and 57 . 1907 . ] On Light Polarised by Reflexion . displacement perpendicular to the plane of incidence , lags behind , the displacement parallel to that plane , the difference of phase We have seen that the components of the displacement in the reflected beam are given by and . If or , then or , so that the reflected is plane polarised in or perpendicular to the plane of incidence . In other cases , in general , it is elliptically polarised , the elliptic orbit , obtained by from the above equations for and . In this way we obtain as the equation of the ellipse In the special cases of direct or incidence the ellipse enerates into a straight line . If the reflected light is plane in an azimuth iven by , tau , while if the light is plane ised in an azinluth , where . These two cases would represent the state of affairs below and above Brewster 's angle respectively , if the transition from one medium to the other were abrupt , so that in such circumstances the reflected ] would be plane By considering the of and in the formulae above , it appears that the motion in the elliptic orbit takes ) lace in a counter clockwise sense . To give precision to this statement we express the matter thus : the ray ( whether incident or reflected ) in the dilection of the propagation of the . Turn counter clockwise from plane of incidence through an acute until the direction of the incident vibrations is reached . The motion in the orbit is then clockwise.7 We proceed to consider the elements of the ellipse referred to above . Putting , the equation of ) ellipse becomes If be the azimuth oi the major axis , we have * Of course , if were rreater t , this statement would } to be reversed . Moreover , if we were dealing with the curl stead of the displacement , vould be interchanged ) , so that the component palallel to the plaue of cidellCO old ehind the other . we were with the curl , instead of the , the nnotiuu would be counter clockwise . Prof R. C. Maclaurin . [ Jan. 14 , The eccentricity ( e ) is given by Putting , this gives while for the semi-axes and b ) we have and We shall develop various laws regarding the variation of the elliptic elements from these simple formulae , and by way of numerical illustration shall apply them to the of reflexion from diamond and realgar . These substances are selected , because , for them , we have the cal.eful experiments of Jamin to compare with theory , and so to assure us of the firm foundations on which we are , and also because while their refractive indices are almost identical , their coefficients of ellipticity at the Principal Incidence differ very considerably , so that their comparison should bring into strong relief the influence of this ellipticity . The ellipticity in the case of realgar is abnormally high ; it stands near the head of Jamin 's list , while diamond occupies a place near the middle . In realgar we shall take and , and for diamond and . This makes in the case of realgar , and in the case of diamond . he difference of phase and the coefficient of ellipticity 1907 . ] On Light Elliptically Polarised by Reflexion . These results are represented graphically in figs. 1 , 2 , 3 , and 4 below . In these figures the crosses indicate the results of ; experiments , so that the agreement between theory and experiment is readily estimated . FIG. l.\mdash ; Difference of phase for realgar . FI 2.\mdash ; Coefficient of ellipticity for realgar . We have seen that the azimuth of the major axis of the ellipse is given by the formula , where At direct incidence and , so that ; at grazing incidence and , so that . Thus as the incidence increases will diminish from , and for most azimuths it will pass through the value zero at the Prinoipal Incidence where Prof R. C. Maclaurin . [ Jan. 14 , FIG. Ditierence of phase for diamond . . 4.\mdash ; Coefficient of ellipticity for diamond . However , for azimuths greater than , where this will not be the case . In such circumstances will pass through infinity at the Principal Incidence , and will change from Since , it will be seen that if be less than the Principal Incidence , is negative , and is less than ; while if be greater than the Principal Incidence , is greater than\mdash ; 90o . Henoe . for such azimuths the graph for will , in the neighbourhood of the Principal Incidence , have the form represented in figs. 5 and 6 below . There must , therefore , be some incidences for which the azimuth is a minimum or maximum . To find them we note that is stationary when 1907 . ] On Light Polarised by . The minima will be found in the bourhood of the Principal Incidence . , we have , therefore Also . This makes a minimnm when , and , as the is very near will be very small . ; where is a small quantity . Thus the equation for becomes . is positive , so that for real ( small ) values of we must have ' negative . This requires and or It is then only for such azimuths that is stationary anywhere . From the equation we see that increases from to as increases from to . Hence in this varies from to-l , and we may put , where is snlall when is near . The equation for then becomes . ( 1 ) If , and be all of the same order of small quantities , then by retaining only the lowest terms in ( 1 ) we get , so that One root is positive and the other negative , the positive root being larger . Thus the maximum beyond the Principal Incidence is soulewhat further from that angle than the minimum that occurs before the Principal Incidence is reached . If be so small as to be } ible , then and ( 1 ) becomes on terms of the fourth order of small quantities . This gives a positive root , , and a negative root , . If be negative , the positive root is numerically the larger ; while if be ) ositive , the negative root is the . It will be found that ) , so that the sigll of depends on syhethcr Prof. R. C. Maclaurin . is greater or less than . It will be negative for such highly refringent substances as diamond and realgar , but more usually positive . If be not zero , but small compared with , we get for the positive root of ( 1 ) above , , so that , and for the negative root and The following tables give the values of for the azimuth in the neighbourhood of the Principal Incidence for diamond and realgar . It will be seen that the maxima and minima are much nearer the Principal Incidence in the first case than in the second . The figures that follow represent the same results graphically , fig. 5 referring to diamond and to realgar ; the scale of in the former figure being four times that in the latter:\mdash ; Diamond . From these tables and figures it appears that , in the case of diamond , the maximum value of about 1 minutes beyond the Principal Incidence and the minimum about 5 minutes below that angle ; while the corresponding quantities for realgar are 5 degrees and 4S degrees respectively . For azimuths less than we have , seen that there are no such maxima and minima , and that decreases throughout from to as the incidence increases , and passes through zero at the Principal Incidence . The 1907 . ] On Light Elliptically by Reflexion . . 5.\mdash ; Diamond . FIG. 6 . \mdash ; Realgar . Prof. R. C. Maclaurin . [ Jan. 14 , table sets out the values of for various azimuths and incidences in the case of diamond and realgar . The first entry in each case refers to realgar and the second to diamond . These results are exhibited in figs. 7 and 8 below , the first dealing with realgar and the second with diamond . FIG. 7.\mdash ; Realgar . 1907 . ] Light Elliptically Polarised by Reflexion . . 8.\mdash ; Diamond . We have seen that if the transition from one medium to another were abrupt instead of radual , the reflected would always be plaue polarised . The azimuth of the plane of polarisation would be or , according as the of incidence were less or greater than the Principal Incidence . The angle is } iven by the equation , and it must be rememl ) ered that is not the same in the neighbourhood of the Principal Incidence in the two cases of abrupt and gradual transition . represents an ellipse whose FIG. 9 . centre is and of which is the semi-major axis . Of and OP pnrallel and perpendicular ) ectively to the of incidence . are fents parallel to Ol ' OI ectively . represents of the cement palallcl to the plane of incidence , and Ol the Prof. R. C. Maclaurin . [ Jan. 14 , amplitude for the perpendicular plane . Thus OE and OF HOE , so that HOE represents the angle . It will be seen from such a figure , or from the equation , that is numerically less or greater than , according as is less or greater than . Let represent the amount of turning tou nrds the plane of incidence in passing from the azimuth of plane polarised light in the case of abrupt transition to the axis of the elliptic orbit when the layer of transition is taken into account . will be positive or negative according as is less or greater than , i.e. , according as is less or greater than unity . Thus will be negative for all angles of incidence when the azimuth is greater than . It will also be negative for high and low incidences , when is nearly unity , for azimuths greater than ; in all other cases it will be positive . At the Principal Incidence , is zero for azimuths less than and for greater azimuths . Thus the layer of transition not only replaces linear by elliptical polarisation , but , when the azimuth exceeds , it turns the direction of the " " major axis\ldquo ; from the plane of incidence through a right an gle . * It will be seen later that the ) is circular at the azimuth , so that there is no discontinuity in passing through that . The following table sets out the values of for various azimuths and incidences , the first entry referring to and the second to diamond:\mdash ; We shall next consider the variation of the quantity , the ratio of the axes , on which the eccentricity of the ellipse depends . We have See figs. 21 and 22 below . 1907 . ] On Light Elliptically by where and . Thus vanishes when or , or when or . These , of course , are the cases of plane polarisation , or S being azimuths in or perpendicular to the plane of incidence , and or being direct or grazing incidence at any azimuth . For any given azimuth begins at zero for direct incidence , and ends at zero for grazing incidence . It must pass through certain maxima or minima in this interval . From the equation for V we see that is stationary when sin2 This is satisfied at the Principal Incidence where , and since is stationary with . As we move in either direction from the Principal Incidence , diminishes and , for all azimuths less than increases . For substances such as diamond , for which the variation of is very rapid in the neighbourhood of the Principal Incidence , the variation of will be mainly controlled by that of , and we shall have a maximum at the Principal Incidence . With other substances , such as , for which the variation of is less rapid , the increase in may more than counterbalance the decrease in . In such circumstances will be a minimum at the Principal Incidence , and there will be two maxima on each side of this and not far from it . Especially with substances of high refractive index , the increase of beyond the Principal Incidence is much more rapid than its decrease before , so that the maximum beyond the Principal Incidence will be further from it than the one below that incidence . For azimuths greater than , we have , so that diminishes with the increase of . In this case , therefore , diminishes as the incidence increases beyond the Principal Incidence . There can thus be no maximum beyond that incidence , the only maximum possible being one very near the Principal Incidence and below it . The following tables set out the values of and of the eccentricity ( e ) for realgar and diamond , and the results for are exhibited graphically in figs. 10 and 11:\mdash ; Prof R. C. Maclaurin . [ Jan. 14 , \mdash ; \mdash ; coco t 5 5 ( r o oo oo oo oo oo oo oo oo oo oo oo oo oo oo co co o r 5oeLO O oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo os oo oo oo oo oo oo os oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo 5 oo oo oo oo oo oo oo oo oo oo oo co oo oo \mdash ; oo oo oo oo oo oo co oo oo oo oo oo oo oo 5 oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo o-r cooo oo oo oo oo oo oo oo oo oo oo oo co oo e- e- e- e- e- e- e- S 907 . ] On Light by Reflexion : . 496 Prof C. Maclaurin . [ Jan. 14 , FIG. ll.\mdash ; Diamond . On p. 493 are considered the variation of for different incidences at a given azimuth . Its variation for a given incidence at different azimuths is very simply discussed . Under such circumstances and are given , so that varies as , and is greatest when , in which case or , according as the incidence is below or beyond the Principal Incidence . Thus at a given incidence begins at zero with , and ends with zero at . It passes through a maximum at the azimuth , and its maximum value is or , according as the incidence is less or greater than the Principal Incidence . The following table gives the position and magnitude of the maxima for various incidences:\mdash ; 1907 . ] On Light Elliptically Polarised by Reflexion . These results are represented in figs. 12 and 13 below , the first representing the plan ( ) and the second the elevation . FIG. 12.\mdash ; The continuous curve represents the results for realgar , the dotted one for diamond . VOL. LXXIX.\mdash ; A. Prof R. C. Maclaurin . [ Jan. 14 , FIG. 13.\mdash ; The continuous curve corresponds to realgar , the dotted curve to diamond . The axes of the elliptic orbit are given by the equations and At direct or grazing incidence we have and , so that for all azimuths . Wae shall consider how a-varies with the incidence and azimuth . We have Thus for a given incidence , where is a constant.-Hence we have Since an , we have and and both being less than . Moreover , is never greater than , so that is positive and less than unity . Hence if be less than , so that is positive , we have is consequently negative , and diminishes as increases . However , this argument is no longer good when is greater than . We shall , therefore , proceed to 1907 . ] On Light Elliptically by Reflexion . investigate the roots of the equation . Combining this with , we the positive sign being taken , as is positive . For brevity , write , so that we have an equation obviously satisfied by , corresponding to , and clearin of fractions and of the root , we get ; The process of squaring introduces an irrelevant root . To exclude this the sign of is to be positive , and as is necessarily positive this requires to be positive . The value of given above makes and as is positive or ative according as the incidence is less or greater than the Principal Incidence , we must take the lower sign below the Principal Incidence and the upper sign beyond it . Thus below the Principal Incidence we have But is positive , and is also positive , except very near the Principal Incidence . Hence , except in the immediate neighbourhood of the Principal Incidence , would be negative if were stationary , so that there is no real value of for which is stationary . Beyond the Principal Incidence our formula gives . The numerator of this fraction is positive and the denominator negative , except very near the Principal Incidence . We see then that is negative throughout , except in the immediate vicinity of the Principal Incidence , that diminishes as the azimuth increases for all incidences outside a small region near the Principal Incidence . This extends on each side of the Principal Incidence from to . Suppose that Prof R. C. Maclaurin . [ Jan. 14 , when , where is the Principal Incidence and is small . We have , so that ( approx. ) , where , as we have seen , is very smalL This equation gives , very approximately and owing to the smallness of this is usually very small . For diamond we have and for realgar At the Principal Incidence is stationary when , i.e. , when and , the azimuth giving circular polarisation . The formula for and are and where At the Principal Incidence , so that or . If we have and , and we must interchange and if we take S- . As is the greater of the two , the first or second of these values must be assigned to , according as is greater or less than , i.e. , according as is less or greater than Thus , at the Principal Incidence , if be less than we have while if be greater than we have . Hence , after passing the azimuth increases from to It is , therefore , a minimum at the azimuth . It must be remembered , however , that in passing through this azimuth , the angle which the major axis makes with the plane of incidence suddenly changes irom to This means , of course , that the axis is perpendicular to the plane of incidence , instead of being in that plane . At the Principal Incidence the axis in the plane of incidence is throughout , while the axis perpendicular to that plane is . As the azimuth increases , the first axis diminishes steadily from to zero , while the second increases steadily from zero to We have still to consider the variations of with the incidence for a given azimuth . From the formula for , viz. , we see that when , and when . Thus as the azimuth increases from one of these values to the other , the curve for must 1907 . ] On Light Ellipfically by Reflexion . pass from that representing , which rises steadily as the angle of incidence increases , to that representing , which is equal to at direct and incidence , but falls to a minimum in the interval at the Principal Incidence . All these statements as to the variation of are illustrated in the table and figures that follow . The table gives the values of for various incidences and azimuths , the first entry referring to realgar , and the second to diamond . Figs. 14 and 15 below represent the same results graphically . FIG. 14.\mdash ; Realgar . Prof. R. C. Maclaurin . [ Jan. 14 , FIG. 15.\mdash ; Diamond . We have next to consider the mode of variation of the other semiaxis , with the incidence and azimuth . The formulae already obtained give where is a constant for a given incidence . This enables us to discuss the variation of with the azimuth . We see that vanishes with when and , so that we should expect it to pass through a maximum somewhere in the interval . The above equation for gives Thus is a maximum when . Except for the of sign , this is the same equation as that dealt with above on p. 499 . It corresponds , in the notation of that , with the equation In the present case we require to be negative , and , as before , we have Hence below the Principle Incidence we must take the upper , and the lower sign beyond it . We thus obtain 1907 . ] On Light Polarised by Reflexion . the upper or lower sign being taken according as the incidence is less or greater than the Principle Incidence . In both cases we get a real value for for any iven incidence . The magnitude of the corresponding maximum is A simple geometrical construction for and the maximum of is easily obtained . In fig. 16 , take AB , an the angle BAC equal FIG. 16 . to or , according as the incidence is less or greater than the Principal Incidence . Draw AD perpendicular to , and in it take a point so that Then AP represents the maximum value of , and represents To prove this , draw BE and CF perpendicular to CA and AB respectively . Then and Hence . AC ; also ; but . AB , and . CE CD . , so that The changes in the magnitude of and are readily discussed by m..eans of this construction . As increases from to increases from unity . It afterwards diminishes to unity , so that increases from to and then diminishes to . Also , as increases from to S , AD increases from zero to and also increases , so that increases steadily in this range from to . After this AD diminishes to zero . In Prof. R. C. claurin . the neighbourhood of the Principal Incidence we have so that in this region . As we go from the Principal Incidence , BC increases , so that diminishes . Thus the maximum value of is found the Principal Incidence , and its value is . The following table gives the position and magnitude of the maximum value of for various incidences:\mdash ; The ridge of maxima is represented in plan and elevation in figs. 17 and 18 below . * See . Proc , .vol . 76 , 1905 , p. 61 . 1907 . ] On Light Elliptically Polarised by Reflexion . FIG. 18.\mdash ; The continuous curve refers to realgar , the dotted curve to diamond . In considering the variation of with the incidence for a given azimuth , we take As the incidence increases from direct incidence to the Principal Incidence , increases throughout , except at the end where it is stationary . * Tan and also increase , so that increases from zero upwards . When the Principal Incidence is passed , decreases again to zero , so that does likewise . It is evident then that passes a maximum between the Principal Incidence and grazing incidence , and that , as the azimuth increases to the position of this maximum draws closer and closer to the Principal Incidence . The following table gives the values of for and diamond for various incidences and azimuths:\mdash ; * See ' Boy . Soc. Proc , vol. 76 , 1905 , p. 61 . Prof R. C. Maclaurin . [ Jan. 14 , These results are represented in figs. 19 and 20 below . FIG. 19.\mdash ; Realgar . FIG. 20.\mdash ; Diamond . The area of the elliptic orbit is 1907 . ] On Light by Reflexio FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 21.\mdash ; Realgar . FIG. 22.\mdash ; Diamond . On Light Elliptically by Reflexion . For a given incidence this is proportional to , it therefore grows from zero to a maximum when , and diminishes again to zero as approaches For a given azimuth the area is proportional to . As increases from zero to the Principal Incidence , increases , and Rsin increases , except near the Principal Incidence , where it is stationary . Hence the area of the ellipse constantly increases within this range . In the neighbourhood of the Principal Incidence is constant , so that the area is proportional to , and continues to increase throughout a short range beyond the Principal Incidence . When this region is passed , diminishes rapidly to zero , so that the area diminishes to zero , passing through a maximum between the Principal Incidence and grazing incidence . Figs. 21 and 22 represent half of the elliptic orbit , drawn to scale for various azimuths at the Principal Incidence .

rspa_1907_0059

0950-1207

The fluted spectrum of titanium oxide.

509

518

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

A. Fowler, A. R. C. S., F. R. A. S.|H. L. Callendar, M. A., LL. D., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0059

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0059

10.1098/rspa.1907.0059

Atomic Physics

Thermodynamics

Atomic Physics

509 The Fluted Spectrum of Titanium Oxide . By A. Fowler , A.R.C.S. , F.R.A.S. , Assistant Professor of Physics , Royal College of Science , South Kensington . ( Communicated by H. L. Callendar , M.A. , LL. D. , F.R.S. , Professor of Physics , Royal College of Science , S.W. Received May 18 , \#151 ; Read June 20 , 1907 . ) [ Plate 6 . ] In a previous paper* it was shown that most of the dark flutings which are characteristic of the spectra of Antarian or third type stars correspond with flutings which appear in spectra obtained from oxide and chloride of titanium , but it was then uncertain whether the flutings originated in the vapour of the oxide or in that of the metal itself . The purpose of the present communication is to give an account of the observations which have led to the conclusion that the flutings in question are produced by a compound of titanium with oxygen , and to give a revision of the table of wave-lengths based upon photographs taken with increased dispersion . The Oxide Origin of the Flutings . The general principle underlying the investigation was the very simple one that if the " Antarian " flutings were due to the element titanium they should appear , under favourable conditions , in the spectra of compounds of the metal with different elements , whereas if they were produced by the oxide they would only appear when the metal was combined with oxygen , or was able to combine with it during the experiment . The most decisive results have been obtained from experiments with titanium chloride ( TiCl4 ) , a heavy volatile liquid , the vapour of which rapidly combines with oxygen on exposure to moi\amp ; t air and forms dense fumes of titanium oxychloride . On account of this affinity for oxygen , considerable care is necessary in attempting to obtain the spectrum of the chloride without contamination with that of the oxide . The observations have shown , however , that not only is the spectrum of the chloride free from the Antarian flutings , but that it is characterised by a perfectly different group of flutings in the blue which does not occur in the stellar spectra . This " chloride group , " as it may be conveniently called for purposes of reference , is a somewhat complicated cluster of flutings fading towards the violet , having three principal heads at wave-lengths 4199*5 , 4192*7 , and 4188*0 , of which the middle one is the brightest . * 'Roy . Soc. Proc. , J vol. 73 , p. 219 , 1904 . Mr. A. Fowler . [ May 18 , Experiments with metallic titanium have also indicated that the Antarian flutings are only produced in the presence of oxygen . Particulars of the experiments are as follows:\#151 ; ( 1 ) Vacuum tubes containing the vapour of titanium chloride were prepared in the usual manner , but it may be remarked that , in consequence of the low conductivity of the vapour , the most satisfactory results were obtained with tubes giving a total length of discharge not exceeding two inches . When the capillary tube was very narrow , little more than a line spectrum was observed , even when there was no jar in the circuit there was just a trace of the chloride flutings already mentioned , and enhanced as well as are lines of titanium were well brought out . In the spectrum of the bulb , however , the chloride group was a conspicuous feature , and enhanced lines were not seen , while arc lines were numerous . When a tube of wider bore was chosen , the spectrum of the capillary corresponded very closely with that of the bulb in the previous experiment . In each case , the passage of the jar spark resulted in the appearance of the line spectrum of chlorine and the almost total suppression of that of titanium . No traces whatever of the Antarian flutings were obtained in these experiments , although the presence of the chloride group of flutings indicated that the electrical conditions in some cases were not unfavourable for their production , if their existence depended only upon the presence of titanium . ( 2 ) The spectrum of titanium chloride was further investigated by introducing some of the liquid into a tube containing dry nitrogen at atmospheric pressure . A tube 2 cm . in diameter and about 10 cm . in length was sealed at one end and provided with platinum electrodes , having a sparking distance of about 1 cm . Through a rubber stopper at the other end two smaller tubes were passed , one for the admission of any desired gas and the other for the escape of the gas driven out . The admission tube was of ( - form , and attached to the vertical arm by a rubber connection was a previously prepared tube containing a small quantity of titanium chloride . This receptacle consisted of a piece of glass tubing about 3 cm . long , drawn out and sealed at its lower end , and scratched with a file so that it might be easily broken ; a short piece of rubber tubing was attached at the other end , and when a sufficient quantity of the liquid had been poured in to fill both glass and rubber tube , the latter was closed with a pinch-cock . In this way a sample of the liquid practically free from oxide was secured , and it could be introduced into the sparking tube when desired without further exposure to the external air . The apparatus having been thoroughly dried by a current of warm dry air , 1907 . ] The Fluted Spectrum of Titanium Oxide . 511 it was filled with nitrogen , and the titanium chloride was then admitted by breaking off the end of the tube containing it . Even after all the precautions taken to exclude moisture , there was a very slight formation of fumes on the exposure of the liquid , which , however , subsided in a few minutes . On passing the spark ( without jar ) numerous lines of titaniumland the chloride group of flutings were seen , but there was no trace of the Antarian series of flutings . When the jar spark was passed , the chloride flutings were abolished , and enhanced lines of titanium were strongly marked . To carry the experiment a stage further , the nitrogen was replaced by dry oxygen , and the trace of oxychloride fumes again resulting from residual moisture was allowed to subside . On passing the spark the Antarian series of flutings formed the most prominent feature of the spectrum , but the chloride group was also visible . ( 3 ) A similar experiment in which the sparking tube was filled with dry hydrogen gave an identical result . That is , the chloride group of flutings was visible , while the Antarian series was absent . In this experiment a purple deposit , presumably of titanous chloride ( Ti2Cl6 ) , was formed on the walls of the tube . ( 4 ) Experiments on the arc spectrum of titanium chloride ( on iron poles ) in an atmosphere of dried nitrogen were also made . Under these conditions , the line spectrum of titanium and the chloride group of flutings were well developed , but the Antarian flutings were excessively feeble and the traces observed were probably due to residual oxygen or moisture , as a thin white deposit was formed on the poles . With an atmosphere of oxygen , however , the Antarian flutings came out strongly . ( 5 ) In another series of experiments , the arc was passed between iron poles , charged with metallic titanium , in an atmosphere of dried nitrogen . Only feeble traces of the Antarian flutings were seen , and these may again be sufficiently accounted for by residual oxygen or moisture . The flutings , however , were well developed when oxygen or air were substituted for nitrogen , but in neither case was the chloride group observed . ( 6 ) As already noted in the previous paper , the Antarian flutings are also visible under the following conditions:\#151 ; ( a ) Arc in air between carbon poles well charged with oxide of titanium , the flutings being best seen in the " flame " when the arc is long . ( b ) Spark , without jar , through fumes of oxychloride of titanium ; with a spark of suitable intensity , the line spectrum is almost eliminated , but there is a continuous spectrum of considerable strength which doubtless arises from particles which are incompletely volatilised . Mr. A. Fowler . [ May 18 , ( c ) Oxy-coal-gas flame , fed with the fumes of titanium oxychloride ; the flutings are in this case not easily seen on account of the bright continuous spectrum which is also present . These observations do not seem to admit of any other conclusion than that the flutings represented in the spectra of Antarian stars are produced by a compound of titanium with oxygen , and not by the vapour of the metal itself . The result is of some importance as indicating that the source of the fluted absorption in the Antarian stars is at a temperature low enough to permit the formation of a chemical compound , and also as demonstrating the presence of oxygen , of the existence of which in these stars there is otherwise no direct evidence . The investigation has lately gained additional interest in consequence of Professor Hale 's discovery of some of the less refrangible flutings in the spectra of sun-spots.* The Wave-lengths of the Flutings . The identification of the flutings of the Antarian stars with those of titanium rested upon such a great number of apparent coincidences in position , and similarity of appearance , that it was almost independent of a very precise knowledge of the wave-lengths , and was sufficiently justified by the wave-lengths derived from photographs taken with the moderate dispersion then available . No further determinations of the positions of the stellar bands have been published , but the application of a more powerful spectrograph has made it possible to determine the wave-lengths of the terrestrial flutings with much greater precision . The instrument employed was a very efficient one of the Littrow form , having one prism of 60 ' = 1*6467 ) and a focal length of 12 feet , the effective aperture employed being 1^ inches . The spectrum is photographed in sections on plates 12 x 2\#163 ; inches , and the linear dispersion ranges from 16 tenth-metres per millimetre at A. 7100 to 2*7 tenth-metres per millimetre at A 4350 . With this dispersion the heads of many of the flutings are found to be more complex than was formerly suspected , but neither this nor the corrections of the wave-lengths affects the probability of identity with the stellar flutings . Many experiments have been made in order to produce the fluted spectrum as free as possible from superposed lines . The uncondensed spark passed through the fumes from titanium chloride is possibly the best way of obtaining this result , but the photographic registration with high dispersion is difficult . The most convenient method yet found is to volatilise titanium * ' Astrophysical Journal , ' vol. 25 , p. 75 , 1907 . 1907 . ] The Fluted Spectrum of Titanium Oxide . 513 oxide in the electric arc between iron poles , and the photographs reproduced in Plate 6 were obtained in this manner . Under these conditions , the " line " spectrum of titanium is not strongly marked , and iron is only represented by the brighter lines of its flame spectrum . Nearly all of these metallic lines appear on the more refrangible side of D , and are strongest towards the blue . The flutings which occur in the flame of the iron arc do not appear to contribute appreciably to the combined spectrum of iron and titanium oxide . Incidentally , the photographs admirably illustrate the simplicity of the line spectrum of iron in the arc-flame . For the determination of wave-lengths , the reference lines employed were those of iron and titanium occurring with the flutings , whenever suitable lines were available for the purpose . In many cases , however , and in the whole region on the red side of D , the reference lines were selected from a spectrum of the iron arc photographed in juxtaposition with the fluted spectrum ; the shutter for exposing the two parts of the slit was entirely detached from the spectrograph , and there was no evidence of relative shift of the two spectra in the plates measured . The adopted positions of the reference lines were those given by Eowland in his table of solar spectrum wave-lengths , and the interpolation was made in the usual manner by the Cornu-Hartmann formula . For the part of the spectrum less refrangible than 6860 , in which Eowland does not tabulate any lines of iron , lines of the arc spectrum were first identified with solar lines and the corresponding solar wave-lengths adopted . The wave-lengths given in the table are stated to two places of decimals , except in the extreme red , where .the dispersion is relatively small , and in cases where the edges of the flutings are not very sharply defined . No attempt has yet been made to tabulate the thousands of fine " structure lines " which compose the flutings , but all the " heads " and " sub-heads " which could be identified as such have been included . Some of the more marked details in the heads , probably consisting of relatively strong structure lines , or ( dusters of such lines , have also been measured ; for want of a better term , they are described as " maxima . " The classification into heads and sub-heads is somewhat arbitrary in many cases , and it should be explained that some of the heads are classed as such , not because they are prominent features of the spectrum , but because of their probable association in series with stronger heads in the groups to which they belong . With the high dispersion employed , the heads of some of the fainter flutings , especially in the region more refrangible than F , almost lose their ? distinctive characteristics , and their identification has only been possible in vol. lxxix.\#151 ; -Jl . 2 N Mr. A. Fowler . [ May 18 , some cases by comparison with photographs taken on a smaller scale . It has been considered desirable to include these for reference in comparisons with stellar spectra , which are usually photographed with moderate dispersion , and also because of their possible use in investigations of the series relationships of the various flutings . The relative intensities of the flutings are roughly shown by the numbers in the second column of .the table , and an attempt is made in the third column to indicate the general characteristics by symbols having the following significance:\#151 ; ( a ) The fluting fades out rapidly , and is not clearly resolved with the dispersion employed . These appear as lines with a slight shading towards the red . ( b ) The fluting fades away more gradually , and the structure lines are very closely crowded together . ( c ) The fluting resembles those of class ( \amp ; ) , except that the structure lines are more clearly separated . ( d ) The structure lines are widely separated , and extend over a long range . For convenience of description in the table , the flutings are classed in numbered groups , into which the spectrum seems naturally to divide itself . It is not possible , however , to convey an adequate idea of so complex a spectrum by means of a table alone , and reference should be made to the reproductions of the photographs given in Plate 6 . The first four strips , representing the spectrum from 4580 to 7200 , have been enlarged 1*8 times from the original negatives , and the attached scale of wave-lengths will facilitate comparison with the table . Lines due to iron are separately indicated , as also are those arising from impurities of sodium , calcium , and lithium in the material employed . The superposition of iron lines on the flutings beginning at 4954*8 , 5167*0 , and 5448*5 , ' tends to conceal the character of the heads , and reproductions of photographs taken with carbon poles are accordingly given in the fifth strip , the enlargement here being 3*5 times . In this case most of the iron lines are absent , but titanium lines are generally more numerous throughout the spectrum . The photographs of the less refrangible parts of the spectrum were taken on Messrs. Wratten 's " Verichrome " and " Panchromatic " plates , which gave uniformly good results . 1907 . ] The Fluted Spectrum of Titanium Oxide . The Fluted Spectrum of Titanium Oxide . 515- Wave- length . Intensity . Character . Remarks . 4353 *68 2 d 1st head of 14th group . 4395 *05 2 d 2nd head . 4421 -66 1 d Sub-head . 4436 '68 2 d 3rd head . 4462 *34 3 d 1st head of 13th group . 4462 70 3 \#151 ; A " maximum * ' in head . 4506-08 2 d 2nd head . 4506 -62 2 \#151 ; A maximum in head . 4548 -04 2 d 3rd head . 4548 *30 2 \#151 ; A maximum in head . 4584 -62 3 d. 1st head of 12th group . 4584 -92 3 \#151 ; A maximum in head . 4586 -78 3 d Sub-head . 4587 *20 3 \#151 ; A maximum in sub-head . 4626 -49 4 d 2nd head . 4628 -68 4 d Sub-head . 4668 *82 4 d 3rd head . 4669 *19 4 \#151 ; A maximum in head . 4671 *26 3 d Sub-head . 4671*66 3 \#151 ; A maximum in sub-head . 4761 *08 5 d 1st head of 11th group . 4761 -37 5 \#151 ; A maximum in head . 4761 *86 5 - \#151 ; 4764 *52 5 d Sub-head . 4804 *55 4805 *61 } 5 d 2nd head , included in cluster . 4807 *42 4 d Sab-head . 4848 *20 4849 *03 } 3 d 3rd head , included in cluster . 4893 *00 2 d 4th head . 4954 *78 6 d 1st head of 10th group , sharply defined . 4955 *26 6 \#151 ; A maximum in head . 4957*21 6 d Sub-head . 5002 -88 5050 -5 3 3 d d 3rd head 9 } Identification difficult with high dispersion . 5167 -00 7 d 1st head of 9th group , sharply defined . 5167 -50 7 \#151 ; A maximum in head ( not Mg line ) . 5169 -51 7 d Sub-head . 5240 -71 5 d 2nd head , structure lines very wide apart . 5241 *00 5 \#151 ; A maximum in head . 5307 *92 3 d Sub-head . 5308 *14 3 \#151 ; A maximum . 5356 -21 2 d Sub-head . 5356 -86 2 \#151 ; A maximum . 5359 *07 3 \#151 ; A maximum , or ? sub-head . 5359 *51 2 \#151 ; A maximum . 5361 -22 3 \#151 ; \#187 ; A maximum , or ? sub-head . 5391 *05 2 \#151 ; 5448 -48 7 d 1st head of 8th group , sharply defined . 5449 *07 7 \#151 ; A maximum in head . 5451 *32 7 d Sub-head . 5496 *79 5 d 2nd head . i . Mr. A. Fowler . [ May 18 Wave- length . Intensity . Character . Remarks . 5597 -92 10 a 1st head of 7th group , sharply defined . 5603 -98 5 b Sub-head . 5629 *53 8 a 2nd head . 5635 *54 5 b Sub-head . 5661 *68 6 a 3rd head . 5667 -81 4 b Sub-head . 5694 -56 5 a ? 4th head . 5728 -13 4 a ? 5th head . 5760 '15 4 b 1st head of 6th group ( followed by Ti 62 *48 and Fe 63 *22 ) . 5790 '86 4 b Sub-head . 5811 *28 4 b 2nd head . 5815 *14 4 \#151 ; A maximum , or line . 5846 -70 4 b Sub-head . 5863 *55 4 b 3rd head ( probably ) . 5872 -9 3 b Sub-head . 5905 *1 3 b a 5954 '66 3 b 1st head of 5th group ( relatively inconspicuous ) . 6006 *5 3 b 2nd head . 6057 *6 2 b 3rd head . 6149 -2 5 a ? A doubtful head . 6158 *86 10 a 1st head of 4th group . 6162 *37 8 \#151 ; Sub-head P Perhaps wholly Ca line . 6174 -60 10 a 2nd head . 6183 *83 4 b Sub-head . 6186 *77 8 a 3rd head . .6190 *07 5 b Sub-head . 6215 *35 8 a 4th head . 6222 *72 6 b 5th head . 6268 *35 4 b Sub-head . 6275 *70 3 b 6321 *0 2 c 6321 -8 2 \#151 ; A maximum in sub-head . 6350 *6 2 b Sub-head . 6357 *9 3 * c 1st head of 3rd group ( relatively inconspicuous ) . 6384 -4 3 c 2nd head . 6400*1 2 b Sub-head . 6416 *0 3 b 3rd head . 6448 *2 4 b 4th head . 6479 *4 4 b 5th head . 6484 *0 4 Sub-head ? or cluster of lines . 6512 *8 4 b 6th head . 6544 *5 4 c 7th head . 6550 *2 4 \#151 ; - A maximum . 6551 *8 4 \#151 ; 6562 *5 3 c Sub-head . 6579 *5 3 c 6594 *5 3 \#151 ; A maximum . 6626 *3 3 \#151 ; a 6634 *4 3 b Sub-head . The Fluted Spectrum of Titanium Oxide . Wave- length . Intensity . Character . Remarks . 6651*5 8 b 1st head of 2nd group . 6681 *0 8 b 2nd head . 6714 -1 8 b 3rd head . 6748 *0 8 b 4th head . 6782 *0 8 c 5th head . 6815 *1 5 c 6th head . 6850 -0 5 i c 7th head . 6852 *5 6883 '8 5 4 J c 8th head . 6919 -4 4 c 9th head . 6951 -8 2 c 10th head . 6988 -8 2 . c 11th head . 7054 -5 10 a 1st head of 1st group . 7059 -6 4 b Sub-head . 7087 -8 10 a 2nd head . 7092 9 4 b Sub-head . 7125 -5 10 a 3rd head . 7130 -6 4 b Sub-head . 7158 -9 3 a 4th head ? 7197 -7 2 a 5th head ? Reference to Stellar Bands . The use of greater dispersion has removed*the doubt as to the agreement of the 7th group of flutings with Duner 's stellar band No. 4 , to which reference was made in the former paper . It is now evident that the appearances described as " lines " near 5598 , 5630 , and 5662 are really the heads of short flutings of class a , as might have been suspected from the near equality of the intervals separating them from the weaker but more obvious flutings ( when seen with small dispersion ) at 5604 , 5636 , and 5668 . This group , therefore , begins with the fluting at 5597*9 , and there is no longer any uncertainty as to its general correspondence with the stellar band , for which Father Sidgreaves gives the wave-length 5597 . Evidence as to the presence in stars of the first group of titanium oxide flutings , beginning at 7054*5 , is afforded by the recent photographs of the spectrum of Omicron Ceti taken by Mr. Slipher , of the Lowell Observatory.* It is stated that " the star spectrum stops so suddenly at A , 7040 as to leave little doubt that another of these bands begins at that point and outruns the sensitiveness of the plate into the red . " There can be no doubt that the abrupt ending to which reference is made owes its origin to absorption by the 7054*5 group of titanium flutings . Still more recently , Mr. Newall has informed me that he has identified the three heads of the 7054*5 group in photographs of the spectrum of a Orionis . * 4 Astrophysical Journal,5 vol. 25 , p. 236 , April , 1907 . 518 The Fluted Spectrum of Titanium Oxide . All the stronger groups of flutings have accordingly now been traced in stars , and it may be assumed that the fainter flutings of groups 3 , 5 , and 6 will also be present when the banded spectrum is well developed , as in a Herculis and o Ceti . It still seems improbable , however , that titanium oxide can sufficiently account for all the stellar bands . As remarked in the former paper , ,the stellar intensities of Dun\amp ; r 's bands 1 and 3 , beginning near 5862 and 6493 , appear to be too great to be wholly accounted for by the titanium oxide flutings which occur in these parts of the spectrum . This is especially the case with the band at 5862 , which is very frequently a wide and dark band in the stars , whereas the fluting at 5863*5 is an inconspicuous feature of the titanium oxide spectrum . The flutings in the neighbourhood of 6493 also seem to be too feebly marked in the titanium spectrum to produce a conspicuous absorption head in the stars . More accurate wave-lengths of the stellar bands in question are urgently required for further investigations of their origin . The author is anxious to express his indebtedness for assistance rendered at different times by students in training assisting in the Astrophysical Department of the Koyal College of Science . Valuable aid in carrying out the experiments described in the paper was given by F. W. Jordan , B.Sc. , and J. Prescott , M.A. , and the large-scale photographs were taken by H. Shaw , A.R.C.S. , and E. J. Evans , B.Sc. The author is alone responsible for the determination of wave-lengths . FLUTED SPECTRUM of TITANIUM OXIDE

rspa_1907_0060

0950-1207

The osmotic pressure of compressible solutions of any degree of concentration.

519

528

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Alfred W. Porter, B. Sc.|Professor F. T. Trouton, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0060

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0060

10.1098/rspa.1907.0060

Thermodynamics

Biochemistry

Thermodynamics

]\gt ; The Osmotic Pressure of ) Solutions of Degree of By ALFRED W. PORT B.Sc. , Fellow of , and Assistant-Professor of Physics in , Uniyersity College , London . ( Communicated by Professor F. T. outon , F.R.S. Received May 22 , \mdash ; Read June 6 , 1907 . ) This paper is an attempt to make more complete the theory of solutions , at the same time as great simplicity of treatment as is possible without sacrificing precision . Renewed attention has been called to the subject , owing to the success of the experiments of the Earl of Berkeley and Mr. E. J. Hartley on the osmotic pressure of concentrated solutions of Diversity of opinion has existed in regard to the interpretation of these experiments , insufficient attention having been previously paid to the inflnence of the hydrostatic pressure of the pure solvent upon the value of the osmotic pressure . The principal advances made in this paper consist iu simply demonstrating the influence of pressure upon osmotic pressure for ) solutions and in including the effect of the variability of vapour pressure with hydrostatic pressure . The influences of accidental properties ( such as the effects of ooravitation ) are excluded . Snmmary of iVotation . The is the notation employed . All the values are isothermal values . Solution.\mdash ; Hydrostatic pressure Vapour pressure corresponding to hydrostatic pressure when solution is in contact with its own vapour alone Volume at hydrostatic pressure Reduction of volume when 1 gramme of solvent escapes Osmotic pressure for hydrostatic pressure Solrent.\mdash ; Pressure of solvent when solution is at pressure Corresponding vapour Vapour pressure when hydrostatic pressure is that of its own vapour Mr. A. W. Porter . The Osmotic Pressure of [ May 22 , Volume at hydrostatic pressure . Specific volume at hydrostatic pressure , , , Vapour of Specific volume at pressure , , , , . . A few special symbols are defined in the text . between Osmotic and Vapour Pressures . The following isothermal cycle enables the above ] ation to be foumd . Jarge ( practically infinite ) quantity of a solution ( unacted upon by any bodily field of force , such as gravity ) is separated from a quantity of pure solvent by a semi-permeable membrane . The solute is supposed to be inyolatile . The solution is under a hydrostatic pressure , while the solvent is under the hydrostatic pressure for which there will be equilibrium . It is not intended that either of these pressures shall be restricted to be the vapour pressure of the corresponding liquid . FIG. 1 . ( 1 ) Transfer 1 ramme of solvent from the solution to the solvent by moving the.semi-permeable membrane to the left ; the work done upon the system is ( 2 ) Separate 1 gramme of the pure solvent ( at ) from the rest by partitioning off the lateral tube ; change its pressure to ( by aid of the lateral piston ) , so that it will be in equilibrium with its own vapour , and then evaporate it ; the work done is ( 3 ) Change the pressure of the vapour to , so that it may be in 1907 . ] Compressible Solutions ofConcentration . equilibrium with the solution when under the hydrostatic pressure of its vapour alone ; the work done is ( 4 ) Close the semi-permeable membrane by a shutter to which hydrostatic ressure p can be applied ; also enclose the solution by a second shutter , to which a pressure may be applied ; the solution may now be removed . Change its pressure to } it into contact with the separated vapour of solvent , which is also at a pressure ; condense this vapour into it , thereby increasing the volume of the solution by , and then compress to a pressure . The work done is . The connection the ) ermeable membrane must now be restored , and then everything will be in its initial state , and the total work done , since the cycle is isothermal , must be zero . Adding the several terms , integrating by parts , and simplifying equation , we obtain ; or , remembering that . ( 1 ) This the expression which gives the osmotic pressure for any concentration and temperature in terms of the vapour pressures , etc. , correS } ) onding to the same concentration and temperature . It includes the influe1lce of compressibility , and states with precision the particular circumstances to which the various physical data correspond . For example , the vapour pressures and are the vapour pressures of the solvent and solution the h.ydrostatic pressure of its own vapour , and not under the hydrostatic pressures and respectively , as might perhaps have been expected . In order to compare this equat1on with those hitherto given , we will first assume that and are constants nor compressibility ) , and that the vapour follows the gas laws . equation then becomes where is the gas constant for solvent vapour . This may also be written . ( 3 ) The special cases are of interest . 522 Mr. A. W. Porter . The Osmotic Pressure of [ May22 , 1st . Let be the osmotic pressure when the solvent is under the hydrostatic pressure of its own vapour ; then . ( 4 ) This is identical with va n't Hoff 's case , except that he writes it in of molecular quantities and pays no attention to the variation of and with hydrostatic pressure . 2nd . Let be the osmotic pressure when the solution is under the hydrostatic pressure of its own vapour ; then . ( 5 ) This is identical with the Earl of Berkeley 's solution , in which , however , no attention was paid to the influence of pressure . It is precisely the result naturally given by the method he employs when attention is paid to pressure . of Hydrostatic Pressure of Solution . By rentiating formula ( 2 ) with respect to , the concentration ( c ) and , therefore , the value of being maintained constant , we get , or This does not allow for compression . By differentiating the accurate expression equation ( 1 ) , we get , ( 6 ) which is of the same form as before , but the terms have now more precise meanings . Similarly , the rate of change of osmotic pressure with change in the hydrostatic pressure of the solvent is ooiven by . ( 7 ) Comparison of Osmotic Pressures of Solutions of different the same Solvent . If we have several solutions of different substances in the same solvent , and if the pure solvent against which they are tested osmotically is under the pressure of its own vapour , then equation ( 1 ) shows in eneral if the vapour pressures of the solutions have the same values ( when measured for a hydrostatic pressure of the solution equal to their own vapour pressure ) the osmotic pressures will be different , for the equation defining is in this case , ( 8 ) where and varies considerably for different solutions . 1907 . ] Compressible Solutions of any Concentration . If , however , the solutions , instead of the solvent , be under the hydrostatic pressures of wheir own vapours , and if these pressures be equal , then the solutions will have the same osmotic pressure . For equation ( 1 ) then becomes , ( 9 ) and both these terms depend only upon the properties of the pure solvent and the pressul.es in question . It is easy to show , however , that this two-fold isotony ( for vapour and for osmotic pressures ) holds for any hydrostatic pressures of the solutions ( the same for all ) , provided that the vapour pressures be measured for the solutions when same hydrostatic pressure . This can be shown at once by considering the arrangement represented in fig. 2 . FIG. 2 . Two solutions having the same solvent are contained in a vessel and separated one from the other by a semi-permeable membrane . The space above contains the vapour ether with an inert whose pressure is A. The vessel is supposed to be in a region free from ravitational action . Then it is obvious that if the osmotic pressures be equal , but the vapour pressures be different , , a circulation must ensue which will upset the initial oslnotic equilibrium in such a direction as to maintain the difference of vapour pressures and thus to cause perpetual flow ; the possibility of this we are entitled to deny . In order to show how this result is consistenlt with equation ( 1 ) , it is necessary to find the mode in which the vapour pressures vary with hydrostatic pressure . Variation of Vapour Pressure with drotatic An approximate formula for this variation has been obtained by Professor J. J. Thomson in his " " Applications of Dynamics to Physics and Chemistry\ldquo ; . A. W. Porter . The Osrnotic Pressure of [ May 22 , by means of the Hamiltonian method . We will proceed to find cm exact formula for this variation by means of an isothermal thermodynamic cycle , consisting of several stages:\mdash ; A large volume of solution is taken with a space above containing an inert gas ( say , air ) and vapour enclosed by a piston semi-permeable to the vapour alone , which is enclosed by a non-per1neable piston . The semi- permeable piston will experience the pressure A due to the inert gas ; the pressure on the non-permeable piston will be the pressure of the vapour alone , which is . The volume of and vapour is initially ( 1 ) Evaporate 1 gramme of solvent from the solution by withdrawing the outer piston , leaving the inmer one fixed ; work done upon the system in this process is equal to or where is the specific volume of the yapour at the pressure ( 2 ) Increase the total pressure to by moving both pistons such amounts that no further liquid condenses or evaporates . The work done by the inner piston is and that done by the outer piston is , where is a volume which represents the fact that the vapour which at the first pressure was to the left of the inner piston may have passed through it on the of pressure taking place , since the law of compressibility of the vapour will not in general be the same as for the inert gas A. ( 3 ) Condense 1 gramme of the vapour by moving outer piston from to left , keeping inner piston fixed . Work done is 1907 . ] Compressible Solutions of any 5 25 ( 4 ) Restore the original state of the system by suitably moving the two pistons ; work done upon the systelu is , must be the same as before . Since the above represents a complete isoChermal cycle the total work is zero ; that is , after rating by parts , whence . ( 10 ) It is convenient to take as the upper limits of the two rals and This result is for a solution of any concentration ; hence , for the pure solvent we have and . ( 11 ) This last result is identical with the result obtained by Professor J. J. Ihomson as an approximate solution ; * we now see that it is accurate , provided that precise meanings be given to the variables concerned . It is convenient to take as the upper limits of these integrals and By means of these equations we can now transform equation ( 1 ) . We have Inserting this in ( 1 ) , . ( 12 ) These integrals depend only upon the properties of the solvent and upon the limits of integration . If all the limits but one are the same for two solutions under comparison , the remaining limit must also be the same , since the volumes are positive and single-valued functions of the pressures . That is , equality of values of involves equality of the values of , where is the same for both solutions . of Dynamics , ' p. 171 . Hence Dr. Larmor 's proof ( Earl of Berkeley 's paper , 'Roy . Soc. Proc , vol. 79 , p. 130 ) that they have also the same freezing-point can be extended to solutions at any hydrostatic pressure . Mr. A. W. Porter . The Osmotic Pressure of [ May 22 , roximate form of the above equation is . When is the value for which the hydrostatic pressure of the solvent is , the left-hand side of this is zero ; consequently , in this case ( from the right-hand side ) . This is simply a special case of a general relation to be proved next . Again , inse.rting the value for both and into equation ( 1 ) , or , whence That is , when a solution is in osmotic equilibrium with the pure solvent , the vapour pressure of the solution is equal to the vapour pressure of the pure solvent , each measured for the actual hydrostatic pressure of the fluid to which it refers . That this is so is almost immediately evident from the following case : FIG. 4 . The solution and solvent are placed in a vessel and separated by a semipermeable membrane . The space above is also separated into two parts by a partition semi-pernleable to the vapour of the solvent , but not to an inert gas . A pressure difference is maintained between the two sides by aid of an inert gas . Then , unless the vapour pressures and are equal , flow of vapour will occur with such consequent evaporation and condensation on the two fluids respectively as to upset the initial osmotic equilibrium in a direction which will maintain the difference of vapour pressures and thus cause perpetual flow , the possibility of which we are entitled to deny . This conclusion may be taken as a check upon the equations which we have derived . We have considered only the case of a non-volatile solute , but it is easy to see that this theorem must be equally true if the solute is volatile ; for the 1907 . ] Compressible Solutions of any Concentration . upper partition may be taken impermeable to the vapour of the solute ; and the argument is , in such a case , in no way Standard Conditions of JIeasurement . In whatever experimental ways osmotic pressures may be determined , it is necessary to decide on the standard conditions to which the obtained values shall be reduced for the purposes of tabulation and comparison ; that is , to what hydrostatic pressure shall they refer ? When osmotic pressures are compared by De Vries ' method , as they still often are ( by means of etable or animal cells ) , the solution is under only a moderate pressure . On the other hand , when values obtained by the method adopted by the Earl of Berkeley , it is the pnre solv that is under a moderate pressure . The values of the osmotic pressure will differ in general in the two cases . Now it seems most natural to reduce always either to the value corresponding to the solvent under its own vapour alone or to that corresponding to the solution under its own vapour alone ; and of these two , the latter seems the better . It is indeed most natural of all to think of the osmotic pressure as being a property of the solution ( just as its pressure , volume , etc. , are ) , the pure solvent bein only brought into consideration in a secondary way in connection with an experimental mode of determinin , the osmotic pressure . It may be objected that if this standard be adopted the equilibrium pressure of the pure solvent will , even for moderate strengths of solution , usually be negative ; that is , the solvent would require to be under tensiou . The difficulty is relieved when it is remembered that a certain amount of tension in liquids is practically , and the osmotic pressure for a strong solution always be conceived as being lmeasured against } less strong solution , and this in turn against a less , and so on , till the pure solvent was reached . If this standard be adopted , we have , from equation ( 1 ) , an equation which is capable of being graphically represented on the indicator diagram for the pure solvent ( fig. 5 ) . The equation , in fact , states that the hatched area must be taken equal to the dotted area ; the vertical height of the former then the osmotic pressure . of The chief results obtained iu this paper are:\mdash ; 1 . An exact equation is obtained connecting the osmotic pressure and vapour pressure for a solution of any given concentration , of any degree of The Osmotic of Compressible Solutions . compressibility , and under any hydrostatic pressure . This equation is applicable , therefore , even in the neighbourhood of the critical point . 2 . Exact equations are obtained giving the dependence of osmotic pressure and vapour pressure upon hydrostatic pressure . FIG. 5 . 3 . It is shown that when a solution at any pressure is in equilibrium through a semi-permeable membrane with the pure solvent , its vapour pressure is equal to the vapour pressure of the solvent , these being measured for the hydrostatic pressures to which the solution o.Jld solvent are respectively subjected . 4 . It is shown that if two solutions , at any hydrostatic pressure the sam for both , are isotonic as regards vapour pressure , they are also isotonic as regards osmotic pressure and they have the same freezing point .

rspa_1907_0061

0950-1207

Note on the use of the radiometer in observing small gas presures; application to the detection of the gaseous products produced by radio-active bodies.

529

532

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir James Dewar, M. A., Sc. D., LL. D., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0061

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0061

10.1098/rspa.1907.0061

Thermodynamics

Optics

Thermodynamics

529 Note on the Use of the Radiometer in Observing Small Gas Pressures ; Application to the Detection the Gaseous Products produced by Radio-active Bodies . By Sir James Dewar , M.A. , Sc. D. , LL. D. , E.R.S. ( Received June 24 , \#151 ; Read June 27 , 1907 . ) Some time ago I exhibited at a soiree of the Royal Society a few experiments with the Crookes radiometer , the object being to show that when helium is the residuary gas filling the instrument , an attached charcoal condenser , even when placed in liquid hydrogen , is unable to diminish the pressure by absorption to such an extent that the radiometer will not rotate ( when subjected to the concentrated beam of an electric arc lamp focussed upon the black surface of the mica vanes ) ; while , on the other hand , if the gas instead of being helium is hydrogen , all radiometer motion is suspended . Even when the charcoal condenser of the helium radiometer was cooled in solid hydrogen under exhaustion so that a temperature of 15 ' absolute wTas reached , the rotation of the instrument was still very marked . If the radiometer is repeatedly washed out with the mixed oxygen and nitrogen got from the evaporation of liquid air , the charcoal and the whole of the glass being thoroughly heated and the apparatus finally exhausted to a fraction of a millimetre and sealed off , then , on placing the charcoal tube in liquid air , generally after an hour or two the vacuum is so high that no motion is induced by the beam of the electric arc . But if instead of liquid air the cooling agent is liquid hydrogen , then two minutes ' immersion is sufficient to effect the same result , provided the radiometer is small and the gases get down a quill tube direct into the charcoal . Instead of the gases from liquid air being used to clean out the radiometer as described , it is for some purposes better to seal on a side tube containing perchlorate of potassium , which , when heated , gives pure oxygen . Further , in many experiments it is advantageous to exhaust the radiometer with its little charcoal condenser by means of a larger quantity of charcoal placed in liquid air for a night and then to seal the latter off before cooling the special charcoal bulb attached to the radiometer . When a McLeod gauge was sealed on to the end of the bulb containing the charcoal condenser which is cooled in liquid air ( no stop-cocks of any kind being used ) , all the mercury vapour was eliminated from the radiometer , and the pressure of the permanent gas was found to be O'OOOOl mm. , or one seventy-six millionth of an atmosphere . In this condition the radiometer moved when the image of the poles was focussed on the black VOL. LXXIX.\#151 ; A. 2 0 Sir James Dewar . On Use of the [ Jime 24 , vanes and after some 15 minutes ' heating the pressure was found to be only one twenty-five millionth of an atmosphere and the pressure remained at this after 10 hours ' cooling of the charcoal condenser in liquid air . The gas produced was no doubt hydrogen , got from the lamp black of the mica vanes , this being the first time the instrument was used . As a rule the radiometers require to be refilled , exhausted and tested more than once in order to get the motion reduced to a minimum . The importance of the removal of traces . of gases like helium , hydrogen or neon is shown from the fact that a radiometer which has the charcoal removed from the attached bulb , and the latter cooled in liquid hydrogen ( the instrument having been previously filled with dry air and exhausted to a fraction of a millimetre of mercury ) , will not reach such a vacuum as to stop the radiometer motion . Now , as the pressure of nitrogen at the boiling point of hydrogen must be of the order of a millionth of a millionth of an atmosphere , the action must come either from uncondensable gases , or the persistent adhesion of gas molecules to the glass and vanes of the radiometer or to some solid matter volatile under the conditions of the experiment . The lowest pressure reached in a charcoal vacuum after 10 minutes ' cooling in solid hydrogen was still one hundred millionth of an atmosphere . The pressure observed is thus far too high and it may he that some of this is due to hydrogen coming from the charcoal . To get really high vacua by the charcoal method , even when liquid hydrogen is the cooling agent , it seems necessary to allow the absorption to go on for an hour or more , when the space to be exhausted is relatively large , and where narrow tubes or orifices constitute part of the apparatus , as in the McLeod gauge . Further , the presence of any organic matter on the vanes is fatal . No amount of cooling of the charcoal in liquid hydrogen of a radiometer filled as usual and tested in the ordinary manner , in which the vanes were made of pith , makes a vacuum sufficient to stop the radiometer motion . The concentrated beam , each time it was applied , was generating gas . In all the experiments the arc used was expending 10 amperes and the focus was adjusted to about 3 feet from the lamp . The radiometers had a volume of from 150 to 20 c.c. Finding the McLeod gauge very difficult to use , a new method of defining the maximum limit of the working pressure ( under the defined , circumstances ) depending upon the vapour-pressure of mercury was devised . For this purpose a side tube was sealed on to the top of the ladio-meter and this , after being bent twice at right angles , ended in a little bulb containing a globule of mercury . After the radiometer and chaicoal were heated and exhausted and repeatedly washed out with the gas from liquid air , the charcoal was cooled in liquid air and the mercury allowed to 1907 . ] Radiometer in observing small Gas , etc. 531 distil for an hour or two . After this treatment , on cooling the mercury with liquid air , the radiometer in a short time became inactive . In this condition the mercury was placed in an alcohol bath at \#151 ; 80 ' C. and the temperature allowed to rise slowly . In this way it was found the radiometer action began in the instrument used at \#151 ; 23 ' C. The pressure of mercury vapour for the temperature derived from the Hertz formulae is found to be about a fifty millionth of an atmosphere . All the time of the experiment the mercury vapour was being sucked out of the radiometer by the liquid air cooling of the charcoal tube , so that the pressure might be less than the saturated pressure . This result at once suggested that the method ought to be applicable to the detection of the gaseous products derived from the transformation of radio-active bodies . In order to test this application , a side tube containing a little radium bromide was sealed on to the bottom of the charcoal condenser , in order to remove the emanation by absorption in the charcoal kept in liquid air . The radiometer , after thorough washing with the gas from liquid air , heating and exhaustion by a subsidiary charcoal condenser placed in liquid air that was sealed off , was found inactive after the small charcoal receptacle was cooled for an hour in liquid air . The radiometer was again tested after standing 15 hours and was found to be quite active . It would seem that the gas produced must be hydrogen , helium , or the alpha particles . In order to eliminate any hydrogen that might be produced , the charcoal condenser of the radiometer was transferred from liquid air , in which it had been kept for some two days , into liquid hydrogen . After half an hour 's cooling the motion was active when the image of the arc lamp was focussed on the black surface of the mica vanes of the radiometer , and even after one hour 's immersion of the charcoal in the liquid hydrogen the motion suffered no diminution . The active gas must , therefore , have been helium along with it may be the alpha particles ; unless one is being deceived by some solid deposited on the radiometer vanes sufficiently volatile when the arc light is concentrated on them to cause the motion . A similar radiometer to that which was used in the radium experiment had a side tube attached containing some 50 grammes of thoria , and after the usual treatment was found inactive . After keeping a fortnight it is now active , but I have not had the opportunity of cooling the charcoal in liquid hydrogen , so that the possibility of the gas being hydrogen has not been eliminated . We might anticipate that monadic gases of t*he type of helium and mercury would be more effective than the ordinary gases in inducing radiometer motion . A radiometer with a helium residue will still work under fixed conditions when the gas pressure is four or five times higher than one containing an oxygen residuum . Again , the sensibility of the Hon. C. A. Parsons . [ June 20 , instrument ought to increase , provided it was subjected to the same intensity of radiation while immersed in liquid air or liquid hydrogen . The experiments , in any case , seem to show that the radiometer may be used as an efficient instrument of research for the detection of small gas pressures and the study of radio-active products . For quantitative measurements the torsion balance or bifilar suspension must be employed . It would be interesting to repeat light repulsion experiments in the highest attainable charcoal vacuum . Later on I hope to extend the investigation . Some Notes on Carbon at High Temperatures and Pressures . By Hon. C. A. Parsons , C.B. , Sc. D. , F.E.S. ( .Received June 20 , \#151 ; Read June 27 , 1907 . ) Following the subject of my paper of 1888 to this Society , which will be referred to in a subsequent communication , attempts have recently been made to melt carbon by electrical resistance heating under pressure , and the following is a short summary of the results of about 100 experiments . The procedure has been on two lines . In the first , carbon is treated in bulk in a thick tube of 8 inches internal diameter of gun steel closed below by a massive pole of steel insulated from but gas tight with the mould and above by a closely fitting steel ram packed by copper rings imbedded in grooves in the ram or by leather and steel cups according to whether solids , liquids or gases are to be contained . The bore of the mould is generally lined with asbestos and after being charged the whole is placed under a 2000-ton press , the head and baseplate being insulated and connected to the terminals of a 300-kilowatt storage battery with coupling arrangements for 4 , 8 , 16 or 48 volts . It was hoped that the greater thermal and electrical conductivity of steel as compared with carbon or graphite at moderate temperatures would with the help of water jackets keep the outer layers comparatively cool and that the increased conductivity of the central portions consequent on their higher temperature and conversion to graphite would so centralise the current on the core lying between the poles as to melt it . Further* concentration of current was obtained in the initial stages of heating by packing the central portion with carbon rods on end or by a compressed graphite core , and filling in around with coarsely broken arc-light carbon , or with wood charcoal ( which is a bad conductor until highly heated ) . With pressures of about 30 tons per square inch , and currents commencing

rspa_1907_0062

0950-1207

Some notes on Carbon at high temperatures and pressures.

532

535

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Hon. C. A. Parsons, C. B., Sc. D., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0062

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0062

10.1098/rspa.1907.0062

Thermodynamics

Measurement

Thermodynamics

Hon. C. A. Parsons . [ June 20 , instrument ought to increase , provided it was subjected to the same intensity of radiation while immersed in liquid air or liquid hydrogen . The experiments , in any case , seem to show that the radiometer may be used as an efficient instrument of research for the detection of small gas pressures and the study of radio-active products . For quantitative measurements the torsion balance or bifilar suspension must be employed . It would be interesting to repeat light repulsion experiments in the highest attainable charcoal vacuum . Later on I hope to extend the investigation . Some Notes on Carbon at High Temperatures and Pressures . By Hon. C. A. Parsons , C.B. , Sc. D. , F.E.S. ( .Received June 20 , \#151 ; Read June 27 , 1907 . ) Following the subject of my paper of 1888 to this Society , which will be referred to in a subsequent communication , attempts have recently been made to melt carbon by electrical resistance heating under pressure , and the following is a short summary of the results of about 100 experiments . The procedure has been on two lines . In the first , carbon is treated in bulk in a thick tube of 8 inches internal diameter of gun steel closed below by a massive pole of steel insulated from but gas tight with the mould and above by a closely fitting steel ram packed by copper rings imbedded in grooves in the ram or by leather and steel cups according to whether solids , liquids or gases are to be contained . The bore of the mould is generally lined with asbestos and after being charged the whole is placed under a 2000-ton press , the head and baseplate being insulated and connected to the terminals of a 300-kilowatt storage battery with coupling arrangements for 4 , 8 , 16 or 48 volts . It was hoped that the greater thermal and electrical conductivity of steel as compared with carbon or graphite at moderate temperatures would with the help of water jackets keep the outer layers comparatively cool and that the increased conductivity of the central portions consequent on their higher temperature and conversion to graphite would so centralise the current on the core lying between the poles as to melt it . Further* concentration of current was obtained in the initial stages of heating by packing the central portion with carbon rods on end or by a compressed graphite core , and filling in around with coarsely broken arc-light carbon , or with wood charcoal ( which is a bad conductor until highly heated ) . With pressures of about 30 tons per square inch , and currents commencing 1907 . ] On Carbon at High Temperatures and Pressures . 533 at 6000 amperes , increasing up to 50,000 amperes , with about 2 volts between the terminals of the mould , the carbon rods were partially converted to graphite and firmly welded together ; in the case of the graphite core the flakes were much increased in size . The heating was in all cases limited by the melting of the steel poles and ' resulted in short circuits in the mould from the permeation of the asbestos by the molten iron . Neither the internal water-jacketing of the poles nor the substitution of copper poles for steel have remedied this trouble . It appears that the thermal conductivity of the carbon or graphite at or near the temperature of vaporisation is very greatly in excess of that anticipated , or that the rapid transfer of heat is caused by carbon vapour , which appears to have a great power of penetration through carbon at high temperatures . The melting of the poles and the destruction caused by short circuits which reached 80,000 amperes in the mould were not only costly to remedy , but caused contamination of the carbon from the metal of the poles and the insulating material . In several experiments a nucleus of very soft graphite about 2f inches in diameter was found in the centre . And in several experiments small masses of iron , highly charged with graphite , were found in varying positions among the carbon or graphite . This method , however , would probably be more successful if carried out on a much larger scale , as for a given central temperature the transfer of heat to the poles and mould would be less , and water-jackets would then prove more effective . It is ; however , difficult to construct water-jackets to withstand more than 30 tons per square inch , and unless made of hard steel they crush in . The maximum power of the press is 2500 tons , and with the apparatus at hand if the size of the mould was much increased the pressure in the mould would have to be decreased . Another plan was then adopted of interposing an insulating barrier of some refractory material with a hole in it between the poles , the charge in the first instance being graphite . It was hoped that by means of electrical currents of higher potential and large volume the energy would be so concentrated on the small volume in the neck as to melt it before it had time to form carbides with the material of the barrier . This was to some extent achieved in that the graphite in the centre was converted to a softer and more flaky nature . In one of these experiments the barrier was formed out of a block of fused magnesium oxide , specific gravity 3*65 , and the pressure in the mould , which was 4 inches in internal diameter , was in this case raised to 100 tons per square inch . The strongest steel poles were required for this pressure Hon. C. A. Parsons . [ June 20 , also the mould of gun steel became permanently strained and required reboring after each experiment . A current at about 12 volts at the terminals in the mould , developing about 100 kilowatts , was turned on for seven seconds . The initial diameter of the hole in the barrier was inch and the thickness about f inch.* This barrier was converted to magnesium carbide of a green colour to a radial depth of about f inch . Thus this magnesium oxide when heated under pressure with graphite readily'forms a carbide . The graphite in the centre was altered to large and very soft flakes . Neither the graphite nor the magnesium carbide contained any hard crystalline carbon . Similar experiments were tried with carbon rods surrounded by silica , and as a guide to the temperature reached , current was turned on of just sufficient voltage to convert the rod to graphite ; the mould was then set up afresh and double the voltage applied , when the rod was vaporised and disseminated throughout the molten silica , principally in the form of graphite of very small grain , very little silicon and still less silicide of carbon being formed . Another series of experiments have been made to investigate the behaviour of vaporised carbon under fluid or gaseous pressures of about 30 tons per square inch . The general arrangement of the mould consisted of a central carbon rod with a lining of marble ; in some cases the space between the rod and marble was packed with coarsely powdered charcoal . Several compounds of carbon were treated , perhaps the most interesting being carbon dioxide . The liquid was run into the mould and a pressure of 30 tons per square inch applied . It was found that its volume diminished to about 80 per cent. , due to its compressibility . Current was then passed through the rod , and the liquid must then have existed as gaseous carbon monoxide in the hotter zones . When cooled , the liquid and gas were allowed to escape ; a sample of this gas on analysis was found to contain 95 per cent , of carbon monoxide and 3 per cent , carbon dioxide , the residue consisting apparently of nitrogen . As the pressure of 30 tons was maintained throughout the experiment , it would seem that the compressibility of carbon monoxide diminishes rapidly at such high pressures , but this experiment will be repeated and will form the subject of a subsequent paper on the compressibility of liquids and gases . Part of the central carbon was converted to graphite , and in one place there was found a nest of woolly deposited carbon , showing that under a pressure of 30 tons per square inch carbon vaporised in carbon monoxide is deposited in the form of amorphous carbon . * The heat units delivered on to the neck being about four times that required to raise the graphite column through 5000 ' C. , taking the specific heat at 0'5 . 1907 . ] On Carbon at High Temperatures and Pressures . Conclusions . From these experiments several hundred samples have been carefully analysed . In none of the experiments designed to melt or vaporise carbon under pressure has the residue contained more than a suspicion of black or transparent diamond . In no experiment we have made has there been any sign of the carbon becoming a non-conductor , and the impression derived is undoubtedly that soft crystals of graphite are the resulting stable form of carbon after heating to very high temperatures . At very high temperatures and pressures graphite has a great tendency to permeate or diffuse into its cooler surroundings . It should , however , be noted that in all the experiments so far made it has been found impossible to exclude from the graphite other substances in the liquid or gaseous state . Though in many of the foregoing experiments the molten steel of the poles became highly charged with graphite , further experiments have been made to ascertain the influence of pressure upon iron highly charged with carbon . Cores formed of iron rods , iron tubes filled with carbon or with various proportions of iron filings and lamp black , surrounded with various substances such as charcoal , magnesia , olivine , etc. , were melted or vaporised and disseminated throughout the charge . Thus iron highly charged with carbon under a pressure of 30 to 50 tons was cooled at various rates according to its proximity to the sides of the mould , the analysis showing in most cases no residue at all , but occasionally a suspicion of very minute diamond . As a further experiment , a small carbon crucible containing iron highly charged with carbon from the electric furnace was quickly transferred to a steel die and subjected , while still far above the melting point , to a pressure of 75 tons per square inch . The analysis showed scarcely any crystalline residue and probably less than if the crucible had been cooled in water at atmospheric pressure , and as it would seem that 75 tons or even 30 tons per square inch must be a greater pressure than can be produced in the interior of a spheroidal mass of cast iron when suddenly cooled , the inference from these experiments seems to be that mechanical pressure is not the cause of the production of diamond in rapidly cooled iron . We hope to be able to communicate further experiments on this subject during the course of next session . I would wish to add that most of the analyses have been made by Mr. J. Trevor Cart .

rspa_1907_0063

0950-1207

Ranges and behaviour of rifled projectiles in air.

536

549

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

A. Mallock, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0063

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0063

10.1098/rspa.1907.0063

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; Behaviour of Rifled Projectiles in Air . By A. MALLOCK , F.R.S. ( Received June 6 , \mdash ; Read June 27 , 1907 . ) In a former paper it was shown that the distance which a pointed projectile*would travel in air , when air resistance was the only force acting on it , could be very closely expressed by the formula . In the present paper I propose to examine the nature of the motion of such a projectile when gravity acts on it , as well as air resistance . Suppose that projectile is started at an angle ( il with the horizon . Without the action of gravity at the end of time , the projectile will have attained a height of above the surface of the ground . It is easy to see ( the proof , however , is given in the notes ) that , if gravity acts and is the only force which has a component normal to the trajectory , the position of the projectile at will , if and are the horizontal and vertical co-ordinates , be . Thus if we put , i.e. , if the projectile reaches the ground after time , the range for an elevation is , so that . Experiment , however , shows that this relation does not hold , and it must be co1lcluded , therefore , that gravity is not the only force acting which has a component normal to the trajectory . Experiment also shows that the axis of an elongated rifled projectile tends to set itself in the direction of the tangent to the trajectory , and it will appear that the small angle between the axis and the tangent is the origin of the normal force which causes the simple relation to fail ; the fact being that the long projectile with its axis slightly inclined to the direction of motion behaves as a rather imperfect sort of flying machine , the upward component of the resistance on the underside of the shot acting to diminish the effect of gravity . That this was so was well known to the late W. E. Metford , who did so much for the improvement of small arms ; but I cannot find that it has been taken into account by artillerists , nor , as far as I know , has any dynamical explanation of the tendency of the axis of a rifled shot to follow the direction of the tangent to the trajectory been published , though part , at any rate , of the true 1eason was given in conversation by the late W. Froude more than 30 years ago . The projectile here referred to is ogival-headed , the radius of the ogive being two diameters . Ranges Behaviour of Rifled Projectiles in We know that if a rifled shot were fired ? vacno its axis of rotation would remain parallel to its initial position throughout its flight . In order to examine the reason why the same shot fired in air should keep its axis of rotation nearly parallel to the tangent of the trajectory , it will be convenient to take at first a simpler case . Imagine a top or gyrostat of any shape ( any surface of revolution ) supported in gymbals and placed at one end of a long arm , in a vertical plane , the other end of the arm being fixed to a horizontal axis ( see fig. 1 ) . FIG. 1 . If the gyrostat be set spinning , and the arm is then made to rotnte about its horizontal axis , we know that , in the absence of any external force , the axis of the gyroscope will always remain parallel to the position it occupied when first set spinning . Suppose this direction to be the tangent to the circle described by the C.G. of the shot about the horizontal axis AB , I will first inquire what the nitude and direction of the couple must be which will cause the axis of the shot to remain tangential to the circle when the arm revolves at a definite angular speed . The mathematical expressions for the required couple are iven in the notes . It appears that the axis of the requisite couple is parallel to the arm ; ( b ) that it must tend to cause rotation in the same direction as the projectile would be spinning if the head of the latter was pointing towards the axis AB ; Mr. A. Mallock . [ June 6 , ( c ) that its magnitude is directly proportional to the angular speed of the arm about AB and to the angular speed of the gyrostat about its axis ; and ( d ) to the power of the linear dimensions of the projectile . If , now , in imagination , we make the arm equal in length to the radius of curvature of the trajectory of a projectile and the angular speed of the arm such that its end has the speed of the projectile , and give the gyrostat the spin which would be given by the rifling , we know that , iu some way or other , the air must call into action a couple with the above specified direction and magnitude . As a numerical example showing the order of magnitude of the required couple , I give the following figures relating to a inch , 6-inch , and inch projectile . The couple which must act about the radius of curvature of the trajectory through the C.G. of a projectile having a velocity of 2000 . and making one whole turn about its axis while it travels 30 diameters 12-inch gun . . ft.-lbs . 6-inch gun . . -inch rifle ft.-lb . about -inch grains . The action of the air in producing this couple may best be illustrated by the action of a jet of water on a rotating body . It is evident that if the axis of the jet and the axis of rotation are identical , the rotation communicated to the fluid by friction , as it spreads over the surface of the body after impact , will be symmetrical about the axis , and the speed of rotation of the projectile will , therefore , unless maintained from ithout , gradually decrease , but beyond this there will be no effect . The case is different , however , if the axes of the jet and of rotation are inclined . Suppose in the first place that these two axes intersect at a point in the projectile ( which may be called the centre of pressure ) independent of the angle ( provided the angle remains small ) , and that the mass in the projectile is so distributed fore and aft as to make this point the centre of gravity . In this condition the jet , although it impinges obliquely on the projectile , exerts no couple in the plane containino o two axes . There is a couple , however , acting in a plane through the jet perpendicular to the plane containing the axis of the jet and the axis of rotation ; for the jet impinges on the surface of the projectile at some distance from the axis of rotation . Surface friction therefore imparts sideways velocity to the jet after impact . Thus the reaction constitutes a force urging the surface of the projectile , at the point of impact , in a direction opposite to that in which the surface is moving , and this force can be calculated . If the effect on 1907 . ] Ranges and of Rifled Projectiles in Air : 539 impact were the only action of the jet , the force just mentioned , together with the inertia of the shot , would constitute a couple acting in the direction required to bring the axis of rotation towards the axis of the jet . * As a matter of fact , however , the fluid in leaving the surface of the projectile also exercises a force there , the resultant of which is in the opposite direction to that called up by the impact of the jet . The magnitude of this force cannot at present be calculated from dynamical principles , but can be shown to exist by experiment , and by appropriate experiments could be measured . Its can be explained thus : Suppose a cylinder immersed in a current of fluid with its axis at right angles to the stream . If the fluid were the perfect fluid of mathematicians , the stream iines would flow in behind the cylinder in curves precisely similar to those they followed while oachincy it . A real fluid , such as air or water , does not behave in this way . In approaching the solid the stream lines conform nearly to the theoretical flow of a perfect fluid , but , instead of closing in behind , the streams leave the solid surface altogether near its greatest diameter , and enclose between them a body of fluid constituting a wake . The motion of the fluid in the wake is of a very complicated character , of eddies which are always being formed in the immediate neighbourhood of the solid , and away from it when they have reached a certain size . The which the average of the wake makes with the direction of flow is unstable within certain limits , so that the wake tends to trail away from the solid at some small angle to the general direction of the stream , implying a lateral force on the solid . If the cylinder is stationary , the direction which the instability takes varies quickly , and , looking back along the wake for some distance , its mean direction will appear to be that of the stream , but its course will be sinuous , owing to the successive changes in the direction of instability . If , however , the cylinder is made to revolve , the direction of the instability is settled , and the wake leaves with a sideways component of velocity in the direction of the motion of the rear surface of the cylinder . Even a slow rotation of the cylinder ( i.e. , a rotation giving a surface velocity less than the velocity the stream ) suffices to give the wake a considerable lateral deviation ; but the angle between the wake and the stream increases with the velocity of rotation of the cylinder , though in what proportion I do not at present know ( the curious of a golf ball with underspin depends on the action just described ) . * This was the explanation given by W. Froude . Mr. A. Mallock . [ June 6 , The cylinder has hitherto been supposed to have its axis at right angles to the direction of flow , but now let it be gradually turned so as to bring the axis of rotation towards the direction of the stream . When the two are nearly coincident the greater part of the wake , of course , belongs to the base of the cylinder , but part still belongs to that part of the side which is , as it were , in shadow ; and as long as any shadowed part remains , some of the wake leaves with a sideways velocity the direction of the surface motion of the shadowed part . This necessarily implies a force on the cylinder in the opposite direction . What the angle between the axis of the projectile and its direction of motion is at which the shadow vanishes , I have not determined . It is certainly small , and varies with the shape of the head ; with flat heads it is probably less than a degree . The statements above depend only on experiments and observations I myself have made . I have no doubt about the existence of the forces , but cannot their magnitude . We are left , however , with the fact that a projectile rotating in air , with its axis nearly in the direction of motion , experiences a force in opposite directions at either end which constitute : ( a ) a couple tending to bring the axis of rotation towards the direction of motion , and ( b ) a force ( equal to the difference of the forces at the head and tail ) tending to move the projectile bodily sideways . * This force is one element of drift , So far I have supposed that the C.G. of the projectile was at the centre of pressure . In all real projectiles , however , the centre of pressure is , in general , some way in front of the C.G. , and , as has often been pointed out , this produces a couple in the plane containing the axis of rotation and the tangent to the trajectory whose magnitude is proportional to the between the two , and to the distance between the centre of pressure and the centre of gravity , that is to OC by OCA . The effect of this couple on the spinning proje.ctile is to cause its axis to a cone round the direction of the motion . The time , , required for the axis to make one complete turn about the direction of motion ( the precessional period ) is given in the notes . The air resistance also gives rise to a force , to move the projectile bodily sideways ( in the plane containing the axis of rotation and the direction of motion ) which is directly proportional to the angle between them and to the resistance . ( The horizontal component of this force is the other element of drift . ) * If the views here expressed are correct , the axis of rotation of a spherical rifled shot should tend to follow the tangent to the trajectory . 1907 . ] Ranges and Beh of Rffled Projectiles in Air . 541 FIG. 2 . Now consider the trace of the axis of the projectile on a plane , at angles to the direction of motion , the plane the same speed as the projectile , and being the point where the ent to the trajectory meets the plane . FIG. 3 . In virtue of the couple in the plane , would describe a circle about with a velocity proportional to In virtue of the couple in the plane at angles to OAP , would describe the line PO with a velocity also proportional to PO . The combination of the two movcments makes the trace of into an equiangular spiral . In a real trajectory the direction of the is always Let be the distance which the tangent vould trace in time Mr. A. Mallock . [ June 6 , on the plane in virtue of the curvature of the trajectory of course . If the point is now on the equiangular spiral at a position where the tangent to the spiral is parallel to the radius of curvature of the trajectory , the element of the spiral is equal to where , constant angle of spiral , and precessional period , and if is independent of time , the axis of the shot in virtue of its precessional and inward motion changing its position at the same rate as the direction of the tangent to the trajectory . With a well-formed shot the angle POY is small , this proves that the motion due to the couple C2 ( which may be called the extinctive couple , from the analogy of its effect with the effect of resistance to the motion of a conical pendulum ) is large compared to the couple If we take the algebraic sum of the horizontal and vertical components of the force at the C.G. of the projectile , the first produces drift and the second acts to diminish the effective force of gravity . It appears , then , that the complete effect of the air resistance on the shot is to produce , in addition to the general retardation of its velocity , two couples : one in the plane containing the axis of the projectile and the tangent to the trajectory , and one in the plane through the tangent at right angles to the first plane ; also two forces both normal to the direction of motion , parallel and perpendicular to the radius of curvature of the trajectory . The reduction in the apparent force of gravity is very considerable and increases with the curvature of the trajectory , that is as the velocity of the projectile diminishes . The relation found between the lifting force and the apparent force of ravity is given in the notes , and is also shown in the , fig. 4 . The meaning attached to " " apparent value of gravity\ldquo ; in this paper is defined by the relation where is the lifting component due to the obliquity of the axis of the shot and direction of its travel and is the " " apparent value of gravity In other words , is the uniform acceleration which , acting for a time on a projectile started at an angle to the horizon for which the range is causes the proj to fall through a distance . In diagram 4 the values of are the esult of the analysis of a large number of range tables collected during many years . These tables , which refer to nearly all the calibres of rifled guns which have been in use , are based , for the most part , on the ballistic theories given in the text-books , but corrected by the use of If this were not so , the drift would be greater than it is . 1907 . ] and of Rifled ojectiles in . 543 suitable multipliers to make them agree with practice . It is clear from the diagram that quation ghethe value oexpressed b ranges tequire , ubject taken anity , ncewrite -ondition tenoughose oindi . ( A ) . ( B ) when is as large as , that is when agreement is still very close . terms ooften convenient thus getting Perms oaper senSma 1nity bthethe areat accuracy wisbetween hich hebei osity)ameequation ( hich teated astaken iccount iQsame amount ancrease oange diminished density ohefor vtmospheric density iiven ithough experiments which woubt these fconstruction oange tesThe reason fifferenceThe object oaper ihatgrap ncorrecwith t parts of the trajectory . the notes . directly what the action of the air is on an Mr. A. Mallock . [ June 6 , obliquely moving rifled projectile are very desirable , it is possible , nevertheless , even with existing knowledge to compute with sufficient accuracy the of any projectile in terms of its initial velocity , weight and diameter , and without the use of any arbitrary constants , except such as are derived from resistance experiments and the constants in the expression for To be able to do this is an important matter , for it is not such a simple thing as be supposed to the true ranges of a large gun by direct experiment . Range Tables , calculated by Formulae ( A ) and ( B ) for 12-inch Gun , ; and 6-inch Gun , . 2575 . Columns III and give the differences between the Calculated Values and the Values given in the ordinary Range Tables for the same Guns . 1907 . ] Ranges )of Rifled Projectiles in Air . 545 VOL. LXXIX.\mdash ; A. Mr. A. Mallock . [ June 6 , The accidental differences due to a variety of causes between the successive rounds of the same gun make it necessary that a large number of rounds should be fired in order that anything like a true mean should be arrived at , and in the case of large guns such as the 12-inch the alteration in the gun itself ( whose life is only about 200 rounds ) makes it almost impossible to determine by experiments on a single gun what the true range is when the gun is new . Any formula , therefore , which will give the range with accuracy is not only a matter of convenience , but of economy , both in ammunition and wear of guns . In the examples given ( p. 544 ) of of elevations and ranges computed by equations ( A ) and ( B ) , the third and fifth columns give the difference between the computed angles and times of flight and those given in the most trustworthy of the ordinary range tables . An example is also given ( p. 545 ) of the actual computation of part of a range table for a 12-inch gun and it may be remarked that the whole of the work can be done without reference to any table except that for in Column III . NOTES . Let X , be principal axes of a solid of revolution , being the generating axis . Let the solid have an angular velocity about ( fig. 5 ) . FIG. 5 . Now impose an angular velocity about X , being small . ; then OP is the instantaneous axis of rotation , and OP ( to the first degree of approximation ) Imagine the solid compresHed in the direction of until it becomes a circular disc in the plane , and let be its mass and its radius of gyration about a diameter . The disc is revolving about OP with velocity . The components of the centrifuga 1907 . ] Ranges and Beho , viour of Rifled Projectiles in Air . 547 force of the disc parallel to exactly balance one another , but as regards the components parallel to X , since half the disc is on one side of the plane through perpendicular to OP and half on the other , there will be a couple acting on the disc in the plane tending to make the plane of the disc coincide with the plane perpendicular to the instantaneous axis . The magnitude of the couple is the of ( components of force parallel to X of all parts of the disc ) ( their distance from Y ) ( angle AOP ) , or , say . This shows that if the gyrostat is to turn with velocity about X , the mechttnical axis exerts a couple on its bearin gs about the axis of , i. e. , in the plane of Conversely , if a couple is made to act on the axis in this plane , the gyrostat will revolve velocity about X. Suppose the axis of the couple to make the angles with X , , and respectively , the resolved couples about X , , and are , and . The effect of be merely to slightly alter the value of , and we need not further consider this component . and will each cause the mechanical axis to resolve with elocities and in the planes XZ and respectively . Two particular cases may be noted with reference to a projectile:\mdash ; ( a ) When the plane of the couple is always in the plane containino ) o axis of and the instantaneous axis of the projectile , the axis of symmetry will describe a cone about the axis of the couple with velocity ( b ) If the axis of the couple makes an with the axis of symmetry of the projectile , these two axes will approach one another with the velocity ( or if is small ) . Case ( a ) corresponds to the action set up by the line of resistance not passing through the centre of gravity of the projectile , and case ( b ) to the action of the couple due to air friction and wake . The precessional period ( or the time in which the mechanical axis describes a complete cone ) is given by the following relations . If is the radius of curvature of the trajectory and the linear velocity of the projectile , . And since and , we have , ( 1 ) , ( 2 ) . ( 3 ) If we take , the angular velocity due to rifling , as being such that the shot makes one turn in calibres , , hence the couple becomes ; or , since for a circular disc , and modern rifling makes , we find or Thus the couple varies as the fourth power of the linear dimensions of the and is independent of its velocity . This would be true for the whole length of the trajectory if remained equal to 2 ; but there is good reason to believe that the actual value of , which is only affected by air friction , does not decrease nearly as rapidly as , whose variation depends on air resistance . The couple set up by the air friction and wake at the head and tail of the shot is presumably proportional at any instant to , to the angle which the axis of the projectile makes with the direction of motion , and to some at present unknown function of velocity . So that must be equal to if the axis of the projectile is to keep at a nearly tant angular dista1ice from the direction of motion , or . ( 4 ) Mr. A. Mallock . [ June 6 , Hence as diminishes , have to increase , and it is only while moderate increments of , such as leave itself small , satisfy the conditions in ( 4 ) the motion is approximately steady . The upward force ( f ) due to the inclination of the axis of the projectile to the tangent of the trajectory may be taken as proportional to being the air resistance , and the projection of on the vertical plane . So that the effective downward acceleration of the shot is If the shot is fired at an inclination of to the horizon , it would , in the absence of any force other than air resistance , have travelled in the time a distance and have attained a height equal to above the ground . If the acceleration be resolved parallel and perpendicular to the original direction of motion , the distance traversed in time be parallel to the direction defined by the elevation and normal to that direction . The result is that at the projectile will be exactly under the position , having fallen through a distance If we put ( may be called the apparent value of gravity ) and make \ldquo ; then small , is the range for elevation By the analysis of a large number of range tables , I find that is well represented by the formula , where , if the units are feet and seconds , The values thus found are accurate enough for range-table purposes , but experiments are much wanted to determine the real relations between , and In the foregoing formulae no account is taken of the variation of density of the air at different levels . Many projectiles , however , reach heights at which the variation of density cannot be ected . A comparatively simple method of correcting the range for varying density is as follows : height ( h ) which projectiles reach with ' ' direct fire\ldquo ; is small compared to , the height of the homogeneous atmosphere . Thus the ( a ) of the foregoing formulae becomes , for a shot at altitude . FIG. 6 . vary with the shape of the projectile . 1907 . ] Ranges Behaviour of Projectiles in Air . 549 In the expression for , nameIy , suppose constant and differentiated with respect to Thus , but ; therefore . , with the range as abscissa , draw a curve with ordinate such that Then the length of this curve is the range corrected for variation of density . The form of the curve is shown in the diagram , fig. 6 , and an approximation to its length is It will be found that for the larger guns the angle is of the same order of magnitude as , that the corrected range is nearly equal to ; and it is for this reason that the formula range ( instead of ) is practically correct , even when the angle of elevation is as large as . For small arms the range given by the formula would be slightly in excess of the true range with elevation as large as height which the projectile reaches in time varies with the density of the air , but for the purpose of correcting the range it is sufficient to take as what it would have been with air of constant density .

rspa_1907_0064

0950-1207

On the force required to stop a moving electrified sphere.

550

563

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

G. F. C. Searle, M. A., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0064

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0064

10.1098/rspa.1907.0064

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; On the Force required to Stop Moving Electrified Sphere . By G. F. C. SEARLE , M.A. , F.B.S. , University Lecturer in Experimental Physics , Cambridge . ( Eeceived June 13 , \mdash ; Read June 27 , 1907 . ) S 1 . of a Charged Sphere in Steady Motion : Heaviside 's Method.\mdash ; When the velocity of a system of electric charges is changed in any manner , waves of disturbance travel out from the system in all directions with velocity , the speed of light , and carry both energy and momentum*to the distant parts of the electro-magnetic field . Dr. Oliver was the first to notice that these waves might be made to yield important information as to energy and momentum of the moving system . Thus , when a charged sphere is in steady motion the electro-magnetic field possesses electric energy magnetic energy and momentum M. If , now , the sphere be suddenly brought to rest , the forces which hold it at rest do no work , since their points of application do not move , and hence the total energy in the field is the same after the sphere is brought to rest as it was before . When the sphere is jtopped , a pulse with depth equal to the diameter of the sphere travels outwards . The electric and magnetic forces in this pulse ultimately vary inversely as the distance and hence the energy and the momentum in the pulse tend to constant values as the pulse travels out to infinity . Outside the pulse the electric and magnetic forces are the same as if the sphere had continued in steady motion and therefore are , after an infinite time , inversely proportional to the square of the distance from the point which the centre of the sphere would have reached had its motion continued . Hence the energy and momentum outside the pulse ultimately vanish . On the other hand , the field within the spherical region bounded by the pulse is the same as that due to the sphere at rest and hence the energy in this part of the field is ultimately , the electrostatic energy of the sphere at rest . Thus , if be the limiting value of the energy in the pulse , the energy in the field is ultimately . But , before the sphere was stopped , the energy was . Hence , . ( 1 ) Dr. Heaviside calculated for the pulse due to a sphere with a surfacecharge and so found , his value for agreeing with that which I * The momentum per unit volume is , where VEH is the vector product of the electric and magnetic forces . The Electrician , ' November 29 , , p. 210 . See also Searle , ' Phil. Mag January , 1907 , p. 131 . Force required to Stop Moving Electrified Sphere . had previously found by a direct integration of the energy in the field of a moving sphere , the integration extending through all space . * Dr. Paul Hertzj has applied this method to a sphere with a uniform volumecharge and has shown that the energy and momentum of the sphere in motion are six-fifths of the energy and momentum of a sphere of the same radius with an equal surface-charge . He has also indicated how the method may be applied to any system whatever , and I have shown how to carry out the details of calculation in the cases of a charged ellipsoid of revolution moving along its axis and of a charged disc in its own plane . S 2 . Force to Start a Charged Sphere : Hertz 's Method.\mdash ; But this list does not by any means exhaust the possibilities of the method of pulses . S For Dr. Hertz has applied it to determine the force which must be applied to a sphere with either a volume-or a surface-charge to cause the sphere to start suddenly from rest and then to move uniformly along a line with any velocity 21 not greater than , the velocity of light . If be the required force , the work done by when the sphere has been in motion for a time is Before the sphere began to move the energy in the field was . After the time it is Fudt . If at the time the sphere be suddenly brought to rest , the stopping forces do no work and hence the energy in the field remains unchanged . After an infinite time the in the field consists of together with , the energy in the compound pulse formed by the pair of pulses generated by starting and stopping the sphere . Hence or . ( 2 ) It must be noticed that the two pulses are not concentric , since their centres are separated by the distance . In the case of a sphere with a surfacecharge , the pulses destroy each effects where they overlap , since the electric and magnetic forces caused by the sudden stopping of sphere are ' Phil. Mag Oct. , 1897 . " " Untersuchungen uber unstetige Bewegungen eines Electrons 'Inaugural Dissertation , ' Gottingen , 1904 , p. 49 . See also Searle , ' Phil. Mag January , 1907 , p. 132 . Phil. Mag anuary , 1907 . S 'Dissertation , ' p. 65 . Mr. G. F. C. Searle . On the Force required to [ June 13 , equal in magnitude and opposite in direction to those caused by the starting of the sphere , and are also constant throughout the depth of each pulse . For a sphere with a volume-charge , and are not constant throughout the depth of each pulse and the calculation then becomes a little more complicated . It is necessary to distinguish three stages in the process of the sphere . If be the radius of the sphere , the first stage lasts from to , the second from to and the third from onwards . If , F2 and denote the forces required in the three stages and if stand for , Dr. Hertz 's results are as follows:\mdash ; Sphere with Uniform -charge Q. , ( 3 ) Thus , in the first stage the force is constant , while in the third stage it is zero . When tends to equality with , the expressions tend to the following limits : There is no third stage now , since the second extends from to infinite values of the time . Sphere with Uniform Volume-charge Q. , ( 4 ) 1907 . ] Stop Moving Sphere . , so that , the expressions become . S3 . Force required to stop a Ioving S. Pulse Method.\mdash ; I find that , if Dr. Hertz 's work be slightly extended , the force required to suddenly stop a charged system is easily calculated . For the sake of simplicity , the investgation will be limited to the case in which the momentum of the system in stea motion , as well as the momentum in the pulse formed when it is stopped , are parallel to the direction of motion . If be the force which must be applied to the system at any time , after it has been brought to rest at , the positive direction ] opposite to that of ? , then is also the force which the electro-magnetic field exerts on the system in the direction of The momentum given up by the electro-magnetic field from to is During this period the force does no work , since the system is at rest , and hence the energy of the system is unchanged during this period . At the time let the system be restarted with the same velocity without change of direction , and let be the force which must be applied to the system at any subsequent time in the direction of in order to maintain the velocity This force lasts from to , where is determined by the condition that in the time the pulse formed on the system has completely passed over the system . When , the time is infinite . During the interval , the momentum of the system is increased by and hence the total gain of momentum is During the interval , the energy of the system has been increased by The stopping and the restarting of the system each give rise to a pulse , and the compound pulse so formed carries off energy and momentum Mr. G. F. C. Searle . On the Force required to [ June 13 , Before the system was stopped the energy of the electro-magnetic field was and its momentum was , and at an infinite time after the stopping and restarting the energy is and the momentum is , since the energy and momentum in the parts of the field outside the compound pulse ultimately vanish . Equating the two expressions for the gain of momentum , we have Similarly , Hence , ( 5 ) and thus we find that the force required to stop the system is given by . ( 6 ) This force will become zero as soon as becomes constant , which will occur as soon as is so great that the two pulses due to the stopping and restarting do not overlap . Since the system is restarted from the position in which it was stopped , the two pulses are concentric , though their radii differ by , for one pulse is formed at and the other at the time . The fact that the pulses are concentric introduces an element of simplicity into the . calculations . The whole momentum I , given up by the electro-magnetic field during the time for which the stopping force lasts , is found by taking so great that the two pulses do not overlap . In this case each pulse has the same energy and the same momentum , and hence , if and be the energy and the momentum in each of the separate pulses , and Hence . ( 7 ) S4 . Force to stop a Sphere Surface-charge.\mdash ; We may now apply the results of S3 to find the force required to stop a sphere of radius with a uniform surface-charge Q. If be the energy and the momentum sent out in the pulse formed when the velocity is suddenly destroyed , we have* ( 8 ) . ( 9 ) See Searle , ' Phil. Mag. , Jan. , 1907 , pp. 131 , 132 1907 . ] Stop a Moving Electrified Sphere . Hence . ( 10 ) If the time be less than , the two pulses will overlap over a depth , and in this part the electric and magnetic forces due to one pulse will exactly neutralise those due to the other , since these forces are constant throughout the depth of either pulse . There remain two shells , each of depth , where the forces do not cancel . The total and the total momentum in the compound pulse are therefore given by Hence , if be the force required to stop the sphere with a surface-charge , we have , by ( 6 ) , . ( 11 ) Hence the force is constant the time for which it acts . The impulse , , of this force , or the momentum which the elect ( field ives up to the Uent stopping the sphere , is Hence . ( 12 ) When tends to equality with , so that the initial velocity of the sphere becomes more and more nearly equal to the velocity of light , the expression for the tends to a limit . For as tends to zero , tends to the limit zero , and hence tends to the limit . ( 1:3 ) The formula ( 11 ) gives us no information as to the value of when is equal to , since the expression then becomes indeterminate . But , instead of deducing the from the energy and momentum in the compound pulse , we can ( as in S6 ) calculate its value , when , by direct integration of over the surface of the sphere , where is the component , parallel to the direction of , of the electric force in the pulse . We then find that the value of for is identical with the limit of the general value of the force . Hence , there is no discontinuity in the force when When is very small , we have , by ( 11 ) , . ( 14 ) Mr. G. F. C. Searle . On Force required to [ June 13 , S 5 . Force required to Stop a Sphere with Volume-charrf e.\mdash ; When the sphere of radius has a uniform volume-charge , the calculation of the force required to stop the sphere is a little more difficult , because the electric and magnetic forces are not constant throughout the depth of the pulse fo1med on suddenly starting or stopping the sphere . If we take two parallel planes at distances and from the surface of the sphere , and if be the charge between them , As H. A. Lorentz*and Paul Hertz have pointed out , at a great time after the formation of one of these pulses the electric and magnetic forces at a point on the radius normal to these planes , and at a distance from the outer surface of the pulse , are proportional to There are parts of the compound pulse where the separate pulses due to the stopping and the restarting of the sphere do not overlap , and in each of these parts , of depth , there are equal amounts of energy and of momentum . Now , when a pulse is generated by starting or stopping an equal sphere with a surface-charge , the per unit depth of pulse is , where is given by ( 8 ) , while for this case Hence , if be the energy in the part of the compound pulse where the separate pulses do not overlap , In that part of the compound pulse where the two separate pulses overlap , the effective value of is 3 ( z-vt ) ' or since the electric and magnetio forces have opposite directions in the two separate pulses , and since the outer surfaces of the two pulses are separated by the distance . This part of the compound pulse extends from to , and hence , if be the energy in this part , we have ' Encyklopadie der Mathematischen Wissenschaften , ' " " Electronentheorie p. 188 . 'Dissertation , ' p. 36 . See also Searle , ' Phil. Mag January , 1907 , p. 123 . 1907 . ] Stop Moving Electrified Sphere . Hence , if be the energy in the compound pulse , . ( 15 ) Similarly , if be the momentum in the pulse formed on starting a sphere with a surface-charge , where is given by ( 9 ) , the momentum in the compound pulse is given by . ( 16 ) We can now find the force required to stop the sphere , for we have , by ( 6 ) , . ( 17 ) If I be the total momentum given up by the ] -magnetic field when the sphere is stopped , we have , by . But , as Dr. Hertz*has shown , and , and , hence , where is given by ( 12 ) . The same result follows if we integrate the expression ( 17 ) with respect to the time from to , for When tends to equality with , we see , by ( 17 ) , that tends to the limit . ( 18 ) 'Dissertation , ' p. 49 . See also Searle , ' Phil. Mag January , 1907 , p. 132 . Mr. G. F. C. Searle . On the Force required to [ June 13 , It is proved by another method in S7 that the value of for is equal to the limit ( 18 ) . When is very small , we have , , ' and then ( 17 ) becomes . ( 19 ) If be the force required to stop the sphere with a surface-charge , so that is given by ( 11 ) , we can write ( 17 ) in the form . ( 20 ) The maximum value of occurs when and the maximum value is S6 . Force required to Stop aSphere with when now pass on to calculate by a direct method the force required to stop a sphere with a surface-charge , when the initial velocity of the sphere is equal to that of light . We now find the force experienced by each element of the charge at a time after the sphere has been brought to rest , and then integrate over the surface of the sphere . When an elementary charge is suddenly stopped , the electric force in the pulse is given ( 21 ) Here is the distance from the point where the charge is stopped and is the angle between the radius , drawn from that point , and the direction of the initial velocity . Further , is the infinitesimal width of the charge measured in a direction parallel to . The electric force is in the plane of and , and is at right to , while it has a positive component in the direction of If be the component of in the direction of , we find that , when . ( 22 ) Let be the centre of the sphere after it has been brought to rest and let OA be the direction of its initial velocity . Let be a point on the surface of the sphere and let POA . About as centre describe two * See Searle , ' Phil. Mag January , 1907 , p. 121 . The expression was first given by Heaviside , ' The Electrician , ' October 11 , 1901 . 1907 . ] Stop ring Electrified Sphere . 5 9 FIG. 1 . spheres of radii . and the sphere in two circles . Let be a point on the band bounded by these circles , let NPO , and let the plane NPO be inclined at an to the plane POA . Since , we have . But the subtended at by the width of the band is twice the subtended at , and is , therefore , , and thus the width of the band is or . If the charge on that element of the ring which is defined by the planes and be , then while Hence , and thus , by ( 22 ) , . ( 23 ) It is only the band defined by ; where , which acts upon by its pulse at the time , and hence we obtain the complete value of the part of which is due to the action of pulses by rating ( with respect to Now is the projection of NP ( not ) upon OA , and thus we easily find\mdash ; . ( 24 ) Hence ) but , and thus . The element of charge at is also acted on by the charges on the sphere whose distanceS from are less than , as well as by those whose distances Mr. G. F. C. Searle . On the Force required to [ June 13 , are greater ihan v. The elements within the distance act on the element at according to the ordinary electrostatic law , and the element at acts on them in the same way . Hence the actions between the element at and the elements within the distance are in equilibrium , and may be left out of account in estimating the force exerted on the sphere as a whole . The elements outside the distance act on the element at in the same way as if they had continued to move on with the speed of light . The electric forces due to these elements are therefore at right angles to the direction of and therefore contribute nothing to the total force . Hence , if be the total experienced by the sphere at time , we can find by intergrating ( 25 ) over the surface of the sphere . Thus\mdash ; . ( 26 ) This value is equal to the limit ( 13 ) to which ( 11 ) , the general expression for the force , tends as tends to equality with . The force experienced by the sphere has this value for the time during which the pulse is passing over the sphere . As soon as the pulse is clear of the sphere the force vanishes . S7 . Force required to Stop a Sphere with when \mdash ; The method of S6 may be applied to find the force required to suddenly stop a sphere with a uniform volume-charge , when the initial velocity is equal to that of light . In fig. 2 , is the centre of the sphere after it has been brought to rest , OA is the direction of its original velocity , and is any point within the FIG. 2 . sphere . Let OP and POA , and let OA be taken as the axis of Let be a point in the sphere at a distance from , let NPO , and let the plane NPO be inclined at an angle to the plane POA . 1907 . ] Stop Moving Sphere . 561 The charge per unit volume is , and thus the -component of the electric force at due to the pulse arising from stopping the charge ( of thickness ) included in the elementary volume is , by ( 22 ) , where is given by ( 24 ) . Since , we have The -component of the electric at time due to pulses is obtained by integrating this expression over that part of the surface of the sphere of centre , and of radius , which lies within the sphere . For the reasons explained in S6 the force experienced by the whole sphere is equal to that due to the action of the pulses alone . When the sphere of radius lies entirely within the charged sphere , goes from to and from to . In this case we have ( 27 ) When the sphere of radius lies partly outside the charged sphere , goes from to , while goes from to , where is the angle subtended at by a radius drawn from to a point on the circle of intersection of the two spheres . From the triangle having this radius as base and as vertex we have . ( 28 ) In this case we have . ( 29 ) The time of of the whole pulse across the sphere ma be divided into two stages . In the first stage , which lasts from to \ldquo ; some complete spheres of radius can be described , but in the second stage , lasting from to , the spheres of radius are all incomplete . VOL. LXXIX.\mdash ; A. Mr. G. F. C. Searle . On the Force required to [ June 13 , In the first stage we can describe complete spheres of radius about every point within the sphere of centre and radius Now , by ( 27 ) , has the constant value throughout the sphere of radius . The charge within that sphere is , and hence , if be the force on this part of the charged sphere , If be the force on the spherical shell of radii and , then is due to the action of incomplete spheres , and thus\mdash ; where is now given by ( 29 ) . When we integrate with respect to , the term in involving vanishes , and thus , substituting for from ( 28 ) , we find The resultant force is equal to , and thus . ( 30 ) In the second stage from to , no complete sphere of radius can be described about any point within the charged sphere . But in this case we need not integrate throughout the whole volume of the sphere , since the pulses due to all the elements of the sphere have now completely passed over the part enclosed by the sphere , and have left this part free from any force due to pulses . Integrating throughout the spherical shell of radii and , we find , for the force during the second stage , where is given by ( 29 ) . Thus 1907 . ] Stop a Moving Electrified Sphere . This expression is identical with that given by ( 30 ) for the force during the first . Hence , the force is expressed by the same formula during the whole time of its action . The value also agrees with the limit ( 18 ) approached by ( 17 ) , the general value of the force , as found in S5 , when tends to equality with S8 . parison of Furces required for Starting and a ChaJged Spher \mdash ; It is to compare Dr. Hertz 's value for the force required the first of starting the sphere with value obtained in the present paper for the force required to stop the sphere . From ( 3 ) and ( 11 ) it will be seen that the stopping force is identical with the starting force during the first stage of the motion . This result could have been foretold without any detailed calculation . For it is easily seen that Dr. Hertz 's method leads to a force which is constant during the first , while my method leads to a constant stopping force . When , the two forces must be equal , since the sphere is at that time in the same position relative to the pulses as it is when it is suddenly stopped . Thus , since each force is constant , they remain equal up to the time . with a -charge . The method employed in the case of a surface-charge that the forces must be equal at . But since is zero at the surface of the , sphere , it is easily seen that both the starting and the stopping forces must vanish at . This result also follows from the detailed , since each expression contains as a factor . But when is infinitesimal , the displacement of the sphere during the time , when it is started , is also infinitesimal , and hence for such a value of the force required during the first stage of the starting of the sphere must be equal to that required to stop it . The latter force lasts for , but , since is infinitesimal , the first may be considered to last for the same time . Comparing Dr. Hertz 's expression ( 4 ) with ( 19 ) , it will be seen that they agree when is negligible in comparison with unity . The length of the second stage is from to ) , and thus may be considered as zero . When , it appears from and ( 31 ) that , as long as is negligible compared with , the stopping force is three halves of the starting force . VOL. LXXIX.\mdash ; A.

rspa_1907_0065

0950-1207

Studies of the process operative in solutions.-Parts II-V. - II. The displacement of chlorides from solution by alcohol and by hydrogen chloride.

564

597

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

H. E. Armstrong, F. R. S.|J. V. Eyre, Ph. D.|A. V. Hussey|W. P. Paddison

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0065

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0065

10.1098/rspa.1907.0065

Biochemistry

Chemistry 2

Biochemistry

564 Studies of the Processes operative in Solutions.\#151 ; Parts II-V . By H. E. Armstrong , F.R.S. , and others . ( Received and read June 20 , 1907 . ) [ International Catalogue of Scientific Literature . Author 's title slips :-C Y D II-V . Subject slips :\#151 ; II D 7175 III D 7065 7090 7190 IY D 7065 7090 Y E 6250 D 7050 7175 7255 Title . Title . ( Hydrolysis ) Title . Degree of hydration of salts in solution . Title . ( Hydrolysis ) Title . Electrolysis an effect of association . The ionic association hypothesis . Title . The dissociation hypothesis criticised . ] II . The Displacement of Chlorides from Solution by Alcohol and by Hydrogen Chloride . By H. E. Armstrong , F.R.S. , J. Y. Eyre , Ph. D. , A. Y. Hussy and W. P. Paddison . Although innumerable determinations of solubility have been placed on record , little has been done to elucidate the phenomena of what may bn termed competitive dissolution . A comprehensive series of determinations of the solubility of chlorides in presence of hydrogen chloride made by Engel* led him to the conclusion that , up to a certain point , the hydride displaces the salt approximately equivalent by equivalent , the sum of the equivalents being practically constant ; eventually , however , in every case , the chloride falls off in displacing power . Almost the only attempt to deal with the problem in a rational manner is that made by Nernst in 1888 , who discussed the mutual influence which salts exercise on one another on the assumption that the gas laws are applicable to liquids and from the ionic dissociation standpoint . Having in mind the fact that , although neutral gases are without influence , a separation of ammonium chloride at once takes place if either hydrogen chloride or ammonia be introduced into a space in which these products of its dissociation are in equilibrium with the chloride , Nernstf advocated the view that the degree of dissociation of a dissolved salt\#151 ; and therefore its solubility\#151 ; will be diminished if a compound containing either of the ions of the salt be introduced into the solution . In support of this contention , results were put forward showing that the solubility of silver acetate is diminished and to about an equal extent by equivalent amounts of * 'Ann . Chim . Phys. , ' 1888 , [ 6 ] , vol. 13 , p. 370 . t ' Zeits . Phys. Chem. , ' 1889 , vol. 4 , p. 372 . Studies of the Processes operative Solutions . 565 the electrolytes sodium acetate and silver nitrate\#151 ; which are supposed to undergo dissociation in solution to about equal extents ; whilst acetic acid\#151 ; which is supposed to exist in aqueous solution almost undissociated\#151 ; has little if any influence . The subject was subsequently dealt with more fully from the same point of view by A. A. Noyes * The circumstance that " unionisable " ( by hypothesis undissociated ) neutral substances such as methylic and ethylic alcohol are powerful precipitants was ignored by Nernst and Noyes . Unfortunately , the data which have been placed upon record ( irrespective of difficulties arising from the irregularity of the curves which they afford ) are seldom sufficient for the satisfactory discussion of the problem of competitive solubility . In but few cases has the influence of one substance on another been determined in a graduated manner , saturated solutions alone having been dealt with by most observers . In making the experiments to be referred to in this communication , alcohol and hydrogen chloride were chosen as precipitants of a number of chlorides because the one may be regarded as a representative nonelectrolyte and a weak dehydrant , the other as a representative electrolyte and moderately powerful dehydrant . The main object in view being to determine their relative " concentrating effects " in competition with that of the salts selected , weight-normal solutions were used throughout the inquiry\#151 ; i.e. , solutions containing in 1000 grammes of water a known proportion of the substance whose effect was to be determined in competition with that of another.f By operating in this wav , the effect was ascertained which the * Ibid1890 , vol. 6 , p. 491 . . + The saturated solutions were prepared by vigorously stirring the solid salt with the solvent in a large test tube ( 21 cm . by 3 cm . ) supported in a large water bath , either a rectangular tank provided with a glass front and back or a deep circular pan ; the temperature was carefully maintained at 25 ' by means of a spiral toluene gas regulator , whilst both bath and solvent were constantly stirred by means of a motor . The saturated solution was withdrawn by means of a pipette provided with a graduated neck and stop-cock ( comp . Lowry , 'Chem . Soc. Trans. , ' vol. 89 , p. 1036 ) . The density of the alcohol used was d y)- 0'79405 ; the alcoholic solutions were prepared by weighing . In the actual experiments , while the solid was being stirred with the solvent , the dried , weighed pipette was kept in a cylinder standing in the bath . Usually stirring was interrupted at the end of an hour ; then as soon as the liquid was clear a sample was withdrawn by means of the warmed pipette . By weighing the pipette full of solution , the quantity withdrawn as well as the density of the liquid was ascertained . A second sample was taken in like manner at the end of another hour . In most cases the samples were diluted to a known volume and titrated either with silver nitrate alone or ( when hydrogen chloride was used ) first with standardised alkali . In the case of potassium iodide , the contents of the pipette was washed into a tared , wide mouth , conical flask , Prof. H. E. Armstrong and others . [ June 20 , substances brought into competition exercised upon and within a given mass of water , the vehicle or medium within which the interchanges were effected being present in constant amount ; emphasis is laid on this point , as the consideration is one which is commonly neglected , although probably it is the most important to bear in mind in dealing with mixed solutions . Table I is given in illustration of the method followed in reducing the observations ; the subsequent tables contain the actual data :\#151 ; Table I.\#151 ; Solubility of Sodium Chloride . Dilute alcohol at 25 ' C. [ 1000 grammes Water at 25 ' C of Water +1 mol . Et(OH ) . ] Sample . A. B. Sample . A. B. Density of saturated solution . d \#151 ; 1 -2015 25 1 -2019 Density of saturated solution . d 25 1 -1794 25 1 -1793 Weight of saturated solution Weight of salt found Weight of water present grammes . 12 -0758 3 -2057 8 -8701 grammes . 12 -0915 3 -2100 8 -8815 Weight of saturated solution Weight of salt found Weight of water + alcohol 1 Weight of alcohol present ( calculated ) Weight of water present grammes . 11 -8480 2 -9340 8 -9140 0 -3920 8 -5220 grammes . 11 -8368 2 -9300 8 -9068 0 -3917 8 -5151 Calculated from above , 100 grammes * of water dissolve 36 T4 sodium chloride . 36 -14 sodium chloride . Taking the value 36 T4 grammes j the salt saturates the alcohol controls ... . 46 grammes alcohol control 1 mol . alcohol controls grammes of water . 8-1184 8-1073 0 -4036 0 -4078 47-36 . 47-81 2 -63 ! 2 -66 molecules of water which was heated in an air oven kept at about 110'\#151 ; 120 ' ; it was found possible , in this way , to prevent the salt from creeping up the side of the vessel . In reducing the observations , the weight of salt present was deducted from that of the solution ; the weight of hydrogen chloride or alcohol in the remaining liquid was then calculated and deducted , the remainder was the amount of water present . The weight of water required to form a saturated solution with the amount of salt present was then calculated and deducted from that of the water present ; assuming that the remaining water was associated with the precipitant , its molecular ratio to the latter was then calculated . The graphs are drawn to represent the variation of the presumed state of hydration of the precipitant with the variation in the amount of the precipitant ; they therefore serve to picture the dehydrating activity of the precipitant . Studies of the Processes operative in Solutions . Table II.\#151 ; Sodium Chloride . Displacement of Salt by addition of Ethyl Alcohol to 1000 grammes of Water at 25 ' C. Precipitant . Saturated solution . Weight of salt dissolved in 1000 grammes of water . Molecular proportion of salt in 1000 grammes of water . | i Apparent molecular hydration of precipitant . Molecular proportion of alcohol per 55'5 mols . of water . Weight of saturated solution taken . ,25 ct . 25 Weight of salt present . Weight of alcohol present . grammes . grammes . grammes . grammes . r A. 12 -0758 1 -2015 3 -2057 nil 361 -4 6-18 \#151 ; i B. 12 -0915 1 -2019 3 -2100 nil 361 -4 6 18 \#151 ; i r A. 12 -0192 1 1959 3 -1303 0 -1010 356 -2 6-09 3-20 * 1 B. 12 -0020 1 *1957 3 -1275 0-1009 356 -5 6-09 3-04 JL I A. 11 9553 1 -1899 3 -0616 ; 0 -1999 352 -2 6-02 2 -84 2 i B. 11 -9516 1 -1896 3 -0616 0 '1998 352 -3 6-02 2-80 A. 11 -8480 1*1794 2 -9340 0 -3920 344-3 5-88 2-63 1 i B. 11 8368 1 -1793 2 -9300 ; 0 -3917 344 -1 5 -88 2-66 9 I A. 11 -6426 1 -1592 2 -7135 0 -7522 331 -8 5-67 2-27 2 i B. 11 -6462 1 -1593 2 -7109 0 -7528 331 -3 5 -66 2-31 A. 11 '1688 1 -1111 2 -1642 1 -6837 295 -6 5-05 2-02 5 i B. 11 -1656 11115 2 -1602 1*6839 295 -0 5 -04 I 2 -04 Table III.\#151 ; Potassium Chloride . Displacement of Salt by addition of Ethyl Alcohol to 1000 grammes of Water at 25 ' C. Precipitant . Saturated solution . Weight of Molecular proportion of salt in 1000 grammes of water . Molecular proportion of alcohol per 55 '5 mols . of water . Weight of saturated solution taken . ,25 a \#151 ; 25 Weight of salt present . Weight of alcohol present . salt dissolved in 1000 grammes of water . Apparent molecular hydration of precipitant . _ / grammes . ! A. 11 -8600 1 -1816 grammes . 3 1676 grammes . nil i grammes . 359 -7 4-83 t B. 11-8561 1 1813 3 -1376 nil 359 -8 4-83 \#151 ; * { A. 11-8196 1 -1755 3 -0621 0 -0995 353 -7 4-75 3-73 ; B. 11 -80G0 1 -1754 3-0611 0 -0994 354 -0 4-75 3 '45 1 * { A. 11-7386 1 -1687 2 -9681 0-1971 346-2 4-64 4-2 : B. 11 -7363 1 -1689 2 -9681 0 -1971 1 346 -3 4-64 4 1 i ; A. 11 -6073 1 -1567 1 2 -8051 0 -3870 333 3 4-47 4*08 i B. 11-6178 1 -1568 i 2 -8138 0 -3871 , 1 334 -3 4-49 3 *93 2 J j A. 11-4002 1 1353 2 -5530 0-7453 315 1 4-23 3*44 i B. 11-4046 1 1 -1357 2 -5C04 0 -7451 316 1 4-24 3*37 5 j A. 10-9018 1 -0847 1 -8943 1 -6843 258 -6 3-47 3 *12 1 B. 10-9012 1 -0847 1 -8977 | 1 -6836 259 -2 3-48 3*10 Prof. H. E. Armstrong and others . [ June 20 , Table IY.\#151 ; Ammonium Chloride . Displacement of Salt by addition of Ethyl Alcohol to 1000 grammes of Water at 25 ' C. Precipitant . Saturated solution . Weight of salt dissolved in 1000 grammes of water . Molecular proportion of salt in 1000 grammes of water . Molecular proportion of alcohol per 55 *5 mols . of water . Weight of saturated solution taken . ,25 Weight of salt present . Weight of alcohol present . Apparent molecular hydration of precipitant . - { grammes . A. 10-8494 B. 10-8456 1 -0808 1 -0805 grammes . 3 -0719 3 -0719 grammes . nil nil grammes . 395 -0 395-2 7-39 7-39 \#151 ; j { A. 10-8244 B. 10-8178 1 -0779 1 -0780 3-0468 3 0414 0 -0884 0 -0884 396 -2 395 -6 7-40 7-40 -0-64 -0-28 \#187 ; { A. 10-8000 B. 10-7994 1 -0753 1 0753 2 -9862 2 -9818 0-1756 0 -1757 390 -9 390 -2 7 31 7 -29 1 -16 1-38 . { A. 10-7542 B. 10-7682 1 -0706 1 -0704 2 -9051 2-9074 0 -3452 0 -3457 387 -1 386 -9 7-24 7-23 1 12 1-16 3 . { A. 10-5739 B. 10-5708 1-0528 1 -0528 2-6007 2 -6007 0 -9668 0 -9665 371 -1 371 -3 6-94 6-94 1 -12 1 11 5 { A. 10-4192 B. 10-4202 1 -0377 1 -0376 2 -3537 2 -3519 1 -5082 1 -5088 358-9 358 -5 6-70 6-70 1 -02 1 -03 Table V.\#151 ; Potassium Bromide . Displacement of Salt by addition of Ethyl Alcohol to 1000 grammes of Water at 25 ' C. Precipitant . Saturated solution . Weight of salt dissolved in 1000 grammes of water . Molecular proportion of salt in 1000 grammes of water . Apparent molecular hydration of precipitant . Molecular proportion of alcohol per 55*5 mols . of water . Weight of saturated solution . Density of saturated solution , 7 25 25 Weight of salt present . Weight of alcohol present . grammes . grammes . grammes . grammes . i r A. 13-8815 1 -3830 5 -6579 nil 688 -0 5 -78 \#151 ; i B. 13-8652 1 -3824 5 -6548 nil 688 -7 5-79 \#151 ; i r A. 13-7849 1 -3725 5 -5609 0 -0935 683 -9 5 -75 1 -40 * 1 B. 13-7968 1 -3727 5 -5657 0 -0936 683 -9 5 -75 1 -40 i i A. 13-6846 1 -3634 5 -4111 0 -I860 669 -7 5-63 ! 3-10 4 1 B. 13-6864 1 -3634 5 -4110 0 -I860 668 -9 5 -61 3 -13 . r A. 13-4906 1 -3445 5 -1818 0 -3654 652 -3 5 -48 2-90 1 i L B. 13-5155 1 -3443 5 -1902 0 -3661 652 -1 5 -48 [ 2 -92 A. 12-8715 1 -2815 4 -4026 1 -0269 591 -5 4-97 2-60 Q 3 I B. 12-8742 1 -2815 4 -4995 1 -0277 590-8 4-97 2 -62 - f A. 12-3792 1 -2318 3 -8232 1 -5999 | 549 -6 4-62 2 -24 B. 12-3773 1 -2322 3 -8261 1 -5990 | 1 550 -3 4-62 2-23 Studies of the Processes operative in Solutions . Table VI.\#151 ; Potassium Iodide . Displacement of Salt by addition of Ethyl Alcohol to 1000 grammes of Water at 25 ' C. Precipitant . Saturated solution . Weight of Molecular proportion of salt in 1000 grammes of water . Molecular proportion of alcohol per 555 mols . of water . Weight of saturated solution . Density of saturated solution , ,25 a \#151 ; . 25 Weight of salt present . Weight of alcohol present . salt dissolved in 1000 grammes of water . Apparent molecular hydration of precipitant . r - i grammes . A. 17-3318 B. 173565 1 -7273 1 -7268 grammes . 10 -3802 grammes . nil grammes . 1487 -9 8-96 \#151 ; * { A. 17-2382 B. 17-2387 1 -7157 1 -7154 10 -2440 10 -2440 0 -0795 0'-0795 1481 -5 1481 -4 8-92 8-92 0-97 0*97 * { A. 17 -1095 B. 17-1111 1 -7036 1 -7042 10 -0920 10 -0916 0 -1578 0 -1578 1471 -2 1470 -7 8 -87 8-86 1 -25 1-29 1 { A. 16-8938 B. 16-9156 1 -6833 1*6833 9 -8122 0 -3114 1449 -3 8-73 1 -47 3 { A. 16-1388 B. 16 -1244 1 -6059 1 -6063 8 -8498 8 -8535 0 -8839 0 -8817 1381 -6 1385 -7 8-32 8-33 1-32 1 -27 3 { A. 15-4879 B. 15-4940 1 -5425 1 -5420 8 -0694 8 -0690 1 -3872 1 -3885 1337 -9 1336 -6 8-06 8-06 1 -12 1 13 Table VII.\#151 ; Ammonium Chloride . Displacement of Salt by addition of HC1 to 1000 grammes of Water at 25 ' C. Precipitant . Saturated solution . Weight of salt dissolved in 1000 grammes of water . Molecular Molecular proportion of hydrogen chloride per 55*5 mols . of water . W eight of saturated solution used . A25- 25 Weight of salt present . Weight of HC1 present . proportion of salt dissolved in 1000 grammes of water . Apparent molecular hydration of precipitant . - { grammes . A. 21-5398 B. 21 -5380 1 -0797 1 -0800 grammes . 6 -1154 6 -1154 grammes . ; grammes . 1 396 -48 396 -52 7-41 7 -41 \#151 ; * { A. 21 -5674 B. 21-5276 1 -0810 1 -0790 5-949 5 -970 0 -1446 0 -1437 385 -1 384 -7 7-19 7-18 6-33 6-61 21 -5816 1 -0815 5 -7346 0 -2835 368 -48 6-88 7-85 1 { A. 21 -6044 B. 21-6020 1 -0827 1 -0827 5 -3531 5 -3435 0 -5783 0 -5768 341 -5 340 -7 6-38 6-37 | 7-75 5 21 -9393 1 -0992 1 2 -4890 3 -0255 174 -24 3-25 6-9 [ June 20 Prof. H. E. Armstrong and others . Table VIII.\#151 ; Sodium Chloride . Displacement of Salt by addition of HC1 to 1000 grammes of Water at 25 ' C. Precipitant . Saturated solution . Weight of salt dissolved in 1000 grammes of water . Molecular proportion of hydrogen chloride per 55 *5 mols . of water . Weight of saturated solution used . A25 A \#151 ; . 25 Weight of salt present . Weight of HC1 present . Molecular proportion of salt in 1000 grammes of water . Apparent molecular hydration of precipitant . - { grammes . A. 239584 B. 23-9810 1 -2012 1 -2018 grammes . 6 -3570 6 -3760 grammes . *** grammes . 362 15 362 -33 6-19 6-19 \#151 ; * { A. 23-8920 B. 23 -8862 1 -1972 1 -1970 6 -0396 6 0253 0-153 0 154 341 -2 340-2 5 93 5-92 12 -559 12 -601 * 23 -7810 1-1915 5 -8076 0 -3175 328 -93 5 -62 10 19 1 { A. 23 -5816 B , 23 -6174 1 1814 1 -1822 5-2600 5 -2674 0 -6385 0-6408 297 -5 297 -4 5-08 5 -08 | 9-91 5 { A. 22-4010 B. 22 -4218 1 -1241 1 -1238 1 -5841 1 -5776 3 -2471 3 -2525 90-16 89 -6L 1 -54 1 -53 | 8-34 Table IX.\#151 ; Potassium Chloride . Displacement of Salt by addition of HC1 to 1000 grammes of Water at 25 ' C. Precipitant . Saturated solution . Weight of salt dissolved in 1000 grammes of water . Molecular proportion of salt in 1000 grammes of wrater . Apparent molecular hydration o ! precipitant . Molecular proportion of hydrogen chloride per 55*5 mols . of water . Weight of saturated solution used . ! A25 . j 25 Weight of salt present . Weight of HC1 present . ; grammes . grammes . grammes . grammes . r A. 23 -5746 1 -1810 6 -2297 \#151 ; 360 -83 4-84 \#151 ; i B. 23 -5952 1 1811 6 -2407 \#151 ; 359 -60 4-82 \#151 ; a. r A. 23-4750 1 -1766 5 -907 0-159 338 -6 4 54 12 -99 4 1 B. 23 -4370 1 1764 5 -899 0-157 339 -33 4-548 13 02 23 -3786 1 -1742 5 -6321 ! 0 -0770 323 -15 4-33 ' 11 -42 t r A. 23-1776 1 -]617 5 0551 0 -6397 289 -2 3-87 | 11 -03 1 1 B. 23 -1592 1 1611 5 0350 0 -6485 288 -1 3-86 q J A. 22-5708 1 1320 3 -023 1 -9218 171 -51 2-29 9-74 3 1 B. 22-5800 1 -1326 3 040 1 -9206 172 -50 2 -31 | 9-68 * f A. 22-3344 1 -1184 1 -5134 3 -2392 86 -07 1 -02 1 | 8 -42 5 i B. 22-3244 1 1184 1 -5477 3 -2169 88 -14 1 18 i 1907 . ] Studies of the Processes operative in Solutions . If the apparent dehydrating power of the precipitant be taken as the measure of its activity in competition with the dissolved salt , it will be obvious , on reference to Diagram 1 ( below ) , in the first place , that although alcohol is less active than hydrogen chloride , the same kind of influence is exercised by both precipitants , as the two sets of graphs correspond in most respects . Diagram 1 . HYDROGEN CHLORIDE AS PRECIPITANT . Apparent Mol. hydration of Precipitant It is important to consider Engel 's results , and especially his conclusions , in connection with our determinations ; as his observations were made at 0 ' they afford data for a comparison of the effects produced at 0 ' and 25 ' . Engel did not adequately take into account the proportion of water present , but assumed that the phenomena would be the same if considered with reference Prof. H. E. Armstrong and others . [ June 20 , to a constant amount of water ; * when his observations are recalculated from our point of view ( Table I ) and the results are expressed by graphs , it is obvious that they correspond very closely with our own ( Diagram 2 ) . Diagram 2 . 1IYBR ALCOHOL 3QEN Apparent Molecular hydration of Precipitant . The graphs afford a most interesting picture of the state of the salts in solution at various stages . As the precipitant has the largest effect when present in least amount , it is clear that the condition of the salts in highly concentrated solutions is peculiar and different from that which they assume in presence of a considerable proportion of the precipitant : sodium and potassium chlorides both exist in an eminently precipitable form in the * His statement on this point is as follows :\#151 ; 6 . Tant que le chlorure est precipite equivalent a equivalent par l'acide chlorhydrique , la quantite d'eau contenuedans un mdrne volume de la solution du chlorure en presence de quantiles variables d'acide est sensiblement constante . II en rtisulte que le ph6romene reste le meme si l'on rapporte \amp ; un meme poids d'eau la quantite de chlorure en solution en presence de quantites variables d'acide chlorhydrique . 7 . L'acide chlorhydrique n'agit pas en fixant de l'eau et empechant ainsi celle-ci d agir comme dissolvant sur le chlorure . La quantite d'eau laissee libre par la precipitation d'un equivalent du sel varie , en effet , dans chaque cas , et , par suite , l'acide chlorhydrique s'opposerait a la dissolution de chaque chlorure en s'unissant lui-meme a une quantity d'eau variable dans chaque cas et sensiblement egale a celle qu'exige , pour se dissoudre , un equivalent du chlorure consider^ . 8 . Enfin , l'eau qui se combine avec l'acide chlorhydrique et 1 eau de cristadisation du chlorure semblent intervenir comme dissolvant , au meme titre que le reste de 1 eau , 1907 . ] Studies of the Processes operative in Solutions . concentrated solutions , water being held by them far less firmly than it is subsequently ; ammonium chloride , on the other hand , is present in a form in which at first it is more soluble in the mixed solvent than in water . As ammonium chloride is readily volatilised and , when vaporised , has a density corresponding to the formula NH4C1 , it may be assumed that it enters into and exists in solution at least largely in the monadic form ; but in concentrated solutions , in which , probably , there is not sufficient water to hydrate all the molecules , a considerable proportion of the monads are unhydrated and capable of combining with substances such as hydrogen chloride and alcohol . As the amount of precipitant is increased , the amount of salt in solution is diminished and a proportion is soon reached which permits of the hydration of most , if not all , of the salt molecules . Ere this stage is reached , however , the proportion of hydrogen chloride molecules present becomes sufficiently large once more to exert a solvent action on the salt , which , in consequence , is thrown out of solution in a diminishing proportion . It can scarcely be doubted that the easily precipitable form of potassium and sodium chlorides is a complex , polymerised molecule , closely related , perhaps , to the solid form : in fact , the solution may be regarded as saturated puisque le phenomene est le meme pour les chlorures anliydres et pour les chlorures qui cristallisent avec de l'eau de eristallisation . Engel 's data for ammonium chloride are given by way of example in the following table , together with ( in the last two columns)the corrected values we have calculated from them on the assumption that water is present in constant amount throughout . Quantite de chlorure d'ammonium dans 10 c.c. de solution presence de quantitesvariables d'aeide I Calculated from data given in table\#151 ; i NH4C1 . HC1 . Comme des equivalents . Densite . Eau Molecular proportion of HC1 in 1000 grammes of water . Molecular hydrate value . ' I 1 : 46 -125 0 46 -125 1 -076 8 *29 grammes . i II j 43 '6 2 -9 46 *5 1 -069 8 *25 0-351 7 -49 1 III 41 -0 5 -5 46 -5 1 070 8 -31 0 -661 9 -477 IV 39 15 7 -85 47 -0 1 -071 8 *33 0 -912 9 -05 V 36 -45 10 -85 47 -30 1 -093 8 *39 1 29 9-43 t VI ; 27 -37 21 -4 48 -7 1 -078 8 *53 2 -50 9:29 VII i 10 -875 53 -0 63 -875 1 106 8 *54 6 -21 6 -88 VIII 1 8-8 61 -0 69 -8 1 114 8 *12 7 -51 4-96 Prof. H. E. Armstrong and others . [ June 20 . with the solid with which it is in equilibrium . Comparison of the observations at 0 ' and 25 ' seems to show that this " solid form " persists in presence of a larger proportion of the precipitant at 0 ' than it does at 25 ' , at least a molecular proportion of hydrogen chloride being required to destroy it at 0 ' and only about half as much at 25 ' . Moreover , to judge from the shortness of the horizontal branches of the sodium and potassium chloride graphs at 0 ' in comparison with those at 25 ' , it would seem that at the higher temperature these chlorides are also to some extent present as unhydrated monads soluble in the precipitant . In the case of ammonium chloride , the increased solubility is noticeable at 0 ' at a somewhat " higher level " than at 25 ' , probably because the more soluble chloride NH4CI : C1H is more stable at the lower temperature . It will be seen that in the case of ammonium and potassium chloride the 0 ' graphs curve more and more to the left as the concentration of the hydrogen chloride is increased ; no such marked trend is noticeable at 25 ' . It is to be supposed that the difference arises from the instability of the double chlorides at the higher temperature in competition with water . The fact that the alcohol graphs resemble the 25 ' hydrogen chloride graphs affords support to this view , as it is to be expected that alcohol would have but little chance in competition with water . From the ionic dissociation point of view , dissociation should be repressed as the amount of hydrogen chloride is increased : therefore , instead of increasing , the solubility should diminish proportionally as the concentration of the hydrogen chloride is increased . It will be observed that the behaviour of potassium bromide and iodide in presence of alcohol is similar to that of the chloride and that the greater the molecular solubility of the salt the more closely it approximates to ammonium chloride ; probably the proportion of monads in the concentrated solution is larger in the case of the more soluble salt , which also has the lower melting point ( Diagram 3).* Except , perhaps , in the case of ammonium chloride , the greater proportionate solubility of the salts in regions represented by the upper portion of the diagram , as well as the lower state of hydration of the precipitant which is indicated by the backward slope of the graphs , can only in part be ascribed to the formation of a soluble compound with the precipitant ; probably it is mainly due to the production of the more soluble monads in increasing " * It is perhaps appropriately suggested here that probably the great increase in molecular solubility of ammonium chloride ( from about 6 to 13'5 proportions per 1000 grammes of water ) between 0 " and 100 ' is to be correlated with the low melting , point of the salt . 1907 . ] Studies of the Processes operative in Solutions . proportion as the number of interposed molecules of the precipitant is increased . The same kind of effect is reciprocally exercised by two salts such as potassium and sodium chloride , a saturated solution containing per 1000 molecules of water of the former 88 and of the latter 111 molecular proportions , whilst a solution saturated with both salts contains 39 of the former to 89 of the latter : or , in sum , 128 , an excess of 128 \#151 ; 111 = 17 monadic proportions over the number contained in a saturated solution of the more soluble salt . The monads of the two salts evidently interfere with one another 's freedom of combination : consequently , the mixed solution contains , in the aggregate , a greater number of molecules than can coexist in the Diagram 3 . solution of the more soluble salt ; evidence in support of this view is to be found in the fact that the solution of the mixed salt has a lower vapour pressure ( 16'84 mm. ) than has the solution of sodium chloride ( 17*7 ) or that of potassium chloride ( 19-2 ) . In the mixed solution , at 25 ' , the more soluble sodium chloride is present in a proportion somewhat larger than that corresponding to its solubility in comparison with the solubility of potassium chloride ; evidently , therefore , it is able to compete somewhat more successfully for the water . This preponderance of the more soluble salt is even more obvious in cases in which the competition is with a salt which is but moderately soluble and which , therefore , presumably has but a slight hold upon the water\#151 ; for example , whereas potassium chloride and sulphate are present in their saturated i solutions in the relative molecular proportions of 88 to 12 , a solution saturated with both salts contains to 84 of the former only 1*5 molecular proportions of the latter , and its vapour pressure ( 19 mm. ) is 576 Prof. H. E. Armstrong and others . [ June 20 , but slightly less than that of chloride alone ( 19*2 ) . The solubility of sodium chloride in the presence of potassium chloride , it is well known , diminishes slightly bet ween 0 ' and 100 ' ; this is probably due to the diminution in its affinity for water as the temperature rises and the concomitant increase in the tendency to reform complex molecules\#151 ; the decomposition of which at lower temperatures must be regarded as determined largely by the affinity of water for the monads . At 100 ' potassium and sodium chlorides are almost equally soluble ( 4'4 : 4'6 molecular proportions ) , the former having the advantage\#151 ; probably because it can hold water more firmly . The distinction between monadic and polymerised molecules has been almost left out of account by those who have attempted to apply the ionic dissociation hypothesis to the discussion of solubility . It is clearly necessary , however , to acknowledge the existence in solutions of a great variety of molecular conditions simultaneously : of monadic and polymerised molecules both in the anhydrous and hydrated states and , in some cases , of compounds formed by the association of the admixed solutes ; and also to recognise that the solvent itself as well as the dissolved substances is in a state of continued flux . The interplay of these conflicting and competing elements is sufficient , probably , to account for all the varied phenomena afforded by solutions without the introduction of hypothetical considerations based on the presumed occurrence of dissociation into independent ions . And even if , on other grounds , it were necessary to postulate the occurrence of ionic dissociation in solution , the phenomena are clearly of so complicated a character that it is impossible to apply such an interpretation without introducing the many other considerations which obviously demand attention . The variables are so numerous that it may be doubted whether it will ever be possible to develop any simple treatment of solutions . III . The Sucroclastic Action of Nitric Acid as influenced by Nitrates . By I\#163 ; . Whymper , Salters ' Company 's Research Fellow , City and Guilds of London Institute , Central Technical College . The experiments carried out by R. J. Caldwell on the hydrolysis of cane sugar by chlorhydric acid in presence of various chlorides , described in the first of these studies , * have afforded a means of judging of the extent to which such salts exercise a concentrating effect and of determining the average degree of hydration of the chlorides in solution . In the present * 'Roy . Soc. Proc. , ' 1906 , A , vol. 78 , p. 272 . 1907 . ] Studies of the Processes operative in Solutions . communication it will be shown that the method is equally applicable to nitrates and that these are nearly as fully hydrated in solution as are the corresponding chlorides\#151 ; a conclusion of some interest , as nitrates are not usually credited with any considerable dehydrating power . My observations have been made with the apparatus* which was used by Caldwell and in the manner described by him ; throughout the enquiry I have also enjoyed the advantage of his experience and have to thank him for the advice which he has given me . The salts examined were recrystallised until neutral , the ammonium nitrate from alcohol . The acid used in preparing the solutions was approximately twice normal ; it was titrated against calcite and also against a solution of baryta standardised by another worker . The solution to be examined was filtered into the polarimeter tube at as near to 25 ' as possible and the tube was then placed in position in the heated jacket attached to the instrument . To give time for the liquid to acquire the temperature of the thermostat , it was found to be advisable to wait before taking the initial reading until about 20 minutes later , when the rotatory power was about 10 ' to 11 ' ; by operating in this manner , the error due to initial disturbances is avoided . Mean time readings were taken at 30 , 35 ... ... ... 100 minutes after the first : a final reading was taken todetermine the end point at least 24 hours later , when the action was practically at an end . Each reading reported represents the mean of five-readings taken at minute and half minute intervals on either side of the mean time . The results obtained in two complete experiments entirely representative of the series are recorded in Tables I and II . It will be noticed that the 30-minutes values are both high : this is almost uniformly the case and appears to be due to the fact that the eye was less sensitive just after coming into the dark room than it was subsequently . The thermometers attached to the jacket were watched throughout the experiment and it was usually possible to correlate marked changes in the value of the constant with any unusual variation of the temperature . An illustration of this fact is given in Table I : it will be seen that the value of K at 35 minutes is given as-12 units above the mean value ; a fall in temperature of about 0'T was noticed when the reading was taken at this time . * To adjust the rate of flow of the water through the jacket of the polarimeter tube , the water was passed through a tube in which a. glass rod , of nearly the same diameter , , could be moved up and down ; this tube was provided with inlet and exit tubes and the water passed through the interval between the rod and the main tube . By shifting the rod , the rate of flow of the water could be adjusted far n^pre delicately than by means of the ordinary screw clip arrangement . Prof. H. E. Armstrong and others . [ June 20 , Table I.\#151 ; \ gramme-molecule of Cane Sugar+ 1 gramme-molecule of HN03 + 1 Gramme-molecule of LiN034-1.000 grammes of H20+13H20 . t. a25 . 1 ) a \#151 ; x. / 10\ a \ K(t1o8^ ) ' 0 9 433 14 766 30 5-35 10 -683 468 35 4-733 10 -066 475 40 4-333 9-666 460 45 3-8 9 133 463 50 3 -333 8-666 463 55 2 -883 8-216 463 60 2 -417 7 -75 467 65 2-033 7-366 465 70 1 -667 7-0 463 75 1 -333 6-666 461 80 0-967 6-3 462 85 0-65 5-983 462 90 0-333 5-666 462 95 0-017 5 -35 464 100 00 -0-2 -5-333 5-133 459 Mean 463 Table II.\#151 ; ^ gramme-molecule of Cane Sugar + 1 gramme-molecule of HjST02 + 1 gramme-molecule of AgN03+1000 grammes of Water . t. a5 . D a \#151 ; x. k(t1osA ) ' 0 11 1 17 -767 30 5 -533 12 -2 544 35 4-85 11 -517 538 40 4-233 10 -9 531 45 3-567 10 -234 533 50 3 013 9-68 528 55 2 -367 9 -034 535 60 1 -883 8-55 530 65 1 -333 8-0 533 70 0-85 7-517 534 75 0 -4 7-067 534 80 0-033 6-7 530 85 -0 -367 6-3 530 90 -0 -683 5-984 525 95 -1 -033 5 -634 525 100 00 -1 -4 -6-667 5 -267 528 Mean 531 The data relating to the various salts which were studied are collected in Table III . 1907 . ] Studies of the Processes operative Solutions . Table III.\#151 ; \ gramme-molecule of Cane Sugar+ 1 gramme-molecule of HN03 + 1 gramme-molecule of Salt+ 1000 grammes of Water+ X gramme-molecules of Water . Salt . V olume K / i'5iog-cb_y V t Ba-x ) X ( gramme - K. Average of solution . molecules ) . hydrate . c.c. Sugar alone ... 1136 4 463 1136 '6 467 1137 -1 466 Mean 465 AgN03 1173 -3 531 20H . , O 339 9H20 429 6H20 459 5H20 f 465 t 466 ; 5H20 . nh , no3 1167 -9 570 ioh2o 444 7H20 f 466 i 466 7H.,0 . ' KNO , 1180 -1 566 IOHoO 453 8H.,0 f 462 1 465 8H20 . NaNO ; i 1172 -1 607 20H , O 373 * 12H,0 444 11H20 f 464 \ 466 11H.O . LiN03 1179 -3 578 7H20 488 IOHoO 478 11-5H.,0 477 13H.'0 463 13H20 . 15HsO 432 Sr ( NO A 1197 9 733 23H,0 420 20H2O 443 18H20 J 463 t 463 18H20 . The results call for little remark , as the hydration values arrived at , given in the last column of the table , seem to be entirely rational . It is difficult to avoid the conclusion that they dispose of the contention that nitrates exist in solution unhydrated . IV . The Hydrolysis of Methylic Acetate in Presence of Salts . By H. E. Armstrong , F.RS . , and J. A. Watson . In principle , the method developed in the first of these studies of determining the average " concentrating effect " of a salt on the activity of an acid hydrolyst is applicable to all cases of hydrolysis other than those VOL. lxxix.\#151 ; a. 2 s Prof. H. E. Armstrong and others . [ June 20 , induced by enzymes ; moreover , the results obtained with chlorides and nitrates with cane sugar are so entirely rational that there can be little doubt that it is valid generally as a means of determining the average degree of hydration of a salt in solution . But as the substances in a solution share the solvent and are in competition , it is to be expected that hydration values will be found to vary from case to case and that it will not always be possible to approximate to the true hydrating effect of a salt : indeed , cases are known in which salts apparently retard hydrolysis . To determine the limitations of the method , therefore , it is necessary to investigate the behaviour of hydrolytes other than cane sugar . That chosen for the experiments referred to in this account was the ethereal salt methylic acetate , CH3.CO . OCH3 . This substance is entirely different in constitution from cane sugar and is present in solution , presumably , in the form of simple molecules which are hydrated to but a very slight extent , whilst cane sugar doubtless exists in solution more or less in the form of associated complex molecules and in a moderately hydrated condition\#151 ; perhaps as a " hexhydrate " at least . Presumably , therefore , the system consisting of water , chlorhydric acid and cane sugar contains less " free water " than the equivalent system in which methylic acetate takes the place of sugar : a salt dissolved in the latter system should , at least in concentrated solutions , therefore have a greater chance of becoming hydrated than it would have if dissolved in the former . From this point of view it was to be expected that the hydration values deduced with the aid of methylic acetate , if not coincident with those determined by means of cane sugar , would be higher ; as a matter of fact , lower values are obtained . The average degree of molecular hydration arrived at with the aid of the two hydrolytes is as follows:\#151 ; 1 1 I Hydrolysis by chlorhydric acid . \#151 ; Hydrolysis by nitric acid . Sugar . Acetate . Sugar . Acetate . _ Silver nitrate ... 5 Ammonium chloride ... 10 5 Ammonium " 7 -2 Potassium " 10 8 Potassium " 8 1 Sodium , , 13 10 Sodium " 11 3 Lithium " \#151 ; \#151 ; Lithium " 13 Barium " 19 18 Barium " Strontium " \#151 ; \#151 ; Strontium " 18 + 5( ? ) Calcium " 22 20 Calcium " 7 The results are very remarkable\#151 ; evidently some special influence comes 1907 . ] Studies of the Processes operative in Solutions . into play , particularly in the case of the nitrates . It is not difficult to diagnose the character of this influence . It has been shown by Arrhenius* and by Spohrj* that chlorides and nitrates , but not sulphates , exert a slight retarding effect on the hydrolysis of ethylic acetate by alkali : therefore it is probable that a similar retarding influence c5mes into play when hydrolysis is effected by an acid and that this to some extent masks and counteracts the proper accelerating effect of the salt . Probably the effective hydrolyst is the hydrated acid : assuming , however , for the sake of simplicity , that water acts alone , the hydrolysis of the ethereal salt doubtless involves the association of the two molecules and subsequent partition of the complex into acid and alcohol , thus\#151 ; OH CH3.COOMe + OH2-^ CH3.COH CH3.COOH + HOMe . OMe A simple explanation is afforded of the interference of a salt and of the diminished acceleration or retardation observed in the case of methylic acetate , if it be assumed that the salts ( M'X ' ) also enter into association with the ethereal salt\#151 ; X CH3.COOMe + M'X'-^ CH3.COH OMe and that consequently they hinder to some extent the association of ethereal salt and hydrolyst . } The keto-group , CO , is so generally admitted to be unsaturated and capable of combining with compounds of the form R'X ' that such an explanation cannot be regarded as otherwise than simple and rational . We are not aware , however , that it has been suspected up to the present time that nitrates are peculiarly active in thus combining . Results such as we have described are altogether irreconcilable with the tenets of those who accept the doctrine of ionic dissociation . They serve , however , to explain the results obtained on hydrolysing ethereal salts with alkali in presence of metallic salts , and we venture to think that it is no * ' Zeit . Phys. Chem. , ' vol. 1 , p. 1107 . According to Arrhenius , the effect on the rate of hydrolysis by sodic hydrate of the corresponding salts is greater than that exercised by the potassium salts on the activity of potassic hydrate . Potassium iodide has a greater influence than the bromide , which in turn is more active than the chloride . Arrhenius speaks of the retardation as a perturbation of the second order , due to forces the true nature of which will not be easily determined . t Ibid. , vol. 2 , p. 194 . } In the case of hydrolysis by alkali , the experiments have been made with quite dilute solutions , between limits within which concentration has but little influence , so that the concentrating effect of the salt cannot well become apparent merely as a diminished acceleration and there is consequently an actual retardation . 2 s 2 582 Prof. H. E. Armstrong and others . [ June 20 , longer necessary to associate any element of mystery with such hydrolytic phenomena ; the long recognised conventional articles of belief of the chemist afford a sufficient and satisfactory explanation of the observed departures from uniformity . The hydrolysis of methylic acetate by acids was first investigated systematically by Ostwald in 1883 and developed by him into a method of appraising the relative activity of acids . Trey , at Ostwald 's instigation , shortly afterwards studied the effect of several neutral salts on the action of the corresponding acids and showed that they exercised an accelerating influence ; as Trey 's and all subsequent experiments , however , were made with volume-normal solutions , it has remained uncertain to the present time whether or to what extent the increased activity of the acid is due to the mere displacement of water by the salt . It was , therefore , desirable to institute experiments in which the water was no longer a variable , so that the specific influence of the salt might be ascertained and its degree of hydration determined , following the plan developed in Part I of these studies . The solutions we have used contained , as a rule , 1000 grammes of water , \ gramme-molecular proportion of methylic acetate and 1 gramme-molecular proportion of hydrogen chloride or nitric acid ; when a salt was added , 1 gramme-molecular proportion was always used . In carrying out the experiments , 100 c.c. of twice weight-normal acid ( chlorhydric or nitric ) was introduced into a Jena flask and when the temperature of the liquid was 25 ' a like quantity of a weight-normal solution of methylic acetate , also at 25 ' , was quickly added ; the two solutions having been mixed , 10 c.c. were promptly withdrawn and run into 10 c.c. of a solution of twice normal sodic acetate , the time being noted ; the flask containing the main bulk of the solution was forthwith placed in the thermostat , which was carefully kept at 25 ' . Samples were withdrawn every 10 minutes up to two hours from the commencement of the experiment . The end point was determined the next morning . An important improvement was effected by using the sodic acetate to check the action of the strong acid . The titrations were made with N/ 5 baryta , using phenolphthalein as indicator . When salts were added , the weighed quantity of salt was dissolved in the acid solution before the solution of methylic acetate was run in . In some cases , in order to dissolve the necessary amount of salt , 50 c.c. of water were added to the acid and the solution of methylic acetate was made of double strength . The first reading was taken only after 30 minutes from the commencement of the experiment . Two complete series of observations are given in Table I. 1907 . ] Studies of the Processes operative in Solutions . Composition of Solution\#151 ; 14 *92 grammes KC1 . 100 c.c. 2N/ HC1 . 100 c.c. N/ MeAc . Table I. KC1.8H20\#151 ; 14 *92 grammes KC1 . 100 c.c. HC1 . 100 c.c. MeAc . 28 *82 c.c. water . Time . Titration . a \#151 ; x. 105 -i a Time . Titration . a\#151 ; x. 1051 a log . t a \#151 ; x 0 c.c. 52 3 23 3 j 0 c.c. 45 9 21 -3 30 57 4 18 -2 357* 30 49-9 17 3 301 40 : 58-5 17 -1 336 40 51 -2 16 0 310 50 59 -7 15 '9 332 50 52 2 15 -0 304 60 1 60-9 14 *7 333 60 53 -25 13 -95 306 70 62 2 13 *4 342 70 54 2 13-0 306 80 63 1 12 5 338 80 55 -05 12 15 305 90 64 1 11 5 340 90 55 9 11 3 305 100 65 -05 10 -55 344 100 56-7 10-5 307 no 65 -7 9-9 337 no 57 -4 9-8 306 End point 75 6 Mean ... 338 End point 67 -2 Mean ... 1 305 * The values entered in italics were neglected . The following ( Table II ) are the values of the velocity constant obtained with acetate alone or with salt present in the solution and those on which the determinations of the hydration values are based . It will be noticed that the values are not as accordant as those determined with the aid of the polarimeter , but this was only to be expected , as the possibility of error is so much greater , owing to the numerous measurements to be made with pipettes and the difficulty of taking samples at exactly the right times , as well as of checking the action ; moreover , titration is not nearly so accurate a process as the estimation of optical activity . Prof. H. E. Armstrong and others . [ June 20 Table II . MeA + HCl . + KC1 . KC1.8H20 . + NaCl . NaC1.10H2O . + NH4C1 . i 1 ' 1 NH4C1.5H20 . 303 291 357 301 318 385 299 292 313 301 310 296 300 336 310 316 359 300 298 2:6 290 . 300 303 300 332 304 294 341 305 313 314 307 301 290 312 333 306 303 361 316 302 321 322 305 307 308 342 306 295 360 309 299 316 307 310 304 310 338 305 301 361 302 303 325 310 309 301 303 340 305 297 361 314 298 329 310 \#151 ; 305 344 307 303 360 \#151 ; 301 316 \#151 ; 308 337 306 \#151 ; \#151 ; - 301 302 304 338 305 303 360 303 301 320 306 306 V. j i ^ j ) 303 304 . 302 306 BaCl2.18H20 . + CaCl2 . CaCl2.20H2O . MeA + HN03 . + KN03 . KN03 , H20 . + NaN03 . 304 297 307 420 292 281 234 265 289 | 268 311 312 316 418 304 298 270 282 284 2~9 318 311 306 428 304 266 278 284 273 290 314 307 311 421 305 284 283 284 274 294 314 291 307 430 302 276 279 280 275 290 301 310 313 429 299 272 279 285 269 290 298 304 309 \#151 ; 299 278 272 286 277 284 \#151 ; 295 302 \#151 ; 299 277 282 \#151 ; 276 \#151 ; 307 \#151 ; \#151 ; 282 \#151 ; \#151 ; I 309 v 304 308 \#151 ; ' 424 300 27 8 \ 278 283 277 290 307 278 277 NaN03.3H20 . nh4no3 . NH4N03-2H20 . + LiNG3 . Ca ( N02)2.7H20 . 291 254 242 257 260 274 245 2.0 267 277 270 256 273 276 274 272 274 279 278 272 273 261 278 277 274 277 266 269 280 277 272 268 273 277 276 274 278 273 263 275 278 275 1907 . ] Studies of the Processes operative Solutions . The results obtained are summarised in the following Table III:\#151 ; Table III.\#151 ; Rate of Hydrolysis of Metliylic Acetate by Chlorhydric and Nitric Acids in Solutions of different Compositions . Composition of solution . 0991 N/ HCl + N/ MeAc ... ... ... ... ... ... ... + N/ 2 MeAc ... ... ... ... ... ... . . + N/ 4 Me Ac ... ... ... ... ... ... . . + N/ 2 MeAc + N/ 2MeOH ... ... ... + N/ 2CH3C02H ... ... . . N/ HC1 +N/ 2 MeAc ... ... ... ... ... ... ... ... . + IvCl , 1 gramme -molecule . + NaCl , 1 gramme-molecule ... + NH4C1 , 1 gramme-molecule ... + CaCl2 , 1 gramme-molecule ... + BaCl2 , 1 gramme-molecule ... N/ HN03 +N/ 2 MeAc ... ... ... ... ... . ' ... ... . + KN03 , 1 gramme-molecule + NaN03 , 1 gramme-molecule Amount of water added . gramme-molecules . 304 \ 308 J 278 278 283 277 290 + LiN03 , 1 gramme-molecule ... . . + NH4N03 , 1 gramme-molecule ... . Less 2 gramme-molecules of water Although , as hydrolysis proceeds , both methylic alcohol and acetic acid are formed and accumulate in solution , the results afford no evidence that they influence the rate of change . The effect of these substances when added in advance is different , methylic alcohol being apparently without action , whilst acetic acid has a distinct accelerating influence*\#151 ; as it has in the hydrolysis of cane sugar . That the alcohol has no influence is * It has practically no hydrolytic effect perse during the time occupied in carrying out an experiment . Prof. H. E. Armstrong and others . [ June 20 , somewhat surprising in view of the fact that ethylic alcohol retards the hydrolysis of cane sugar to a not inconsiderable extent ; this difference between the two cases is , perhaps , significant and deserving of further study . Apparently , the concentrating effect which the methylic alcohol may be supposed to exercise is just balanced by the extent to which it acts in neutralising acid ; on the other hand , it would seem that the acid alcoholate is not much less active than the acid hydrate , although in the case of cane sugar it is relatively ineffective . The effect of increasing the concentration of the ethereal salt appears to be very similar to that observed in the case of cane sugar . It is proposed to extend the experiments to other ethereal salts . V. The Discrimination of Hydrates in Solution . By H. E. Armstrong , F.B.S. , and B. J. Caldwell , B.Sc. , Leathersellers ' Company 's Besearch Fellow , City and Guilds of London Institute , Central Technical College . There are many signs that the uncertainty which has so long attended the interpretation of the peculiarities manifest in solutions may be dispelled at no distant date and a common understanding arrived at , as the old belief in the existence of hydrates is once more coming to the front* and there is a growing tendency to admit that the phenomena are more complex than is commonly supposed . Inasmuch as there are no arguments from the chemical side which either compel or even require belief in ions as independent entities and not a few incompatible with such an assumption , which support the view that asso-ciationf\#151 ; not dissociation\#151 ; is the precedent of chemical interchange , physicists may well be challenged to reconsider the grounds on which they are led to suppose that ionic dissociation takes place in solution : the cogency of their arguments has been frequently questioned from the chemical side without the objections being met . To state the case briefly : apart from the fact that it is irrational and inapplicable to compounds generally ( only to electrolytes ) , three main lines of argument appear to militate directly against the assumptions postulated by the advocates of the ionic dissociation hypothesis . 1 . The complex sugars and ethereal compounds generally are hydrolysed by all acids ; and these latter differ only in the degree of activity which they * Comp. Nernst , ' Zeits . phys . Chem. , ' 1889 , vol. 4 , p. 372 ; ' Centralblatt , ' 1900 , vol. 2 , p. 620 . t Comp. E. Fischer , ' Deut . chem . Ges . Ber . , ' 1907 , vol. 40 , p. 495 . 1907 . ] Studies of the Processes operative Solutions . manifest towards the various hydrolytes . Enzymes , on the other hand , act selectively . The strength of the case which this argument affords is probably in no way realised by those who are not fully conversant with the phenomena . It is assumed by the ionic dissociation school that the action of acids is exercised by the free hydrogen ions and that the activity of the acid is proportional to the extent to which the acid is dissociated in solution into positive and negative ions . But as enzymes do not behave as electrolytes in solution , although extraordinarily active in comparison with acids , some other explanation must be found to account for their activity as hydrolysts . The proof that the enzyme enters into association with the liydrolyte appears to be complete* and as there is reason to believe that acids also combine transiently with ethereal compounds , there seems to be no reason why an explanation should be given of their action which is inapplicable to enzymes . 2. . From the ionic dissociation standpoint , the dissociation of an acid into free ions should be repressed by a neutral salt containing the negative ion of the acid ; consequently , when present together with the acid , as the salt is inert per se , the salt should diminish the activity of the acid : in point of fact , it increases it . As non-electrolytes sometimes exercise an accelerating influence similar to that of salts , although to a less extent , there is again no reason to attribute altogether special properties to electrolytes and to account for their activity by an explanation which cannot be applied to non-electrolytes.f 3 . This same argument may be applied to the precipitation of salts from .solution , as non-electrolytes are active as well as electrolytes.* * 'Roy . Soc. Proc. , ' B , 1907 , vol. 79 , p. 360 . t An argument to the same effect may be based upon the fact that hydrogen chloride , calcium chloride and alcohol produce similar effects in altering the absorption spectrum of cobalt salts ( Hartley , Royal Irish Academy , 1900 , IT , vol. 7 , p. 253 ) . I In tracing the development of the theory of electrolytic dissociation , in a lecture which he gave at the Royal Institution on June 3 , 1904 ( ' Proceedings of the Royal Institution . ' vol. 17 , p. 552 ) , Arrhenius laid stress on the fact that in the case of permanganic acid and its various metallic salts , as well as in the case of the salts of pararosaniline with acids , the absorption spectrum does not vary from salt to salt except in intensity , whereas the spectrum of fluorescein is modified by the smallest chemical change of the molecule : he advances the explanation that the uniform behaviour of permanganates and of rosaniline salts is due to the fact that the spectra are all produced by the dissociated permanganate ion in the one case and by the rosaniline ion in the other . Those who have made use of this argument have paid little attention to what is known of the relation of colour to structure : it is well established , in the case of fluorescein , that the action of alkali extends beyond the formation of a salt and involves the formation of an isodynamic compound of entirely different structure and very* differently coloured ; no such change of structure is involved in the formation of the permanganates and of the ordinary rosaniline salts . In the case of rosaniline it is possible , by varying the proportions of acid , to produce salts of different structure , in which case the colour Prof. H. E. Armstrong and others . [ June 20 , , The one respect in which electrolytes and non-electrolytes undoubtedly differ is in their affinity for water\#151 ; which appears to enter into combination with the former in some particularly intimate maimer ; it is reasonable to suppose that their special behaviour towards an electric current is conditioned by this peculiarity . From this point of view , the study of the phenomena of ' hydration is of exceptional importance . It appears to be now so widely admitted that hydrates are formed in solution that it is unnecessary to discuss the subject from the general point of view ; the question to be decided is rather what particular hydrates are present . Passing over evidence such as has been adduced by Mendeleeff , . Pickering , Hartley and others , the recent work of Harry C. Jones may be specially referred to , as he has brought forward a large amount of what purports to be new experimental evidence bearing on the determination of the extent to which salts are hydrated in solution.* also varies . The argument from colour , far from supporting the dissociation hypothesis , in reality is opposed to it . * The values which this observer arrives at are in many cases so remarkable that his methods appear to be more than open to doubt . Thus he considers that sodium , potassium and ammonium chlorides have little , if any , attraction for water and that the nitrates are even less hydrated than the corresponding chlorides . Magnesium and other sulphates give abnormal results ; this salt " appears to form no hydrates in aqueous solution , notwithstanding that it crystallises with 7 molecules of water ... it has . considerable hydrating power , but this is masked by the large amount of polymerisation which the sulphates undergo . " As the concentration is increased , the degree of hydration of caustic soda falls to zero and then rises . And whilst ammonium hydroxide is regarded as being as highly hydrated as caustic soda and potash , the mineral acids are uniformly represented as anhydrous in dilute and hydrated in concentrated solutions . The method adopted by Jones on which these conclusions are based involves , in principle , the assumption that the number of units\#151 ; whether ions or molecules\#151 ; in solution can be deduced directly from observations of the electrical conductivity ; it also involves the assumption that this value can be deduced equally well from the depression of the freezing point even in concentrated solutions made on the volume-normal plan . - In cases in which the two values differ , the difference is attributed to the formation of a hydrate and the magnitude of the difference is the basis on which the degree of hydration is calculated . Apart from the fact that the method involves both the . acceptance of the ionic hypothesis and the application throughout of the 1 '86 factor in calculating the theoretical depression of the freezing point , it is noteworthy that Jones also leaves out of account in his calculation the effect of hydration on the ionic mobilities ; and that no allowance is made for polymerisation effects . Biltz ( 'Zeits . phys . Chem. , ' 1902 , vol. 40 , p. 185 ) , who recognises that the formation of hydrates in solution may be the cause of some of the abnormal properties of strong electrolytes , has endeavoured to support this view by the argument that as caesium nitrate\#151 ; which he assumes is but slightly , if at all , hydrated in solution\#151 ; depresses the freezing point in accordance with the Ostwald dilution law , it is to be regarded as behaving normally . The electric conductivity of such solutions is not that to be expected from the freezing point results , however ; it therefore follows that conductivity cannot be taken as a true measure of the state of dissociation even in the case of salts which are- 1907 . ] Studies of the Processes operative Solutions . The method adopted in Parts I , III and IV of these studies is in principle independent of the assumptions made by those who accept the ionic hypothesis as a basis of calculation . Using cane sugar as hydrolyte , the average values arrived at in the case of a number of chlorides and nitrates appear to be such as are to be expected ; the fact that somewhat lower values are obtained with the aid of methylic acetate can be accounted for without difficulty , as already pointed out . It was our intention to discuss our results in connection with the observations of previous workers , especially with reference to the influence of salts and certain non-electrolytes on the solubility of various gases ; in this we have been somewhat anticipated by Philip , who , in a recent communication to the Chemical Society , * has developed the method of calculating the degree of hydration of a salt from existing data as to the influence of salts on the solubility of gases . Although no attempt had been made previously to deduce hydration values from changes in solubility , Setschenow , f TildenJ and RothmundS had contemplated the possibility of explaining the diminution in solubility of non-electrolytes as a consequence of the diminution in the amount of free water by the fixation of water by the dissolved salts . JahnJ moreover , had foreseen the importance of referring the solubility to the weight of solvent used instead of to the volume of solution . Philip has only called attention to a few cases of close agreement\#151 ; but it will be seen on reference to Table I , in which the results deduced from the various available observations are collected together , that the agreement is far from being close in many cases . In some cases , doubtless , the determination is affected by relatively large experimental errors , as , for example , Braun 's determinations made with nitrogen ; Euler 's determinations may also be regarded with doubt in view of the use of an unstable substance such as ethylic acetate . The values deduced with the aid of carbon dioxide excite the suspicion that some carbonate may have been formed ; the values obtained with thiocarba-mide and salicylic acid are open to a similar criticism . In fact , few of the values to the right of the nitrous oxide column command confidence . not liydrated . Taking the cases of sodium and potassium chlorides\#151 ; which do not obey the dilution law either as regards freezing points or conductivity\#151 ; and assuming that they are dissociated to about the same extent as caesium nitrate , Biltz calculates that the former can be associated with from 19\#151 ; 26 and the latter with 15\#151 ; 24 molecules of water , according to the concentration of the solution ; these results are altogether different from those arrived at by Jones . * ' Chem. Soc. Trans. , ' 1907 , vol. 91 , p. 711 . t ' M6m . de l'Acad . de St. Petersb . , ' 1875 , vol. 22 , p. 6 . 1 A lecture delivered to the Bristol Naturalists ' Society , February , 1878 , Chemical Society 's Pamphlets . S 'Zeits . physik . Chem. , ' 1900 , vol. 33 , p. 401 . || Ibid. , 1897 , vol. 24 , p. 114 . Table I.\#151 ; Average Hydration of Salts in Solutions of gramme-molecular Strength . Criterion . Hydrolysis . Solubility . Cane sugar . Methyl acetate . Hydrogen . Oxygen . Nitrous oxide . Nitro- gen . Carbon dioxide . Phenyl . tliiocarbamide . Salicylic acid . Ethyl acetate . Observers ... Caldwell \amp ; Whymper . s 1 Gordon . Steiner . i n=i \#163 ; Braun . Knopp . S3 'S \#163 ; i Geffcken . Knopp . Braun . i .8 Setschenow . Biltz . Rothmund . Bogdan . Hoffman \amp ; Langbeck . 1 Euler . Temperature 25 ' . 25 ' . 15 ' . 15c . 25 ' . 25 ' . 20 ' . 25 ' . 25 ' . 25 ' . 20 ' . 25 ' . 25 ' . 15'-22 ' . 20 ' . 20 ' . 25 ' . 1 25 ' . 28 ' . CaCl , 22 20 19 1 19 -8 BaCl , 19 18 \#151 ; \#151 ; \#151 ; 27 *0 \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; 37 -o \#151 ; \#151 ; 22 -0 NaCl ' 13 10 11 2 11 -2 \#151 ; 10 *5 \#151 ; 14 *0 12 0 \#151 ; -V- 20 -9 \#151 ; 10-1 14 -9 \#151 ; \#151 ; 13 18 -1 KC1 10 8 9-9 10 1 \#151 ; \#151 ; 10 \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; 6 4 5 -7 12 0 \#151 ; \#151 ; 8 15 -6 Lid \#151 ; 8-5 8-3 \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; 9*4 NH4d ... 10 5 \#151 ; \#151 ; \#151 ; 4 2 1 7 KBr ! - \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; 8*8 \#151 ; \#151 ; \#151 ; 7 3 Sr(N03)2 ... 18 NaN03 ... 11 3 9-5 10 -i \#151 ; \#151 ; 11 \#151 ; \#151 ; 10 \#151 ; \#151 ; 7-0 \#151 ; 4-0 5*8 kno3 8 1 9-2 9-0 \#151 ; 7 7 3-2 5 -8 2 5 3 -6 \#151 ; 5-1 LiN03 13 0 nh4no3 ... 7 \#151 ; ve \#151 ; * 2 \#151 ; ve \#151 ; - ve AgN03 ... 5 5-4 NaOH \#151 ; 16-0 19 -5 KOH \#151 ; \#151 ; \#151 ; \#151 ; 14 -0 \#151 ; \#151 ; 18-0 \#151 ; 14 -0 h3po4 \#151 ; _ 4*4 HC1 \#151 ; \#151 ; \#151 ; \#151 ; 2 -6 \#151 ; \#151 ; 2-7 1 4 \#151 ; 0*6 HNOo 1 *4 \#151 ; 0-9 \#151 ; \#151 ; ve \#151 ; \#151 ; \#151 ; ve 590 Prof. H. E. Armstrong and others . [ June 20 , 1907 . ] Studies of the Processes operative in Solutions . The values in the other part of the table are both rational and in agreement with those given in the first column , except in the case of the ammonium salts , certain nitrates and the acids . An explanation has already been advanced of the low values obtained with the aid of methylic acetate in the case of certain chlorides and nitrates ; to account for the irrational values given by the acids and in some cases by ammonium salts , it appears necessary to suppose that these exercise a specific solvent influence in presence of water . Setschenow has shown that carbon dioxide is about equally soluble in sulphuric acid and in water ; the monohydrate H2S04.H20 , however , is a less effective solvent than either of its constituents separately and it is the mixture which has the minimum solvent power . This observation shows clearly both that acids can act as solvents of gases and that the association of water with another substance may lead to a diminution in its solvent power . Taken as a whole , the outcome of the comparison of the values arrived at in various ways is very striking ; it is certainly remarkable that it should be possible to deduce the degree of hydration of a salt from the diminution in solubility of a gas such as hydrogen , which dissolves only to the extent of 13 molecules per 1,000,000 molecules of water . Such a result , taken in conjunction with the conclusions deduced from our hydrolytic studies , lends support to the view that solubility is to be regarded as a chemical phenomenon , as a manifestation of chemical affinity , even in the case of gases . If it be supposed that the gas molecules merely become interposed in the free spaces between the solvent molecules , it is to be expected that equal numbers of molecules would dissolve and that , within limits , the solubility would be independent of the nature of the gas . Again , if the molecular interspaces are limited in volume , some relation should obtain between the molecular volume of a gas and its solubility : gases of low molecular volume should dissolve the most readily . The facts do not fit in with either view* ( Table II ) . The great difference in solubility between ethane , ethylene and acetylene , is especially remarkable , the solubility increasing to a marked extent in passing from the saturated paraffin hydrocarbon to the unsaturated olefine and to an altogether extraordinary extent in passing to the still less saturated acetylene.f * Jahn ( 'Zeits . phys . Chem. , ' 1895 , vol. 18 , p. 1 ) has suggested that the decrease in solubility should be proportional to the amount of surface covered by the solute . Drude and Nernst ( ibid. , 1894 , vol. 15 , p. 79 ) consider that when ions are present the water is compressed by electrostriction . t In this behaviour of the unsaturated hydrocarbons there is , perhaps , foreshadowed the altogether astonishing power possessed by charcoal\#151 ; doubtless an ethenoid form of carbon\#151 ; of absorbing gases at low temperatures which has been disclosed by Dewar'a remarkable observations . [ June 20 , Prof. H. E. Armstrong and others . Table II . Gas . Molecular weight . Solubility at 25 ' . Molecules per 1,000,000 molecules of water . He 4 c.c. per litre . 13 -71 9 -9 n2 28 14 -32 10 -3 h2 2 17 -54 12 -7 CO 28 21 -42 15 -5 o2 32 28 -31 20 -4 ch4 16 30-06 21 -7 A 40 34 -70 25 -6 c2H6 30 41 -04 29 -6 NO 30 42 -23 30-5 n2o 44 59 -42 42 -9 c2h4 28 108 -0 78 -0 c2h2 26 930 -0 671 -0 The solvent power of water for gases , etc. , is modified by dissolved solids presumably in a variety of ways : ( 1 ) by the combination of water with the solute and the consequent diminution in the amount of free water ; and ( 2 ) by the change in the equilibrium ( H20)rej=r^H20 conditioned by the presence of the molecules of the solute , whether hydrated or unhydrated ; the extent to which the gas is soluble in the dissolved substance or its hydrate is another influence to be taken into account ; changes which the dissolved salt itself undergoes in its state of molecular aggregation in consequence of the interposition of the neutral molecules , when these are sufficiently numerous , will also affect the equilibrium . These various influences may come into play to counteract one another ; consequently , the values obtained cannot be regarded as more than approximations . The problem before us is to separate the cases in which there is minimum interference with the first-mentioned factor . Taking into account the low hydration values deducible from Knopp 's determinations of the solubility of hydrogen in presence of potassium and ammonium nitrates , it appears that hydrogen cannot be used safely in all cases . The determination of the effect produced by neutral salts on the hydrolysis of cane sugar appears to be the most likely means of arriving at probable values\#151 ; but even the values thus deduced must be regarded as minima , inasmuch as it must be supposed that the acid to some extent combines with the hydrolyte and that when the salt is added it may compete with the acid and alter the proportion of active acid as well as interfere mechanically with its action.* It can scarcely be doubted that the forces at work in solutions are too * Cf . IV , above . 1907 . ] Studies of the Processes operative Solutions . complex in character to be expressed as simple mathematical laws . The fact that water is itself a complex material , which varies greatly in composition as the conditions are changed , has been left almost wholly , if not entirely , out of account in discussing electrolytic and hydration phenomena ; and far too little attention has been paid also to the existence of salts in solution in various states of molecular aggregation . The discovery of liquid crystals and the observations of Miers and his co-workers on the separation of solids from solution in the absence of nuclei capable of determining crystallisation , as well as the peculiarities manifest in saturated solutions such as are referred to in No. II of these studies , all afford indications of complexities which must not be omitted from consideration in dealing with solutions . The average extent to which a salt becomes hydrated is obviously more or less dependent upon the amount of water available ; this is clearly brought out in Table III , in which the values are given which may be deduced from various solutions of sodium chloride . Table III.\#151 ; Average Degree of Hydration of Sodium Chloride at various \#166 ; Concentrations . Criterion . Hydrolysis of cane sugar . ( Caldwell . ) 25 ' . Solubility of nitrous oxide . ( Rotli . ) 25 ' . Solubility of hydrogen . ( Steiner . ) 15 ' . 5 normal 9*6 7-5 4 " \#151 ; \#151 ; 8 -4 3 11 \#151 ; 9 '5 2 " \#151 ; \#151 ; - 10 -4 1 ' " 13 12 11 . 2 0-5 " \#151 ; 13 *6 0 '25 " \#151 ; 17 *4 As the results obtained by the cane sugar method apply to weight-normal solutions and those obtained by the solubility method to volume-normal solutions , the values are not strictly comparable . The agreement appears to be closer when the results are expressed in terms of the number of molecules of free water present per equivalent of hydrate ( Table IV ) ; to obtain these values , it is assumed that the cane sugar and the chlorhydric acid appropriate between them 15H20 , leaving - 15 40 at the disposal of the salt . If the average hydration and the concomitant free water are expressed as co-ordinates , it becomes evident that the hydration value at infinite dilution will probably not exceed 20H2O . 594 Prof. H. E. Armstrong and others [ June 20 , Table IY.\#151 ; Equilibrium between hydrated Sodium Chloride and free Water . Sugar hydrolysis . ( Caldwell . ) Weight-normal solutions at 25 ' . Solubility of hydrogen . ( Steiner . ) Volume-normal solutions at 15 ' . 5N NaCl 9 -6H"0 ^ 8H20 3N NaCl 11 -0H2O 13H20 N NaCl 13 -0H2O ^ 4011,0 5N NaCl 7-5H20^ 2-911,0 4N NaCl 8-4H20^* 4-711,0 3N NaCl 9-5EUO 5=2 8 '2H20 2N NaCl 10 -4H20 16 -5H,0 N NaCl 11 -2H20 5= 43 -4ILO Even the values in Table IY are not strictly comparable , as they refer to different temperatures . The influence of temperature is well brought out in Table Y , deduced from Roth 's observations on the solubility of nitrous oxide . Table Y.\#151 ; Hydration of Sodium Chloride in volume-normal solution of gramme-molecular strength . Temperature . Hydration . o 25 NaCl 12 011,0 42 -411,0 20 NaCl 12 -3H20 ^ 42 -211,0 15 NaCl 12 -6H,0 ^ 42 -0H , O 10 NaCl 13 -3H20 ^ 41 -4H"0 5 NaCl 13 -9H20 40 -9II20 We believe that we are not justified in giving an absolute interpretation of any of the physical properties of solutions which involves the assumption that such properties are the outcome of the simple changes postulated by the advocates of the ionic dissociation hypothesis . It is only when water is regarded as a changeable and ever changing substance that the full significance of the complex phenomena afforded by solutions becomes apparent . In future it will be necessary to pay more attention to the changes which the solvent itself undergoes and instead of thinking of interchanges as carried out in a mere space to contemplate their occurrence within a medium itself sensitive to every alteration occurring within it . It will be desirable , therefore , to abandon the use of solutions made up to particular volumes\#151 ; except for analytical purposes\#151 ; and always to use those instead which contain a known mass of solvent . In discussing the phenomena of electrolytic conductivity in 1886 , * the increase in molecular conductivity which attends dilution was attributed by * ' Roy Soc. Proc. , ' vol. 40 , p. 268 . Studies of the Processes operative in one of us to the gradual resolution of the more or less polymerised molecules of the salt into simple molecules or monads ; conducting solutions were pictured as containing a composite electrolyte formed by the association of these monads with the solvent molecules ; and the conclusion was formulated that " there is no satisfactory evidence that the constituents of the electrolyte are either free prior to the action of the electromotive force or are primarily set free by the effect produced by the electromotive force upon either member separately of the composite electrolyte but that an additional influence conies into play , viz. , that of the one member of the composite electrolyte upon the other while both are under the influence of the electromotive force . This influence , " it was imagined , " is exerted by the negative radicle of the one member of the composite electrolyte upon the negative radicle of the other member . " It is possible now to go somewhat further in explaining the process . The electrolytically effective monads must be thought of as hydrated in some particularly intimate manner , perhaps as hydroxylated , e.g. , H HCl + OH2 ^ HC1 : OH2 ^ H C1 OH The proportion of the firmly hydrated or hydroxylated molecules in a solution of hydrogen chloride\#151 ; which probably exists in solution , judging from its gaseous nature , entirely in a monadic form\#151 ; will depend on the proportion of water present as well as on the affinity of the chloride for water and the correlated stability of the effective hydrate . From this point of view , the differences observed between salts in solution are conditioned both by the different extents to which they exist as polymerised molecules and as monads and by the different extents to which they exist as effectively hydrated monads ; the underlying causes of these differences would be the different degrees Bf affinity inherent in the monads for one another and for water . The process of electrolysis in a solution , say , of potassium chloride , may be pictured as involving a complete series of interactions among the hydroxylated monads polarised in a manner which may be represented diagrammatieally thus:\#151 ; 2 t VOL , lxxix.\#151 ; A. 596 Studies oj the Processes operative in Solutions . H K)C1 OH H b K Cl OH H c K Cl OH H d KC1 OH H e K(C1 \#151 ; ? The attraction of the potassium and chlorine ions* to the electrodes may be supposed to determine an alteration of the " affinity " relationships within the molecules such as would permit , in the case of molecule of the hydrogen ion and the chlorine ion uniting if the OH ion attached to the chlorine ion at the same time were to become associated with the potassium ion of molecule b\#151 ; and so on throughout the chain . The contiguous nascent molecules of hydrogen chloride and potassium hydroxide would interact forthwith . But the substances in solution would he hydrated beyond the hydroxide stage ; and presumably both the hydrogen chloride and the potassium hydroxide would attract more water immediately they were formed . Probably in the rearrangement water would be carried in both directions but in different amounts corresponding to the different degrees of hydration of the two compounds . The mobilities of the " ions " would be more or less affected by and dependent on the extent to which the compounds were hydrated . * I have more than once pointed out that the modern use of the term ion\#151 ; and of its correlative ionisation\#151 ; is not such as was contemplated by Faraday . It is desirable that some agreement were arrived at and that the conception of dissociation were separated implicitly from both terms . Words are never idle used wrongly , they give rise to false impressions :\#151 ; " through a very imperceptible but still very dangerous , because continual influence , they do great injury to science by contracting and limiting the habitual views of those pursuing it " ( Faraday ) ; " those who are not familiar with a subject are very liable to be misled by the deceptive appearance of simplicity conferred by particular names " ( FitzGerald ) . There are now three partially synonymous terms in use , each of which has its special value\#151 ; the first is atom , the second radicle , and the third ion . The term atom , of course , applies to the elementary , undivided unit ; the term radicle is of more general use , being applicable both to atoms and to groups of atoms which can function as atoms ; both these terms have only a structural significance . The ion , however , is the movable , transferable radicle ; a radicle may be said to be an ion and to be ionised to a particular extent , if it be movable by chemical means to the particular extent to which it is said to be ionised.\#151 ; H. E. A. The Effect of Pressure upon Arc Spectra . 597 Although the water is thought of as attached only to the negative ion , both ions would appear to he hydrated , on this hypothesis . The arrangement suggested is but a modification of the Grotthus ' chain . It is difficult to avoid the conclusion that the facts on the chemical side are such as require some such explanation of the phenomena , and that we are justified in asking physicists to re-examine the arguments which have led them to take exception to the Grotthus explanation . FitzGerald has already spoken with no uncertain voice and given us his support , in his memorial lecture on Helmholtz . Of late years probably no one has shown greater power of appreciating all sides of the position : his adverse criticism of the dissociation hypothesis is therefore of peculiar value . The Effect of Pressure upon Arc Spectra . No. I.\#151 ; Iron . By W. Geoffrey Duffield , B.Sc. , B.A. ( Communicated by Professor A. Schuster , F.R.S. Received July 4 , 1907 . ) ( Abstract . ) The first part of the paper contains a description of the mounting and adjustment of the large Rowland Concave Grating in the Physical Laboratory of the Manchester University . The feature of this is the stability of the carriages carrying the grating and camera , and the novel construction and attachment of the cross-beam , which secure the absence of any disturbance which might be caused by bending or sagging . The second part describes experiments made with a pressure cylinder designed by Mr. J. E. Petavel , F.R.S. , in which an arc is formed between metal poles opposite a glass window , through which the light is examined by means of the Grating Spectroscope . A system of mirrors allows the image of the arc , however unsteady it may be , to be kept almost continuously in focus upon the slit . Two sets of photographs of the iron arc in air have been taken for " pressures ranging from 1 to 101 atmospheres ( absolute ) , and the results are given below for wave-lengths X = 4000 A.U. to =4500 A.U. I. Broadening . 1 . With increase of pressure all lines become broader . 2 . The amount of broadening is different for different lines , some almost

rspa_1907_0066

0950-1207

The effect of pressure upon arc spectra. No. I.\#x2500;Iron.

597

599

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. Geoffrey Duffield, B. Sc. B. A.|Professor A. Schuster, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0066

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0066

10.1098/rspa.1907.0066

Atomic Physics

Thermodynamics

Atomic Physics

The Effect of Pressure upon Arc Spectra . 597 Although the water is thought of as attached only to the negative ion , both ions would appear to he hydrated , on this hypothesis . The arrangement suggested is but a modification of the Grotthus ' chain . It is difficult to avoid the conclusion that the facts on the chemical side are such as require some such explanation of the phenomena , and that we are justified in asking physicists to re-examine the arguments which have led them to take exception to the Grotthus explanation . FitzGerald has already spoken with no uncertain voice and given us his support , in his memorial lecture on Helmholtz . Of late years probably no one has shown greater power of appreciating all sides of the position : his adverse criticism of the dissociation hypothesis is therefore of peculiar value . The Effect of Pressure upon Arc Spectra . No. I.\#151 ; Iron . By W. Geoffrey Duffield , B.Sc. , B.A. ( Communicated by Professor A. Schuster , F.R.S. Received July 4 , 1907 . ) ( Abstract . ) The first part of the paper contains a description of the mounting and adjustment of the large Rowland Concave Grating in the Physical Laboratory of the Manchester University . The feature of this is the stability of the carriages carrying the grating and camera , and the novel construction and attachment of the cross-beam , which secure the absence of any disturbance which might be caused by bending or sagging . The second part describes experiments made with a pressure cylinder designed by Mr. J. E. Petavel , F.R.S. , in which an arc is formed between metal poles opposite a glass window , through which the light is examined by means of the Grating Spectroscope . A system of mirrors allows the image of the arc , however unsteady it may be , to be kept almost continuously in focus upon the slit . Two sets of photographs of the iron arc in air have been taken for " pressures ranging from 1 to 101 atmospheres ( absolute ) , and the results are given below for wave-lengths X = 4000 A.U. to =4500 A.U. I. Broadening . 1 . With increase of pressure all lines become broader . 2 . The amount of broadening is different for different lines , some almost Mr. W. G. Duffield . [ July 4 , becoming bands at high pressures , and others remaining comparatively sharp . 3 . The broadening may be symmetrical or unsymmetrical ; in the latter case the broadening is greater on the red side . II . Displacement . 1 . Under pressure the most intense portion of every line is displaced from the position it occupies at a pressure of 1 atmosphere . 2 . Reversed as well as bright lines are displaced . 3 . With increase of pressure the displacement is towards the red side of the spectrum . 4 . The displacement is real and is not due to unsymmetrical broadening . 5 . The displacements are different for different lines . 6 . The lines of the iron arc can be grouped into series according to the amounts of their displacements . 7 . Three groups can in this way be distinguished from one another ; the displacements of Groups I , II , III bear to one another the approximate ratio 1:2:4 . ( The existence of a Fourth Group is suggested by the behaviour of two lines , but further evidence is needed upon this point ; 1:2 : 4 : 8 would be the approximate relations existing between the four Groups . ) 8 . Though all the lines examined , with two possible exceptions , fall into one or other of these Groups , the lines belonging to any one Group differ to an appreciable extent among themselves in the amounts of their displacements . 9 . The relation between the pressure and the displacement is in general a linear one , but some photographs taken at 15 , 20 , and 25 atmospheres pressure give readings incompatible with this relation . Other photographs at 15 and 25 atmospheres present values which are compatible with it . 10 . The abnormal readings are approximately twice those required by the displacements at other pressures , if the displacement is to be a continuous and linear function of the pressure throughout . 11 . On the photographs showing abnormal displacements the reversals are more numerous and broader than they are on plates giving normal values , and there is some evidence in favour of a connection between the occurrence of abnormal displacements and the tendency of the lines to reverse . III . Reversal . 1 . As the pressure is increased , reversals at first become more numerous and broader . 2 . The tendency of the lines to reverse reaches a maximum in the 1907 . ] The Effect of Pressure upon Arc Spectra . neighbourhood of 20 to 25 atmospheres , and a further increase in pressure reduces their number and width . 3 . Two types of reversal appear on the photographs , symmetrical and unsymmetrical . 4 . Within the range of pressure investigated , the reversals show no tendency to change their type . 5 . In the case of unsymmetrically reversed lines in the electric arc , the reversed portion does not in general correspond to the most intense part of the emission line , being usually on its more refrangible side . 6 . The displacements of the reversed parts of the unsymmetrically reversed lines of Group III are about one-half the displacements of the corresponding emission lines . Indeed , the reversed parts of the lines of Group III fall approximately in Group II . 7 . No relation between the order of reversal and the frequency of vibration , such as exists in the spark , has been observed in the iron arc for the ranges of wave-length and pressure examined . IY . Intensity . 1 . The intensity of the light emitted by th\#174 ; iron arc is , under high pressures , much greater than at normal atmospheric pressure . 2 . Changes in relative intensity of the lines are produced by pressure . Lists of enhanced and weakened lines are given . 2 t 2

rspa_1907_0067

0950-1207

The annealing of copper: with special reference to dilatation.

1

12

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

T. Turner, M. Sc., A. R. S. M.|Professor J. H. Poynting, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0067

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10.1098/rspa.1907.0067

Measurement

Thermodynamics

Measurement

PROCEEDINGS OF THE ROYAL SOCIETY . Section A.\#151 ; Mathematical and Physical Sciences . The Annealing of Copper : with Special Reference to Dilatatioru By T. Turner , M.Sc . , A.R.S.M. , Professor of Metallurgy , and D. M. Levy , A.R.S.M. , Assistant Lecturer in Metallurgy , University of Birmingham . ( Communicated by Professor J. H. Pointing , F.R.S. Received May 21 , \#151 ; Read June 27 , 1907 . ) It is well known that copper is met with in two distinct forms , viz. , the soft state as in cast or annealed metal , and the hard variety which is the result of mechanical work . There is more difference between the mechanical properties of hard and of soft copper than is observed in the case of two distinct metals ; such , for example , as nickel and cobalt . For instance , one of the most important of these differences , from a practical point of view , is in connection with the tensile strength of the material , which is only about 10 to 14 tons per square inch in cast or in annealed copper , while in hardened copper the tenacity is about twice as great , and usually runs from about 20 to 28 tons per square inch , or even more in special cases . The difference between hard and soft copper can be also readily illustrated by bending two rods about \#163 ; inch square section , one in the hardened and the other in the annealed condition . The latter can be easily bent in the hands or even tied in a knot , while the mechanically worked bar is rigid and elastic , and can only be bent by the application of considerable force . It is common knowledge that hard copper becomes perfectly annealed by heating to 500 ' C. ; that the heating need not be for any lengthened period , and the rate of cooling afterwards is unimportant . VOL. lxxx.\#151 ; A. B Prof. Turner and Mr. Levy . Annealing of [ May 21 , Changes of properties which are so marked , and so far-reaching in the applications of metallic copper , have naturally been the subject of investigation by metallurgists and physicists , among whom may be specially mentioned Roberts-Austen , * Kudeloffj* Thurston , J and Heyn . S These researches deal chiefly with the mechanical properties of copper in various conditions , and at various temperatures . In addition to the foregoing , reference should be made to the work of Beilby , || who has investigated the microstructure of copper in different states ; while the expansion of copper , over a considerable range of temperature , was observed byDittenberger and G-ehrke.f Ho particulars are given in their report as to the condition of the metal under examination ; but its expansion up to a temperature of 625 ' C. is stated to be in agreement with the formula \ = 10~9 ( 16070+ 4D3(H2 ) , while a rod 487 mm. long showed a permanent extension of 0*01 to 0-02 mm. on resuming the original temperature . In the course of an investigation recently conducted at the University of Birmingham on the volume changes during the solidification of cast metals , it was shown that corresponding with each temperature arrest during the cooling of cast iron there was also a definite volume alteration.** It was also shown that copper zinc alloys expand during solidification . For these experiments a simple form of extensometer was employed , and the indications of this instrument show that at certain temperatures , which marked well defined changes in the properties of the solid metal , there were well marked alterations of volume , which were rendered very evident by the extensometer . It was thought that by the application of somewhat similar methods , information might be obtained as to any abrupt or definite change which may occur when metal , which has been subjected to mechanical work , is , by annealing , converted into the soft variety . * Roberts-Austen , W. , 2nd Report Alloys Research Committee , 'Proc . Inst. Mecb . Eng. , ' April , 1893 , p. 114 . + Rudeloff , M. , " Influence of Temperature on Tensile Strength of Metals , " \#163 ; Mittheil . Konig . Technische Versuchs-Anstalt , ' 1894 , vol. 11 ( b ) , pp. 292\#151 ; 330 ; " Influence of Heat , Chemical Composition and Mechanical Treatment on Strength and Ductility of Copper , " ' Mittheil . Konig . Technische Versuclis-Anstalt , ' 1898 , vol. 16 ( a ) , pp. 171\#151 ; 219 . J Thurston , 'Materials of Engineering , ' Part III , pp. 477\#151 ; 573 . S Heyn , E. , " Overheating of Mild Steel " ( refers to copper ) , 'Journ . Iron and Steel Inst. , ' 1902 , vol. 2 , p. 101 . || Beilby , G. , 'Journ . Soc. ' Chem. Tnd . , ' 1903 , pp. 1107\#151 ; 8 ; 1904 , p. 788 . IT Report of Physikalisch-Technische Reichsanstalt , by Holborn and Griineisen , 1902 , abstracted in 'Engineering , ' vol. 4 , No. 24 . ** T. Turner , " Volume and Temperature Changes during the Cooling of Cast Iron , " 4 Journal of the Iron and Steel Institute , ' 1906 , vol. 1 , p. 48 . 1907 . ] Copper : with Special Reference Dilatation . In order to make the desired observations an extensometer was devised capable of indicating the changes of length of a bar of copper at temperatures from that of the atmosphere to about 700 ' C. At the same time the temperature of the bar was ascertained by a pyrometer of the Le Chatelier thermo-junction type . The general arrangement of the apparatus is shown in fig. 1 ; whilst fig. 2 represents , on a larger scale , details of the method of connecting with the extensometer . vyVvV^ Inches Arramgememt of Apparatus for Measur/ /\g Fig. 1 . Numerous forms of apparatus were tried before the final design was adopted , as it was essential to heat the bar uniformly and to ensure that the expansion of the whole length and of that alone should be recorded , the difficulty being b 2 Prof. Turner and Mr. Levy . Annealing of [ May 21 , to connect the bar , which was of considerable length and entirely in the furnace , with the extensometer , which was situated at some little distance away . The bars used in the series of experiments were all \#163 ; inch in square section and 35 inches long . Each bar ( B ) was heated in a gas fired tube furnace as subsequently described ; and , in order to confine the rise of temperature to the bars , they were fitted at each end with a copper tube ( A ) 4 inches in length . This tube was screwed on to the bar for a distance of about ^ inch , and projected about 3 inches beyond the end of the furnace . The bar itself was thus entirely in the furnace , and in order to prevent the expansion of the connecting tubes being recorded they were water cooled , while the end of Inches o i 2 I 1 II I 1 I \#187 ; l"lT l T Tenths Scale . DetE/ LS OE EETE/ VSOMETE/ ?CO/ VA/ ECT/ OA/ . Fig. 2 . the bar inside the tube was covered with an asbestos plug ( c ) so as to prevent the water having any cooling effect in it . One of these copper tubes was firmly clamped so as to be kept quite rigid , while to the tube at the other end the extensometer was attached . In this way the expansion of the whole length of the bar was obtained , while the rest of the system was maintained at a constant temperature . In order to allow freedom of motion in the direction of its length , the rod rested on a number of small porcelain rollers ( D ) which were supported on a trough made of steel bars , ^ inch thick and 3 inches wide . The trough is open at both ends , and in order to prevent buckling effects due to the heat it was well braced , whilst the rollers , instead of running directly on the bottom 1907 . ] Copper : with Special Reference to Dilatation . of the trough , were supported by two thin strips of steel . In the earlier experiments with a thinner trough , there was sufficient buckling to seriously affect the observations . The trough was heated by a series of bunsen burners , controlled by a common tap , and so placed as to ensure , as nearly as possible , uniformity of heating . It is known that tube furnaces are usually cooler at the ends than in the middle , and pyrometric tests were made throughout the trough in order to determine the proper number and spacing of the gas burners . By surrounding the trough with brickwork , covering the ends and top with asbestos cardboard , and providing a considerable covered air space around the trough , it was ultimately found possible to ensure very considerable uniformity of temperature throughout the tube . The extensometer consisted essentially of a bell crank lever ( F ) mounted on pivots ; the indicating arm was 25 inches long , whilst the short arm was so fashioned that at a distance of | inch from the pivots it took the form of a finely rounded projection ( G ) . This pressed against a brightly polished disc ( H ) screwed on to one of the connecting tubes , by means of which the forward motion of the disc the expansion of the rod ) was indicated on a scale ( K ) , which was an arc of a circle divided in millimetres . The extensometer worked in a vertical plane , and was very delicately mounted so as to reduce the effects of friction to a minimum . On being tested by a micrometer screw its indications were found to be fairly uniform in all positions , and the millimetre scale denoted a magnification of 48 ; in other words , 1 mm. scale-division corresponded to an expansion of 1/ 1200 of an inch . The indicating arm was extended backwards for some distance beyond the pivots , so as to accommodate a balance weight ( L ) , which was , however , placed at such a distance as to always insure a small positive pressure against the brass disc in whatever position the indicator arm might happen to be situated . As the copper connecting tube at the other end was firmly clamped , it was only necessary to take the extensometer readings from one end in order to measure the expansion . The extensometer was made in the Metallurgical Department of the University of Birmingham , by Mr. J. Ward , the University steel melter , and the authors desire here to acknowledge the value of the assistance thus rendered by Mr. Ward . The temperatures were recorded by a thermocouple , * the junction ( M ) being placed in an ^-inch hole bored in the centre of the bar under examination . The leads from the cold junction were connected with a dead-beat galvanometer of the D'Arsonval type , in the mirror of which the 6 Prof. Turner and Mr. Levy . Annealing of [ May 21 , reflections of a graduated scale were observed through a telescope placed some distance away . The adjustments of the apparatus required careful attention , and the precautions detailed in the foregoing paragraphs were adopted as the result of a very large number of experiments at the commencement of the work . These tests showed that minute frictional effects , slight draughts , and other very small deviations led to irregularity in the results obtained . The quantity of asbestos used as a non-conducting plug at the end of the rod , the use of steel strips for the rollers to run upon , the adoption of movable bunsens instead of the usual form of combustion furnace , and the careful adjustment of the counter-balance on the extensometer were all decided on after a number of early failures . More uniform results were obtained when the junction was inserted in a hole in the metal instead of fastening it on the surface , whilst the exclusion of draughts by employing brickwork and asbestos protection was most important . Marked effects were also produced by any irregularity in the supply of cooling water to the ends of the rod , and it was considered advisable to run the water under a constant head from a fixed reservoir some feet above the level of the apparatus . The actual operations were conducted as follows . The adjustments of the apparatus being made so that the indicator was near , but not at the bottom of the scale , the clamps were made tight , and a gentle stream of water was set flowing through the connecting tubes for some minutes , zero readings were noted , the bunsens were then lighted at the full , and observations taken of the indicator and the galvanometer at intervals of 15 seconds . The changes , which were at first rapid , become gradually smaller , and after a red heat had been attained , half-minute , then one-minute , and finally two-minute intervals were allowed between the readings until the maximum temperature had been reached , at which point the readings had become practically constant . The gas was then turned off , and readings were taken during the cooling of the bar . The results were then plotted so as to give a continuous record of the changes of length and of the increments of temperature . Preliminary Experiments . The first series of experiments was undertaken in order to test the delicacy of the apparatus and the trustworthiness of the method . The object was to ascertain whether , when a material was employed which is known to undergo abrupt changes of length at certain critical points , these changes could be readily and accurately observed , and , secondly , to determine 1907 . ] Copper : with Special Reference to Dilatation . whether , in the case of a material which undergoes no such abrupt changes , a perfectly continuous curve could be obtained . . The materials which suggested themselves as being most suitable for the above purposes were steel and wrought iron , as it is well known that with high carbon steel there is an abrupt change of volume at about 680 ' C. , while no such change takes place with wrought iron . The change in volume in the case of steel is known to be connected with the state of combination of the carbon which is present , and this volume change is accompanied by marked differences in hardness and other properties . The wrought-iron bars used for these tests were of best Staffordshire iron , and contained 003 per cent , of carbon . The steel was made in the Siemens furnace , and contained 0'94 per cent , of carbon . The bars were , as before described , 35 inches long , | inch square section , and the experiments were all conducted exactly as previously mentioned . ( a ) Wrought Iron.\#151 ; The curves obtained from heating and cooling a bar of wrought iron are shown on fig. 3 . From these it will be seen that within the range of temperature employed the curves are regular and continuous , and the absence of any break or arrest may be taken to indicate that the apparatus was satisfactory , and that the precautions previously mentioned had eliminated all important sources of error . ( b ) Steel.\#151 ; The curves obtained from the steel with 0*94 per cent , of carbon are also given in fig. 3 , and these indicate that a marked diminution in length occurs at the temperature arrest point , Ari , which corresponds with about 680 ' C. On cooling the bar a corresponding increase of length occurs at the same temperature . M. H. le Chatelier* has already , by an entirely different method , determined the expansions of iron and steel at various temperatures , and the results of the present experiments given above are in practical agreement with his observations . Messrs. Charpy and Grenetf have also studied the transformations of steel by the dilatometric method , using the method of Le Chatelier . These observers point out that in order to obtain satisfactory numerical values it is necessary to heat at a sufficiently slow speed , and state that about 200 ' per hour is a suitable increment , a rate which does not differ ver]f markedly from that adopted in the present series of experiments . Charpy and Grenet also found that in all steels , and cast iron containing only carbon , the transformation took place at about 700 ' C. ; that with low carbon steels the contraction at this temperature was inappreciable ; and that the * ' L'Etude des Alliages , ' Paris , 1901 , p. 403 . + The Metallographist , ' 1903 , p. 240 ; ' Comptes Kendns Academy des Sciences , ' May 10 , 1902 . 8 Prof. Turner and Mr. Levy . Annealing of [ May 21 , maximum contraction was observed in steels which contained 0'93 per cent , of carbon . As the curves obtained both for iron and steel by the extensometer apparatus agreed with those of previous experimenters , alike in the character and extent of the changes which take place , and the temperature at which any irregularity is noted , it may be assumed that the accuracy and suitability of the method of investigation was sufficiently proved . It was therefore possible , with confidence , to approach the real object of the research . Dilatation of Hard-drawn Copper . The rods used in these tests correspond in every way with those employed in the tests for iron and steel , being 35 inches long , a \#163 ; inch in square section , and screwed to water-cooled copper connecting-tubes as before . The rods were supplied by Messrs. Thos . Bolton and Sons , of Oakamoor , Staffs , and were of electrolytic copper of selected quality and uniformity . They had been rolled while hot down to f inch square , and were afterwards cold drawn until \ inch square . The curve obtained on heating a bar of this hard-drawn copper to about 580 ' C. is given in fig. 4 . At this temperature the metal is completely annealed , and , on cooling , is dead soft . It will be observed that both the heating and cooling curves are quite regular , there being no break such as would be caused by the slightest abrupt change of volume at a critical temperature . There was nothing observed which would serve to indicate at exactly what temperature . hard copper passes into the soft variety . As a check upon the results obtained by the extensometer , the rod was marked before being placed in the furnace , a length of 30 inches being taken , and when the metal was cold , after the conclusion of the experiment , there was no perceptible alteration of length in the marked portion . Dilatation of Annealed Copper . The annealed rod , as used in the previous experiments , was now heated to about 600 ' 0 . , and afterwards allowed to cool slowly to the temperature of the ttmosphere . From the curves obtained ( fig. 4 ) it will be observed that the dilatation was as regular as with wrought iron , and quite similar to what was observed with the hard-drawn copper . It thus appears that the change from the hard elastic condition of worked copper to that of extremely soft metal , such as is obtained with fully annealed copper , is not accompanied by any alteration of length . It may be recalled that it is usual to make allowances in practice for the volume changes which accompany the cooling of cast iron or the hardening of steel ; while we are informed , by Mr. F. Platten , of Copper : with Special Reference to Dilatation . 3yrut/ i/ Jc/ W3J_ / !/ / 3S/ JJ \#166 ; ( 20Sl/ *c"V3J.-7V/ JL/ /V/ J 3\lt ; y 3S-/ J/ = -AKJ f ( A/ O/ QA/ l/ a/ Xp ) 3313h/ O S'A/ 31 3J/ 00 P___00\#163 ; ____002____001____0_____p0\#163 ; 002 Prof. Turner and Mr. Levy . Annealing [ May 21 , oo 9/ - un .u it/ u/ w/ J syn\#177 ; i/ dJdW3jL u/ isty Oa Q/ = yHJ3JL 1VIX/ A/ /J 3 6/ t/ d3dlM3\#177 ; N/ 35/ \#163 ; ! 200 300 0 100 20 0 300 Extensometer Deflection ( Expansion ) Fig. 4 . 1907 . ] Copper : with Special Reference to Dilatation . Elliott 's Metal Company , Limited , that , on the other hand , no allowance is made , when annealing hard copper in the processes of rolling or drawing , for any alterations in length or thickness . Dilatation of Copper Alloys . It was now considered advisable to examine certain well-known copper alloys which are of commercial importance ; which are hardened by work , and which may be annealed at a relatively low temperature like copper itself . For this purpose Mr. Flatten kindly supplied hard-drawn |-inch-square rods having the following composition:\#151 ; 1 . Brass ( copper 70 , zinc SO ) 4 . Gun metal . 2 . " ( " 66 , " 34 ) 5 . Phosphor bronze . 3 . " ( " 60 , " 40 ) These were examined in 35-incli lengths exactly as in the previous experiments , and the results plotted . No satisfactory curve was obtained of the 60:40 brass as all the rods of this composition which were tested behaved in a curious manner , showing a normal expansion up to a certain point and then beginning to develop a helical twist which rendered it impossible to obtain any trustworthy indications wTith the extensometer , as the bars were no longer straight . The other four alloys , namely 70:30 brass ; 66:34 brass , gunmetal , and phosphor bronze gave perfectly regular and uniform curves as the temperature rose , and no indication was afforded as to the point at which the hard metal became annealed . The cooling curves were all quite regular , and similar to each other , though the contraction was very slightly more rapid above 400 ' and slightly less rapid below 400 ' than might have been expected from the heating curve . The conclusion to be drawn from these experiments would appear to be that the alterations which take place when hard copper is by annealing converted into the soft variety are unaccompanied by any change in linear dimensions . It is known that the separation of a constituent , as of graphite from cast iron or pearlite from steel , is accompanied by marked dilatometric changes . Le Chatelier* has shown that a dimorphic transformation such as that which ferrous sulphide undergoes between 100 ' and 150 ' , is accompanied by a marked change of volume . Allotropic changes in an element are also usually accompanied by marked alterations of volume , as in the case of pure iron at about 880 ' C. It is evident , therefore , that such changes in the properties of copper and of copper alloys as are caused by mechanical work or * ' Metallographist , ' 1903 , p. 23 ; ' Bulletin de la Societe d'Encouragement , ' September , 1902 . Prof. Ayrton and Messrs. Mather and Smith . [ June 5 , annealing respectively are of a different order to those which are due to allotropic or dimorphic transformations , or to the separation or rearrangement of constituents . The results here recorded lead us to believe that mechanical work produces only internal rearrangement of the metallic grains or molecules , but does not lead to any chemical or physical changes such as are correctly regarded as allotropic . We have met with no evidence to support the view that allotropic change results from mechanical work . A New Current Weigher , and a Determination of the Electromotive Force of the Normal Cadmium Cell . By Professor W. E. Ayrton , F.R.S. , and T. Mather , F.R.S. , Central Technical College , London , and F. E. Smith , A.R.C.S. , National Physical Laboratory , Teddington . ( Received June 5 , \#151 ; Read June 27 , 1907 . ) ( Abstract . ) Introductory . The instrument described is the outcome of conversations between the late Professor J. Viriamu Jones , E.R.S. , and one of the authors ( W. E. A. ) , on their return from the British Association Meeting held in Toronto in 1897 . Its object was to determine " the ampere " as defined in the C.G.S. system , to an accuracy comparable with that attained in the absolute determination of the ohm by Lorenz 's apparatus , an account of which was given by Professors Ayrton and Jones at the Toronto Meeting.* Professor Jones had previously developed a convenient formula for calculating the electromagnetic force between a helical current and a coaxial current sheet , viz. , F = YA7 ( M2\#151 ; Mi ) , f where \lt ; yh is the current in the helix , the current per unit length of the current sheet , and Mi , M2 the coefficients of mutual induction of the helix and the two ends of the current sheet respectively . By using coaxial coils with single layers of wire wound in screw-thread grooves , advantage could be taken of the above formula . * See 'B . A. Report , ' Toronto , 1897 , p. 212 . t ' Roy . Soc. Proc. , ' vol. 63 , p. 204 .

rspa_1907_0068

0950-1207

A new current weigher, and a determination of the electromotive force of the normal weston cadmium cell

12

18

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Professor W. E. Ayrton, F. R. S.|T. Mather, F. R. S.|F. E. Smith, A. R. C. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0068

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0068

10.1098/rspa.1907.0068

Electricity

Measurement

Electricity

12 Prof. Ayrton and Messrs. Mather and Smith . [ June 5 , annealing respectively are of a different order to those which are due to allotropic or dimorphic transformations , or to the separation or rearrangement of constituents . The results here recorded lead us to believe that mechanical work produces only internal rearrangement of the metallic grains or molecules , but does not lead to any chemical or physical changes such as are correctly regarded as allotropic . We have met with no evidence to support the view that allotropic change results from mechanical work . A New Current Weigher , and a Determination of the Electromotive Force of the Normal Cadmium Cell . By Professor W. E. Ayrton , F.R.S. , and T. Mather , F.R.S. , Central Technical College , London , and F. E. Smith , A.R.C.S. , National Physical Laboratory , Teddington . ( Received June 5 , \#151 ; Read June 27 , 1907 . ) ( Abstract . ) Introductory . The instrument described is the outcome of conversations between the late Professor J. Viriamu Jones , E.R.S. , and one of the authors ( W. E. A. ) , on their return from the British Association Meeting held in Toronto in 1897 . Its object was to determine " the ampere " as defined in the C.G.S. system , to an accuracy comparable with that attained in the absolute determination of the ohm by Lorenz 's apparatus , an account of which was given by Professors Ayrton and Jones at the Toronto Meeting.* Professor Jones had previously developed a convenient formula for calculating the electromagnetic force between a helical current and a coaxial current sheet , viz. , F = YA7 ( M2\#151 ; Mi ) , f where \lt ; yh is the current in the helix , the current per unit length of the current sheet , and Mi , M2 the coefficients of mutual induction of the helix and the two ends of the current sheet respectively . By using coaxial coils with single layers of wire wound in screw-thread grooves , advantage could be taken of the above formula . * See 'B . A. Report , ' Toronto , 1897 , p. 212 . t ' Roy . Soc. Proc. , ' vol. 63 , p. 204 . A New Current , etc. 1907 . ] A preliminary apparatus was made at the Central Technical College in 1897- 8 , and used to obtain experience as to the conditions necessary for successful operation.* The design of the proposed instrument was then proceeded with . By employing the arrangement devised by one of the authors ( W. E. A. ) , of having double-threaded screw grooves wound with separate bare wires subsequently connected in series , it wTas possible to prevent any uncertainty existing regarding leakage between adjacent turns of a spiral . At the same time , the absence of any silk covering on the wires wound on bare marble cylinders enabled very great precision in the measurement of the dimensions of each coil to be attained . Complete working drawings and specifications of the proposed instrument and its adjustable support were prepared at the Central Technical College in 1898- 99 , Mr. J. P. Gregory , a then student of the College , rendering very valuable assistance in this work . Grants amounting to \#163 ; 300 , for the construction of the balance , were made by the British Association for the Advancement of Science in 1897 and 1898 , and Sir Andrew Noble , F.R.S. , kindly presented the adjustable phosphor bronze stand , designed to support the instrument . The physical balance was built by Mr. L. Oertling , of London ; and the electrical portions were made at the National Physical Laboratory under the supervision of the Director , Dr. R. T. Glazebrook , F.R.S. General Description . The instrument consists of a very sensitive physical balance , with a 20-inch beam , f supporting from each end a coil with vertical axis ; these coils hang coaxially within fixed coils carried from the base . All the coils are wound in single layers on hollow marble cylinders having double-threaded screw grooves cut on their surfaces , the fixed cylinders being about 13 inches diameter , 11 inches high , and 2 inches thick , and the suspended cylinders 8 x 6 x | inches . Each fixed cylinder carries two windings , an upper and a lower , in which the current circulates in opposite directions , so that one repels and the other attracts , the current carrying winding on the suspended cylinder hanging symmetrically between them . Each winding , on both fixed and suspended cylinders , consists of two helices occupying adjacent grooves of the double-threaded screws ; there are thus 12 wires in all on the four cylinders , and these are connected all in series in the ordinary use of the balance . Connection with the suspended coils is made by flexible silver wires 1 mil * 'B . A. Report , ' Bristol , 1898 , p. 157 ; also ' Journ. Inst. Elec . Engrs . , ' vol. 35 , p. 12 . + The balance carries about 5fr kilos , and turns with 1 / 10 milligramme . Prof. Ayrton and Messrs. Mather and Smith . [ June 5 , in diameter , arranged 80 in parallel , and all other leads to and from the coils are of small concentric cable . These cables run to a plug board and commutators , whereby the current in any or all of the 12 helices may be reversed . Adjacent helices can also be disconnected from each other , and electrically grouped so that the insulation between all the pairs may be found by a single test . When in use for measuring current , the directions of circulation in the several coils are arranged so that they all produce a torque in the same sense on the balance beam , and this torque is balanced by suitable masses placed on the scale pans . Reversal of the current , in the fixed coils only , produces an apparent change of weight , which is a measure of the square of the current employed . The position of the beam of the balance is observed by viewing through a microscope a finely divided scale carried by the pointer . The masses used to balance the electromagnetic forces can be manipulated .quickly and conveniently without opening the case of the instrument , four weight lifters being provided for this purpose . To prevent change of level of the suspended cylinders on removing or replacing the weights , the scale pans are carried on separate planes resting on the knife edges from which the suspended coils hang . For convenience in erection and adjustment the fixed coils are supported on phosphor bronze slide rests , capable of about half an inch movement in two horizontal directions and of 14 inches vertical displacement . Advantages of Duplication of Coils . The arrangement of having a set of coils at each end of the balance beam has several advantages . Independent determinations may be made on the two sets , or , by using both together , the forces are approximately doubled . Differential tests can also be made so that one set serves as a check on the other . The chief advantage , however , is the symmetry obtained , which neutralises to a very great extent the disturbances arising from convection currents of air and change of air buoyancy . The double winding is also of great utility in this respect , as it permits of an electromagnetic weighing being made with one set of coils without introducing the error , due to drift of zero , which would occur if that set alone were heated by the passage of the current . This is effected by arranging the connections so that the currents in adjacent helices on one pair of cylinders are in opposite directions ; they have then no electromagnetic effect , and yet are heated by the passage of the current just as much as the coils on the other pair . 1907 . ] A New Current , etc. Magnetic . Before constructing the parts of the balance , magnetic tests were made on all the materials intended to be used , and in cases where the permeability differed appreciably from unity those parts were rejected . When the instrument was completed it was used to test itself , but no trace whatever of magnetism could be detected . Construction and Winding . The material employed for the fixed and suspended cylinders is Carrara Statuary Marble , which , after being turned approximately to size , was baked in an oven at 140 ' C. for 30 hours and then immersed in hot paraffin wax . The turning was then completed , the V grooves cut and bare copper wire , No. 24 S.W.G. , wound in them under tension , numerous measurements of the diameter of the wire being made during the winding . Special arrangements were made to ensure that each helix contained an exact number of turns , and that the two helices of one pair start and end in the same diametral plane . The pitch of the screw grooves is 1/ 18 inch : each helix on a suspended cylinder has 92 turns , making 184 in all , and those on each fixed cylinder 90 turns , making a total of 360 . These turns on the fixed cylinders are in two portions , upper and lower , with an unwound space of 2/ 18 inch between them . The axial length of the suspended coil is , therefore , equal to the distance between the central planes of the upper and lower windings on the fixed cylinder . On all the cylinders the total number of turns is 1088 and the total length of wire about 980 metres . Measurement of Coils . Measurements of the axial lengths of the windings were made by a cathetometer , and of the diameters by a special measuring machine obtained from Messrs. Stanley , of London . An optical lever used with the latter instrument gave a deflexion of 2 mm. for a movement of the micrometer of 1 g(1/ 1000 of a millimetre ) , so the dimensions could be determined with great precision . Such accuracy in the measurement of the diameters was rendered possible owing to the use of bare wire wound on bare marble . About 120 diameters were measured on each suspended cylinder , and about 220 on each fixed one , the probable error of the mean diameter of any cylinder amounting to about five in a million . All the cylinders are very nearly perfect , the ellipticities and the conicalities being extremely small . Prof. Ayrton and Messrs. Mather and Smith . [ June 5 After measuring the coils and insulating adjacent helices , the windings were coated with melted wax , and again measured in numerous places from which the wax was temporarily removed ; no appreciable change in dimensions could be found . Erection and Adjustment . To facilitate the setting of the cylinders , two spirit-levels are mounted on the upper plane end of each , and adjusted so that when these indicate level the axis of the corresponding cylinder is truly vertical . Mechanical indicators are also provided for showing when the cylinders are co-axial and when the middle planes of the windings on the fixed and suspended cylinders coincide . The vertical and horizontal adjustments can also be tested by electrical methods which are simple and very accurate ; these were adopted in the final settings , the error introduced by faulty adjustment amounting to something less than 1 part in 5 millions . Calculation of Mutual Inductions and Forces between the Coils . The formulae employed are given in Professor J. Y. Jones ' paper , mentioned on p. 12 , and were employed by two of the authors ( T. M. and F. E. S. ) to calculate independently the mutual inductions and the forces between the fixed and suspended coils when a current of 1 ampere circulates in them . The values of M2\#151 ; Mi , defined on p. 12 , calculated ( a ) with logarithms and ( 6 ) by calculating machine , were in very close agreement , the difference being less than 1 in a million . The actual numbers are 25962 02 cm . and 25962-04 cm . respectively for the left-hand set of coils , and 25960-45 cm . and 25960-43 cm . for the right-hand set . This order of accuracy in the values of the coefficients of mutual induction is rendered quite real by a knowledge of the exact position of the bare conductors and the certainty that no current leaks from one convolution of wire to any other . In both cases the sum for both sets of coils is 51922-47 cm . , and this number was used in most of the determinations . Taking the value of g , the acceleration of gravity at Bushy , as 981*20 , and the length of winding on the suspended cylinders as 12-9830 cm . , the change of apparent mass on reversal of 1 ampere in both sets of coils becomes m \#151 ; 14*99 928 grammes . This assumes that no forces exist between the fixed coils on one side of the balance and the suspended ones on the other side . As a matter of fact , such forces are present , but can be eliminated by taking two sets of readings , one set in which the cross actions assist the direct ones and the other set in which A New Current Weigher , 1907 . ] these forces oppose each other . These sets give what we have called ( D + S ) ( direct + secondary ) and ( D \#151 ; S ) observations respectively . The change from one condition to the other is effected by simply reversing the direction of current in all the coils on one side of the balance ; this leaves the direct forces unchanged in direction but reverses the secondary forces . In the majority of the determinations ( D + S ) and ( D \#151 ; S ) observations were taken in succession and the current calculated from the expression amperes = v/ ( w/ /29'99856 ) , where mf is the sum of the balancing masses in the ( D + S ) and ( D \#151 ; S ) tests . Tests on Cadmium Cells . To determine the E.M.F. of a cell , an electric current supplied by a 110-volt storage battery was passed through a standard resistance of approximately 1 ohm , in series with the current weigher , and adjusted in strength until the P.D. between the terminals of the resistance balanced the E.M.F. of the cell . The magnitude of this current was then determined by the instrument , the cell and the resistance being kept at very nearly constant temperature during the measurements . Switches with copper contacts and terminals , to minimise thermal E.M.F. 's , were used in the cell circuit , and reversals of current and of the cell were sometimes made to eliminate inaccuracies which might otherwise be introduced by such E.M.F. 's . As the steadiness of the balance was much greater when the instrument was cold than when heated by the long continued flow of the current in the coils , our usual procedure was to make one complete set of observations , ( D + S ) and ( D \#151 ; S ) , in the morning and another in the afternoon . The interval between the morning and afternoon readings was often devoted to silver deposit determinations , the combination of cell and standard resistance being used as a secondary standard of current during the depositions . An account of work on silver is well advanced , and will be published shortly . In all some 71 observations have been made on a certain cadmium cell ( N.P.L. , No. 2 ) , using both sets of coils on the balance , and 13 observations in which one or other of the two sets was employed . The agreement between the individual results obtained with the two sets of coils is remarkable , the average difference from the mean amounting to only six parts in a million . The whole series of observations extended over a period of 19 months ( September , 1905 , to April , 1907 ) , and during that interval the coils of the balance were reset five times . No determination made has been omitted , except those in which the observations were of such a nature that A New Current Weigher , etc. a decision to disregard the result was arrived at before its computation . Such occasions were very rare . Of the 71 observations made , 7 are within 1 in a million of the mean , 14 are within 2 , 28 within 5 , 53 within 10 , 66 within 15 , and 70 within 20 in a million . Only 1 determination out of the whole 71 , and this one of the earliest , differs from the mean by so much as 1 part in 59,000 . The above facts constitute important evidence of constancy in both cell and balance . In fact , both current weigher and cell proved to be much more constant and trustworthy than the standard resistance , although the latter was very carefully made and annealed with a view to ensuring permanency . Expressed in terms of the international ohm , as realised at the National Physical Laboratory , and of the ampere as given by the new current weigher , the value of C x E for the normal Weston cadmium cell is P018305 at 17 ' C. This assumes that the value of g at Bushy is 981T9 , a number probably correct to within 3 parts in 100,000 . An uncertainty of this amount in g introduces a possible error of 1| parts in 100,000 in the value of the ampere , and , as all other probable errors are smaller in magnitude , it is important that a more accurate determination of g at Bushy should be made . To realise the volt with an accuracy approaching that of the ampere as now known , it is necessary that an absolute determination of resistance of corresponding precision be undertaken . At the present time the uncertainty in the absolute value of the international ohm approximates to 4 parts in 10,000 . From the above value of C x E for the cadmium cell , together with the ratio of Clark to cadmium , viz.:\#151 ; Clark at 15 ' C. cadmium at 17 ' C. = l'406fi , the E.M.F. of the Clark cell at 15 ' becomes 1*4323 . Two Appendices accompany the paper : one of these gives the numerical values of the constants in the series for calculating F and E , the complete elliptic integrals of the first and second kinds respectively ; the other relates to the corrections in the forces between the coils of the balance arising from the finite thickness of the wire used , and from the fact that helices are substituted for current sheets . Neither of these corrections affects the results appreciably . Some historical notes are given in the paper .

rspa_1907_0069

0950-1207

On luminous efficiency and the mechanical equivalent of light

19

25

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Charles V. Drysdale, D. Sc.|Silvanus P. Thompson, D. Sc., F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0069

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0069

10.1098/rspa.1907.0069

Optics

Tables

Optics

19 On Luminous Efficiency and the . Mechanical Equivalent of Light . By Charles V. Drysdale , D.Sc . ( Communicated by Silvanus P. Thompson , D.Sc . , F.R.S. Received June 8 , 1907 . ) ( Abstract . ) The determination of the efficiency of various forms of illuminants , and of the power expended in light production , does not appear to have received the attention it deserves in this country , nor have the labours of workers in Germany and in the United States as yet sufficed to permit of definite values being adopted for luminous efficiencies , or for the mechanical equivalent of light . In what follows , an account of some observations made by Mr. A. C. Jolley and the writer , with the object of determining the mechanical equivalent of light , will be given . For this purpose an attempt was first made to find the luminous efficiencies and total consumption of some of the newer highly incandescent electric lamps ; and this was followed by a direct determination by a bolometer in the spectrum . I. Luminous Efficiency . Let Q be the total power consumption of a source . f ' ' R the " total radiation " = I the remaining power , Q \#151 ; R being 0 dissipated by conduction or convection . r ^2 L the " luminous radiation " = where and are the limits of ' V the visible spectrum , say , 039 / / . and 076 y , respectively . La the " equivalent luminous radiation " = where kk is a factor 0 which is proportional to the luminosity and taken to be unity for a wave-length of which is that of maximum luminous utilisation of energy . Then the " luminous efficiency " in its ordinary acceptance is = L/ Q. This is the quantity which is called by Nichols* the " total efficiency . " Methods which take no account of conduction or convection losses seek to determine the ratio yR = L/ R , which Nichols terms the " radiant efficiency . " Lastly , a suggestion of Dr. Guilleaume'sf leads to a new definition , yK = LA/ Q , which might be termed the " reduced luminous efficiency , " as it is reduced in terms of the standard monochromatic light . It is obvious that while * 'Phys . Rev. , ' vol. 17 , p. 267 . t ' Soc. Int. Elec . , ' Bull . Y , pp. 363-400 . VOL. LXXX.\#151 ; A. n 20 Dr. C. V. Drysdale . On Luminous Efficiency [ June 8 , with the ordinary definition a source would have unit efficiency if L = Q , or the whole of the energy were within the spectrum , and might yet be a very ineffective source as an illuminant if its radiation were confined to near the ends of the visible spectrum ; Dr. Guilleaume 's definition would only lead to unit efficiency in the case of a monochromatic source of wavelength 054 fx . II . Measurement of the Mechanical Equivalent of Light . The most direct mode of procedure is obviously to allow a beam of light of any required quality to fall simultaneously on some form of radiometer and a photometer ; and to compare the indication of the radiometer with that obtained from a known source of radiation at a given distance . As nearly all devices for measuring low intensities of radiation are liable to troublesome variations , it is of the greatest importance that the comparison between the radiation in the beam under test , and the known radiation , should be effected as quickly and easily as possible , and with the minimum of disturbance . Fig. 1 shows the arrangement of apparatus adopted after consideration of the above points . A small intense source of light such as an arc or Nernst filament was employed , in conjunction with a lens , L , and carbon bisulphide prism , P , to form an approximately pure spectrum at the photometer and radiometer box , B. By using a narrow slit an approximately monochromatic light of any required ' wave-length could be projected on to the photometer , while by widening the slit a band of any width up to the entire limits of the visible spectrum could be employed , the integration being automatically performed without any other collecting device . The known source of radiation consisted of a glow lamp which will be referred to as the " comparison lamp , " C.L. , placed close to the prism ( in some cases beneath it , so that both were approximately on the axis of the bench ) . A standard glow lamp , S.L. , was kept continuously burning on the other side of the photometer box , B. A fixed screen , S , with an aperture , served to block off all radiation but that from the prism , P , or comparison lamp , C.L. , while a sliding metal screen , S ' , actuated by a cord , could be rapidly moved in front of one or the other . In taking the readings the light from the prism was allowed to fall on the bolometer , and the current through the comparison lamp varied until on moving the screen , S ' , in front of P or C.L. alternately , no change could be noticed . In this way all disturbances due to external changes of temperature could be eliminated , and the observations were much more rapidly obtained than by waiting for slow deflections . A glow lamp was used as the standard source of radiation for the following and the Mechanical Equivalent of Light . 1907 . ] reasons : ( a ) The total power is easily measured by the P.D. and current , and can be readily regulated ; ( b ) the ratio of convection and conduction to radiation is very small , owing to the high temperature of the filament . These advantages render the glow lamp immeasurably superior to low temperature sources such as employed by Thomsen and others . On the other hand the radiation is not uniformly distributed . But this difficulty can be overcome by determining once for all the relation of the intensity in any given direction to the mean spherical emission , and this may conveniently be determined photometrically . The photometer employed was of a special form devised by the writer for ordinary and heterochromatic measurement . It consists simply of two totally reflecting right-angled prisms , mounted with their edges in contact . When this combination is set up between two lamps , the light from each is reflected forwards , and can be received on a screen placed in contact with the front face of the prism . This screen may be simply of translucent paper , or opal glass , in which case the appearance is identical with that of the Joly paraffin block photometer ; or in the form of a discrimination diagram which serves for heterochromatic work . This diagram is made up of letters and reticulations of different sizes , and both on light and dark backgrounds , the letters and designs being absolutely symmetrical . The advantages of this arrangement are , briefly , that it serves either for isochromatic or heterochromatic photometry ; it is absolutely symmetrical ; it is not affected as are the wedge photometers by a slight inclination to the axis of the photometer bench ; it forms a very sensitive cross staff for indicating whether the lamps and the photometer are in line , and whether there is any inclination to the axis ; and , lastly , it permits any portion of a spectrum to be brought exactly to the dividing line so that the comparison may be made with a fairly short spectrum on one side . For the measurement of the energy a pair of thermo-junctions on the lines employed by Professor Fery* was at first made up , but was found insufficiently sensitive . They were therefore replaced by a bolometer , which was made of 50 cm . of 2-mil copper wire wound backwards and forwards on a mica frame , and had a resistance of about 7'5 ohms . Two such bolometers were made and mounted in the same case with the photometer prisms , the centre of the bolometer being carefully adjusted to be over the edge of the prisms so as to be in the part of the spectrum under photometric examination . To protect the bolometers from draughts the two ends of the box and the observing window were covered with quarter-wave mica sheets . The two bolometers were separated by an asbestos screen , and * " Rayonnement Calorifique et Lumineux , " Theses , Paris , Serie A , No. 1111 . C 2 Dr. C. Y. Drysdale . On Luminous Efficiency [ June 8 , were connected to three terminals on the top of the box , from whence three flexible conductors were taken to a Carey-Foster bridge . By having the two bolometers , changes of the air temperature are of less importance , and the whole photometric and radiometric arrangement is reversible . The ratio coils were of 10 ohms each , and a moving coil galvanometer having a resistance of 7'5 ohms and a sensitiveness of 22 mm. per microvolt was employed . The current in each of the bolometer grids was from 004 to 0T ampere . * In taking the readings the photometer head was first fixed in the middle of the bench , and the spectrum moved until the required colour appeared at the dividing edge between the prisms . The standard lamp was then brought up and balance obtained at a distance , d , from the photometer . Next , the comparison lamp was regulated as above indicated , until the heat balance was obtained , the comparison lamp being at a distance , D , and supplied with power , W , watts . Then , on the assumption that the heat from the comparison lamp was radiated equally in all directions , we have:\#151 ; Intensity of radiation at bolometer p = rW/ 47rD2 watts per square centimetre , where r is the ratio of radiation to total power . Intensity of illumination of beam I = / K/ d2 , where K is the candle-power of the standard lamp , and / the ratio of the illumination in the direction of the beam to the average illumination . the mechanical equivalent in watts per candle . A careful determination of the candle power of the comparison lamp in various directions , when kept at a constant P.D. , was made by Mr. Jolley , resulting , for the horizontal direction , in a reduction factor of 0-862 , agreeing very well with the 0-865 given by Paterson . For the direction in which the radiation was measured the value of the factor was found to be 0'78 . The amount of heat lost by convection was estimated experimentally by measuring the amount of heat communicated to a suitable calorimeter by the warm air rising from the glow lamp . It was found that the convection loss was not more than 2 or 3 per cent. , which could be neglected in view of the accuracy which could be obtained . The greater number of the observations were made in the yellow-green , which were judged by eye to be in the neighbourhood of X = 0-54 ^ proposed by Gfuilleaume . Having regard to the fact that the mounting- hardly justified accurate determinations of wave-length ; that the point A , = 054 fx can hardly be said to have been definitely determined as the point of maximum Hence , the mechanical equivalent of light 2a 1907 . ] \lt ; me7 the Mechanical Equivalent of Light . efficiency ; that in the region of maximum efficiency the variation would not probably be great , as was confirmed by test ; and lastly , that in order to avoid trouble , owing to the Purkinje effect , it was considered advisable to work at illuminations not exceeding two or three candle-feet , in which case the sensitiveness was not very great , it was considered superfluous to determine the wave-length with greater accuracy . It may be said that the sensitiveness of the arrangement seemed to allow of the definite detection of half a watt at a distance of about 2 metres . In making determinations on white light , the slit was broadened considerably , and by covering it up from each side successively , it could be adjusted so that light passing one edge of the slit gave a very dark red light on the photometer screen , while that from the other edge gave a deep violet light on it . In this case the result produced by the whole slit was of a pure white light , from which all the invisible radiation was cut off , instead of o being only cut off from one end , as in the experiments of Angstrom.* A number of preliminary observations were taken with arc and Hernst lamps as sources of light , and reversing the photometer box , etc. Considerable trouble was , however , found with drifting of the galvanometer , and this was traced to the presence of the observer . The mean result , however , from 24 observations was 008 watts per candle power . After this the whole of the apparatus was removed , the photometer bench , sliding screen , etc. , being set up in a dark room , through the wall of which an aperture was made for the projection of the spectrum , and a second small aperture for the observation of the photometer . In this way the whole of the observations could be taken without entering the room , and the readings were much more satisfactory . The results obtained are collected in Table I. The final result of about 0T2 watt per candle power for the white light from the Hernst filament agrees almost exactly with the value found by ' Angstrom for the Hefner lamps . Thomsen and Tumlirz both used absorption methods , and little value can be attached to their results . Other values can be deduced from investigations on the efficiencies of illuminants , but these values range from O'OOll to O0289 watt per candle found by Wedding , and 0'02 to 039 by Eussner , to 0T9 to 049 watt per candle from the results of Merritt . The lower value of 0 08 watt per candle found in the present tests for o * In Angstrom 's experiments the glass in the lenses , etc. , employed would probably have cut oil the major part of the ultra-violet radiation , and the energy in the ultraviolet is generally very small for ordinary sources of light . Hence probably the agreement with our results . Dr. C. Y. Drysdale . On Luminous Efficiency [ June 8 white light from the arc is probably due to the higher temperature of the source . Pending more exact determinations , therefore , it may be assumed that an ideal source of white light should give us about 10 candles per watt , and a monochromatic yellow-green source nearly 17 candles per watt . Table I.\#151 ; Observations on the Mechanical Equivalent of Light . Standard lamp . Comparison lamp . Mechanical equivalent , m = oWk(l)2 ' Distance , d. Candle power , K. Distance , D. Current , amperes . P.D. , volts . Watts , W. ( a ) Light approximately monochromatic , yellow-green . 80 -0 24 -5 116 -7 0-145 31 -8 4-61 0 -0555 80-0 24-5 1(36 -7 0-13 29 -0 3-77 0 -0455 70 -6 24 -5 165 -5 015 32 -6 4-9 0 -0468 78 -0 20 -6 165 -5 0-145 31 -8 4-48 0 -0620 78 -0 20 -6 165 -5 0 16 34 -5 5-52 0 -0765 78 -0 24 -5 165 -5 0-17 36 -2 6 15 0 -0715 85 -0 24-5 165 -5 0-15 32 -4 4-85 0 -0670 76 -3 24 -5 165 -5 0-155 33 -2 5 -15 0 -0573 7676 -3 20 -6 165*5 0-145 31 -6 4-58 0 -0605 76 -3 24 -5 165 -5 0-15 32 -2 4-83 0 -0536 57 -4 24 -5 165 -5 0-23 45 -0 9-9 0 -0622 121 -0 24 -5 165 -5 0-095 22 -2 2-11 0 -0590 Mean ... 0 -0598 ( B ) White ligl it from wi de slit . 149-0 16 -0 206 -0 0 -115 26 -3 3 -03 0 -127 I Nernst 86 -0 13 -0 263 -0 0-225 47 -0 16 -6 0 *1115 J filament Mean ... 0 -1193 76 -1 16 -0 263 -5 0-23 47 -5 10-9 0-073 75 -0 16 -0 263 -5 0-25 50 -5 12 -6 ''082 La\#153 ; 89-6 24-5 166 -5 0-16 34 -4 5 -5 0 -0835 fArc 89 -6 24 -5 166 -5 0-16 34 -4 5-5 0 -0835J Mean ... 0 -0805 Table II.\#151 ; Mechanical Equivalent of Light . Collected Values . to o Observer . Date . Method . Source . Unit . Mechanical Calories per second . equivalent . Watts . Per Hefner . Per C.P. Per Hefner . Per C.P. T Tli nm QAn 1863 A. Sperm candle 0-065 0-0733 0-276 0 -3075 1 a Sperm 0 -0585 0 -065 0-245 0-272 ; | Moderator lamp \lt ; L candle , 0 -0615 0 -0683 0-257 0-286 \gt ; ) . r [ 8*2 grammes 0 -063 0 -070 0-264 0 -293 )9 \gt ; \gt ; " } Gas name \lt ; per hour 0 -0553 0 -0615 0 -232 0-258 0 . Tumlirz and 1888 A. Incandescent platinum Hefner 0-041 0 -0455 0 -1715 0 19 Krug wire O Tnmlirz 1889 A. Hefner lamp Hefner 0 -0455 0 -0505 0-191 0 -212 o K. Angstrom ... 1903 c. Hefner lamp Hefner 0 -0259 0 -0288 0-1085 0 121 " Writer and 1907 c. Nernst filament Candle 0 -0256 0 -0284 0-107 0 -119 A. C. Jolley Arc 0 -0173 0 -0192 0-0725 0 -0805 yy yy Monochromatic , yellow- jj yy 0 -01285 0 -0143 0 -0538 0 -0598 green Method . A.\#151 ; Thermopile and absorptive screens . Method C.\#151 ; Direct measurement of energy in spectrum . In this table the Hefner has been taken as 0'90 C.P. See Paterson , * Proc. Inst. E. E. , ' vol. 38 , p. 286 , and Fleming , p. 311 . |\gt ; C S2 a \lt ; s\gt ; . ar- to Cn and the M

rspa_1907_0070

0950-1207

On the surface-tension of liquids investigated by the method of jet vibration.

26

27

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

P. O. Pedersen|Lord Rayleigh, P. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0070

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Tables

Fluid Dynamics

Tables

26 On the Surface-tension of Liquids investigated hy the Method of Jet Vibration . By P. 0 . Pedersen , Copenhagen . ( Communicated by Lord Rayleigh , P.R.S. Received June 11 , \#151 ; Read June 27 , 1907 . ) ( Abstract . ) 1 . According to Lord Rayleigh 's theory* of jet-vibrations , measurement of the length of the standing waves and the velocity and cross-section of a jet , together with the density of the liquid , affords the necessary constants for the calculation of the surface-tension . Notwithstanding the great fundamental advantages of this method , it has only been used in very few cases , and only for relative measurements of the surface-tension , j* The explanation hereof is to be found in the great difficulties connected with the adequate exact determination of the wave-length , and cross-section or velocity of the jet . As none of the methods in use for the measurement of these quantities could be taken as satisfactory , the main object of this investigation has been to work out really good methods for them . 2 . The determination of the cross-section of the jet is accomplished in the following manner:\#151 ; To the lower end of a pendulum is connected an apparatus , the " jet-catcher , " consisting of two parallel vessels with rectangular openings , the short sides of which are cutting-edges . The two vessels are parallel to the horizontal jet and symmetrical to each other with regard to a plane through the axis of the pendulum . When this is oscillating the jet-catcher is cutting pieces out of the horizontal jet . From the weight and the length of these pieces " cut out " the cross-section of the jet is calculated . The different sources of errors are discussed , and it is shown that it is easy to obtain very reliable results by this method . For a water-jet , velocity 273T cm . per second , diameter = 0T3415 cm . , the mean error in the measured cross-section has been determined to 0T4 per cent. The velocity of the jet is calculated as the ratio between the discharge and the cross-section . 3 . Production of the desired deviation from the cylindrical form of a jet:\#151 ; * Lord Rayleigh , ' Roy . Soc. Proc. , ' vol. 29 , p. 71 , 1879 . t F. Piccard , 'Arch . d. Sc. phys . et not . , ' ( 3 ) , vol. 24 , p. 561 , 1890 ; G. Meyer , ' Wied . Ann. , ' vol. 66 , p. 523 , 1898 . On the Surjace-tension of Liquids , etc. In the paper is shown the importance of the jet only executing one single vibration , as in other cases the determination of the wave-length is difficult and becomes inaccurate . In the measurements that , up to now , have been made with this method , only little attention has been paid to this condition . I have succeeded in making some orifices so exact , that jets issuing from them practically only execute one vibration . 4 . The influence of the amplitude on the period of vibration has been investigated , and it is shown that only for very small amplitudes is the period independent of the amplitude . 5 . The determination of the wave-length is very difficult . By all the previous measurements it is determined as the distance between the summits of the jet , and the determination has taken place by direct measurement either on the jet itself or on a photograph of it . As the amplitude of the vibration must be small , this method is very unsatisfactory , and cannot give good results . An exact determination of the wave-length can be made by using the jet itself as an optical , image-forming system . The following method was found to be very convenient:\#151 ; The jet is illuminated from a parallel , linear , incandescent lamp , and the twice refracted and once reflected rays form an image of the lamp on a photographic plate ( compare the theory of the rainbow ) . If the jet is cylindrical , the image will be a straight line , but for a jet with standing-waves the image will be wavelike . And as the amplitude of the image is much larger than that of the jet , it is much easier to measure the wave-length on the image than on the jet itself . 6 . Results.\#151 ; The surface - tension of the following liquids has been determined :\#151 ; Water ( T15oC . = 74'30 din ./ cm . ) , Toluol ( T15oC . = 28'76 " ) . Aniline ( T15o C- = 43D0 " ) . 3 aqueous solutions of NH3 . 1 " solution of C11SO4 . 1 " " H2SO4 . 15 " solutions of alcohol . For the three first named the results are given above . 7 . Used in this manner the jet method gives very consistent results , and is highly deserving of use in the future on account of its great fundamental advantages .

rspa_1907_0071

0950-1207

The dispersion of double refraction in relation to crystal structure.

28

44

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

T. H. Havelock, M. A., D. Sc.|Professor J. Larmor, Sec. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0071

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10.1098/rspa.1907.0071

Fluid Dynamics

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Fluid Dynamics

]\gt ; The ersion of Double cxction in to By T. H. HAVELOCK , M.A. , D.Sc . , Fellow of St. John 's College , Cambridge , Lecturer in Applied Mathematics in Arnlstrong College , Newcastleon-Tyne . ( Communicated by Professor J. Larmor , Sec. R.S. Received July 5 , 1907 . ) In a previous communication , writer discussed the double refraction of a medium composed of similar particles arranged in rectangular order , the results })plied especially to the produced in colloidal solutions by mechamcal stress and by a magnetic field ; the present paper is the discussion of a similar problem , a ) method of procedure suggested by Professor Larmor . The object is to investigate to what extent it is possible to consider double , whether produced artificially or occurring in natural crystals , as due simply to an oeolotropic distribution of similar particles ; the questions which arise when one considers whether the aeolotropy occurs naturally or is produced by the action of mechanical , electric , or mag1letic force are not specially considered , but the various cases are classified in the section . In the next sections we considel a lnediul1l ) osed of a homogeneous assemblage of optically isotropic molecules and obtain an expression giving the dispersion of the double acCion . This is applied first to artificial double refraction produced by mechanical stress and by an electric field ; then on the same basis the dispersion in quartz is examined . Certain divergences in natural crystals and cially such lnomalous cases as ylite and vesuvian to an exCenfflon of theory . This is , bl'ieiiy , all aeolotropic ibution of optically cnles , each of which disperses regularly ; it is exalnined first uniaxal crystals and finally in general for biaxal cryfitals , and is to contain the possibility of all the varieties of dispersion of double tion which occur in natural crystals . 1 . Thjorics of The ordinary theory of double refraction . in as it is ecular , amoumts to considering the as a collection of crystal molecules in ical order , the vckrieties of ) ) ostulated of the single particle . Thus with the principal inate { be the . Proc , vol. , 170 , 1906 . . 180 . Daspersion ofDouble in Relation to Crystal Struct ure . 29 polarisation of a typical particle at which the ective electric force , we have equations of the form . ( 1 ) These equations mean that the aeolotropy is assumed to inate w in the individual crystal molecule , and that it affects the quasi-elastic force under which the polarisation electrons are supposed to vibrate . The same method has usually been followed in attempts to electron theory to the double refraction due to mechanical stress . It we consider the equations for an isotropic medium , to ( 1 ) with a single constant , then Voigt*lmes that is altered by amounts proportional to the stresses in the medium ; this is a direct effect on the internal forces of the molecule , while on the other hand a theory which confines the effect to a rearrangenlent of the molecules in space will the result by a modification of the effective force in the previous equations . The latter theory appears to comprise the double refraction effects obtained by Majorana by placing certain colloidal solutions in a field . These effects appear to be quite distinct those involved in the Zeemann effect . The double refraction obtained in the latter way is explained by a direct action of the magnetic field on the electron , and a result of the is that the extraordinary and ordinary indices both from the index of the isotropic medium under no netic a the variation of the two indices is in the same direction , one three tlmes the other , and the difference varies sely as the of the In the Majorana effect , on the other hand , the of the two indices are in opposite directions , one ately tvice the other . The same distinction occurs in the theory of the effect , that is , of double refraction produced by an electric field . has extended his theory of the Zeemann effect to cover an effect by an elpCtriC field , the results being of the same character . Now Kerr 's experiments appeared to prove that only the index for vibrations parallel to the { ield was altel'ed ; , in some experiments , claims to have observed in Voigt , ' Annalen der ysik , ' vol. 6 , p. 461 , 1901 . Voigt , ' Annalen der ysik , ' vol. 4 , , 1901 . .eckerlein , 'Physikalische hrift , ' vol. 7 , ) , 1906 ; also , ? bicl . , p. 811 , Dr. T. H. Havelock . Dispersion of Doubfe [ July 5 , certain liquids a change in both indices , the variations being in opposite senses and one apparently twice the other . It is , of course , possible that there may be some direct effect of the electric field upon the periods of the electrons , in addition to a merely mechanical effect of rearrangement of molecules . For the present we are concerned more with working out the possibilities of the latter supposition ; that is to say , although Cauchy 's theory of optical dispersion , as caused by simple discreteness of the medium , was insufficient to account for ordinary dispersion , it is gested that it may be capable of application to the differences of dispersion occurling in different directions in a doubly refracting medium . 2 . Optical Properties of a Homogeneous Assemblage of Molecules . In a dielectric medium , if we write for the electric force , for the magnetic force , and for the total electric displacement , we have the usual equations curl , curl The total displacement is given by equations of the form , ( 3 ) where refers to the polarisation of a typical particle and is the number of such per unit volume . For we have an equation , ( 4 ) where is the component of effective electric intensity considered as acting on the given particle . The determination of the mean value of is the problem in question , and in particular , the estilnation of the influence of neighbouring particles . In the ordinary procedure , we consider round the given particle a sphere whose radius is small compared with the wave-length of the radiation medium , but such that it contains a large number of particles ; then we evaluate separately the influence of the particles outside and within this spherical region . 1907 . ] to Structure . The first part is taken to be the force within a sphel.ical cavity cut a medium uniformly polarised Go the value at the point in question of the vector ; this , then , contributes a force . The second part is due to the average effect of the immediately ing particles within the sphere , and is enerally written as , where are constants depending upon the arrangement of the particles . For a simple cubical arrangement , we the -constants to be all ; thus , as in the similar argument in the case of liquids , we are to eliminate the consideration of the purely localpart of the hbouring action . Now , for any other regular ement of particles , the -constants of this method will not all be equal and zero ; but suppose that of a sphere we can choose some other form of surface , such that we can ) the local effect of the particles within , then we are left with the evaluation of the force within a cavity in a medium uniformly polarised to the value of the material polarisation vector at the point in question . In particular , it is clear that for a approx tion for a ular arrangement of particles ering slightly from a simple cubical systeln , we may assume to be an ellipsoid whose axes are nearly equal . If we take co-ordinate axes in the ections of the principal axes of the ellipsoid , the force due to the particles outside is giyen by ( 5 ) where ( 6 ) with similar expressions for and C. Hence , if we put , we have to the first power in , . ( 7 ) .32 1 Dr. T. H. Havelock . Dispersion of Dispersion of Writing these for the moment as have , from ( 4 ) and ( 5 ) , ( 8 ) If the quantities vary as , we find from this equation an expression for ; this can be substituted in equation ( 3 ) to give a relation between and X which must necessarily be of the form , where is refractive index . Hence we obtain a value whioh is expressed most in the form here is the refiactive index of the same substance if isotropic and of the same mean density . Now we substitute from ( 7 ) the values for and expand from ( 9 ) to the first power in the small quantities ; we find the following values for the refractive indices of the medium:\mdash ; ( 10 ) The mean value is given by . The medium , then , is doubly , and we shall consider first some consequences when it behaves like a crystal . In this case we may take and as zero , and we have the extraordinary index and the ordinary index given by\mdash ; where . The mean index , that is the index for the same medium if isotropic and of the same density , lies unsymmet rically between the ordinary and extraordinary indices , being twice a , s far from the latter as from the former . Further , if we measure the double refraction by the difference between the two principal indices , we have 1907 . ] Refraction in ltelc , to , then , that the ellipticity of the eflective ellipsoid is constant , if we know varies with the wave e , this tiun gives of dispersion of the double refraction ; we shall this with some experimental data in the following sections . 3 . Donble Dnc The most suitable test for the bove formula would ) in the of artificially produced double refraction , as , . instance , when isotropie medium behaves like a uniaxal crystal if ected to mechanical stress . However , in these cases t , he effect is extrelnely small , and the pl.incipal indices and ? have not usually been measured separately , but ) } ) their difference . If the dispelsion of the unstrained isotropic known either by a curve or a dispel'sion formula , then it would be possible to calculate the dispersion of the difference for instauce , if for the isotropic medium of the same density , were given by then , ince we should have given pproximately by a relation of the . ( 14 ) Further , the separations of and from should be in opposite directions , with the former approximatel . twice the latter . consequences rest on the initial assumption of the theory , namely , that the isotropic medium is , in fact , an semblage of optically isotropic molecules , and not a collection of crystalline molecules , their distributed equally in all possible directions . 4 . Electric Refraction . For the double refraction produced in lnedia by the action of all electric tield , Kerr observed a dispersive effect , and supposed that the double refraction varied inversely as the square root of the , but this has beeu shown to be erroneous by Blackwell . * His experiments deal with carbon disulphide , and curves are given for variation of the double refraction with the wave-length for two ferent temperatures with a field strength of 56,000 volts per centimetre . These esults give the only data suitable for the present purpose . * H. L. Blackwell , ' American Academy Proceedings vol. 41 , p. 647 , 1906 . Dr. T. H. Havelock . Dispersion of Double [ July 5 , We have , then , two sets of values for the double refra.ction of at the temperatures of C. and C. , each set ving values for six differenf , wave-lengths with the value of for and taken as 100 ; absolute values can be obtained by means of a determination of for at the latter point . For the present theory we require actual values of and iu order to calculate mean value equal ; vever , it is sufficient to take for the refractive index of under the same conditions in regard to density and temperature . To obtain these values for required , we have a dispersion formula for at obtained by Martens , *which ives values correct to four decimal places at least ; the formula is where ; ; ; The correction for temperature can be made to sufficient accuracy by decrease of index of for } degree rise of teml ) Making these calculations , we have the of used in the following Tables I and II . The first column gives the , the second the third the observed values of the double refraction ; the fourth column gives the calculated values of , which , according to the theory , ought to be constant . Table I.\mdash ; Carbon ) isulphide at Mean value of ; greatest divergence per cent. approx. The fifth column in each table was obtained by the mean value of , together with the values of , in order to recalculate the values of comparison of the third and fifth colunlns shows the amount of reement between the ) served and calculated values of ; it may be ) arked that * Martens , ' Annalen der Physik , ' vol. 6 , p. 632 , 1901 . Landolt , ' ' 3rd edition , p. 671 . ( I Iosr.edmoo j aqt XUB qonm saop J0E aas . puooas ' . 08 III ' . ns tSTP 0 aq Iqnop $13 \mdash ; : pug ) } puti xoJl ? : 6 . . Z9 9 989 I 86 T9 I 889 TI 7 899 I . I9 4 8 . IZT . T9 . IZT 9 08 T9 689 Sb ' c- .36 Dr. T. H. Havelock . Dispersion of Double [ July 5 , calculate the values of some other relation which might suggest itself ; for instance , the quantity decreases ntinuously throughout the whole range , its extreme from a mean value by as much as 16 per cent. Table III.\mdash ; Quartz . In consequence of the use of Babinet 's } ) sator in determining the double refraction of minerals , the dispersion of double refraction in quartz has been studied extensively . From experimental observations in the visible and ultra-violet spectrum , Mac6 de found that could be represented very accurately by a formula\mdash ; * Mace de Lopinay , ' Annales de la Faculte des Scieuces de Marseille , ' vol. 50 , p. 1 , 1891 . to Structure . The numerical values of the constants were found by to fit also his observations in the infra-red . This relation is of the form to be expected our formula and , assuming to be explessible ) a dispersion formula of the usual type . We have assumed in the calculations that the effective cavity was an ellipsoid of small ellipticity . We might then examine the order of magnitude of the second order terms which have ected , but it is simpler to obtain now a more coeneral relation free from this approximation . Using the notation of equations ( 5 ) to ( 9 ) , the only assmnption we make about the effective cavity is that the force within it , due to the polarised medium outside , has components , ' , ( 16 ) where are constants . Then assuming as before that the molecules are isotropic , we a principal index iven by The quantity differs by a constant from its value in any other state ; or , more simply , we have Consequently , if the medium is uniaxal , we have the relation constant , ( 18 ) where and are the extraordinary and ordinary indices . Using the values given in Table III , we can examine this relation for quartz ; the result is shown in Table . Mean value Dr. T. H. Havelock . of Double [ July 5 , 6 . Some Exceptional The relation obtained in ( 18 ) does not cover all the cases of regular dispersion , as we see from the ures for Iceland Spar given in Table . But it may be noticed that in this the double refraction is 20 times reater than in quartz ; thus simple distribution of isotropic molecules is apparently not quite sufficient to account for so large a difference between the two indices . able VIceland Spar . Further , we have exceptional cases in which decreases with the waveIength , but much more rapidly than in other crystals . For instance , in strontium hyposulphate , the rate of decrease is about 10 times that of quartz , and we find that the quantity . the previous calculations is by no means constant , but decreases with the wave-length . If we have , given by the relation we see that the substance ) be either a sitive or ative uniaxal crystal , according as is ative or positive ; but in either case the absolute value of decreases with , that is , in general , will decrease as increases . Now this is the rule in most actual crystals , but there are a few for which increases with , although diminishes ; the figures for apophylite are given in Table for the purpose of comparison with a later set of figures . * B. Trolle , ' Physikalische Zeitschrift , ' vol. 7 , p. , 1906 . 1907 . ] Refi.action in Relatton to S9 Also , there are crystals for which passes , and some for which the double raction c from positive to \mdash ; the substance being isotropic for some defi1liCe It appears , then , that a theor olotropic d of isotropic molecules which may serve for the al.tificial double lefiRction produced in bodies and for simple crystals is not sufficient to cover the varieties of dispersion found in natural crystals . This is naturally to be expected ; for , in addition to the varieties of dispersion in biaxal crystals , to be considered later , we see that if such a simple theory were sufficient , then the symmetry of all the physical properties of a crystal would be the as its optical symmetl'y , and this is not the case . The direction in which to modify the theory is clear ; we shall consider a crystalline as a homogeneous assemblage of crystal molecules . Whether or no the crystal molecule can be identitied with the chemical molecule need not be considered here . the general later , we shall consider the case of a uniaxal crystalline medium . 7 . Modified of The previous theory can be extended in the manner : molecules ( or crystal units ) of the medium are not necessarily to be supposed ellipsoidal in shape , but are optically aeolotropic , so that the subsidiary equations connecting the polarisation of a particle with the effective electric force are aeolotropic , with an axis of symmetr ; the particles are supposed to be arranged in a homogeneous such that the effective cavity may be taken as an ellipsoid of revolution of ellipticity , and having its axis of symmetry coincident in direction with that of the unit . Then , instead of equation ( 9 ) , we have now . ( 19 ) with a similar equation in and In these , and are the and ordinary indices for the substance , with a regular cubical arrangement of the same molecules in the same density . Hence , substituting for , and their values in terms of , we have the two principal indices given by , ( 20 ) Dr. T. H. Hayelock . ispersion of Double [ July 5 , And the double refiaction is given by . ( 21 ) These equations ( 20 ) ) would represent the effect of deformation in a natural uniaxal crystal . ) purpose we apply them to a natural unstrained crystal . They cannot be vel.ified by actual calculation in this case , but we shall see that they cover all the nomalous cases mentioned in the previous section . To find how varies with the wave-length , we have , from ( 21 ) , 22 ) Now the object is to account ) anomalous dispersion of in regions free from absorptio ] ) . Then if and follow the regular law of diminishing as increases , we have both and negative ; and as we can have greater or less than and positive or ative , we see that it is possible to have positive . In fact , it is possible to have the varieties of change of aa increases : ( i ) slow decrease , ( ii ) decrease , ( iii ) slow increase , ( iv ) passing through a minimuln , and ( v ) changing in sign . hese cases all occur , typified by quartz , strontium phate , apophylite , and for the latter cases by varieties of vesuvian and melilite . * The theory can be illustrated best by np from a known crystal of ular dispersion of double refraction one which behaves like apophylite . Suppose we consider the uniaxal crystal phenakite , for which there are available determinations of the principal in dices for five diHerent wavelengths ; we denote these indices by and we find their difference diminishes as the wave-length increases . Suppose , now , that the crystal molecules of phenakite are so that the effective cavity has an ellipticity of , and has its axis along direction of the axis of symmetry of the crystal units ; then by equation ( 21 ) we may calculate double refrac , tion of the medium thus built up . The results are shown in Table . We see that although the doul ) refraction of the phenakite crystals follows the regular law of decreasing as increases , yet the double refraction of the distorted medium increases as increases , and is of about the same order as that of apophylite ) . This is , of course , only intended as an illustration of the possibility of explaining the irregular dispersion in regions which are not in the vicinity of absorption bands . Hlawatsch , ' Tschermak 's Mitteilungeu , ' , p. 415 , 1904 . 1907 . ] Refractio in to Crystal Table \mdash ; Phenakite with 8 . Dispersion in Bic We consider now the previous theory in the most general form , namely , the double refraction of a medium composed of optically aeolotropic particles with the same orientation and so as to rive an ellipsoidal effective cavity with its principal axes in any three fixed mutually perpendicular directions ; we shall indicate briefly the general character of the results . We take the principal axes of a typical particle as co-ordinate axes , and have , , and , as the direction cosines of the principal axes of the effective cavity . Then if is the polarisation of the medium , the -component of the force within the cavity due to the polarisation is given by , ( 2.3 ) where , are the usual constants for the cavity and can be written as\mdash ; Further , if we write for the principal indices of a medium composed of the same units , but in regular cubical order , we three ations of the form We can obtain now three equations connecting the components of electric force with the polarisation ; but if are the direction cosines of a principal axis of the resulting ellipsoid of polarisation and if is the corresponding principal index of refraction for this direction , we must have . ( 25 ) Hence , for the detelmination of the principal axes and indices of the medium we obtain three equations of the type , ( 26 ) Dr. T. H. Havelock . Dispersion of Double [ July 5 , where the -constants are given by relations of the form ; . ( 27 ) We shall examine now the various types of crystals covered by these equations . ( a ) system.\mdash ; If we take simplest case , we have the principal txes of the crystal unit coinciding with those of the ctive cavity ; then evidently the three principal polarisation axes are in the same directions , and llaintain these directions for all wave-lengths , as in crystals of the prismatic type . From equations ( 26 ) and ( 27 ) we see that the plincipal refractive indices are give by ; , 2 , 3 . ( 28 ) Thus we have ( 29 ) Hence , as in the theory of S7 for xal crystals , we may have the indices varying differently with the wave-length and consequently the possibility of such crystals as brookite , in the order of magnitude of the indices changes and the plane of the optic axes is turned through a right angle . ( b ) Alonoclinic Suppose , now , that one principal axis of a particle coincides with a principal axis of the cavity , then this will be an axis of the polarisation ellipsoid which is fxed in direction ; thus we obtain the monoclinic system of crystals with a single plane of symmetry . Without discussing the equations in detail , we consider , as an illustration , the dispersion of the other two isation axes . These are at right angles to each other and lie in the plane of symmetry of the crystal . Let be the angle giving their position with reference tu the fixed co-ordinate axes , and the corresponding for the position of the axes of the effective cavity in the same plane . Then , supposing the plane of symm to the plane , we find , after substitution in ( 26 ) and ( 27 ) and reduction , that . ( 30 ) Now , and are assumed to be of the wave-length ; suppose , then , that indices and for crystal molecules in cubical order decrease arly with the wnve-length , so on the simplest supposition we have dispersion formulae of the type 1907 . ] in to Crystal Then from ( 30 ) we see that the dispersion of the angle is by a rel tion of the form . ( 31 ) Sufficient } ) imental data on the dispersion of the principal axes of monoclinic crystals are not available to test this ) a similar ation without terms in has been suggested on other rounds b and found to well with some cases . ( c ) Anorthic .\mdash ; Finally we have the general case in which none of the axes of the crystal unit coincides with a principal axis of the cavity , and consequently the three principal axes of risation all chan , both in nitude and direction , with the includes , then , all anorthic crystals . 9 . inning with a theory intended apply to artificial double refraction produced in an isotropic medium , we found that the consequences could be expressed simply in the following mallner:\mdash ; If is a refractive index of the substance , the quantity is altered by an amount independent of the wave-length , and varying only with the direction ; this implies a small which is proportional to , where ? refers to a standard state of arrangement in ular cubical order . to natural stals , we find anomalous dispersion of the double refraction in regions away from absorption bands , and a theory modified to account for these cases leads to a consideration of the optical relations of crystal structure . In this connection it is of interest to compoxe some recent work in two directions . On the one hand we ttempts to explain crystal structure as a of chemical constitution ; the crystal is described as a homogeneous of spheres which are combined into sub-groups defining the crystal unit or nolecule . On the other hand , we have work connecting dispersion of double refraction in ronps of minerals with their chemical constitution , some members being found to possess a lninimum of double refraction . Consequently , it should be possible to explain the varieties of dispersion of double refraction by means of the structure of the Cl.ystal , and we have attempted this in the previous sections , with the mptions : The crystal unit contains electrons , so that their ffect is expressed by principal equations connecting the } ) tion of the Nakamura , ' rift , ' vol. 6 , , 190 Hlawatsch , loc. 44 ofDouble Refraction in Relation to Structure . unit with the effective electric field ; if , then , these units are in regular cubical order , we have a medium with principal refractive indices along hree fixed directions in space , and we assume that in this case we have regular declease of the double refraction with increasing wavelength in regions away from absorption bands . considering in general any other homogeneous , we ) the eff'ect by a change in the effective electric field acting on the crystal unit ; this effect we have estimated by supposing , as a cient approximation , that the effective cavity is htly ellipsoidal instead of being spherical . Thus differences of packing of the crystal molecules are represented opticalIy by variations in the ratios of the axes of the effective cavity and in their directions in space compared the polarisation axes of the individual unit . Combining these assumptions , we have shown that they are sufficient for a descriptive theory covering the varieties of dispersion of double refraction found in natural crystals .

rspa_1907_0072

0950-1207

Experiments on a new cathode dark space in helium and hydrogen.

45

49

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

F. W. Aston, A. I. C.|Professor J. H. Poynting, F. R. S.

experiment

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0072

en

rspa

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10.1098/rspa.1907.0072

Tables

Atomic Physics

Tables

]\gt ; iments on Dnrk in Helium Hydrogen . F. W. A , A.I.C. , Research choler , the University of ( Communicated by Professor J. H. Pointing , F.R.S. Received June 14 , \mdash ; Read June 37 , 1907 . ) In a paper recently read before this Society , author described some eriments on the length of the Crookes dark space under eonditions in diff'erent gases . While ) was under this inequality of was noticed very close to the , which , un the . conditions , as not defillite enough to wal.rant further attention at the time . When , vever , heliuul introduced into the : this phenomenon clear , itself to be hitherto undescribed dark } ) close ainst the cathode and inside the dark space , possessing very properties from the latter . By the time the measurements of the space in helium were completed , the behaviour of the new dark ) had ested a simple explanation , which led to a series of experiments , of this paper is a descl.iption . \mdash ; The preliminary ) servations of the new dark space were ulade in the uard ring cathode\ldquo ; tube already described , when it was realised that all acculaCc of the urrent density not required , this was replaced a smaller cylindrical tube , 8 cm . in diameter , with more walls plane aluminium cathode and anode . this exception , the ) parattlS was entirely as described in the previous paper . rement of the of Space.\mdash ; As this is small ( its greatest length under measurable conditions is about cm its lneasulement was found to be a matter of considerable attempt at magnification by a telescope , as with the Crookes vorse than useless , and , after seyelal methods of , the hter used for the latter opted eing the nlost reliable . consisted of a tube about 20 cm . oncr 1 , at one end with a pointer and at the other with a small eye-hole , the whole mounted to move parallel the of the cathode . The were lone in da1kness , the error bein about cm . * F W. Aston , " " Experiments on the of the Cathode Dark ' Proc , 1907 , pp. 80\mdash ; 95 . . cit. Mr. F. W. Aston . eriments on New [ June 14 , Th of the Dark of " " the length of the new dark space , showed that it was practically independent of the pressure and proportional to the inverse square root of the current density . Now the equation expre , sing the distribution of electric force X in the Crookes dark , ] ) was hhown in the previous paper*to be , certain assumptiolJs , where current density , distance f the edge of the Crookes dark space , and of a in a unit field prevailing pressure . If we substitute ( the length of the Crookes dark space ) for in this expression , we obtain the field just outside the and , since is roughly proportional to , this field is independent of pressure and proportional to cl- , ting that the fall of potential across is constant . Now suppose the electrons start from the surface ) the cathode from rest , with a unif.orm velocity not great to ionise the gas . It clear that , if the energy necessary for such ionisation is constant , they can only attain this energy by falling through a delinite potential , so that there will be a space in front of the cathode of definite in which no ionisation will on at all , and where no light would be eYpected . The new dark space may therefore be arded as the which the electrons fall in to attain to collision with rnolecules . The influence of the current density upon this enon explainB the fact 0 it being overlooked during the on the Crookes dark space in hydrogen , since only high-current then employed . The first test of the above theory is the constancy of the fall of potential . This , ) the distribution of force quoted , is where is the total ] of potential russ the Crookes dark space , which , in the absence of any trace of , has been shown to be practically the same as the en ce of ) between the electrodes . Since is very much smaller ) , and the error of its measurement comlJaratively great , the second term may he neglected . The tables for hydrogen and helium show that , over a large ange , the fall of potential across the new dark space is constant within experimental error , is for hydrogen 15 , helium 30 Assuming for the value of the charge on ctron 3 C.G.S. , yives for the to ? atom of hydr.ogin of hdium , , taking as the value of in electromagnetic units , for hydrogcn , helium , cm . per second . 1907 . ] Cathode and Hyclrogelb . of the Darltl oives a mmatic section of the cathode in helium at abont 1 mm. pressure , with a co1nparatively low current densit , The appearance llay be broadly divided FIG. 1 . , cathode ; , new dark space ; , Crookes dark space ; glow . into three bands : an intensely black one of the order of cm . , new dark space , followed by a region of moderate reenish 1 of length about 1 cm . , the Crookes dark space , terminating finally in the brilliant bluish-green " " \ldquo ; Plate 1 , fig. 1 , is an actual hotograph of the discharge , clearly showino . the relative proportions . As the camera was placed close to and level with the cathode , the curvature of the of the Crookes dark space is gerated . Plate 1 , , shows the appearance of the at a very much current density . The Crookes dark space has lost all its distinctness outline , while the new dark space is still sharply defined , and much than in The theory given above is well supported ) the intense blackness of the new dark space in pure helium and hydrogen , and by this theory the following effect was predicted:\mdash ; Consider the motion of the first eneration of electrons starting rest , at the surface of the cathode in a field , for simplicity assumed unifol.m . Let be the distance through which they must freely in such a to obtain sufficient velocity to ionise the gas . If is smaller than the meall free path of an electroll under such conditions , we should expect just beyond a maximum ionisation and a corresponding maximum adnally fading as we recede from the cathode and the energy of the electrons is dissipated . But , by the time a point from the athode is reached , the second generation of electrons , formed by collisions at , will have attained Aston . . Soc. Proc. , A. vol. 80 , 2 . FIG. 3 . white line on the left of each of the figures represents the position of the edge of the cathode . Mr. F. W. Aston . iments on a New [ June 14 , velocity , so that thele shonld ) lotl ) , but less shalply defined , lnaximun of at a point just beyond beyond , and so on , each more indistinct , so the faint in the Crookes dark space bhould be striated near the cathode . It is clear that this effect will at its maximum when is of kIue dimensions as the free path of an under stated conditions . Of effect only the first nlaximum was in ) in elium , at comparatively pressules and very low current densities , the striatio could be plainly seen and photogl a , Plate 1 , is the uction of discharge in helium at a pressure ( beyond the range of the ometer ) of 2 to 3 mm. With a current so as barely to cover the , urface of thode , the curvature of the of the new dark space , due the current density not being uniformly listributed over the cathode , is clearly shown . Three distinct maxima , and traces of a fourth , could be detected on the original negative . It is interesting to note that the potential between the electrodes in this particular experiment was well below 200 volts , so that the effect can be shown with ease by means of a suitable tube and an ordinary lamp circuit . In such striated discharges the distances between the cathode and the firsG maximum and between the first and second maxima , after allowances are made for the distribution of electl.ic force , corre spond to equal falls of potential as nearly as call be estimated . conclnsion is of importance , for , since the second maximum is caused presumably by electrons formed from molecules of the itself , their initial velocity must ) negligible , erefore the initial velocity of those the first inlum must similarly be igible , so that in helium the electrons may be takell as from aluminium cathode at rest , and the values of miniulum ionisation , velocity already evaluated that becon ) approximately absolute . Or.(frrenre of \mdash ; It was naturally expected this interesting phenomenon\mdash ; for which the Ilanle cathode dark space\ldquo ; has been suitably ) detected in other gases when the best conditions for its exhibition had been discovered . Up to the tinle of writing , however , not the slightest indication of it has been observed in air , nitrogen , oxygen , , or carbon monoxide . For this two explanations are ested if the theory given above is substantially correct , either\mdash ; ( i ) molecules of these ases 1 so low an ionisation energy that \ldquo ; is too small to be detected ; ( ii ) The electrons liberated the sulface of by the } ) 1907 . ] Cathode Dark Space ) and of positive ions of these ases stalt with sufficient velocity to ionise at their very outset , in which case the phenomenon would not exist at all . Some results obtained from observation of tho length of in mixtures of belium and , which require further investigation , show that the latter is the more In conclusion , I wish to express my heartiest thanks to J. H. for bis kind help and encoura ement t this research . Table I.\mdash ; Hydrogen . Table II.\mdash ; Helium . VPotential difference in volts between electrodes . Length of Crookes dark space in cm . Length of new dark space in cm . The pressures range in hydrogen from to mm. , in helium from to Bracketed measurements were performed at the same pressure .

rspa_1907_0073

0950-1207

On the presence of sulphur in some of the hotter stars.

50

56

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir Norman Lockyer, K. C. B., LL. D., Sc. D., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0073

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0073

10.1098/rspa.1907.0073

Atomic Physics

Astronomy

Atomic Physics

50 On the Presence of Sulphur in some of the Hotter Stars . By Sir Norman Lockyer , K.C.B. , LL. D. , Sc. D. , F.R.S. ( Received May 8 , \#151 ; Read June 20 , 1907 . ) [ Plate 2 . ] In connection with a particular study of the green region of stellar spectra , photographs of the spectra of several of the brighter stars have recently been obtained at Kensington , using the two 6-inch Henry prisms . An excellent photograph of the spectrum of Rigel is amongst those secured , and the increased dispersion available has afforded evidence which abundantly verified my previous conclusions as to the presence of sulphur in the hotter stars . With regard to the occurrence of sulphur , I stated in ' Inorganic Evolution/ p. 169 , " The evidence also suggests sulphur , and this is all the more probable because of the simplicity of its spectrum series/ ' In the course of the reduction to wave-lengths of the lines in this recent Rigel photograph , an isolated clearly defined line was found at about X 4815*7 , which had not been observed in any previously studied stellar spectra . Reference to Watts ' ' Index of Spectra ' showed that there was a strong line of sulphur close to that position recorded by Hasselberg . On referring to Eder and Valenta 's record* of the sulphur spectrum , a strong line was found of wave-length 4811*967 . This was so large a discrepancy from Hasselberg 's wave-length that a Kensington photograph of the spark spectrum of sulphur was examined , and a very strong and isolated sulphur line was found at X 4815*3 as nearly as could be estimated . It thus became fairly obvious that the wave-length 4811*967 given by Eder and Yalenta was , for some reason or other , in error . Dr. Eder was communicated with in reference to this line , with the result that he explained the discrepancy as being due to a clerical error in publishing the wave-lengths . It should have been 4814*967 . To test further whether there was a real identity between the stellar and the laboratory lines , the new Rigel spectrum was carefully examined in the region covered by the characteristic group of sulphur lines extending from X4142 to X4175 . It was found that there were stellar lines\#151 ; none of them very strong , but undoubtedly genuine\#151 ; agreeing , as nearly as could be estimated , with each of the members of that group . Other parts of the spectrum also showed lines in the position of other strong sulphur lines . In fact , there are only about three of the strongest sulphur lines , in the region * f Beitrage sir Photochemie und Spectralanalyse/ p. 282 , Vienna , 1904 . \#171 ; On the Presence of Sulphur i some of the Hotter Stars . 51 where a comparison is possible , which appear to be lacking in the stellar spectrum . These exceptions will be discussed later . The following table gives the wave-lengths of the strongest sulphur lines as measured from the Kensington photographs of the vacuum-tube and spark spectra , the vacuum-tube wave-lengths of the corresponding lines as recorded by Eder and Yalenta , and the wave-lengths and intensities of the Eigel lines which closely agree in position with the sulphur lines . For the sulphur lines beyond X 4553 , Eder and Yalenta 's wave-lengths of the vacuum-tube lines are used in the tables , as the existing Kensington photographs of the sulphur spectrum in that region are not of sufficient dispersion to furnish accurate reductions to wave-length . In the region 4100\#151 ; 4553 the Kensington reductions of the wave-lengths of the sulphur lines are given in the table for both vacuum-tube and spark spectra . The former were reduced by means of Hartmann 's formula from a photograph taken with the 3-inch Cooke spectrograph , the latter by a direct comparison of the Rowland grating spectra of the sulphur spark and the sun . The wave-lengths of the stellar lines were obtained in most cases by interpolation between lines whose wave-lengths are well known . Foi several of the fainter lines which would not stand magnification under the micrometer the wave-lengths were obtained as accurately as possible by direct comparison with a solar spectrum photographed with the same instrument . The stellar wave-lengths must be accepted as only provisional , but they are probably accurate within 0'3 tenth-metres . A comparison of the wave-lengths of the sulphur lines , as reduced from the spark spectrum and vacuum-tube spectrum respectively , shows that in nearly all cases the vacuum-tube wave-lengths are about 0'5 tenth-metres less than the spark wave-lengths . This has been pointed out before by Eder and Yalenta , * who give a photographic comparison of some of the stronger sulphur lines as they respectively occur in the vacuum-tube spectrum and the spark spectrum , and show that the sharply defined lines of the former occupy positions near the more refrangible edges of the diffuse lines of the latter . Notable exceptions to this , as was also pointed out by Eder and Yalenta , are the two strong lines at XX 4253'8 , 4285-1 which show practically no shift in passing from one spectrum to the other . These two lines occur quite prominently in all the Kensington spectra of sulphur , under whatever conditions they have been obtained , but they are of a different nature to the other strong sulphur lines , being far more compact and sharply defined . In Hagenbach and Konen 's record of the sulphur spectrum , the reproductions of their photographs show these lines as having far inferior intensity to those * ' Beitrage sir Photochemie und Spectralanalyse , ' Plate 15 , Vienna , 1904 . VOL. LXXX.\#151 ; A. E Table of the Strongest Lines of Sulphur and Lines in Eigel . Sir Norman Lockyer . On the Presence of [ May 8 , a O m o O m M '\#169 ; bD Id a -*S 3 ns \#163 ; \#169 ; o \#169 ; \#163 ; ^S's'a .a -S o e-'S fri-ali JSga g\#174 ; 1 ! M l 2 St=J H 03 -ft ^ \#163 ; \#171 ; 2 * *T 2 2 * 9 g gS'Sjj Siig.ts'i ^Jjlg S Bn o P\lt ; S GQ \#169 ; a bo P goo -s k\gt ; \#187 ; 0 Tj\lt ; 'gffi 15 3 S It O o3 PM " r\#151 ; | \#169 ; I =5* \#169 ; i =3 OQ cq co IH I I \lt ; M H H I Ol cq cq I CO H Tf H H I I 00 \gt ; D 1\gt ; 9 \lt ; D cq io co co Tft ^ ^ lO\#169 ; l\gt ; HHHHH Tft Tft Tft Tft Tft CO ID CO GO Oi^OtHt^ipp^OOOi rft lo cq toiot^TftiocqOTfi.t\gt ; -cq 05 cp oq \#187 ; o h h h cq cq 05 h h cq co \#163 ; 2312i2 \#163 ; ;2$\#163 ; 2 9 29999 Tft Tft Tft Tft TftTftTfl-rftTftTftlDiOlOO 08 \#166 ; s J \gt ; Vacuum tube . Int. Max. 10 . oo i\gt ; a \#169 ; i\gt ; 10 8 00 ID CO to TtfTftTftioCDlOCOOOTfioO Ti s * \#169 ; TS H * 4142 39 4145 -27 4153 27 4162 86 4174 -47 4253 -77 4285 -13 4294 *56 4464 -62 4525 *16 4552 *59 4716 -38 4814 -97 4917 -41 4924 -27 4925 49 4992 -15 5009 76 5014 -25 5027 -41 5032 -66 \#166 ; d Int. Max. 10 . *D CD 05 O t\gt ; 10 7 i\gt ; CD 1\gt ; | CQ \#169 ; .1 1 Pi l a 02 \lt ; 4143 -00 4145 -75 4153 -85 4163 -30 4174 -95 4253 -70 4285 -10 4295 *20 4464 *90 4525 *20 # P .S S Vacuum tube . Int. Max. 10 . CD lO CD 05 \#169 ; | ID 10 8 CD l\gt ; | Tft 1 Tft ID CD \lt ; 4142 -46 4145 *25 4153 *31 4162 -81 4174 -46 4253 *63 4285 03 4294 *61 4464 *67 4524 -95 4552 *53 rP \#169 ; 1tf\gt ; CO \#163 ; \#166 ; s a \#169 ; bfi .a c3 Tft \lt ; \lt ; P rP - 9 Pf\gt ; s po is CO 4 ) -SS .\amp ; a \#163 ; | J'Sb .+3 co .a 't i i ii \#169 ; C3 OQ \#169 ; d *1 i ? p \#169 ; 1*8 \#163 ; S H b\#163 ; I \#163 ; pq ^ II 1907 . ] Sulphur in some of the Hotter Stars . 53 of the same lines in the Kensington and Eder and Yalenta 's photographs . It seems fairly probable , then , that under certain conditions these sulphur lines disappear from the laboratory spectra , and that similar conditions pertain in the absorbing atmosphere of the star , in the spectrum of which the lines in question cannot be traced . Another line which is doubtfully present in the star is that at X 4295 . There are several weak lines in Rigel from about 4290 to 4303 , most of them probably due to proto-iron or proto-titanium , but the nearest to the wavelength of the sulphur line appears to be about 4294*3 . With the possible exception of line 4163*0 , none of the Rigel lines given in the preceding list is given by Pickering* in his record of lines in the stellar spectrum . He gives a line at 4163*9 and makes it identical with 4163*9 in \#171 ; Cygni . Comparison of the Kensington two-prism photographs of these two stellar spectra , however , shows most distinctly that they are not identical . The Rigel line is probably 4163*0 ( sulphur ) , that in \#171 ; Cygni undoubtedly 4163*9 ( proto-titanium ) . The following table contains the lines recorded by Keelerj* in the spectrum of Rigel in the region between Hp and D. He did not give any origins for the majority of the lines . The probable origins added to the table are suggested as a result of the Kensington investigations of the relation of the stellar lines to lines in terrestrial spectra . Rigel lines ( Keeler ) . Probable origin A of probable origin . ( Kensington ) . A. Remarks . 4861 H^ . Very strong . 4924 Fairly strong J Asterium \ Proto-iron 4922 -10 4924 *11 6016 Strong Asterium \ Proto-iron 5015 *73 5018 *63 5033 V ery weak Sulphur 5033 *0 5056 Weak Silicum ( Group II ) 5057 *0 5168 Fe ? Fairly strong Proto-iron 5169 *22 5316 Weak Proto-iron 5316 *79 5454 Weak Sulphur 5454 *0 5876 D3 . Very strong . 5890 ? 5896 ? j- Suspected . It will be seen that the only lines not traceable to elements which have\#151 ; from considerations of lines in other parts of the stellar spectrum\#151 ; been * ' Annals Harv . Coll. Obs. , ' vol. 28 , Part I , p. 79 . t ' Ast . and Ast . I'hys . , ' vol. 13 , p. 489 . 54 Sir Norman Lockyer . On the Presence of [ May 8 , found to be represented in the star are the two lines 5033 and 5454 . As there are , according to Eder and Yalenta , two strong sulphur lines at W 5032*66 and 5454*00 respectively , it would appear that this is genuine confirmatory evidence that sulphur is really represented in the Bigel spectrum . The line 5033 is well marked in the Kensington stellar spectrum , but Keeler 's line 5454 is beyond the region over which the Kensington photograph extends . There are several other strongly marked sulphur lines in the region 5400 to 5500 , and it is quite probable that if stellar photographs are obtained extending more into the yellow than the existing one , these lines will also be found to occur in the stellar spectrum . The best-marked Eigel lines which are probably due to sulphur have been looked for in the spectra of a Cygni and Sirius , which represent the next lower stage on the temperature classification . The lines cannot , however , be traced . If they do really exist in these spectra , they are so exceedingly faint \amp ; s to defy detection in the existing stellar photographs . In Bellatrix , however , representing a higher stage than Eigel , some of the stronger Eigel-sulphur lines , of which may be mentioned 4715*9 and 4815*7 , are certainly present , but not so well marked as in Eigel . A really successful photograph of the Bellatrix spectrum has not , however , been yet obtained with the two prisms , and it is expected that when one is obtained other sulphur lines will be traced . It has not yet been possible to investigate whether the lines occur at the Alnitamian stage , as no satisfactory spectrum of a star of this type has yet been photographed with two prisms . The excellent photograph of the Eigel spectrum in which the sulphur lines were traced was obtained by Mr. W. E. Eolston . The stellar lines were found , and their identity with the sulphur lines established , by Mr. F. E. Baxandall , who , with the assistance of Mr. H. E. Goodson , reduced the wave-lengths of the stellar and terrestrial lines . The photographs of the sulphur spectrum used in the discussion were taken by Mr. C. P. Butler . Mr. Baxandall has also taken part in the preparation of the paper . REFERENCE TO PLATE . I # Plate 2 shows the spectrum of Rigel , from X 4123 to X5075 . The stronger sulphur lines which occur in the spark are denoted by S. The origins and wave-lengths of several of the outstanding lines of the stellar spectrum are also indicated . An up-and-down positive was first obtained from the original negative , a direct negative then made from it , and from this a seven-times-enlarged positive print . The scale of the reproduction is about six times that of the original negative . Lockyer . Roy . Soc. Proc. , A. 80 , Plate 2 . Z9\#163 ; *l 1907 . ] Sulphur in some of the Hotter Stars . 55 [ Addendum , October 17 , 1907 . ] Since the foregoing paper was written , further facts have been obtained regarding the occurrence of sulphur lines in the hotter stars . In the paper it was mentioned that two strong sulphur lines of special behaviour , 4253*8 , 4285*1 , are lacking in the Rigel spectrum , in which the strongest ordinary spark lines occur . These two lines have since been found to exist in spectra representing higher stages of temperature than that of Rigel , such as 7 Orionis ( Crucian ) and e and k Orionis ( Alnitamian ) . Reference to Pickering's* records of stellar spectra shows that he also gives the lines in the stars named below , thus :\#151 ; Star ( Pickering ) . Type ( Kensington ) . A. Int. \#163 ; Centauri Crucian J4254*1 \ 4285 T 4 3 t Orionis Alnitamian J 4254 *1 \ 4285*1 3 2 7 Orionis Crucian / 4254 *1 \ 4285 *1 2 2 a Pavonis Crucian J 4254 *1 14285 *1 1 0 V . \#151 ; . It will be noticed that the relative intensity of the two lines is , in general , the same in the different stars , 4254*1 being the stronger . This agrees with their relative intensity in the sulphur spectrum itself . In a paper on " The Spectra of Silicon , Fluorine , and Oxygen/ ' Luntf records an oxygen line at 4254*22 , and associates it with a stellar line at the same wave-length . In the light of the other oxygen lines occurring in the Crucian and Alnitamian stars , the stellar line in question is too strong to be accounted for solely by the oxygen line , which is relatively weak . The true origin is far more likely to be sulphur , especially as the line is generally accompanied by 4285*1 , which cannot be attributed to oxygen . In fact , the two stellar lines under discussion cannot be satisfactorily explained by reference to the lines of any of the other elements already shown to be represented in Crucian and Alnitamian stars . These are helium , hydrogen , silicium , calcium , magnesium , oxygen , nitrogen , and carbon . As these sharply-defined lines in the sulphur spectrum decrease in intensity , relatively to the diffuse lines , when self-induction is introduced , we should expect them to appear at a higher level of stellar temperature than the set of sulphur lines which appears in Rigel ( in which star , it must be remembered , the sharp lines are missing ) . The fact , therefore , that there are * ' Annals Harv . Coll. Obs./ vol. 28 , Part II , p. 236 . t ' Annals of the Cape Observatory/ vol. 10 , p. 33 B. 56 Note on the Association of Helium and Thorium in Minerals . corresponding lines in the Crucian and Alnitamian stars , which come higher up the temperature curve than the Eigelian , seems to leave no doubt as to the genuineness of the identification . The Eigelian group of sulphur lines has not been detected in e Orionis , though one or two of the strongest lines have been traced in the best Kensington spectrum of Bellatrix ( Crucian ) . The following represents the relative and inverse behaviour of the two sets of lines in stellar spectra . Group . Type star . Sharp lines ( 4254 , 4285 ) . Diffuse lines . Alnitamian e Orionis Well shown Absent Crucian 7 Orionis Present , but weaker than in \#171 ; Orionis Strongest lines present , but weaker than in \#163 ; Orionis Eigelian )3 Orionis Absent Well shown Note on the Association of Helium and Thorium in Minerals . By the Hon. E. J. Strutt , F.E.S. ( Eeceived September 10 , \#151 ; Eead November 7 , 1907 . ) The question has been often raised of whether or not helium is a product of thorium radio-activity . My own view throughout has been that it is.* * * S Mr. Boltwood has recently argued that the helium in radio-active minerals may always be attributed to the action of the uranium-radium series of transformations.*)- I wish in the present note to draw attention to a case where that view is clearly untenable . Prof. Julius Thomsen , of Copenhagen , described , in 1898 , j a helium mineral from Ivitgut , Greenland , similar in some respects to fluor spar , but containing rare earths . Eecently he has determined the quantity of helium liberated on heating as 27 c.c. per kilogramme . S Prof. Thomsen kindly sent me a supply of this mineral . I have carefully tested it for radium , and find that it contains no more than the traces which are ubiquitous in rocks and minerals . The quantity found was , in fact , about * 'Boy . Soc. Proc./ vol. 73 , p. 191 , 1904 , also March 2 , 1905 . t ' Am . J. Sci./ vol. 23 , February , 1907 , p. 77 . t ' Zeits . Physikalische Chemie/ vol. 25 , part 3 . S 'Bull , de l'Acad . Boyale des Sciences , Copenhagen/ 1904 , 53\#151 ; 57 .

rspa_1907_0074

0950-1207

Note on the association of helium and thorium in minerals.

56

57

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

the Hon. R. J. Strutt, F. R. S.

article

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http://dx.doi.org/10.1098/rspa.1907.0074

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0074

10.1098/rspa.1907.0074

Atomic Physics

Thermodynamics

Atomic Physics

56 Note on the Association of Helium and Thorium in Minerals . corresponding lines in the Crucian and Alnitamian stars , which come higher up the temperature curve than the Eigelian , seems to leave no doubt as to the genuineness of the identification . The Rigelian group of sulphur lines has not been detected in e Orion is , though one or two of the strongest lines have been traced in the best Kensington spectrum of Bellatrix ( Crucian ) . The following represents the relative and inverse behaviour of the two sets of lines in stellar spectra . Group . ! Type star . Sharp lines ( 4254,4285 ) . Diffuse lines . Alnitamian a Orionis Well shown Absent Crucian y Orionis Present , but weaker than in e Orionis Strongest lines present , but weaker than in p Orionis Eigelian P Orionis Absent Well shown Note on the Association of Helium and Thorium in Minerals . By the Hon. R J. Strutt , F.RS . ( Received September 10 , \#151 ; Read November 7 , 1907 . ) The question has been often raised of whether or not helium is a product of thorium radio-activity . My own view throughout has been that it is.* * * S Mr. Boltwood has recently argued that the helium in radio-active minerals may always be attributed to the action of the uranium-radium series of transformations.-}- I wish in the present note to draw attention to a case where that view is clearly untenable . Prof. Julius Thomsen , of Copenhagen , described , in 1898 , a helium mineral from Ivitgut , Greenland , similar in some respects to fluor spar , but containing rare earths . Recently he has determined the quantity of helium liberated on heating as 27 c.c. per kilogramme . S Prof. Thomsen kindly sent me a supply of this mineral . I have carefully tested it for radium , and find that it contains no more than the traces which are ubiquitous in rocks and minerals . The quantity found was , in fact , about * 'Roy . Soc. Proe./ vol. 73 , p. 191 , 1904 , also March 2 , 1905 . f ' Am . J. Sci./ vol. 23 , February , 1907 , p. 77 . J ' Zeits . Physikalische Chemie/ vol. 25 , part 3 . S ' Bull , de l'Acad . Royale des Sciences , Copenhagen/ 1904 , 53\#151 ; 57 . On Temperatures in the Cylinder of a Gas Engine . 57 the same as in average rocks , and is insufficient to account for one-hundredth part of the helium present . On the other hand , a solution of the mineral gave abundant thorium emanation . I am inclined to think that there is some unknown complicatior about the thorium-emanating power of solutions , which makes it unsafe , in certain cases at least , to infer from it the quantity of thorium present . But enough thorium emanation was given off by the solution to show that thorium was a substantial constituent of the mineral . I regard it as entirely certain that the helium in this mineral has not been generated in situ by uranium or radium , and have no hesitation in connecting it with the presence of thorium . On the Measurement of Temperatures in the Cylinder of a Gas Engine . By Professor H. L. Callendar , F.R.S. , and Professor W. E. Dalby , M.A. , M.Inst . C.E. ( Received October 8 , \#151 ; Read November 7 , 1907 . ) 1 . Introductory.\#151 ; It is important in the experimental investigation of the internal combustion engine to be able to measure directly the temperature of the working fluid at some point of the cycle . If the temperature at a suitable point of the cycle is known , the laws of gases enable us to calculate the temperature at any other point during compression and expansion from the indicator diagram on the assumption that the mass remains constant and that the molecular change occurring in combustion is known . The method usually employed has been to estimate the temperature at the beginning of compression ( the temperature at this point is sometimes referred to as the " suction temperature " ) by computing the total mass of the cylinder contents at this point from a knowledge of the gas and air supply and an estimate of the temperature and mass of the contents of the clearance space . But this is an indirect and troublesome method , and some of the data required are extremely uncertain . Direct measurements of the temperature in the cylinder under working conditions have hitherto failed for various reasons . Professor F. W. Burstall* was the first to employ the platinum thermometer for this purpose . He used wires 0'0025 and 0 0015 inch in diameter , and obtained a good deal of valuable information from his experiments , but he * 'Phil . Mag. , ' June , 1895 .

rspa_1907_0075

0950-1207

On the measurement of temperature in the cylinder of a gas engine.

57

74

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Professor H. L. Callendar, F. R. S.|Professor W. E. Dalby, M. A.

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http://dx.doi.org/10.1098/rspa.1907.0075

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0075

10.1098/rspa.1907.0075

Measurement

Thermodynamics

Measurement

On Temperatures in the Cylinder of a Gas Engine . 57 the same as in average rocks , and is insufficient to account for one-hundredth part of the helium present . On the other hand , a solution of the mineral gave abundant thorium emanation . I am inclined to think that there is some unknown complicatior about the thorium-emanating power of solutions , which makes it unsafe , in certain cases at least , to infer from it the quantity of thorium present . But enough thorium emanation was given off by the solution to show that thorium was a substantial constituent of the mineral . I regard it as entirely certain that the helium in this mineral has not been generated in situ by uranium or radium , and have no hesitation in connecting it with the presence of thorium . On the Measurement of Temperatures in the Cylinder of a Gas Engine . By Professor H. L. Callendar , F.R.S. , and Professor W. E. Dalby , M.A. , M.Inst . C.E. ( Received October 8 , \#151 ; Read November 7 , 1907 . ) 1 . Introductory.\#151 ; It is important in the experimental investigation of the internal combustion engine to be able to measure directly the temperature of the working fluid at some point of the cycle . If the temperature at a suitable point of the cycle is known , the laws of gases enable us to calculate the temperature at any other point during compression and expansion from the indicator diagram on the assumption that the mass remains constant and that the molecular change occurring in combustion is known . The method usually employed has been to estimate the temperature at the beginning of compression ( the temperature at this point is sometimes referred to as the " suction temperature " ) by computing the total mass of the cylinder contents at this point from a knowledge of the gas and air supply and an estimate of the temperature and mass of the contents of the clearance space . But this is an indirect and troublesome method , and some of the data required are extremely uncertain . Direct measurements of the temperature in the cylinder under working conditions have hitherto failed for various reasons . Professor F. W. Burstall* was the first to employ the platinum thermometer for this purpose . He used wires 0'0025 and 0 0015 inch in diameter , and obtained a good deal of valuable information from his experiments , but he * 'Phil . Mag. , ' June , 1895 . 58 Profs . Callendar and Dalby . Measurement of [ Oct. 8 , did not succeed in measuring the temperature under ordinary working conditions . In his latest report* he says:\#151 ; " All attempts to use these wires with an engine firing at every second revolution resulted in the destruction of the wire before a sufficient number of observations could be taken . The temperatures have , therefore , been measured on an engine running dead light , that is firing about one in six of the possible explosions . " These conditions are quite abnormal , and the results from these experiments cannot , therefore , throw much light on the question of the temperatures corresponding to full load conditions."]* Professor B. Hopkinsonf has recently suggested that the suction temperature might be measured with a wire sufficiently thick to withstand the explosion temperature without melting , and has developed an ingenious method of correcting the indications of a thick wire so as to deduce the temperature of the gas in the cylinder . The method of correction , though somewhat elaborate , appears to have been satisfactory for temperatures up to 300 ' C. , but his final conclusion is as follows:\#151 ; " The large size of the wire ( namely , 0'004 inch ) was chosen because it was intended ultimately to use it for measuring the suction temperature when the engine was working in the ordinary way , taking in and firing a charge of gas . But it was found that even this large wire always fused before any observations could be taken . A still thicker wire might of course have been used for the purpose , but the correction would then have been so great as to make the results valueless . " 2 . Method employed by the Authors.\#151 ; In order to avoid troublesome and uncertain corrections , it is necessary that the wire employed should be fine enough to follow the changes of temperature of the gas very closely during suction and compression . To employ such a wire in the cylinder under working conditions , it is further necessary that it should be perfectly screened from the flame during explosion , Any apparatus for the introduction and withdrawal of the thermometer must be such as not to make any change in the usual form and extent of the clearance surface during the time interval comprising the end of compression . Otherwise the normal conditions of working would be changed , and a risk of pre-ignition would be introduced . The arrangement used by the authors was designed to satisfy these conditions . The thermometer was contained in a small valve ( T , fig. 1 ) , called the * ' Proc. Inst. Mech. Eng. , ' October , 1901 , p. 1050 . + The mixtures used were very weak , being one of gas to 12 of air , and the correction for radiation , error at the maximum temperatures is very large . J 'Phil . Mag. , ' January , 1907 . Temperatures in the Cylinder of a Gas Engine . thermometer valve , inserted through the spindle of the admission valve A , which was bored out to receive it . The admission valve casting C is shown detached from the engine cylinder , and the thermometer valve T is shown R / P T open to its fullest extent , the maximum lift being T5 inches . The head W of the valve T has a seating in the head of the admission valve A. The valve T is closed by a spring U , shown in compression , acting on a nut X. The thermometer leads are enclosed in a brass tube B fitting inside the spindle of the valve T. The tube can be inserted or withdrawn without dismounting the valve . It is held in place by a collar D which is screwed home against the nut N. The platinum wires forming the thermometer are seen at P. The head W of the valve T is connected to the tube forming the spindle by the two ribs R and R , which are made as thin as possible in order to leave the platinum wires freely exposed to the gas when the valve is pushed in . Two views of the combined admission and thermometer valves are shown in figs. 2 and 3 reproduced from photographs , fig. 2 showing the thermometer valve opened to its fullest extent , fig. 3 showing it closed . The gear for operating the thermometer valve is shown diagrammatically in fig. 4 . A fixed casting F carries a shaft Q , to which is keyed a long lever L , and a short lever i. The short lever ends in a roller which is held up by a spring against the cam E , keyed to the lay shaft of the engine . The end of the long lever L acts on the nut N at the end of the thermometer valve T , and is forked so as to clear the brass tube B of the thermometer . The end of the lever operating the admission valve A is similarly forked to clear the thermometer valve T. Any desired timing of the exposure of the thermometer valve T in the cylinder may be obtained by adjusting the form Profs . Callendar and Dalby . Measurement of [ Oct. 8 , LAY SHAFT OF GAS ENGINE . ^7/ 77777777777777777 " 1907 . ] Temperatures in the Cylinder of a Gas Engine . and position of the cam E. In the gas trials described below the thermometer valve was arranged to open during suction and close towards the end of compression . 3 . The Platinum Thermometers.\#151 ; The platinum thermometers and accessory apparatus for observing the temperatures were similar to those employed by Callendar and Nicholson in their experiments on the steam-engine , * but the thermometers were of somejvhat simpler construction , since they were not required to be exposed to high pressures or temperatures . The leads were a pair of twin wires , insulated with rubber and cotton , and were fixed gas tight in the brass containing tube . The projecting ends of the copper leads were held in place with mica washers . A loop of platinum wire , 0001 inch diameter and 1 inch long , was soldered to the ends of the thermometer leads . The ends of the compensator leads were similarly connected by a loop of the same wire , $ inch long . The thermometer and compensator were connected to opposite sides of the Wheatstone bridge , so that the bridge reading gave the difference of resistance between them , corresponding to the resistance of the middle -S . inch of the thermometer loop . This provision of a compensating loop has often been overlooked , but is most essential when using short loops of fine wire for the measurement of rapidly varying temperatures . The ends of the fine wire loops close to the leads are affected by conduction of heat to or from the leads , and cannot follow the rapid variations of temperature ; but the end effect is eliminated by observing the difference between two loops of different lengths . The lengths of the loops were chosen so as to give with the wire actually employed a change of resistance of 1 ohm approximately for 100 ' C. Shorter lengths might have been employed without material reduction of sensitiveness , but the above lengths were found to be sufficiently stiff to stand the commotion in the cylinder satisfactorily for long periods . After each run the thermometer was removed and placed in a tube in a vessel of water . Its resistance was then measured at the temperature of the laboratory , in order to test for variations of the zero . It was found that the zero was generally raised after a run of half an hour or so by about one-fifth of a degree C. , owing to slight strain or distortion of the wire ; but it was easy to take account of these small changes , which would not , if neglected , however , have materially affected the accuracy of the measurements . The current employed in measuring the resistance was about the 1 / 200 part of an ampere . The heating effect of this current on the thermometer was measured and found to be less than a quarter of a degree C. The same current was employed in determining the fundamental interval of the thermometers . The heating effect could be safely neglected , as it was nearly * ' Proc. Inst. C.E. , ' 1898 . 62 Profs . Callendar and Dalby . Measurement of [ Oct. 8 , constant and would not produce an error greater than one-twentieth of a degree C. Owing to slight changes in temperature from stroke to stroke during the working of the gas engine , the mean temperature at any part of the cycle could rarely be observed with an approximation closer than 1 ' . As the temperatures to be observed were about 100 ' C. , no great refinements in testing the wire were required . 4 . The Periodic Contact-maker and the Electrical Connections.\#151 ; In order to observe the temperature at a definite point in the cycle , a periodic contact-maker was inserted , either in the galvanometer or in the battery circuit , and was set to close the circuit at the desired point . In this method errors may arise from thermo-electric or induction effects . Both effects were practically negligible with the apparatus employed , but the thermo-electric effects were rather larger and more variable than the induction effects . The periodic contact was , therefore , usually connected in the battery circuit , so as to eliminate the thermo-electric effects . The electrical connections , including the periodic contact-maker , are shown in fig. 5 . In this diagram PS , QS are .AY SHAFT W*\#163 ; A/ CW\#163 ; Clamping Scppn the equal ratio arms of the Wheatstone bridge . The galvanometer G is connected to the point S and to the sliding contact on the bridge wire BW . The thermometer and its leads P are connected on one side of the bridge wire , and the compensator C and the balancing resistance B on the other . The battery circuit includes a mercury reversing key K , an adjustable resistance r , and a storage cell Y ; and the battery is connected to the bridge at the points P and Q , and to the brushes of the periodic contact-maker at E. The brushes E are carried by an insulated arm A bolted to a divided disc 0 1907 . ] Temperatures in the Cylinder of a Gas Engine . riding loosely on the lay shaft of the engine , and capable of being clamped in any position by the screw L. The index I shows the crank angle , corresponding to the middle point of the contact when the insulated copper strip D carried in the fibre bush F passes under the brushes . 5 . Percussion Contact-maker.\#151 ; The common form of wipe-contact-maker illustrated in fig. 5 was employed in the earlier experiments , but was found to possess certain disadvantages . The contact was difficult to keep clean and the timing was liable to vary with speed and wear . The duration of contact could not be readily adjusted or accurately verified . In the later experiments a novel form of contact was adopted which appeared to be free from these defects . The construction of this contact-maker is illustrated in fig. 6 . A brass bush B keyed to the lay shaft of the engine carries two fibreRED E/ B / /VSL/ LRT/ OH INDEX LAY S , LCehtre L\e OR Ci/ J*1 R/ /v$ SCsZeuy See Re 5 washers or cams Wi and W2 which can be clamped in any relative angular position against the flange of the bush by the nut FT . A radial step , as u\ , is made in each washer and the surface gradually rises from the bottom of the step to the normal circular surface of the washer . The brushes of the wipe-contact are replaced by stiff springs Si and S2 , the reflexed ends of which 64 Profs . Callendar and Dalby . Measurement of [ Oct. 8 , rest on the fibre cams . A projection Z carrying a platinum-pointed screwy is riveted to one of the springs and the screw is adjusted so that its point is just clear of the platinum rivet r in the other spring when both springs are riding on the circular surfaces of their respective cams . Contact is made when the rotation of the lay shaft in the direction of the arrow brings the radial step Wiof the cam Wi under the spring Si , thereby allowing it to fall down the step , thus bringing p and r together . Contact is broken when the radial step v-2 of the cam W2 reaches the spring S2 , thereby allowing the second spring to fall down the step w2.The epoch and duration of contact are readily adjusted by adjusting the angular positions of the cams relatively to the bush and also with regard to one another . The distance between the springs and the platinum contacts and the steps w are exaggerated in the diagram in order to make the principle of the apparatus clear . The percussion form of contact with platinum points was found to give more definite and certain results than the wipe pattern . It always kept itself clean , and no trouble of any kind was experienced with it . The duration of contact was generally adjusted to correspond with 20 degrees of the crank angle or 1/ 36 part of a revolution of the lay shaft . 6 . General Arrangement of the Engine.\#151 ; The only engine immediately available for the purposes of the tests was a 10 H.P. Crossley , forming part of the laboratory equipment of the Central Technical College , with a cylinder 7 inches bore and 14 inches stroke , the compression ratio being 4-68 . It was not quite the latest pattern , but was in very good condition and well suited for testing the application of the method . It had porcelain tube ignition . It was directly connected to a four-pole dynamo of 8 kw . capacity , mounted on the same shaft . This arrangement was particularly advantageous , as it permitted the engine to be run under widely varying conditions of speed and load . For measuring temperatures by the periodic contact method , it is most important that the cycle of operations should be perfectly regular , and that there should be no missed explosions ; otherwise it is impossible to take readings accurately , owing to the wide variations of temperature from stroke to stroke . With this object , the governor was disconnected , and the gas-admission valve arranged to open at every suction stroke . The field of the dynamo was separately excited , and the load taken by adjustable wire resistances , so that the engine could be made to run quite steadily at low speeds if desired . By a slight alteration in the electrical connections it was possible to supply the dynamo with current from the external lighting system , and employ it to drive the engine . This was required in some trials made for the purpose of testing the sensitiveness of the thermometers . 7 . Indicator Diagrams.\#151 ; When running the engine with rich mixtures , the 1907.J Temperatures in the Cylinder of a Gas Engine . 65 rapidity of the explosion was so great that satisfactory diagrams could not be obtained with the ordinary piston type of indicator . The sudden rise of pressure caused violent oscillations of the pencil , which continued throughout the stroke and made accurate readings impossible . For this reason , an optical indicator , or " manograph , " of the Carpentier type was employed , with some modifications suggested by previous experience . In this instrument the pressure acts upon a steel disc or diaphragm , the movement of which is transmitted to a short optical lever , which carries a mirror reflecting a spot of light on to a photographic plate . The lever is pivoted on a fixed point and has a second arm at right angles to the first , which simultaneously receives a movement corresponding with the movement of the piston . I his manograph was originally intended for taking diagrams from small high-speed motors with closed crank-chambers . It was supplied with a long , fine copper tube , for connecting the disc chamber to the cylinder , and with a long , flexible coupling to be attached to the crank-shaft , the rotation of which was made to reproduce the motion of the piston by means of a small crank actuating the arm of the optical lever . In adapting the manograph to the gas engine , we found it more convenient to dispense with these connections , which were a source of inaccuracy . The disc chamber was screwed directly on to the indicator cock of the engine . In the earlier experiments the piston motion was obtained from a sprocket wheel on the lay shaft , but later it was reproduced directly by means of a lever driven by a cord attached to the usual indicator rig connected to the piston of the gas engine . Fig. 7 shows the optical indicator in place , and also the sprocket wheel and band driving from the lay shaft . The figure shows incidentally also the general arrangement of the gear for working the admission and the thermometer valves , and the disc and contact-maker on the lay shaft , the details of which have already been illustrated diagrammatically in figs. 4 and 5 . As the pressure scale given by a plane disc is not one of equal parts , and is liable to vary slightly with slight differences in the clamping of the disc , the scale of the indicator was calibrated on each occasion in its actual position on the engine . A gas bottle and a standard pressure gauge were connected to the blow through hole of the indicator cock , and lines were traced on the photographic plate corresponding to equal intervals of pressure , and also lines at right angles to these corresponding to equal displacements of the piston . By using a grill prepared in this manner for measuring the diagrams , errors due to the variation of the pressure scale , or inaccuracy in the reproduction of the piston motion , are practically eliminated . By using discs of different thicknesses , or by different combinations of discs , a considerable range of pressure could be covered with 66 Profs . Callendar and Dalby . Measurement of [ Oct. 8 , satisfactory accuracy . For the lower pressures , and for the tests in which the engine was driven by the electric motor without firing , a steam engine indicator of the Crosby pattern was also employed . This indicator was calibrated by weights placed upon a revolving plunger of known area , and Fig. 7 . was found to be correct and to agree with the optical indicator in those tests in which diagrams were taken with both instruments . 8 . Testing the Platinum Thermometers for Lag.\#151 ; It was well known from previous experiments that a platinum wire , 0'001-inch diameter , was capable 1907 . ] Temperatures in the Cylinder of a Gas Engine . of following the cyclical variation of temperature of a gas during suction and compression with sufficient accuracy for the determination of the suction temperature , but it appeared desirable to measure the lag of the thermometer at various speeds under these conditions , and to test whether a thermometer inserted in the manner already described could be relied upon to give the average temperature of the mixture in the cylinder , and how far its readings might be affected by the temperature of the valve in which it was enclosed . For this purpose the engine was driven by a motor , compressing and expanding a charge of air without firing . Temperature readings were taken throughout the cycle for comparison with the mean temperatures deduced from the indicator diagrams . Two thermometers were employed which differed slightly in the disposition of the platinum loop . In the first , designated Pti , the fine loop was attached in the usual maimer , projecting beyond the ends of the leads . In the second , designated Pt2 , the copper leads were made somewhat longer , and the platinum loop was inverted so as to lie between the leads . It was thought that with this latter method of construction the fine wire loop would be better protected from accidental damage in inserting or withdrawing the thermometer , and would be better able to withstand the shock of opening or closing the thermometer valve . This proved in fact to be the case . It was found , however , that the projecting loop Pti suffered very little distortion , and that although the thermometers agreed very well on the readings of the suction temperature , the readings of Pt2 were appreciably affected by the close proximity of the leads to the fine wire , when the difference of temperature between the leads and the surrounding gas was considerable . Two kinds of motor-driven tests were made . In the first kind the gas-cock was shut and the valves were worked in the usual way , so that a fresh charge of air was taken in and compressed during each cycle . In the second kind the gas-cock was shut , the valve levers were removed , and the thermometer valve was fixed permanently open with the gas admission valve permanently closed , and the tension of the exhaust valve spring was relaxed so as to allow it to act as a non-return valve for admitting a little air to the cylinder to compensate for leakage at the end of each suction stroke . Under these conditions the piston expands and compresses a practically constant charge of air at each revolution , and there is little or no disturbance due to the opening and closing of valves . This made it possible to secure a more accurate comparison of the thermometer with the indicated temperatures throughout the cycle , and to obtain a more satisfactory estimate of the lag . With the valves opening and closing in the VOL. LXXX.\#151 ; A. . F Profs . Callendar and Dalby . Measurement of [ Oct. 8 , ordinary way the cycle occupies two revolutions , and the readings of the thermometer from stroke to stroke are appreciably disturbed by slight variations in the opening and closing of the valves . Moreover , the mass of air contained in the cylinder is constant only for a part of each alternate revolution , so that the comparison with the indicator cannot be extended satisfactorily throughout the cycle . 9 . Comparison of the Temperatures recorded the Thermometer with the Temperatures calculated from the Indicator Diagram.\#151 ; The comparison in the case of the first method of working , namely , valves opening and closing in the usual way , is made in fig. 8 . The broken line represents the reading Fig. 8.\#151 ; Crank Angle from beginning of Suction Stroke . of the platinum thermometer Pti in degrees Centigrade , plotted with reference to crank angle during the compression and expansion strokes . The full line represents the temperatures deduced from the corresponding indicator diagram by calculating the product PY for the period during which the mass of air enclosed remained sensibly constant . The average speed in this trial was 102 revolutions per minute . An appreciable leakage or loss of heat takes place during the period of maximum compression , so that the compression and expansion curves are not exactly superposed on the card , but each is sensibly adiabatic , following the law PY1-4 = a constant within the limits of error of the pressure measurements . It would make very little difference to the form of the curve between 260 degrees and 460 degrees of crank angle if the temperatures at each point were calculated from the pressures alone ( instead of from the product PV ) , assuming the adiabatic law f ? 1,4/ ^0-4 = a constant . The temperatures on the PY curve are calculated on the assumption that the mean temperature of the charge ' is given correctly by the platinum thermometer at 260 degrees of crank angle . It will be observed that the Pt curve is not quite 1907 . ] Temperatures in the Cylinder of a Gas Engine . 69 symmetrical with the PV curve , the lag appearing greater during compression than during expansion . This may have been caused by some peculiarity in the direction of the currents of air in the cylinder with reference to the position of the ribs of the thermometer valve during compression . The thermometer valve was fixed in this experiment with one of the ribs vertically over the other , so that the opening through the valve might be horizontal or parallel to the axis of the cylinder . During expansion , when the turbulent motion of the air due to admission had subsided , the motion is probably parallel to the axis of the cylinder and the lag of the thermometer is seen to be very small . The PIE and Pt curves reunite towards the end of expansion . It was observed in another experiment that the effect of turning the thermometer valve through a right angle , so that the ribs should not obstruct the air current , was to raise the maximum indication 10 ' C. The reading at the lowest point corresponding with the suction temperature was not appreciably affected by the position of the thermometer valve . In a repetition of this test with the thermometer Pt2 having the inverted loop , it was found that the close proximity of the copper leads to the fine wire raised the readings of the suction temperature 2 ' to 3 ' C. and lowered the reading of the maximum temperature nearly 20 ' C. It may be inferred from this test that a thermometer of the type Pti with a projecting loop may be trusted to give the suction temperature with an approximation of 1 ' C. , in spite of the presence of the enclosing valve , providing that the temperature of the valve does not differ greatly from that of the mixture in the cylinder . When the temperature is changing most rapidly and the temperature of the valve differs nearly 200 ' from that of the air , the thermometer lags only 20 ' and a change in the position of the ribs of the thermometer valve does not affect the readings by more than 10 ' C. The comparison in the case of the second method of working , in which the valves are continuously closed , is illustrated in fig. 9 . This method promised to afford a more accurate method of testing the thermometer owing to the greater steadiness of the conditions , which permitted more accurate readings of the temperature . Some unexpected difficulties were encountered owing to the presence of small quantities of water , resulting from the formation of fog , but the observations were in many respects instructive , and may be worth recording as additional evidence . The quantity of water required to saturate the clearance space at a temperature of 100 ' C. was only OD03 of a pound . Nearly half of this quantity was found to have accumulated in some of the experiments , which afforded an interesting study in the adiabatics of fog . The effect of the formation of fog is very greatly to reduce the range of temperature for a given range of pressure , and the presence of water must , Profs . Callendar and Dalby . Measurement of [ Oct. 8 , therefore , be carefully avoided in this method of testing a platinum thermometer . In the test reproduced in fig. 9 , the air in the cylinder was sufficiently dry for the calculation of the temperatures from the card by the PY method . The compression and the expansion curves were very nearly symmetrical and adiabatic . The motion of the air in the cylinder was parallel to the axis in both , and the PY and Pt curves were approximately symmetrical . The lag was greater than in fig. 8 , partly owing to the higher speed ( 130 revolutions per minute ) , but partly also due to the more quiescent Fig. 9.\#151 ; Crank Angle from beginning of Suction Stroke . state of the air in the cylinder . The range of temperature with Pti was from \#151 ; 6 ' to +159 ' C. , as against\#151 ; 10 ' to +173 ' C. , calculated from the card . It must be remembered , however , that there was probably a snow fog in the cylinder at \#151 ; 10 ' , which throws some doubt on the accuracy of the PY curve and would account for part of the lag of the thermometer owing to condensation on the wire . Also that an error of 1/ 1000 of an inchin measuring the card would make an error of 1 ' of temperature in the PY curve at this point . The range given by the inverted loop thermometer Pt2 in this test was from 0 ' C. to 142 ' C. , being reduced by the proximity of the wire leads , the temperature of which was approximately 50 ' C. The experiment was repeated with and without the thermometer valve in place . The presence of the valve lowered the reading of the platinum thermometer about 10 ' C. at the point of maximum temperature when the ribs were placed in the horizontal plane so as to obstruct the flow of the air through the aperture , but it did not make any appreciable difference when the aperture was horizontal . 10 . Suction Temperature in Gas Trials.\#151 ; A number of trials were run under various conditions of speed and load , and gas supply , with the engine driving the dynamo in the ordinary way . Por these trials the thermometer 1907 . ] Temperatures in the Cylinder of a Gas Engine . valve was adjusted to open about the middle of the suction stroke , and close soon after the middle of the compression stroke . The temperatures were observed at the end of the suction stroke , and just after the closing of the admission valve . An observation was also taken at the end of the compression stroke when the thermometer valve was closed in order to give the temperature of the valve itself . The suction temperature was found to vary with the conditions of running from about 95 ' C. on light load trials to about 125 ' C. at maximum load , the air temperature being in all cases nearly 20 ' C. , and the jacket temperature 27 ' C. It should be remembered that in all these trials an explosion occurred at every second revolution , that is , there were no misses , the governor being entirely cut out . The trials were not , however , sufficiently extended to show the dependence of the suction temperature on the various conditions of load and speed and gas supply and jacket temperature . For the present the authors must content themselves with giving an illustration of the method of calculation they propose , reserving further discussion until more complete data are available . The most interesting of the trials from a theoretical point of view are those with rich mixtures in which combustion is practically complete at constant volume and the diagram conforms most closely to the theoretical type . A typical example is shown in fig. 10 , taken from trial 26 , photo 62 . Six consecutive explosions , photographed on the same plate , were practically identical . The following are the data of this trial:\#151 ; Ee volutions per minute , 130 ; Eatio of gas to air , 1 to 7'1 ; Atmospheric temperature , 20 ' C. ; jacket temperature , 27 ' C. ; Temperature of thermometer valve at 360 degrees crank angle , 122 ' C. ; Temperature of mixture in cylinder at 260 degrees crank angle , 111 ' C. ; Pressure in pounds per square inch absolute at 260 degrees crank angle , 18*5 ; Volume of mixture at 260 degrees crank angle , 0*2846 cubic feet . In calculating the temperatures along the expansion line , it is assumed that combustion is complete , and that the gases have undergone a molecular contraction , depending upon the richness of the mixture and the composition of the gas , which in this case amounts to 4*3 per cent. To find the temperature at any point in the expansion curve it is only necessary to divide the product of the pressure and volume at that point by the constant 0*01315 , representing the observed value of the product at the point corresponding to 260 degrees crank angle corrected for contraction . The resulting curve of temperature is shown in the upper part of the diagram ( fig. 10 ) . The temperature thus calculated is the apparent or effective Profs . Callendar and Dalby . Measurement of [ Oct. 8 , temperature , and includes the effect , if any , of dissociation . By comparing and analysing such curves it may be possible to deduce important relations bearing on the phenomena of combustion of gaseous mixtures . The curve shown in the diagram exhibits a marked change of curvature at 04 of the I ooo o 2 + 6 8 10 Fig. 10.\#151 ; Trial 26 . Diagram Photo 62 . o z t ifi 0 z \#163 ; $ t t F Ll 0 Hi i vO stroke , and becomes nearly straight . A peculiarity of this kind might be due to some imperfection of the indicator , but it might also imply a further stage in the combustion . Without an exact knowledge of the suction temperature it would be impossible to investigate such points satisfactorily . By a curious coincidence a diagram ' taken in another trial , fig. 11 , trial 4 , \#163 ; A- \amp ; 8 lO Fig. 11.\#151 ; Trial 4 . Diagram Photo 9 . j ) z i tii 0 H ID $ if O 1907 . ] Temperatures in the Cylinder of a Gas Engine . photo 9 , with a different ratio of gas to air , namely 1 to 5'8 , gave a practically identical expansion curve , not differing by more than 1 pound at any point from the curve of the preceding example recorded on photo 62 . The mean pressures deduced from the brake horse-power were also very nearly identical . Without a knowledge of the suction temperature it might be inferred that the two trials were really identical and that some mistake had been made in the gas measurements . The data for this trial are as follows:\#151 ; Revolutions per minute , 114 . Ratio of gas to air , 1 to 5*8 . Atmospheric temperature , 21 ' C. Jacket temperature , 27 ' C. Temperature of mixture at 260 degrees crank angle , 130 ' C. , and pressure 17'8 lbs. per square inch absolute . Molecular contraction on combustion , 5*1 per cent. The constant for calculating the temperature along the expansion curve comes out ( H)1195 in place of O01315 , and the temperatures are all much higher , as they should be with a richer mixture . The temperature curve in fig. 11 shows the same curious anomaly as that from photo 62 in fig. 10 , although the diagram was taken with a different disc having a different pressure scale , and with an entirely different arrangement of indicator gear , the piston motion being transmitted from the lay shaft in the way shown in fig. 7 , instead of being taken direct from the usual indicator rig as was the case in Experiment 26 . 11 . Conclusions.\#151 ; It appears probable from these experiments that the temperature of the thermometer valve never differs very much from the temperature of the gases shortly after the closing of the admission valve in the method of construction adopted by the authors , in which the thermometer valve is inserted through the spindle of the admission valve . In a specially designed gas engine , a separate opening might be provided for the insertion of the thermometer , but it is probable that the temperature of the valve in this case would not be so nearly equal to the suction temperature to be measured . The method adopted by the authors has the advantage that it can be applied without difficulty to any existing engine by simply making a special admission valve . Since the temperature of the thermometer valve in this method of construction differs so little from the suction temperature at the required point , it appears probable that the thermometer gives the actual suction temperature required with an approximation of the order of 1 ' C. The temperature at this point can probably be measured with a fine wire with a greater degree of accuracy than the pressure . In order to obtain the pressure at this point , it is necessary to take a diagram 74 Temperatures in the Cylinder of a Gas Engine . with a light spring in the indicator , as the pressure cannot be satisfactorily-measured with a spring strong enough to record the explosion temperature . Further , it is absolutely necessary in these investigations that the engine should repeat a perfectly regular cycle at each explosion . No results of any value can be obtained with a hit-and-miss governor in operation , because the conditions vary too greatly from stroke to stroke . This has been repeatedly shown by previous trials . In measuring the expansion and exhaust temperatures by a similar method , it would be most appropriate so far as the temperatures to be measured are concerned to insert the thermometer valve through the spindle of the exhaust valve . The authors desire to record their obligation to Mr. Witchell and Mr. Betterley and to other members of the Laboratory staff for the able assistance they severally gave during the investigation . (

rspa_1907_0076

0950-1207

On the normal weston cadmium cell.

75

76

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

F. E. Smith, A. R. C. Sc.|R. T. Glazebrook, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0076

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0076

10.1098/rspa.1907.0076

Electricity

Chemistry 2

Electricity

On the Normal Weston Cadmium Cell . By F. E. Smith , A.R.C.Se . ( Communicated by R. T. Glazebrook , F.R.S. Received July 13 , \#151 ; Read November 21 , 1907 . ) ( From the National Physical Laboratory . ) ( Abstract . ) The experimental investigations described had as their primary object the improvement of the Clark and cadmium cells as standards of electromotive force . In the past many investigators have pointed out that the mercurous sulphate used as a depolariser may produce variations in the E.M.F. as great as 0'002 volt , and the first thing sought by us was a mode of manufacture of the sulphate which could be relied on to give a constant product . We have prepared the salt in four ways : ( 1 ) Electrolytically ( the method is due to Carhart and Hulett , and Wolff ) ; ( 2 ) by chemical precipitation , mercurous nitrate being added to sulphuric acid ; ( 3 ) by the recrystallisation of purchased samples of mercurous sulphate from strong sulphuric acid ; and ( 4 ) by the action of fuming sulphuric acid on mercury . The mean value of the cells set up with the electrolytic salt is 1'01828 volts ; * with the sulphate prepared by ( 2 ) the E.M.F. is 1'01830 volts ; ( 3 ) gives P01832 volts , and ( 4 ) gives P01831 volts . We conclude that the mode of manufacture of the depolariser is immaterial , provided that certain conditions are observed , and our guiding principle in the manufacture of the salt and the preparation of the paste is to prevent hydrolysis by keeping the salt in contact with dilute sulphuric acid ( 1 to 6 ) or with saturated cadmium sulphate solution . The effect of the size of the crystals of the depolariser , to the importance of which attention has been called by H. v. Steinwehr , was investigated by using crystals of various sizes and measuring the E.M.F. of the cells in which they were inserted . Twenty samples of the salt were examined under the microscope , and in 12 cases microphotographs were taken , the magnification being 250 . The uniformity in the size of the crystals is most marked in samples prepared by method ( 2 ) , and this is recommended as a standard method of preparation of the salt . In general , the crystals varied in size from 5 to 30 microns , and we conclude that no large crystals of mercurous * The E.M.F. is given in terms of the ampere ( 10_1 C.G.S. , measured by the .Ayrton-Jones ampere balance ) and the international ohm . On the Normal Weston Cadmium sulphate which are sufficiently soluble to act as an efficient depolariser can give an E.M.F. appreciably lower than that due to crystals from o to 30 microns long . A very large proportion of the cells dealt with have not varied in E.M.F. by more than two parts in 100,000 since the first month of their preparation , and some of the cells are nearly three years old . A few abnormal cells have fallen in E.M.F. by about 25 parts in 100,000 , but the depolariser in these is of a peculiar colour and suggests hydrolysis of the salt . The recuperative power of the cadmium cell was tested by short-circuiting different cells for 1 minute , 5 minutes , 5 hours , and 5 days . The recovery in each case was very rapid . The lag of E.M.F. with temperature is very small , and the temperature coefficient for the range , 10 ' C. to 30 ' C. , is given by the following equation:\#151 ; Et E17 \#151 ; 3-45x 10-50-17)\#151 ; 0-066 x 10-5(\#163 ; -17)2 . This is in very good agreement with the formula given by the Reichsanstalt . I

rspa_1907_0077

0950-1207

The silver voltameter.

77

79

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

F. E. Smith, A. R. C. Sc.|T. Mather, F. R. S.|T. M. Lowry, D. Sc.|R. T. Glazebrook, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0077

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0077

10.1098/rspa.1907.0077

Electricity

Chemistry 2

Electricity

77 The Silver Voltameter . Part I.\#151 ; By F. E. Smith , A.R.C.Sc . , and T. Mather , F.RS . Part II.\#151 ; By F. E. Smith , A.RC . Sc. , and T. M. Lowry , D.Sc . ( Communicated by R T. Glazebrook , F.R.S. Received July 22 , \#151 ; Read November 21 , 1907 . ) ( From the National Physical Laboratory . ) ( Abstract . ) Part I.\#151 ; On a Comparison oj many Forms oj Silver Voltameters . By F. E. Smith ; and a Determination of the Electrochemical Equivalent of Silver . By F. E. Smith and T. Mather , F.R.S. It has been known for several years that the measurement of electric quantity by the deposition of silver is liable to inaccuracies which appear to be dependent on the size and nature of the anode and cathode and on the electrolyte of the voltameter employed . Hence the necessity of an enquiry to ascertain the possibility of specifying a voltameter which is easily reproducible and in which an ampere-second always deposits the same mass of silver . In some very early experiments it was found that the mass of the deposit was dependent on the mode of preparation of the silver nitrate , but on several crystallisations of the salt constant results were obtained . Very large voltameters were experimented with . Four of the cathode bowls had a capacity of 500 c.c. each , and in general from 300 to 400 c.c. of electrolyte were employed . The anodes were coated with electrically-deposited silver . With a Rayleigh form of voltameter containing an electrolyte of pure silver nitrate 52 determinations of the electrochemical equivalent were made , the current being indirectly measured by the British Association ( Ayrton Jones ) ampere balance . The mean of the 52 determinations was IT 1827 milligrammes per coulomb , and the mean difference was 2'4 parts in 100,000 . With a Richards form of voltameter , in which the anode liquid was separated from the cathode liquid by a porous pot , variable results were at first obtained , but this was found to be due to the presence of acid in the pots . When the pots were baked in an electric furnace before their employment in a voltameter , constant values resulted , and the mean of these was 1T1828 milligrammes per coulomb , i.e. , practically identical with that obtained with the Rayleigh form . Richards originally obtained a difference of eight 78 Messrs. Smith and Mather and Dr. Lowry . [ July 22 , parts in 10,000 between the two forms , his form giving the smaller deposit .later he found the difference to be four parts in 10,000 , and recently van Dijk has found a difference of half this latter amount . Further observations were made with a syphon and other modified forms of voltameter , and the same value , 1'11827 , was found , pointing to little or no irregularities in the large-size Rayleigh form of voltameter . Deposits were made when the voltameter was subject to a gaseous pressure of 2'4 cm . of mercury , and were found to be identical with those made under a pressure of 1 atmosphere . We have thus failed to confirm the observations of Schuster and Crosslev and of Kahle . At a temperature of 90 ' C. we found the deposits to be very slightly heavier than at 15 ' C. , but the calculated temperature coefficient was so small ( 1 x 10-6 ) that we believe the increase to be due to the action of the filter paper on the silver nitrate , as originally suggested by Kahle . The range in the current intensities was from 05 ampere to 8 amperes , and for this range we found no appreciable irregularity . We conclude that the Rayleigh form of voltameter as employed by us is . reproducible to one or two parts in 100,000 , and that the electrochemical equivalent of silver is IT 1827 milligrammes per coulomb . Part II.\#151 ; The Chemistry of the Silver Voltameter . By F. E. Smith , A.RC . Sc. , and T. M. Lowry , D.Sc . Before a definite value could be assigned to the electrochemical equivalent of silver it was necessary to demonstrate the possibility of preparing again and again , from silver nitrate of different origins , solutions which should give identical weights of silver when electrolysed under identical conditions . We prepared silver nitrate from electrolytic silver , from much used silver nitrate , and from commercial samples of the salt , and satisfied ourselves that by taking precautions in recrystallising , etc. , a sufficiently constant product could be obtained . Tests on commercial silver nitrate were gratifying in so far that with one exception all the samples ( eight in all ) examined gave figures agreeing with those obtained from the samples which were specially prepared , and we conclude that , except in measurements of high precision , the commercial salt may be used without purifying . Attempts to confirm the observations of Novak , Rodger and Watson , Kahle , van Dijk and others , on the effect of repeated electrolysis of a solution , show that in our voltameters there may be a very small increase in the deposit with continued use of a solution , but 'nothing comparable with that obtained by the observers mentioned . We also fail to confirm the formation , at the anode , of a complex silver salt , giving rise to The Silver Voltameter . 1907 . ] heavy deposits at the cathode , as suggested by Rodger and Watson and by Richards . High values are obtained for the electrochemical equivalent if the solution contains oxide , carbonate , chloride , nitrite or hyponitrite . Low values are caused by acid . The impurities which raise the electrochemical equivalent appear to be those which are insoluble in water but soluble in silver nitrate solutions ; they are , therefore , precipitated from the impoverished solution at the cathode . There may be slight changes in the electrolyte due to its interaction with filter paper , but the mass of the deposit is not seriously affected thereby in our size of voltameter in the course of one electrolysis . It is inadvisable , however , in measurements of high precision to use an electrolyte more than once . Silver chlorate and silver perchlorate appear to give normal deposits , but are more troublesome in use and have no advantage over the nitrate .

rspa_1907_0078

0950-1207

The diurnal variation of terrestrial magnetism.

80

82

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Arthur Schuster, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1907.0078

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1907_0078

10.1098/rspa.1907.0078

Fluid Dynamics

Meteorology

Fluid Dynamics

80 The Diurnal Variation of Terrestrial By Arthur Schuster , F.R.S. ( Received October 31 , \#151 ; Read November 7 , 1907 . ) ( Abstract . ) 1 . In a previous communication* I proved that the diurnal variation of terrestrial magnetism had its origin outside the Earth 's surface , and drew the natural conclusion that it was caused by electric currents circulating in the upper regions of the atmosphere . If we endeavour to carry the investigation a step further , and consider the probable origin of these currents , we have at present no alternative to the theory , first proposed by Balfour Stewart , that the necessary electromotive forces are supplied by the permanent forces of terrestrial magnetism acting on the bodily motion of masses of conducting air which cut through its lines of force . In the language of modern electrodynamics , the periodic magnetic disturbance is due to Foucault currents induced in an oscillating atmosphere by the vertical magnetic force . The problem to be solved in the first instance is the specification of the internal motion of a conducting shell of air , which shall , under the action of given magnetic forces , determine the electric currents producing known electromagnetic effects . Treating the diurnal and semi-diurnal variations separately , the calculation leads to the interesting results that each of them is caused by an oscillation of the atmosphere which is of the same nature as that which causes the diurnal changes of barometric pressure . The phases of the barometric and magnetic oscillations agree to about If hours , and it is doubtful whether this difference may not be due to uncertainties in the experimental data . In the previous communication referred to , I already tentatively suggested a connection between the barometric and magnetic changes , but it is only recently that I have examined the matter more closely . In the investigation which follows , I begin by considering the possibility that both variations are due to one and the same general oscillation of the atmosphere . The problem is then absolutely determined if the barometric change is known , and we may calculate within certain limits the conducting power of the air which is sufficient and necessary to produce the observed magnetic effects . This conducting power is found to be considerable . It is to be observed , however , that the electric currents producing the magnetic variations circulate only in the upper layers of the atmosphere , where the pressure is too small to affect the barometer ; the two variations have their origin , * ' Phil. Trans. , ' A , vol. 180 , p. 467 ( 1889 ) . The Diurnal Variation of Terrestrial Magnetism . 81 therefore , in different layers , which may to some extent oscillate independently . Though we shall find that the facts may be reconciled with the simpler supposition of one united oscillation of the whole shell of air , there are certain difficulties which are most easily explained by assuming possible differences in phase and amplitude between the upper and lower layers . If the two oscillations are quite independent , the conducting power depending on the now unknown amplitude of the periodic motion cannot be calculated , but must still be large unless the amplitude reaches a higher order of magnitude than we have any reason to assume . The mathematical analysis- is simple so long as we take the electric conductivity of the air to be uniform and constant ; but the great ionisation which the theory demands requires some explanation , and solar radiation suggests itself as a possible cause . Hence we might expect an increased conducting power in summer and in day time as compared with that found during winter and at night . Observation shows , indeed , that the amplitude of the magnetic variation is considerably greater in summer than in winter and we know that the needle is at comparative rest during the night . The variable conducting power depending on the position of the sun helps us also to overcome a difficulty which at first sight would appear to exclude the possibility of any close connection between the barometric and magnetic variations ; the difficulty is presented by the fact that the change in atmospheric pressure is mainly semi-diurnal , while the greater portion of the magnetic change is diurnal . This may , to some extent , be explained by the mathematical calculation , which shows that the flow of air giving a 24-hourly variation of barometric pressure is more effective in causing a magnetic variation than the corresponding 12-hourly variation , but the whole difference cannot be accounted for in this manner . If , however , the conductivity of air is greater during the day than during the night , it may be proved that the 12-hourly variation of the barometer produces an appreciable periodicity of 24 hours in the magnetic change , while there is no sensible increase in the 12-hourly magnetic change , due to the 24-hourly period of the barometer . The complete solution of the mathematical problem for the case of a conducting power proportional to the cosine of the angle of incidence of the sun 's rays is given in Part II . But even this extension of the theory is insufficient to explain entirely the observed increased amplitude of the magnetic variation during summer . We are , therefore , driven to assume either that the atmospheric oscillation of the upper layer is greater in summer than in winter and is to that extent independent of the oscillation of the lower layers , or that the ionising power of solar radiation is to some extent accumulative and that the atmospheric conductivity is , therefore , not com82 The Diurnal Variation of Terrestrial Magnetism . pletely determined by the position of the sun at the time . The increased amplitude at times when sunspots are frequent is explained by an increased conductivity corresponding to an increase in solar activity . All indications , therefore , point to the sun as the source of ionisation , and ultra-violet radiation seems to be the most plausible cause . A good test of the proposed theory may be found in a closer examination of the diurnal magnetic changes in the equatorial regions , because , owing to the inclination of the magnetic to the geographical axis , the magnetic changes ought to have a term which does not depend on local time , but on the time of the meridian containing the geographical and magnetic pole . This term has its greatest importance at the equator and at the time of the equinox . A study of the lunar effects may also lead to interesting conclusions , as , according to the point of view of the present paper , they must be explained by some tidal oscillation . The value of the conductivity necessary to explain the diurnal variation in the manner indicated depends on the thickness of the layers which carry the currents . If e be the thickness and the conductivity and the amplitude of oscillation in the upper layers is assumed to be the same as that deduced from the barometric variation , it is found that pe = 3 x 10-6 . If e is equal to 300 kilometres , the conductivity would have to be as high as 10-13 , while the observed conductivity of air at the surface of the earth under normal conditions is of the order 10-24 ; at a height at which the pressure is reduced to one degree per square centimetre , the conductivity would be 10-18 , assuming the rate of recombination to be independent of temperature , and the ionising power to be the same . This , calculation is based on the assumption that the ions conveying the current are identical with those we observe at high pressures , while it is of course possible that the ionic velocities are much greater . But taking all these possibilities into account , we are led to the conclusion that there must be a powerful ionising agent giving a high conductivity to the upper layer of the atmosphere . If the fundamental ideas underlying the present enquiry stand the test of further research , we are in possession of a powerful method which will enable us to trace the cosmical causes which affect the ionisation of the upper regions of the atmosphere and which act apparently in sympathy with periodic effects showing themselves on and near the surface of the sun .

rspa_1908_0001

0950-1207

Results of the interaction of mercury with alloys of other metals.

83

87

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

J. W. Mallet, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0001

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0001

10.1098/rspa.1908.0001

Chemistry 2

Chemistry 1

Chemistry

83 Results of the Interaction of Mercury with Alloys of other Metals . By J. W. Mallet , F.R.S. , University of Virginia . ( Received August 27 , \#151 ; Read November 21 , 1907 . ) It is well known that alloying metals with each other often modifies in a remarkable way their several relations to acids and other non-metallic reagents . Examples of this are afforded by the addition of silver to platinum , rendering the latter soluble , along with the former , in nitric acid \#151 ; by the great resistance to the action of aqua regia on platinum when alloyed with rhodium or iridium\#151 ; and by the solubility in cold , somewhat dilute sulphuric acid , of copper in alloy with nickel and zinc as common " German silver . " It seemed interesting to see what the behaviour of fluid metallic mercury would be in relation to alloys of metals solid at common temperatures . For instance , if an alloy of two metals\#151 ; one of them when alone amalgamating readily with mercury and the other not\#151 ; should be exposed to the action of mercury , would the former resist amalgamation or the latter be rendered amalgamable , or would each continue to behave as though the other were absent and the mercury take up the one and leave the other intact ? Some experiments of this kind , recently made , seem worth recording , as little or nothing bearing upon the question appears in the principal handbooks of chemistry . It suggested itself first to examine the case of an alloy of two metals presenting evidence of chemical combination between them , not merely of solid solution . Such a case is that of the alloy of tin and platinum which is produced by fusing the two together , the act of union being attendee ! with sudden and very great elevation of temperature , exhibiting brilliant incandescence , and the product being found to have completely changed in respect to cohesion , the two thoroughly malleable metals giving rise to a highly brittle alloy easily crushed to powder . Tin-platinum Alloy . For about 5 grammes of platinum in the form of rather thick foil a piece of pure tin was weighed off representing a trifling excess over the quantity needed for two atoms of tin to one of platinum , this excess being intended to allow for a slight loss of tin by oxidation . The tin was closely wrapped in the platinum foil , and the whole was rapidly heated by a blast-lamp flame . VOL. LXXX.\#151 ; A. G 84 Dr. J. W. Mallet . Results of the Interaction of [ Aug. 27 , Complete fusion took place in a moment , with vivid incandescence . The button of alloy , after cooling , was moderately hard , very brittle , and easily reduced to powder in an iron mortar . It contained : platinum , 45*26 per cent. ; tin , 54*74 per cent. The specific gravity of the button , taken before crushing , was found to be but 10*72 , notably below the calculated value , so that if there were no cavities\#151 ; none were observed on crushing\#151 ; there must have been considerable expansion in the act of union of the metals . The finely pulverised alloy , with about five times its weight of pure mercury , was at once placed in a stoppered glass cylinder , and the vessel was vigorously shaken from time to time for several days . No sign of amalgamation appeared . The larger part of the mercury was run off from the seemingly quite unaltered powder , carefully freed from any trace of the latter by skimming , and distilled at a temperature a little below the boiling point in a hard glass tube , sweeping away the vapour by a current of air produced by a jet pump . No visible residue was left , so that the tin had been completely protected by the platinum from amalgamation , and neither metal had gone into solution . The surface of the particles of the original alloy powder showed under the microscope no sign of adhering mercury . On treating this unaltered powder of the platinum-tin alloy with another portion of mercury to which a very little metallic sodium had been added , amalgamation took place at once , and the amalgam began to adhere to the surface of the glass vessel . The soft amalgam thus formed seemed to contain entangled in it the larger part of the powder , but very little was present in true solution , as on straining off the fluid portion through chamois leather and distilling , only a trifling residue was obtained , containing but a few milligrammes of platinum and tin . The main mass of the buttery amalgam left behind on straining through the leather was treated with moderately diluted nitric acid until all action ceased . It left undissolved pulverulent grey platinum , and a heavy , finely granular residue , of crystalline appearance under the microscope , greyish white and with metallic lustre . This latter was an alloy of platinum and tin which , like the bulk of the original fused alloy , was not acted upon by mercury . Heated in a stream of dry chlorine gas , it gave off tin as chloride and left metallic platinum , weighings showing the composition to be : platinum , 48*08 per cent. ; tin , 51*92 per cent. ; agreeing pretty well with the not very probable formula Pt4Sn7 , which requires platinum , 48*33 per cent. ; tin , 51*67 per cent. It is by no means certain that this material was homogeneous . It would seem that even in an amalgam which as a whole is liquid and Mercury with Alloys of other Metals . 1907 . ] mobile , the mass may be viewed as consisting of a solid part or phase\#151 ; the solid metal moistened by mercury\#151 ; and a liquid part or phase\#151 ; mercury holding the solid metal in solution\#151 ; these parts mechanically separable by straining , or often simply by gravity on standing at rest . In the material just referred to nearly all of the tin and platinum seems to have existed in the former of these states . Silver-platinumAlloy . Platinum as heavy foil and pure silver ( " proof silver " of the United States Mint ) were weighed off in proportions representing four atoms of silver and one of platinum , and fused together in an assay crucible at a temperature high enough to render the alloy perfectly fluid . The ingot which was somewhat hard , but quite malleable , was rolled out to strips not more than about a tenth of a millimetre in thickness . These strips weighing about 12 grammes , were cut up into small bits , washed well with ether to remove any traces of oil from the rolls , dried , put into a stoppered glass cylinder , and shaken with about five times their weight of pure mercury , the vigorous shaking being repeated at intervals for several days . The mercury began almost at once to wet the surface of the solid alloy , and after a few hours practically all running mercury had been soaked up and the strips began to crumble . About half as much more mercury was added , and in three or four days an apparently smooth buttery amalgam had been formed . Almost from the first the amalgam began to adhere with remarkable firmness to the surface of the glass , and before long the whole interior surface of the cylinder was coated with a mirror-like deposit as perfect as that usually obtained by means of silver reduced by aldehyde or Kochelle salt , and remarkably persistent . The perfectly smooth buttery amalgam , containing no visibly solid fragments of the strips of alloy , was strained by squeezing through chamois leather . The solid part which was left behind hardened somewhat on standing , but not nearly as much as amalgam of silver alone , and showed some tendency to crumble . Applied to the surface of clean platinum foil it at once produced amalgamation of the latter . A specimen of simple silver amalgam was strained through chamois leather , and the pasty solid residue was in like manner applied to the surface of clean platinum foil . At first , even with rubbing , no sign of amalgamation of the foil appeared , but on leaving the lump of silver amalgam resting on the surface for an hour or two and then sliding it to one side , a mark was G 2 86 Dr. J. W. Mallet . Results of the Interaction of [ Aug. 27 , left showing where the amalgam had lain , and after 24 hours there was distinct amalgamation of the surface . This increase of adhesiveness given to mercury by the presence of silver displays an interesting additional hit of parallelism between silver and the alkaline metals . Bemoving the lump of amalgam and rubbing the surface of the platinum foil vigorously with a cloth , there was left a visible stain , which changed somewhat in lustre but did not disappear on heating to low redness , showing that silver as well as mercury had adhered to the surface . Whether this silver had been carried down into the platinum by the amalgamation ( as is most probable ) or was partially alloyed with it by the heating to drive off mercury , the stain did not entirely disappear on treatment with nitric acid . About 30 grammes of the fluid part of the amalgam from the silver-platinum alloy , which had been strained through chamois leather , was carefully distilled in a stream of air , keeping somewhat below the boiling point to avoid any mechanical loss by spattering , and left behind 60 milligrammes of solid residue . This was " parted " by repeated boiling with concentrated sulphuric acid . The results of the parting show the following comparison between the composition of the original silver-platinum alloy and of this portion of it which had been taken into solution by the mercury :\#151 ; Original Dissolved alloy . by mercury . Platinum ... ... ... ... ... . 31*09 18*78 Silver ... ... ... ... ... ... . 68*91 81*22 It thus appears that , unlike the case of the tin-platinum alloy , in which the platinum prevented the tin being amalgamated , in the silver-platinum alloy the silver brings about solution of the platinum by mercury , although in smaller proportion than that in which it was present in the original alloy . Copper-tin Alloy . It seemed desirable , in the third place , to see what effect , if any , upon amalgamation would be produced by alloying two metals , each of which is by itself readily taken up by mercury ; and such metals were selected as we have reason to believe , from the experiments of Sir William Bamsay and others , are simply dissolved by mercury , and in the condition of monatomic molecules . With this in view , a specimen of good speculum metal , made with two parts of copper and one of tin , and hence near Cu4Sn in composition , extremely brittle , was reduced to very fine powder in an iron mortar ; 10 grammes of this was placed in a stoppered glass cylinder , about five times as much pure Mercury with Alloys of other Metals . 1907 . ] mercury added , and the whole well shaken at intervals for several days . At first there was no sign of amalgamation , but in a few hours this began to appear , and at the end of 24 hours the greater part of the solid alloy had been taken up by the mercury . There was no adhesion of amalgam to the surface of the glass . About half as much more mercury was added , and after four or five days , with many shakings , there remained but a very little solid alloy in powder . This was carefully removed from the surface of the seemingly smooth , buttery , or thickly fluid amalgam , and the latter squeezed in chamois leather . Forty or fifty grammes of the fluid portion which had passed through the pores of the leather was carefully distilled , guarding against spattering . It left but 2 or 3 milligrammes of solid residue , in which both copper and tin were present , the former probably in rather larger proportion than in the original alloy , but the quantity of residue was too small for an accurate analysis . The pasty amalgam which was retained by the leather showed a strong tendency to crumble , and when examined with the microscope showed numerous particles of the solid speculum metal which had not fully blended with the mercury . It is evident , therefore , that alloying these two metals\#151 ; copper and tin\#151 ; together , greatly diminishes the readiness and extent with which they unite with mercury when they are separately exposed to its action . On the whole , these experiments show that the relations of mercury to alloys are not the same\#151 ; at any rate for those tried\#151 ; as to the component metals taken separately . Many other experiments of the general nature of those now recorded suggest themselves as worth trying . Thus it would be well to examine the behaviour towards mercury of solid alloys , including one of the alkaline metals , the amalgams of which are so peculiar in character , to try the effect of mercury upon two or more alloys of the same metal in widely different proportions , and to extend such experiments to more complex alloys containing three , four , or a larger number of solid metals .

rspa_1908_0002

0950-1207

A method of depositing copper upon glass from aqueous solutions in a thin brilliantly reflecting film, and thus producing a copper mirror.

88

92

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

F. D. Chattaway, F. R. S.

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http://dx.doi.org/10.1098/rspa.1908.0002

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0002

10.1098/rspa.1908.0002

Chemistry 2

Thermodynamics

Chemistry

88 A Method of Depositing Copper upon Glass from Aqueous Solutions in a Thin Brilliantly Reflecting , and thus producing a Copper Mirror . By F. I ) . Chattaway , F.E.S. ( Received September 26 , \#151 ; Read November 21 , 1907 . ) Many organic substances which undergo oxidation easily are able to reduce various metallic oxides . The oxygen is removed with very different degrees of readiness and the property is in consequence often used as a means of recognising particular compounds or atomic groupings . Silver oxide is especially easily reduced , and if it is dissolved in an aqueous solution of ammonia the metal , by an appropriate agent , as Liebig first observed , * may be obtained attached to the glass walls of the containing vessel as a brilliant reflecting film . This observation has received an important industrial application in the manufacture of mirrors , and silver thus deposited has now practically replaced the tin amalgam formerly used , which so often seriously affected the health of the workers . With the view of improving the processes originally used , many chemists have studied the conditions under which glass is coated with silver , but their investigations have generally had for their object the preparation of a liquid which wrould deposit a uniform and coherent layer of the metal over a large glass surface at the ordinary temperature . Liebigj* was the first to solve the problem satisfactorily and his method , in which milk sugar is the reducing agent , was formerly extensively used . Other metals are not so easily laid down upon glass in a firm reflecting film as is silver ; and in particular copper , which is so closely related to it , is not in similar circumstances so deposited . Metallic copper has been attached to glass in various ways . Faradayabout the time when silver mirrors were attracting much attention , made the interesting observation that a mirror-like deposit of the metal upon glass having the proper metallic lustre and colour by reflection , could be obtained by dissolving a little oxide of copper in olive oil and heating plates of glass in a bath of this liquid up to the decomposing temperature of the oil . Mirrors , however , obtained by Faraday 's method , if of any size , are liable to be stained and discoloured in patches by * 'Annalen , ' 1835 , vol. 14 , p. 133 . t ' Annalen , ' 1856 , vol. 98 , p. 132 . j ' Phil. Trans. , ' 1857 , p. 145 . A Method of Depositing Copper upon Glass , etc. 89 decomposition products of the oil and they are , moreover , generally lacking in brilliancy . Further , as the deposition of the metal only takes place at a temperature above that at which the oil decomposes , the process is excessively disagreeable to carry out and , as the oil is spoiled , it is somewhat costly . Faraday also discovered* that a fine deposit of copper upon glass could be produced by deflagrating the metal in the neighbourhood of the glass by a Leyden battery in an atmosphere of hydrogen , and Wright , employing a method essentially the same , f obtained small brilliant mirrors of copper on the inner surface of exhausted glass tubes by passing through them an electric discharge between copper electrodes . Everyone who has reduced Fehling 's solution with excess of grape sugar must have noticed that occasionally the metal produced adheres to the sides of the beaker or flask in somewhat reflecting patches , and much brighter patches are obtained when certain copper salts such as formate or acetate are heated in glass vessels . The firm of Weisskopf , in Morchenstein , has further succeeded in depositing copper upon glass by reducing the hydroxide in presence of zinc chloride together with gold or platinum chloride by a somewhat complicated liquid mixture containing cane sugar , glycerine , and formaldehyde . These facts lead to the conclusion that copper should be capable of deposition in the same way as silver , if a suitable reducing agent were forthcoming ; this I have recently found in phenylhydrazine . Phenylhydrazine , as I have elsewhere shown , J especially in presence of caustic potash , which greatly accelerates the action , is easily oxidised by free oxygen , there being produced in all likelihood hydroxyphenylhydrazine , which immediately breaks down into a molecule of benzene , a molecule of nitrogen , and a molecule of water thus:\#151 ; C6H5\#151 ; X\#151 ; H C6H5\#151 ; 1ST\#151 ; H l+o= ! = c6h6+x2+h2o . H\#151 ; X\#151 ; H H\#151 ; X\#151 ; OH Copper oxide acts similarly upon the base , and under suitable conditions the metal can be deposited upon glass in the form of a fine mirror . The operation may be carried out in a variety of ways , using finely divided black copper oxide suspended in a boiling saturated solution of phenylhydrazine or a liquid made by mixing the latter with a solution of copper hydroxide in alkaline tartrates or ammonia . * ' Phil. Trans. , ' 185V , p. 154 . t Silliman , ' Amer . Journ. , ' 1877 , [ 3 ] , vol. 13 , p. 49 . X 'Trans . Chem. Soc. , ' 1907 . Dr. F. D. Chattaway . [ Sept. 26 , The following procedure , which resembles that employed in silvering glass , gives a uniformly excellent result . Heat a mixture of one part of freshly distilled phenylhydrazine and two parts of water till a clear solution is obtained . To this add about half its bulk of a warm saturated solution of cupric hydroxide in strong ammonia . Nitrogen is freely evolved during the addition , and the cupric is reduced to cuprous hydroxide , which remains dissolved in the ammoniacal liquid , and does not undergo any immediate appreciable further reduction until heated . Add next a hot 10-per-cent , solution of potassium hydroxide until a slight permanent precipitate of cuprous hydroxide is produced . If this colourless or pale yellow liquid be cautiously heated in contact with a perfectly clean glass surface , metallic copper is deposited upon it in the form of a thin , coherent , perfectly reflecting lamina . As nitrogen is evolved during the reduction , and as tarry bye-products are formed in small quantity and float with the benzene produced to the surface of the liquid , if flasks or tubes are to be coppered , devices have to be adopted to keep the inner surface completely covered by the liquid from which the metal is being deposited , whilst allowing the gas to escape . If the glass in any part is not perfectly coated , the process may be repeated , but a uniform deposit is seldom obtained unless the whole surface is covered in one operation . To obtain a film of sufficient thickness to be permanent , and to prevent its superficial oxidation , it is best to allow it to remain for an hour or so in contact with the warm reducing fluid , and not to pour this off till it has cooled to the temperature of the air . The surface of the deposited copper should then be well washed , first with water and afterwards with alcohol and ether , and finally should be protected from the slow oxidising action of the air by one or two coats of some quickdrying varnish . Very little of the phenylhydrazine is actually used up in the reduction , and the same fluid may be employed again and again after filtering while warm through cotton wool and mixing with more solution of copper hydroxide , adding fresh phenylhydrazine when necessary to compensate for the dilution . If required for future use , the liquid must bo kept in a stoppered bottle carefully protected from the air , as free oxygen is very readily absorbed by it and the phenylhydrazine thereby destroyed . The mirrors obtained by this method are very beautiful , for they show the pleasing red colour of copper and are as perfect in reflecting surface and as lustrous as the similar mirrors obtained by the deposition of silver . To carry out the operation successfully , it is essential to cleanse very thoroughly the surface of the glass ; this is best done by well rubbing in turn 1907 . ] A Method of Depositing Copper upon Glass , . with a strong solution of soap , with strong nitric acid , and with strong caustic potash , using a pad of cotton wool soaked in these liquids , and washing well between the successive operations . Surfaces of blown glass are more readily coated with copper than polished surfaces . In any case old glass should not be used , at least without the surface being carefully repolished . Ammonia in excess hinders the deposition of copper , as it does that of silver , while caustic alkali accelerates it . It is interesting to note that the copper is in the monvalent or cuprous state , in which it is analogous to silver , when it shows a similar tendency to be deposited in a metallic film upon glass . Little is known as to the reasons why , when metallic oxides are reduced in aqueous solutions , the metals under certain conditions are deposited upon glass in a thin , reflecting lamina , while under others , apparently equally favourable to such deposition , they separate in a spongy or flocculent state . Vogel* concludes from his experiments with silver oxide that when complete reduction takes place in one stage , a mirror or crystalline deposit is obtained , whilst granular or finely divided silver is produced in two stages , a lower insoluble oxide separating as the primary product of the reduction and being afterwards itself further reduced . The behaviour of copper oxide on reduction makes it , however , very improbable that the various stages of the process affect the result . For the production of a mirror it appears rather to be essential that the compound undergoing reduction shall be in solution and that its concentration shall be small , that the liquid in which it takes place shall be alkaline , and that action shall be more rapid at the surface of the glass than elsewhere . It is certain that the nature of the surface on which the metal is deposited plays an important part in the process , since both silver and copper are deposited much better upon blown than upon polished glass and upon surfaces which have not for long been exposed to the action of the air or of water . It seems probable that the glass surface itself acts as a catalyser and locally accelerates the action . Oberbeck , some years ago , f measured the electric resistances of a number of silver films deposited upon glass from aqueous solution . He made the interesting discovery that such resistances , although very large immediately after the metal had been deposited , continually diminished with time , and although a minimum was not reached in two years , ultimately approximated to the resistances which would have been shown by films of * ' Journ. fur praktische Chemie , ' 1862 , vol. 86 , p. 321 . t ' Ann. der Physik und Cliemie , ' 1892 , p. 282 . 92 Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 , ordinary silver of corresponding thickness and size . The films during this change of resistance altered neither in reflecting power nor in appearance when viewed by transmitted light . As reflecting silver films of very different thickness and initial resistance and produced under very different conditions all showed this great increase in conductivity , Oberbeck concluded that when silver is first deposited from aqueous solution in the form of a mirror , it is in a different molecular condition from ordinary silver , but that in time its state approaches that of the latter more and more . The Electric Discharge Monatomic Gases . By Frederick Soddy , M.A. , Lecturer in Physical Chemistry in the University of Glasgow , and Thomas D. Mackenzie , B.Sc. , Carnegie Research Scholar . ( Communicated by Professor J. Larmor , Sec. R.S. Received October 8 , \#151 ; Read November 7 , 1907 . ) 1 . Scope of the Enquiry . In a recent paper* one of us has described the use of metallic calcium at . high temperature for the production of high vacua , and in spectroscopic work as a very perfect chemical absorbent of all except the chemically inert gases . It was shown that helium and argon purified by calcium from traces of common gases or vapours , with which they are in practice invariably contaminated during manipulation , showed a great disinclination to conduct the discharge . In ordinary spectrum-tubes , helium offered a resistance equivalent to an alternative spark-gap of an inch in air , at a pressure of ( H)5 mm. , and argon at 0-02 mm. of mercury . This behaviour of the monatomic gases , together with the closely-allied phenomenon shown by spectrum-tubes filled with these gases of becoming non-conducting , or " running out , " under the action of the discharge , have now been investigated in detail . A great number of experiments have been performed and a short summary will be given in the present paper . The main object was to settle whether electric conduction in the monatomic gases is essentially different from that in other gases . The first results raised at least a presumption that perfectly pure helium might * ' Koy . Soc. Proc. , ' 1907 , A , vol. 78 , p. 429 .

rspa_1908_0003

0950-1207

The electric discharge in monatomic gases.

92

109

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Frederick Soddy, M. A.|Thomas D. Mackenzie, B. Sc.|Professor J. Larmor, Sec. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0003

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0003

10.1098/rspa.1908.0003

Thermodynamics

Atomic Physics

Thermodynamics

92 Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 , ordinary silver of corresponding thickness and size . The films during this change of resistance altered neither in reflecting power nor in appearance when viewed by transmitted light . As reflecting silver films of very different thickness and initial resistance and produced under very different conditions all showed this great increase in conductivity , Oberbeck concluded that when silver is first deposited from aqueous solution in the form of a mirror , it is in a different molecular condition from ordinary silver , but that in time its state approaches that of the latter more and more . The Electric Discharge Monatomic Gases . By Frederick Soddy , M.A. , Lecturer in Physical Chemistry in the University of Glasgow , and Thomas D. Mackenzie , B.Sc. , Carnegie Research Scholar . ( Communicated by Professor J. Larmor , Sec. R.S. Received October 8 , \#151 ; Read November 7 , 1907 . ) 1 . Scope of the Enquiry . In a recent paper* one of us has described the use of metallic calcium at . high temperature for the production of high vacua , and in spectroscopic work as a very perfect chemical absorbent of all except the chemically inert gases . It was shown that helium and argon purified by calcium from traces of common gases or vapours , with which they are in practice invariably contaminated during manipulation , showed a great disinclination to conduct the discharge . In ordinary spectrum-tubes , helium offered a resistance equivalent to an alternative spark-gap of an inch in air , at a pressure of ( H)5 mm. , and argon at 0-02 mm. of mercury . This behaviour of the monatomic gases , together with the closely-allied phenomenon shown by spectrum-tubes filled with these gases of becoming non-conducting , or " running out , " under the action of the discharge , have now been investigated in detail . A great number of experiments have been performed and a short summary will be given in the present paper . The main object was to settle whether electric conduction in the monatomic gases is essentially different from that in other gases . The first results raised at least a presumption that perfectly pure helium might * ' Koy . Soc. Proc. , ' 1907 , A , vol. 78 , p. 429 . 1907 . ] The Electric Discharge Monatomic Gases . be unable to conduct the discharge at all , so that the running out of spectrum-tubes might be due to the absorption of the impurities only by the electrodes and not by the absorption of the inert gas itself . This view , however , proved to be untenable . The absorption of the monatomic gases during the discharge occurs rapidly and continuously under suitable conditions , and the nature of this action is now fairly clear . But , on the other hand , helium which has been subjected to the prolonged action of the discharge between aluminium electrodes , after initial purification with calcium , exhibits to an altogether extraordinary degree the peculiarity before noticed . In an ordinary spectrum-tube such helium offers a resistance equivalent to that of an inch spark-gap at a pressure of over half a millimetre of mercury , and the discharge is accompanied by all the well-known characteristics\#151 ; intense fluorescence of the tube , production of cathode rays , and the incipient production of X-rays\#151 ; which are usually supposed to be indicative of a high vacuum . But at higher pressures this very pure helium conducts the discharge in the same way as other gases . Our results leave no doubt that the difference between helium and other gases is one of degree only , and that the monatomic gases are relatively electrically as well as chemically inert . It will be shown that the remarkable behaviour of helium in the region of low pressure is intimately bound up with the equally remarkable behaviour of the gas in the region of atmospheric pressure , when , as Ramsay and Collie* have shown , it conducts the discharge so much more easily than any other gas . A spectrum-tube filled with helium at atmospheric pressure conducts the current from a small induction coil with ease . It is only necessary to regard the helium molecule at all pressures as only about one-fifth to one-tenth as effective electrically as a molecule of a common gas like hydrogen , in order to obtain a simple and consistent explanation of the behaviour of both high and low pressure helium to the discharge . In the course of the work it became necessary to examine the common gases also in order to be able to compare their behaviour with the monatomic gases . The result transpired that the electrical effects usually supposed to be indicative of a high vacuum occur in all gases at degrees of rarefaction which cannot with any accuracy be described as " high vacua . " Thus in the previous paper the behaviour of argon , which was found unable to conduct below 0'02 mm. , was regarded as exceptional . In reality , it is similar at this pressure to the common gases , hydrogen and nitrogen , all of which , when pure , cease to conduct at about ( H)4 mm. The pressure in an X-ray tube , filled with hydrogen and giving good X-rays , is above * ' Roy . Soc. Proc.,5 1896 , vol. 59 , p. 257 . Messrs. F. Soddy and T. D. Mackenzie . [ Oct , 8 , 0'01 mm. Some of the possible causes which ma)T have contributed to the mistaken impression that the degree of rarefaction in a Crookes tube is of the order of a thousandth of a millimetre will be discussed in the paper . During the investigation it transpired that the spectrum of one of the rare gases appeared in a set of new spectrum-tubes during preliminary preparation before any of the gas had been introduced ; and it has been put beyond doubt that the aluminium electrodes of spectrum-tubes which have been used with either helium , neon or argon , retain , even after months ' exposure to the air , sufficient of the gas in question to give its spectrum when remounted in a new glass tube into which none of the gas is introduced . 2 . Absorption of Helium in Spectrum-tubes . In our first series of experiments the running out of spectrum-tubes filled with helium was investigated . Six similar spectrum-tubes of about 28 c.c. volume were filled with helium purified by calcium to accurately known initial pressures , ranging from 1 to 32 mm. The tubes were constructed to stand a heavy current without breaking down . The cathode consisted of aluminium wire 4 mm. diameter , and the anode an aluminium disc 16 mm. diameter . A narrow side tube was sealed into the cathode chamber for the purpose of measuring subsequently the residual gas in the tube , and a tube drawn to a fine point , to be broken under mercury at the end of the experiment , was sealed to the anode chamber . These tubes were constructed in batches of a dozen at a time by a well-known London maker especially for the investigation , and none of them have been used in any other experiments . Six tubes at a time were attached to the calcium furnace , an arrangement for admitting known quantities of helium , and a mercury pump , and very thoroughly freed from occluded gases by heating and passing a discharge heavy enough to fuse the electrodes . The remarkable fact must be chronicled that during this treatment , before any helium had been brought into the apparatus , the first batch of tubes developed the helium spectrum . In the two first experiments , each with six new tubes of the first dozen , the full helium spectrum was developed during the preliminary treatment . The second batch of a dozen , made at another time , did not show this behaviour . The phenomenon and its probable explanation are discussed under Section 9 . The practice adopted during this preliminary treatment was to keep the calcium at its absorbing temperature , and by a tap to regulate the flow of expelled gases into the calcium chamber , so as to keep the tube fluorescent without allowing the vacuum to rise to the non-conducting point . When the \#187 ; operation was complete and the calcium had absorbed the expelled gases , 1907 . ] 7%e Electric Discharge in Monatomic Gases . helium was introduced , the fusion of the electrodes repeated , and the tubes again exhausted by the pump . This was necessary , as it is known* that electrodes freed sufficiently from occluded gases by ordinary running and heating tend to evolve a further supply when filled with the monatomic gases and run , owing to the much greater heating of the electrodes in the latter gases . Helium in accurately known amount was then admitted to the calcium chamber and allowed to remain there until the spectrum became perfectly pure , when the tap to the spectrum-tube was opened and the first tube sealed off . The remaining five were then sealed off one by one , each after a further known quantity of helium had been admitted . The total volume of the apparatus had been found , so the initial pressure of helium in each tube could be calculated . The six tubes were then run in series with a heavy current from a 10-incli coil worked with a mercury interrupter from the 250-V . mains . A rectifier was placed in the secondary circuit to keep the current as unidirectional as possible , but it is doubtful if this had any influence . The first four tubes showed a sharp line spectrum , but in the other two , owing to too high pressure , the spectrum was confused . A new clear faint line in the extreme red , about 7266 , was noticed in the helium spectrum of the tubes filled at lower pressure . The first three tubes ran out and became non-conducting without difficulty , and ultimately the fourth also , but the remaining two did not . All the first four tubes went through the same changes in appearance just before they became non-conducting . The glow changed from yellow to green , and the yellow line , at first by far the strongest , became weaker than the green . At this stage the cathode fluorescence extended a distance of 12 cm . to the extreme tip of the side gauge-tube . As soon as the discharge commenced to pass an alternative gap of 1 inch in parallel to the tube , the latter was cut out of circuit and the tip broken under previously heated mercury , with precautions against the admission of air . As the mercury entered , all the gas was compressed into the side gauge-tube and its volume marked by a diamond scratch . The table ( p. 96 ) shows the details of the six tubes . The current after the first 40 hours was considerably increased . The pressures in the last column were obtained from the volume of the residual gas immediately after filling the tube with mercury . It will be seen that the helium is absorbed during the discharge until a residual pressure is reached nearly the same in each case and between 0'6 and 0'7 mm. , independent of the initial pressure . This indicates that at this pressure the * E. C. C. Baly , 'Phil . Trans. , ' 1903 , A , vol. 202 , p. 185 . 96 Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 , Initial pressure . Fluorescence appeared . ! 1 Became non-conducting . Residual pressure . mm. mm. I 1 -1 From start After 25 mins . 0-57 II 2 -3 After 10 mins . After 70 mins . 0-72 III 4-9 After 50 mins . After 7 hrs . 40 mins . 0-62 IV 8-6 After 60 hrs . 30 mins . After 61 hrs . 20 mins . 0-9 V 16 -8 1 Did not appreciably change after over 100 hours ' continuous VI 31-2 / running . helium ceases to conduct the discharge . But it was at once found that as soon as the mercury entered the tube it commenced to dissolve the mirror of aluminium deposited from the electrodes and to liberate the absorbed gas . In the first tube , after the volume of the residual gas had been measured , the mercury was sucked out and allowed to refill the tube , when the volume was found to have doubled . In the second tube the evolution of gas could be watched , and large bubbles made their appearance at the cathode film as the mercury was sucked out . The volume after refilling corresponded to a final pressure of T33 mm. In the third tube , after the mercury had been left in half an hour , the pressure was 3'43 mm. , and after readmitting the mercury and allowing it to remain another four hours the pressure was 3'7 mm. In the fourth tube gas came out from both the anode and cathode mirrors , and the volume increased enormously , but the final measurement was unfortunately lost . The spectrum of the residual and liberated gas was always observed , to detect the entrance of air , but in every case the spectrum , except for mercury , was of absolutely pure helium . These experiments clearly show the nature of the process when a helium tube is run to non-conductance . Contrary to what was given as the explanation in the last paper , * a real absorption of the helium takes place , and the greater part of the absorbed gas is very loosely retained and can be recovered from the aluminium mirror volatilised from the electrodes . On the other hand , non-conductance obtains in pure helium long before all the helium is absorbed , and the gas so treated refuses to conduct the current at a pressure when any other gas would be at about its maximum conductivity . As , however , the residual pressure was practically the same for all the four tubes , one of which had been run for over 60 hours , the experiments do not support the idea that pure helium by itself is a nonconductor . They favour the view that the constant residual pressure is the real limiting pressure for pure helium itself , above which it will conduct in the same way as any other gas . * Loc . cit. , p. 448 . 1907 . ] The Electric Discharge Monatomic Gases . The experiments described are inconclusive in one respect . Owing to the unexpected ease with which the absorbed gas is liberated under the action of mercury , the large residual pressures observed might have been due at least in part to liberation of absorbed gas during the admission of the mercury . This did actually happen in the filling of Tube No. IV with mercury , and accounts for the somewhat high residual pressure observed . Before the cathode chamber had filled actual bubbles had been liberated from the aluminium film in the anode chamber and could be seen passing through the capillary with the entering mercury . It was , therefore , necessary to repeat the observations in a different manner to eliminate this uncertainty . Before describing these it may be mentioned that a similar series of tubes to those used for helium were prepared with argon , but none of the tubes could be run out to non-conductance even after prolonged action of the discharge . During the greater part of the time the cathode in the tube filled at lowest pressure ( 1*3 mm. ) was bright red-hot . Only this tube showed a clear spectrum . All the others filled to higher pressures had a confused spectrum . In filling the tubes we had the mistaken impression that argon was more easy to run out than helium . Argon spectrum-tubes certainly often run out more readily than those of helium , but this is due to the fact that the pressure in an argon tube is necessarily so much lower than in helium in order to get a clear spectrum . A good helium tube may be filled to 6 or 8 mm. without confusing the lines , but in argon the pressure should not be much over a millimetre . To get results with argon comparable with those for helium the tubes should have been filled to about one-tentli the pressures . 3 . The Pressure at which Pure Helium ceases to conduct . The advantage of experimenting with sealed tubes is that thereby the influence of contaminations derived from lubricants and mercury is eliminated . In the present series of experiments mercury vapour was present , and found not to exert any important influence ; but lubricants were completely avoided in that part of the apparatus containing the helium while it was being run . The spectrum-tube was of the same pattern as before , but was kept connected throughout the experiment with a specially designed form of M'Leod gauge ( fig. 1 ) by means of an unconstricted tube . The graduated tube and the connecting tubes were 6 mm. in bore , and to avoid the latter being too long they were provided with glass valves closed by the rising mercury of the kind usually found on Topler pumps . The gauge was worked without rubber tubing by varying the pressure on the mercury in the reservoir . By the special arrangement of tubes shown , the Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 , spectrum-tube and gauge could be connected with or shut off from the rest of the apparatus by lowering or raising the mercury , so that the apparatus constituted a mercury tap as well as a gauge . Thus the vapour of lubricants was avoided , and during the running of the spectrum-tube the mercury sealed off the connection with the rest of the apparatus . With this Spectrum ^etc . IOOc.c . Fig. 1 . apparatus the earlier results were at once confirmed . If helium purified by calcium is admitted in successive small doses to the apparatus and run out till the discharge commences to pass an inch gap , the pressure at which non-conductance obtains reaches a maximum of 0'7 mm. , and then the admission of more helium and further running to non-conductance always 1907 . ] The Electric Discharge in Monatomic Gases . reproduces this same pressure . In common gases the stage of nonconductance is usually reached very abruptly at a definite pressure , but in the monatomic gases a heavy current will partly spark across a given gap when a feebler current would pass entirely through the tube . The observations were , therefore , taken under as nearly comparable conditions as possible as regards the current flowing . Three stages were recognised in the experiments . In the first , sparks passed regularly at intervals of a few seconds ; in the second , sparking was continuous , about half the current going through the gap ; and in the third , only a very feeble current passed through the tube . The initial passage of a single spark or a few sparks at long irregular intervals across the gap was ignored . The pressure of 0*7 mm. corresponds to the first stage . If the pressure is measured after the second stage is reached , it is found to be about 0*55 mm. When the discharge is left to run for several hours until the third stage is reached and hardly any current passes through the tube , the pressure sinks to 035 mm. , and does not further decrease however long the discharge is continued . Increasing the spark-gap to 2 inches only effects a very slight additional absorption of the gas , and external discharges take place over the glass , owing to the condenser effect of the aluminium mirror inside the tube , which involve the risk of puncturing the tube . In this apparatus the pressure at which sparks from a small coil commenced to jump an inch gap was measured in helium which had been purified by calcium only and not subjected to the discharge . It was found to be 0*275 mm. This is over five times the pressure given in the last paper , and is due to a more thorough removal of gases from the electrodes prior to the experiment , and to the absence of vapour of lubricating grease . It is clear that running the tube exerts a further purification of the helium by the absorption of the last remaining impurities in the electrodes , and that an otherwise undetectable trace of impurity makes a very great difference on the pressure at which helium becomes non-conducting . In helium purified by calcium and the prolonged action of the discharge , examined in a straight tube 30 mm. wide by 100 mm. long , with two 10 mm. discs of aluminium 42 mm. apart , continuous sparking across an inch gap occurred at a pressure of 0*39 mm. The total amount of gas admitted to this tube during the experiment was recorded . The tube was pumped out to 0 001 mm. On standing for 20 minutes the pressure had risen to 0*01 , and after 18 hours to 0*034 , due to the spontaneous liberation of helium in the cold . The tube was then heated , and the pressure rose to 0*36 mm. It was pumped out to 0*00.1 , and reheated more strongly , when the pressure of the gas liberated was 0*5 mm. It was VOL. lxxx.\#151 ; A. H 100 Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 , calculated that at least 98 per cent , of the absorbed gas was re-evolved through heating . As at this temperature none of the gas which causes the Campbell Swinton effect ( compare Section 10 ) is liberated , it follows that only a very small fraction of the absorbed gas is driven into the glass itself . Experiments were made to see if helium is absorbed during simple volatilisation of aluminium and magnesium by heating these metals in a furnace similar to that employed for heating calcium . Ho absorption occurred . This suggests that the absorption in the case of helium is electrical or mechanical rather than chemical . The gas molecules moving under the electric force with great velocity resemble the a-particles , and are able , as Campbell Swinton 's results indicate , to penetrate the surface of the glass wall to a very slight extent and remain embedded . If , however , the glass is covered with a mirror of aluminium , most of the gas is stopped there and does not reach the glass . An arrangement was devised to compress helium after it had been purified by calcium and run till non-conducting in a spectrum-tube without thereby contaminating it . A second volume of about 100 c.c. , capable of being filled with or emptied of mercury in the same way as the M'Leod gauge , was attached to the apparatus . The whole apparatus was first filled with helium and run to non-conductance , and mercury was then admitted to compress the helium , and the spark-gap measured . It was found that the gas behaved quite normally . Increasing the pressure lowered the spark-gap , and on expanding the original spark-gap was regained . The helium , owing to the larger volume of the apparatus , was not quite so pure as before , and the pressure in one experiment with the sparks passing an inch gap was 0'43 mm. At 0'68 mm. the gap was 12 min. , and at T64 mm. the gap was 3 mm. An attempt was made to get an approximate value in volts for the various spark-gaps by means of current from a large Wimshursfc machine and a Kelvin electrostatic voltmeter . The gap of an inch or 25 mm. corresponded to 16,800 V. , of 20 mm. to 12,500 , of 10 mm. to 10,400 , of 5 mm. to 7900 , and of 2 mm. to 5100 . 4 . Behaviour of Neon and Argon . The results obtained with neon and argon were quite analogous to those recorded for helium . With neon the first stage of non-conductance with an inch gap occurred at a pressure of 0T8 mm. , the second at 040 mm. and the last at 0-07 mm. With argon a great many observations were made and the three pressures were 04)55 mm. , 0'05 mm. , and 0'04 mm. In one experiment with the latter gas the initial pressure in the tube was 0'27 , and 1907 . ] The Electric Discharge Monatomic Gases . it took four hours ' running before the tube became non-conducting . During this time the pressure steadily decreased until the values given above were reached . Increasing the gap to 2 inches only effected a slight reduction of pressure to 0*037 mm. In an experiment with neon which had been run to the last stage and left , the pressure rose during the night from 0*075 to 0*09 , and on heating the tube next morning a pressure of 0*4 mm. developed . Only 30 seconds ' running sufficed to reduce this to 0*2 mm. , when sparks commenced to jump the gap . 5 . Behaviour of Hydrogen , Nit , and Carbon Dioxide . Similar experiments on the pressure at which non-conductance obtained were performed with the gases hydrogen , nitrogen , and * carbon dioxide . With these the non-conducting point was very well defined . Thus with hydrogen practically no current went through the tube at a pressure of 0*04 mm. for a spectrum-tube , and 0*03 mm. for a wide tube of the kind described ( p. 99 ) . It was found that pure hydrogen , derived from palladium hydride , behaved in the same way as . the gas introduced into the apparatus by heating , with a spirit flame , the palladium wire of a regulator such as X-ray bulbs are now commonly provided with for lowering the vacuum . Cathode fluorescence commences in hydrogen in a spectrum-tube at 0*1 mm. , the gap was 5 mm. at 0*07 mm. , and 10 mm. at 0*06 mm. In nitrogen non-conductance is reached at about 0*035 mm. , and in carbon dioxide at about 0*02 mm. , both for an inch gap . At a pressure at which a hydrogen tube would give an inch gap a carbon dioxide tube would give only a millimetre gap . [ Special experiments were performed with pure nitrogen to ascertain whether , after prolonged running , the pressure at which non-conductance set in was raised as in the case of helium , but with negative result . In a tube in which repeated additions of nitrogen were absorbed by the electrodes under the discharge , the pressure at which non-conductance occurred with an inch gap was the same at the end of the experiment as at the beginning with nitrogen which had not been run.\#151 ; October 21 . ] The gas generated from the electrodes and walls of a new spectrum-tube during running behaved , as its spectrum indicates , like a mixture of hydrogen and carbon dioxide and with an inch gap is non-conducting at 0*03 mm. It is remarkable how abruptly conducting power ceases when the pressure falls lower than 0*04 to 0*02 in common gases . The application of powerful coils may cause a discharge below these pressures , but only by first lowering the vacuum . The facilitation of the discharge by the use of electrodes of the alkali metals or calcium is analogous . H 2 Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 The action of these metals is probably to supply hydrogen sufficient to conduct the discharge . The evolution of hydrogen from calcium during heating formed the subject of frequent reference in the last paper . In operating the calcium furnace enough hydrogen is always evolved on heating a fresh piece of calcium to make the vacuum a far better conductor of heat than air at atmospheric pressure . Probably hydrogen-free calcium has never yet been prepared . There are probably many other reasons , more or less well recognised , that account for the impression that the degree of rarefaction in a vacuum incapable of conducting the discharge is extreme . Apparatus to be exhausted is usually made with a constricted orifice where it is to be sealed off . The free path of the gas becomes comparable with the diameter of this constriction at about 0T mm. , or higher in heavy gases and vapours . Below this pressure there is properly speaking but slight difference of pressure between the two sides of the orifice , using the word pressure in a hydrostatic sense , even though on one side a perfect vacuum is maintained . Diffusion alone , not flow , operates to equalise the concentration of the gas on the two sides , and therefore gauge readings of pressure in apparatus connected to the gauge with a narrow orifice are not strictly pressure readings at all . A more important error , probably , of the readings is the usually invariable presence of vapour which a compression gauge will not detect and a pump will not remove . In the present measurements constrictions were avoided and vapours removed by the action of calcium , and these two facts probably account for the pressures at which 11011-conductance obtains being comparatively high . It is doubtful whether the lower pressure recorded in the case of carbon dioxide is real or due to the property of carbon dioxide of condensing on glass surfaces , vitiating the gauge readings . 6 . Behaviour of Mercury Vapour . In the first series of experiments the mercury was contained in an H-tube provided with two electrodes , and was connected to a shortened fall-tube , which , when the mercury was boiled out , acted as a Sprengel pump worked with the condensed mercury . After the apparatus had been exhausted as completely as possible by the mercury pump , the mercury in the tube was rapidly boiled and the exhaustion continued by means of the condensed globules of mercury falling through the fall-tube . Owing to the liability of the glass to crack during prolonged heating the method was abandoned . But with this apparatus the cathode fluorescence of the discharge was not observed when the temperature of the mercury was above 90 ' , and the tube was non-conducting to an inch gap below 60 ' . 1907 . ] The Electric Discharge in Monatomic Gases . 103 In the next experiments the apparatus was exhausted by means of calcium , the mercury being boiled vigorously , and a heavy discharge being passed through the tube during the operation . After this treatment the mercury remained non-conducting , and fluorescence was observed at much higher temperatures than if the calcium treatment had not been adopted . The cathode fluorescence was observed up to temperatures of about 110 ' , which corresponds to a pressure of 0*5 mm. The spark-gap was 10 mm. at a temperature corresponding to a pressure of about 0*15 mm. , while below 0T mm. the mercury vapour conducted with difficulty . Hence mercury vapour resembles the monatomic gases both in the effect of impurities and the high pressure at which it remains non-conducting . 7 . Pressure in an X-ray Tube filled with Helium or Hydrogen . In order still further to test the view that helium conducts the discharge normally except for the higher pressure at which the various phenomena of the discharge make their appearance , an X-ray bulb of 8 cm . diameter was attached to the gauge in addition to the spectrum-tube , and the whole apparatus thoroughly freed from gas . Helium was admitted and run in the spectrum-tube till the discharge passed an inch gap at a pressure of 041 mm. The mercury in the gauge was then momentarily lowered , and small successive quantities of the helium removed by the pump , and the appearance of the X-ray tube observed . The hemispherical area of fluorescence accompanied by the production of X-rays just able to penetrate the glass was observed at a pressure of 0*31 . At 0*25 mm. rays capable of penetrating 02 mm. of aluminium escaped the tube and the spark-gap was 1'5 mm. At 0*21 the spark-gap was 17 mm. and the bones of the hand could be well seen . At 0T5 mm. the spark-gap was 22 mm. and the flesh of the hand was quite transparent to the rays . It must be pointed out in this experiment that the helium , though pure at the start , must have become contaminated as the pressure was reduced , owing to vapour from the rest of the apparatus diffusing back during the exhaustion , and to gas generated from the electrodes . For this reason the pressures corresponding to the longer spark-gaps are probably too low , and as the exhaustion proceeded , approached more and more closely to the values for a common gas like hydrogen . But , throughout , the appearance of the tube , but for the greenish glow at the commencement , was quite normal . In the same X-ray tube , hydrogen derived from a palladium regulator gave the following values:\#151 ; Fluorescence was plain at 0'13 mm. , the gap was 10 mm. at 0*1 , 20 mm. at 0*08 , 30 . mm. at 0*05 , 40 mm. at 0*035 , and 115 mm. at 0*02 . Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 , An X-ray bulb of the usual simple " bianodal " form and size , 13 cm . diameter , was attached to the gauge and exhausted entirely with the mercury pump in the ordinary way , the tube being heated in an oven and the discharge kept passing after the fluorescent stage had been attained . This operation took all day , whereas with calcium it could have been done easily within the hour . After cooling , the tube was run , and the pressures corresponding to different spark-gaps measured . The pressure varied from 0'008 mm. to 0'005 mm. with a gap from 4 cm . to 9 cm . The tube was then pumped as empty as possible , and subjected to the action of calcium to remove vapours . Hydrogen was then introduced through a palladium regulator . Now it was found that the pressures for corresponding spark-gaps were higher , and ranged from 0'045 with a spark-gap of 2 cm . to O012 with a spark-gap of 9 cm . It is probable that this difference is due to the absence of condensable vapours in the second case , and that in no case the real pressure in an X-ray tube is below the hundredth of a millimetre . 8 . The Relation of Potential to Pressure at High Pressures . On the view put forward to explain the high pressure at which helium becomes non-conducting , a space filled with a certain number of helium molecules conducts the discharge similarly in every way to the same space filled with about one-tenth to one-fifth the number of molecules of a common gas like hydrogen . This point of view at once brings into line the behaviour of helium at atmospheric pressure . At this pressure helium conducts the discharge in a similar manner to hydrogen at a pressure of several centimetres\#151 ; that is to say , the discharge passes through helium at atmospheric pressure as a ribbon or flickering line of light . In order to investigate this point more closely , the curves connecting pressure and voltage in hydrogen and helium were compared in a very long wide tube by the aid of an 8-plate Wimshurst machine and a Kelvin electrostatic voltmeter . The current was kept constant , by regulating the speed of the machine , at about 03 milliampere . The voltage in hydrogen remained at a minimum of about 1100 Y. from 0'62 to 0*3 mm. , rising rapidly above and very suddenly below these limits . In helium the minimum potential was below 1000 V. , the minimum range of the instrument , at from 6 to 0'54 mm. The tube was 70 cm . long , 25 mm. diameter , with two aluminium discs 15 mm. diameter , 64 cm . apart . The helium employed was spectroscopically quite pure at the commencement of the experiment , having been fractionated by charcoal cooled in liquid air , but no special effort was made to remove the unavoidable contaminations from taps , elec1907 . ] The Electric Discharge in Monatomic Gases . trodes , etc. , introduced during the experiment . At 60 mm. the potential in helium was 7750 V. , and in hydrogen this same potential was reached at 12 mm. In hydrogen at 30 mm. the potential was about 16,000 V. , while in helium at the same pressure the potential was- 3400 V. The smoothed curves are shown in the figure . 772,771 . '\#163 ; SSL/ XE . In the curves drawn in dotted lines the scale of the pressure axis is increased 100 times , so that these curves represent the relation of voltage with pressure up to 0'5 mm. In specially purified helium the curve would , of course , be very considerably displaced to the right . The curve for argon at high pressure is also included in the figure , and it will be seen to approach helium more nearly than hydrogen . The fact that argon becomes non-conducting with an inch spark-gap at the same pressure as hydrogen does not truly represent the relation between the two gases , for at higher pressures up to the pressure of maximum conductivity , argon , like helium , conducts *less readily than hydrogen , while in the region of high pressure it , like helium , conducts far more easily . The monatomic gases in general appear to he what has been termed electrically inert , and if the effectiveness of a molecule in allowing or resisting the passage of a discharge Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 , is to be associated with the number of relatively free electrons it contains , the monatomic gases appear from their electrical , as well as from their chemical , inertness to be relatively deficient in easily displaceable electrons . But this point of view carries with it the corollary , since even in the purest state the monatomic gases are undoubtedly capable of conducting and becoming ionised , that their chemical inertness is relative rather than absolute . This was the view taken , we believe , by Dr. Larmor in connection with the previous paper . Possibly the results described may be connected with the observations of Strutt , * who found the spark potential in helium and nitrogen greatly affected by minute traces of impurity , and of Warburg , f who found the cathode-fall in gases greatly affected by moisture and other impurities . But even if impurities exert a specific " catalytic " effect on the electrical properties of the gas with which they are mixed , apart from the effect proper to their partial pressure , it does not affect the conclusion that the monatomic gases are relatively electrically inert . We wish to express our indebtedness to the Carnegie Trust for some of the apparatus used in the measurements given in this section . 9 . Retention of the Rare Gases Aluminium Electrodes . In Section 2 it was recorded that a batch of new spectrum-tubes developed the helium spectrum during preparation , and the matter appeared to call for fuller examination . The conditions under which the spectrum-tubes were prepared were novel , in that the occluded gas was not pumped out , but absorbed chemically within the apparatus . Since six tubes with exceptionally heavy electrodes were treated at once , the conditions were very favourable for the detection of a minute trace of an inert gas produced by the discharge or evolved from the electrodes which otherwise would have been certainly overlooked . At first it was thought that the results might be connected with those of v. Hirsch , | who observed the continuous formation of a gas during the cathode-ray discharge , independently of the nature of the gas initially present , with properties which pointed to a possible molecular weight of 4 . But Dr. von Hirsch about this time came and re-examined his gas in this laboratory by means of the calcium apparatus , and found it was certainly not helium . A quantity of new aluminium wire and discs of the same kind as employed in the spectrum-tubes was procured from the maker of the tubes . This was heated to a very high temperature in a furnace similar to ttfose employed for * ' Phil. Trans. , ' 1900 , A , vol. 193 , p. 377 . t 'Wied . Ann. , ' 1890 , vol. 40 , p. 1 . f ' Phys. Zeit . , ' 1907 , vol. 8 , p. 461 . 1907 . ] The Electric Discharge in Monatomic Gases , calcium , but it failed to give the least indication of helium . Other spectrum-tubes at a later date from the same maker also did not give the least trace of helium when examined under conditions identical to those described . The most probable explanation appeared to be that some of the electrodes in the first batch of tubes , probably the disc anodes , for the cathodes were almost certainly new , must have been old and used in previous experiments with helium before they came into our hands , and that such electrodes must be capable of retaining sufficient gas to show a spectrum when remounted in new tubes . At the close of the investigation the second point was specifically examined . The electrodes of the tubes used in the experiments of Sections 3 and 4 were chosen for the test . The neon tube was first tried . It had been cut down five months before and since left open to the air . The cathode was first mounted in a new spectrum-tube with a new similar electrode fresh cut from a length of new aluminium wire of the same size and quality . It was attached to a calcium furnace through a tap and during the running the flow of gas wras regulated to keep the tube fluorescent . As the spectrum cleared the neon yellow D5 ( 5852*6\lt ; f showed clear and distinct in the sodium , hydrogen , and mercury spectrum , its position being exactly fixed with reference to the two sodium lines . The tube was cut down and the disc anode of the old tube inserted in place of the new electrode , and then the tube was re-examined as before . Again D5 was seen , but much brighter than before . After the calcium furnace had cooled , it was filled with mercury and the contained gas compressed about 15 times into a second spectrum-tube . Now the latter showed unmistakably to the eye the characteristic orange glow of neon , and the spectrum showed all the chief red and orange lines together with the helium line D3 faint , and the lines of hydrogen and mercury . The original neon , which had been prepared by Mr. Berry by Dewar 's fractionation method , showed the helium D3 in about the same relative intensity . It can only probably be removed from the spectrum by fractionating the gas with liquid hydrogen . Contrary to the statement in Travers ' " Experimental Study of Gases " ( p. 312 ) , the neon green line ( 5016 ) was not visible . The helium tube was then examined . It had been cut down five months previously , but in this ease had been sealed up , unexhausted , to exclude moisture . Both electrodes were sealed in a new spectrum-tube . The helium yellow D3 was observed almost immediately after the commencement of running , and later the helium red ( 6677 ) faintly . From previous experience , the quantity of helium present could be accurately estimated . Its partial pressure was about 0-01 mm. , and as the volume of the apparatus was about 200 c.c. , the total quantity was about 3 cubic millimetres , measured at atmospheric pressure . Messrs. F. Soddy and T. D. Mackenzie . [ Oct. 8 , This quantity would have given the whole spectrum brilliantly if the apparatus had been filled with mercury , but the result was certain without this being done . The argon tube , like the neon tube , had been left open to the air for five months . The anode only was sealed into a new tube with a new electrode . It gave , on running , clear but faint argon lines in the blue region of the spectrum , and on compressing the gas at the end of the experiment the blue argon spectrum was clear . [ About a year previously , before any neon had been used in the laboratory , a number of old spectrum-tubes had been broken up and the electrodes recovered . These had since remained in an open dish exposed to air . A dozen of these electrodes , selected at random , were heated in a vacuum furnace to the melting point of aluminium , and the gases evolved absorbed by calcium in a second vacuum furnace . The helium yellow line , D3 , was seen clear but faint . On compressing the gas about 14 times by admitting mercury , the prominent red and green lines of the spectrum were also seen . The quantity of helium was estimated to be about a fifth of a cubic millimetre.\#151 ; October 21 . ] These experiments , therefore , prove that aluminium electrodes tenaciously retain traces of argon , neon , and helium after they have been used in connection with these gases , and indicate that the explanation advanced for the extraordinary appearance of helium in the first batch of spectrum-tubes is probably correct and sufficient . 10 . The Campbell Effect . The glass parts of the spectrum-tubes , of which the electrodes had been used in the experiments described in last section , were examined for the effect described by Campbell Swinton , * who showed that if the glass of a vacuum-tube used with hydrogen or helium is fused in a flame it becomes clouded and under the microscope is seen to be permeated to some depth from the inside surface with a multitude of minute spherical bubbles . All three of our tubes showed this effect with the most remarkable clearness , but the argon tube was by far the best . Indeed , when the glass of this tube was fused it appeared to boil , and the bubbles could be seen and heard bursting . If the heating was stopped sooner the glass surface at first sight appears completely devitrified , but under a very small magnifying power the effect could be seen to be due to bubbles which were quite large where the glass had been most strongly heated . In the helium and neon tubes , and also the argon tube , the cathode chamber showed this effect everywhere where particles travelling at right angles to the surface of the wire cathode could reach the glass , but no effect whatever appeared behind the * 'Roy . Soc. Proc. , ' 1907 , A , vol. 79 , p. 134 . 1907 . ] The Electric Discharge in Monatomic Gases . plane cutting the wire cathode at right angles drawn through the end of the glass tube in which the cathode w*as sheathed . The anode chamber of the helium and neon tubes showred a well-marked line of bubbles corresponding to the edge only of the anode disc , absent on the side where the side tube had been attached . In the argon tube this was absent , but the small part of the anode chamber immediately bordering on the capillary was strongly affected . [ The fact that the argon tubes showed the effect so prominently raised a doubt whether Campbell Swinton 's explanation , that the bubbles are caused by the discharge gases being driven into the glass and remaining embedded below the surface , could be correct . Some of the glass from the argon tube was heated in an iron tube in a vacuum furnace , and the gases absorbed in a second furnace by calcium . The temperature , subsequently determined by a platinum and platinum-iridium couple , was in the neighbourhood of 1300 ' C. The glass frothed copiously , and was largely blown out of the iron tube . Argon , if present at all , could only have been but the merest trace as , although a faint argon spectrum was observed , it was not more than could be accounted for by a slight leak in the apparatus which interfered with the test . Certainly the main frothing of the glass was not due to embedded argon , and probably no argon was given off by the glass . It was considered more satisfactory to try the glass of the neon and helium tubes in a similar way , as the appearance of these gases , if observed , is less equivocal than in the case of argon . No trace of neon was obtained from the glass of the neon tube which showed the Campbell Swinton effect strongly . With the glass of the helium tube the line D3 was faintly visible . Some more of the glass was , therefore , first heated in an exhausted tube of Jena glass to a red heat to drive off gases condensed on the surface . The temperature was not high enough to develop bubbles , and the glass remained quite clear . This glass was then heated in a vacuum furnace as before to about 1300 ' C. No trace of helium was observed , even when the apparatus was filled with mercury . These experiments show that the gas which causes the bubbles is not the discharge gas driven into the glass . The bubbles are in all probability a secondary effect , due to the chemical decomposition of the glass under the influence of local heating produced during the bombardment . _ There are probably in glass always sufficient undecomposed carbonates or sulphates to account for the effect , for porcelain , which is fired at a far higher temperature than glass , gives off a copious supply of gases consisting largely of carbon dioxide and hydrogen when heated in a vacuum above 1000 ' C. If the experiment is prolonged , several cubic centimetres of gas may be pumped off.\#151 ; October 21 . ]

rspa_1908_0004

0950-1207

Note on the sensibility of the ear to the direction of explosive sounds.

110

112

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

A. Mallock, F. R. S.

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10.1098/rspa.1908.0004

Fluid Dynamics

Astronomy

Fluid Dynamics

110 Note on the Sensibility of the Ear to the Direction of Explosive Sounds . By A. Mallock , F.R.S. ( Received October 22 , \#151 ; Read November 21 , 1907 . ) Soon after the introduction of modern rifles , which give their projectiles a velocity much higher than that of sound , I noticed that when standing in a position in front of the gun and not far from the line of fire , the sound seemed to come , not from the firing point , but from some point considerably in advance of the gun . The natural explanation seemed to be that the sound thus heard was not that of the explosion itself , but was caused by the wave-surface , which is generated in the air by the projectile , moving at a velocity higher than sound . In 1898 I made some observations at the ranges at Broundown to see if the apparent directions agreed with this supposition . A large range like Broundown , however , at which many parties are firing at the same time , was not a very good place for such observations , but in the present year I have again made similar experiments under much more favourable circumstances . It is clear ( if the source of the sound is due to the wave caused by the projectile ) that the apparent direction of the sound will be the normal to the wave-surface , and that if the direction of this normal is known , the velocity of the projectile , at the time that that particular portion of the wave-surface was generated which ultimately reaches the observer , can be calculated . I now record these observations , not as giving a practical method of ascertaining the velocity of projectiles , but as showing that the ear can distinguish with considerable accuracy the direction of a sound which consists , not of a train of waves , but , at most , of two waves only . The figure gives the plan of the range and the stations at which the observations were made . The arrows through these points show the direction of the sound as-judged by ear . Each arrow is the mean of eight observations which rarely differed among themselves by more than two or three degrees . That portion of the wave-surface which passes the observer at any station was generated at the point where the apparent direction of the sound cuts the line of fire , and since the trace of the wave on the trajectory necessarily has the velocity of the projectile at the place where it was formed and moves-along the normal with the ordinary velocity of sound , it is plain that at those points the velocity of the bullet is the velocity of sound -*\gt ; the sine of the angle which the tangent to the wave-surface makes with the trajectory . Sensibility of the Ear to the Direction of Explosive Sounds . Ill The spots , + , show the velocities thus computed , and the full curve gives the actual velocity , as determined by firing , at various ranges up to 1000 yards , into a ballistic pendulum . Scale for The arrows show the apparent direction of the sound at the stations ABC ... The dotted lines are the normals to the wave-surface , calculated from the known velocity of the projectile . The full curve is the velocity of the projectile , obtained from experiments with the ballistic pendulum . The spots , + , are the velocities of the projectile , as deduced from the observed direction of the sound . The method by which the observations of the direction of the sound were made rendered it almost impossible for any bias on the part of the observer to affect the result . At each station a piece of paper fixed to a drawing board was placed on the ground and a line ruled on it was directed to the firing point . At each shot the observer determined in his own mind what point in the horizon the sound seemed to come from ( this could be located by reference to some distant tree or other object ) , and a line was then drawn on the paper in that direction . After all the observations had been completed a plan of the range was made from the 25-inch Ordnance Map and the positions of the observing stations were marked . The observed angles between the direction of the sound and the line joining the station with the firing point were then laid off , and thus the angles between the direction of the sound and the line of fire were found . 112 Sensibility of the Ear to the Direction of Explosive Sounds . The agreement of the values of the velocities thus obtained with the true-velocities shows the degree of accuracy with which the direction of the sound was estimated . In this case the difference between the true and observed directions was seldom more than a few degrees and was generally in one direction . A sound which is caused by the detached waves , such as those which accompany a bullet , can scarcely be said to have a pitch , but the wave-length is certainly small compared with the distance between the ears , and is-indeed comparable with the dimensions of the bullet itself . It would seem , therefore , that the ears can determine the direction of a sound , not only by difference of phase , but by the actual difference in the times at which a single pulse reaches them . It may be mentioned that the difficulty in determining the apparent direction of the sound increased considerably as the observer approached the firing point , for there the noise of the actual explosion became comparable with that caused by the bullet . At a distance of 500 yards the noise of the explosion was inconsiderable and at 1000 yards almost inaudible .

rspa_1908_0005

0950-1207

Magnetic declination at kew observatory, 1890-1900.

113

113

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

C. Chree, Sc. D., LL. D., F. R. S.

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10.1098/rspa.1908.0005

Meteorology

Tables

Meteorology

113 Magnetic Declination at Keiv Observatory , 1890\#151 ; 1900 . By C. Chree , Sc. D. , LL. D. , F.R.S. , Superintendent . Observatory Department , National Physical Laboratory . ( Received November 2 , \#151 ; Read December 12 , 1907 . ) ( From the National Physical Laboratory . ) ( Abstract . ) The paper deals with the phenomena exhibited by the magnetic declination at Kew from 1890 to 1900 . The magnetograph curves have been measured on every day of this period , whether disturbed or undisturbed , and the data from days of the different species are contrasted . Diurnal inequalities are got out for ordinary days , excluding those of large disturbance , and separately for the highly disturbed days , and the differences between these , and the points wherein they differ from the corresponding inequalities from quiet days , are investigated . The disturbed days show a well-marked regular diurnal variation , which differs in many notable respects from that observed on ordinary days . When the inequalities are analysed in Fourier series , it is found that the difference mainly centres in the 24-hour term , whose amplitude and phase seem both largely influenced by disturbance . The variation in the phenomena presented by disturbances throughout the year are investigated from several points of view . The absolute range of the declination ( absolute maximum less absolute minimum ) was determined for every day of the 11 years , and special attention is given to the variation of this quantity throughout the year , and from year to year . With a view to throwing light on the theories of Arrhenius , Maunder and others , on the origin of magnetic storms , a minute comparison is made of the relationship between the absolute ranges and ( Greenwich ) sunspot areas throughout the 11 years . Whilst the results do not preclude the possibility that Arrhenius ' theory may be true of a certain number of magnetic storms , they seem to indicate that it cannot be a complete explanation of the facts . The paper aims at reaching results of a novel or critical character , and makes no attempt to chronicle the very bulky material , embracing over 100,000 actual curye readings , on which it is based . The cost of the reductions has been partly defrayed by a grant obtained from the Government Grant Committee in 1904 .

rspa_1908_0006

0950-1207

On the frictional resistances to the flow of air through a pipe.

114

139

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

John H. Grindley, D. Sc. (Vict.)|A. H. Gibson, M. Sc. (Vict.)|Professor Horace Lamb, F. R. S.

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10.1098/rspa.1908.0006

Thermodynamics

Tables

Thermodynamics

]\gt ; On the Resistances to th Flow of Air through Pipe . By JOHN H. GRINDLEY , D.Sc . ( Vict . ) , and A. H. GIBSON , M.Sc . ( Vict . ) . ( Communicated by Professor Horace Lamb , F.R.S. Receired April 19 , \mdash ; Read May 23 , \mdash ; Received in revised form Octci ) , 1907 . ) PAGE S1 114 S2.\mdash ; Description of the appliances 115 S3.\mdash ; The theory of the flow of a gas through a pipe and the deduction of general equations required in the research 118 S4.\mdash ; The determination of the essential di mensions of the experimental tube 121 S5.\mdash ; The method of conducting the experiments and the details of a typical experiment 122 S 6.\mdash ; The results of the experiments 125 S 7.\mdash ; The determination of the critical velocity for the flow of air in the tube 1.30 S \mdash ; The determination of the coefficient of viscosity and its variation with temperature 130 S9.\mdash ; The determination of the resistances to the passa ge of air in eddying motion through the tube , with a determination of the true equation of flow 135 1 . Introduction . The research described in this paper was commenced by Dr. rindley at the suggestion of Professor Osborne eynolds in the Whitworth Engineering Laboratories , the Owens College , Manchester . Mr. Gibson continued the research after Dr. Grindley had left Manchester . The experiments were commenced with the object of determining , on a larger experimental scale than usual , the coefficient of viscosity of air and other gases and the variation of this coefficient with temperature . The present research , however , developed into a more complete investigation of the resistances to the passage of air through a pipe . ] velocities of flow of the air through the pipe in the experimenGs by Dr. Grindley were for the most part above the critical velocity , the critical velocity being the velocity of flow below which the motion is steady or stream line and above which the motion becomes eddying or turbulent , the laws of resistance the passage of the air bein . different in the two kinds of flow . These experiments by Dr. Grindley indicated the value of the critical velocity of flow through the particular pipe used in the experiments , but the few experiments at velocities of flow below the critical were insufficient to On Resistcmces to Flow of . a . 115 permit any deductions on viscosity to be made , and it was left to Mr. Gibson to make all the experiments at velocities of flow belo the critical from the results of which the coefficient of viscosity has been deduced in this paper . The scope of the research may best be shown by the summar of some of the more important deductions . ( 1 ) The coefficient of viscosity , , of dry air at C. is in . sbsolute units . ( 2 ) The law of variation of with temperature has been determined between the limits C. and C. , and is found to represented by an equation of the form where and are constants , and is the absolute temperature . ( 3 ) The absence of dependence of on the density of the air has lreceived experimental verification . ( 4 ) The critical velocity for a small lead pipe\mdash ; about 1/ 8 an inch been determined . In the turbulent motion of air through a pipe , the resistance has been found to be independent of the pressure of air in the pipe , and to be proportional to , where for this pipe . ( 6 ) The law of variation of this resistance with temperature has been determined . 2 . Description of the Appliances . The general arrangement of the apparatus is shown in . It consists two gasholders A and each of a little over 3 cubic feet capacity and connected by a length of lead tubing of roughly 1/ 8 of an inch internal diameter . Part of this length is to be used as the experimental tube , and at the ends of this , arrangements for measuring the pressures are provided . The gasholder A contains air which can be forced through the experimental tube and into by the simple expedients of water into the lower part of A and emptying of water contained by it at the beginning of each experiment . These vessels A and were calibrated so that the volume of air or entering in any time interval could be obtained at once from the graduated gauges and bb by observing the heights of the columns of water in these tubes . The length oftube between A and is practically all wound on a central cylinder of brass , the tube being wound at a constant small tension and fitting into a properly turned helical groove on the outer surface of the drum , VO L. LXXX.\mdash ; A.

rspa_1908_0007

0950-1207

Exterior ballistics. (No. 2.)

140

142

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

George Forbes, F. R. S.

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10.1098/rspa.1908.0007

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; By , F.R.S. Exterior Ballistics . ( No. 2 . ) ( Received November 6 , \mdash ; Read December 12 , 1907 . ) a curve which may be described as the characteristic curve of any gun , aract iensity oibre ients ohese aharge aThat communication contained ( construction feducingI.ommunication tuthor ehich trdinates a new characteristic curve when the muzzle velocity changed ; ( 4 ) a comparison of range-tables showing how , by help of these laws , from the chal.actel'istic curve for a gun of any calibre and muzzle velocity , to deduce the a gun of any other calibre and muzzle velocity ; and ( 5 ) empirical formulae enabling a practical runsight to be so constructed that when set for true range , it is also set for the true elevation , whatever the calibre of the , the muzzle velocity , the air density , and the rate of of may be . 6 . At a ione of the Royal Society last year , a model of this gunsight , made by . W. G. , Whitworth , and Co. , was shown , and later a complete sight for a 6-inch was made by the same firm , and was tested and approved of by Naval experts at Portsmouth , but it has not been adopted for the Britisl ] Navy . allthor had designed this sight use in conn ection with a range-firnler , and also with a new ) in strument , and a mechanical transmission of ranges to the gunsights , so designed that the runs of all calibres are kept by a motor continuously set the varying the speed of the motor is checked by occasional observations of the range . The advantages claimed for this system of gunsighting All guns ) set to the true , a ship may carry guns of various ] , and the abolition of the secondary armament in our battleships is unnecessary , in so . as fire-control is a consideration . ( 2 ) The oflicers , during an action , are relieved from much brain-work . ( 3 ) The best brains of the do ot need to be concentrated on a platfor1n at the -head . ( 4 ) Surrender of a ship when that mast is shot away becomes lmnecessary , because control of all of the ship 's guns can be . Soc. Proc January , 1905 . Exterior Ballistics . cArried on from any turret . These can be only by a sight like the one first exhibited by the author to the Society , which is ahvays set to the true whatever may be the nruzzle velocity , airdensity , and rate of of As the author l.efelTed to this gunsight in his previous on " " Exterior Ballistics he desires thus shortly to record the success ) attended its construction , before now to some new ) allistic theorems . 7 . Angle of Dcscent.\mdash ; A knowledge of the inclination of the tra , jectory of a shot to the horizontal ] at the end of its is necessary for estimating the extent of the zone . to the principle of the rigidity the trajectory , proved in artillery text-books , if the axis of the has to be inclined at an of elevation to the line of to hit a target at the on a horizontal plane , the is correct for any vertically above the former ; so that if the vertical angle between the two target positions be not great , the trajectory is simply raised that angle . Call this angle , and let be the range on the horizontal plane for the elevation . From it is clear FIG. 1 . that , if OR and , and if SOP POR , and , the an gle of descent , when and are educed initely , then in the limit . 8 . The characteristic curve introduced by the author gives the ession of this law very neatly . In , OR is a range and FIb . 2 . Through draw OQ ) arallel to the tangent at , and produced . Then xterior B produced for moderate elevations ; therefore Thus PR is the angle of elevation and the angle of descent , or their ents . 9 . \mdash ; If in the line OQ produced cuts the aracteristic curve at , draw perpendicular to produced . If , as a first approximation , the curvature of OPP ' be taken as uniform , then OR ' and if the angle of descent known at any range , twice this angle is approximate]y the angle of elevation at twice the range . This rule for extending a -table to ranges has been known as approximation . The geometrical form of proof clearly its limitations . 10 . To trace the from the elevations and corresponding ranges given in a range-table:\mdash ; Rule : In fig. ) , let be the range and SO the elevation . Take any other range OR ' , and draw Ox ' so that SOx ' is the corresponding elevation . Through draw vertically , meeting in point P. Then the locus of is the trajectory . This follows directly from the principle of of the trajector For if Ox ' were horizontal , the angle of elcvatio1l vould carry the shot to and that principle says that wheu Ox ' is inclined the shot is carried to the poiIlt P. We must not assume , however , a mathematical accuracy in that principle in cases } ) is not a small angle . But even where not mathematically exact this construction is useful .

rspa_1908_0008

0950-1207

The effects of temperature and pressure on the thermal conductivities of solids. Part II.\#x2014;The effect of low temperatures on the thermal conductivities of pure metals and alloys.

143

145

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Charles H. Lees, D. Sc., F. R. S.

abstract

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en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0008

10.1098/rspa.1908.0008

Thermodynamics

Electricity

Thermodynamics

143 The Effects of Temperature and Pressure on the Thermal Conductivities of Solids . Part II.\#151 ; The Effect of Lorn Temperatures on the Thermal Conductivities of Pure and Alloys . By Charles H. Lees , 11.Sc . , F.R.S. , Professor of Physics in the East London College , University of London . ( Received November 8 , \#151 ; Read December 12 , 1907 . ) ( Abstract . ) The object of the work described in the present paper was to extend the measurements of Thermal Conductivities of Metals and Alloys made by Lorenz , Jager and Diesselhorst , and others at temperatures between 0 ' C. and 100 ' C. down to the temperature of liquid air , and thus provide a means of comparing the Thermal and Electrical Conductivities of these substances over a much wider range of temperature than has hitherto been possible . The method adopted was a modification of that used originally by Wiedemann and Franz . A rod of the metal , 7 or 8 cm . long , 06 cm . in diameter , was placed in the axis of a vertical copper tube of 2*7 cm . internal 33 cm . external diameter , 9'5 cm . long , closed at the top . The lower end of the rod fitted into a copper disc , which in its turn fitted into the lower end of the copper tube . The joints were accurately made and were smeared with olive oil to exclude air and improve the thermal contact . The heat which flowed along the rod was supplied electrically by means of a current through a fine platinoid wire wound on a short thin brass sleeve , which was slipped on to the upper end of the rod . The difference of temperatures at two points of the rod , between the heating coil and the point where the rod entered the disc forming the lower end of the tube , was measured by means of two platinum thermometers , the wires of which were wound on two short thin brass sleeves , capable of sliding along the rod . The three sleeves fitted the rod closely , and thermal contact was improved by smearing rod and sleeves with a little olive oil . The apparatus was placed in a Dewar vacuum vessel , which could be filled with liquid air . When the apparatus had cooled down to the temperature of the liquid , the excess of liquid was poured off , and observations commenced . Owing to the heat supplied to the rod , and the flow of heat from without , the Prof. C. H. Lees . Effects of Temperature and [ Nov. 8 , temperature of the whole apparatus rises , and it is shown in the complete paper under what conditions observations taken under such circumstances can be used to determine conductivities . In making a determination , the difference of resistance of the two platinum thermometers was first measured with the heating current round the rod zero , then with the current flowing , then again with it zero . The difference between the second and the mean of the first and last gives the difference of resistance due to the flow of heat down the rod . The instruments used in measuring the watts spent in the heating coil were standardised , and a correction was made for the heat conducted away from the rod along the wires supplying the current and along the wires to the platinum thermometers . The effect of each sleeve on the flow of heat through the rod in its neighbourhood was calculated and allowed for . The platinum thermometers were standardised by observations of their resistances in steam at about 100 ' C. , in ice at 0 ' C. , and in liquid oxygen boiling under a reduced measured pressure . All temperatures are by this means reduced to the standard constant volume hydrogen thermometer . Resistance coils were standardised by comparison with standards tested at the National Physical Laboratory or at the Reichsanstalt . The rods used were turned from materials supplied as pure by firms , of repute , and have been tested for density and electrical conductivity . The following table embodies the results obtained , together with those given for higher temperatures by Jager and Diesselhorst , and it will be seen that they justify the following statements:\#151 ; The thermal conductivities of most pure metals decrease as the temperature rises within the range \#151 ; 160 ' to 100 ' C. The thermal conductivities of all alloys tested increase as the temperature rises within the range \#151 ; 160 ' to 100 ' C. 1907 . ] Pressure on the Thermal Conductivities of Solids . 145 Table of Thermal Conductivities of Pure Metals and Alloys between \#151 ; 160 ' and 18 ' C. , as deduced from the present Experiments , compared with those at 18 ' and 100 ' C. given by Jager and Diesselhorst as the results of their Experiments . Substance . Chemical and physical state . From the present experiments . Jager and Diesselhorst 's results . At -1603 c. At -80'C . At 0'C . At +18 ' C. At 18 ' C. At 100 ' C. Chemical and physical state . j Copper Pure soft drawn 1-075 0-960 0-924 0-916 0-918 0-908 ! Pure Silver 0*999 Ag 0-998 1 -006 0-981 0-974 1 -006 0-992 0 -9998 Ag Zinc Pure redistilled 0-278 0-269 0-269 0-268 0-265 0-262 Pure cast cast Cadmium Ditto 0-239 0-228 0-219 0-217 ! 0-222 0-216 Ditto Aluminium ... 0*99 A1 0-514 0-493 0-502 0-504 0-480 0-492 0 -99 A1 Tin Pure cast 0-192 0-173 0-160 0-157 0T55 0-145 Pure wire Lead Pure 0-092 0-085 1 0-084 0-083 0-083 ; 0-082 Pure Iron Wrought 0 -152 0-150 OT47 0-147 0-144 : 0-143 0 -9955 Fe Nickel 0*99 Ni 0-129 0-136 1 0T40 0-140 0-142 ! 0T38 0 -97 Ni Steel 0 113 0-115 : o-ii6 0-115 0T08 0-107 o-oi C Brass 0-181 0-223 1 0-254 0-260 German silver 0-043 0-049 ; 0-056 0-059 Platinoid 0-042 0-047 ! 0-058 0-060 ! Manganine ... 0-035 0-040 0-050 0-052 0-053 0-063 j Lipowitz alloy 0-042 0-043 0-044 0-044 1 I

rspa_1908_0009

0950-1207

The action of ozone on water-colour pigments.

146

150

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir William de W. Abney, K. C. B., F. R. S.

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10.1098/rspa.1908.0009

Optics

Chemistry 2

Optics

146 The Action of Ozone on Water-colour Pigments . By Sir William de W. Abney , K.C.B. , F.R.S. ( Received November 21 , \#151 ; Read December 12 , 1907 . ) In 1888 a report* upon " The Action of Light on Water Colours " was-made to the Science and Art Department by Dr. Russell and myself , in which we showed that mineral colours are far more stable than vegetable colours , that the presence of moisture and oxygen are in most cases essential for a change to be effected even in the case of vegetable colours , that every colour is permanent in vacuo , and that the spectrum colours which principally cause fading lie at the blue end . From time to time since then I have occupied myself and experimented with pigments . Amongst others , one set of experiments was made which , is fairly complete , and which I wish to lay before the Royal Society , as it may prove to be a starting point for other investigations . They show that water-colour pigments ( which , by the bye , are usually the same pigments as oil pigments , the only difference between the two being the vehicle in which they are situated ) might fade without any assistance of light when freely exposed to the air , and it is not improbable that the action of light in some measure in the presence of the pigment produces the effective cause in the surrounding atmosphere . It was suspected from the first , and indeed the report alluded to above-implies it , that the fading of colours is due to oxidation . If such be the cause , then the introduction of an active oxidising agent such as ozone ( or peroxide of hydrogen ) into the atmosphere should show the same effect as the prolonged exposure to light . To ascertain if such were the case , strips of varying depths , of different single colours or of mixtures of colours , were prepared , so that the effect might be studied on well-separated particles , and also when they were closer together . In fact , strips were prepared as described in the report . A piece of apparatus was put together , as shown diagrammatically in the following figure ( p. 147 ) . A is a four-cell Grove battery working a coil B , which is connected with C an ozone tube , to which are attached , as shown , a series of wide tubes T ' and T " , in which strips of pigmented paper can be readily introduced . 0 is an oxygen bottle supplying the ozone tube with a slow stream of oxygen . The various strips were well moistened at the back , so that the pigmented surface was damp . * Subsequently printed and presented to both Houses of Parliament . The Action of Ozone on Water-colour Pigments . When everything was arranged , the flow of oxygen was commenced and the coil put in action . The following extract from my note-book of the first day 's work will show the kind of strip and length of time required for experiments with the different colours :\#151 ; June 22 . 11.15 Put into the tubes crimson lake , Payne 's grey , Antwerp blue , and indigo . Bleaching at once began in crimson lake , Payne 's grey , and indigo . 11.45 Took out crimson lake , quite bleached . 12.0 " indigo 12.15 " Payne 's grey Antwerp blue unchanged . 1.35 Put in tubes ultramarine blue , chrome yellow , and a fresh strip of indigo . 1.38 Faint wash of indigo , quite bleached . 2.0 Next 2.15 Took out indigo ; darkest wash gone pale green . 2.30 Put in tube Prussian blue . 3.0 Put in indigo + gamboge* ( i.e. , a green made of these two colours ) , and of Prussian blue + raw sienna ( i.e. , a green made of these two colours ) . Took out chrome yellow and ultramarine blue , and found no appreciable change . * Indigo + gamboge means a green made by mixing indigo and gamboge together ; the + sign always means a mixture . VOL. LXXX.\#151 ; A. . L [ Nov. 21 Sir W. de W. Abney . 3.20 Indigo + gamboge , indigo bleaching ; light washes bleached . Gamboge , light shades quite bleached , and darker shades much lighter . 3.45 Indigo + gamboge , action seemingly over . 4.5 Indigo + Venetian red ( a grey ) , and indigo .+Indian red ( a grey ) put in tube . Rapid disappearance of the blue began immediately , and at 4.20 No trace of the indigo appears but in the darkest wash . 4.30 Action stopped . No further change in the indigo 4- Venetian red or in the indigo + Indian red . No change noticed in Prussian blue , Antwerp blue , or in Prussian blued-raw sienna . Colours exposed to light by Russell and Abney in moist air . Time taken to bleach in damp ozonised air . Composition of colour , according to Winsor and Newton . Unchanged . h. m. Indian red u A variety of iron oxide . Venetian red u Artificially prepared sesquioxide of iron . Burnt sienna u Burnt raw sienna . Yellow ochre u Native earth . Raw sienna u 55 55 Emerald green 0 45 Acetoarsenite of copper . Terre verte u Native earth . Chromium oxide ... u Chromium sesquioxide . Cobalt blue u Alumina tinctured with cobalt oxide . Ultramarine ash u Second quality of blue from lapis lazuli . Chrome yellow u Normal chromate of lead . Altered . V ermilion u Mercuric sulphide . Rose madder 4 0 Lake from the madder root . Brown madder 2 10 55 55 55 Gamboge 0 50 A gum resin . Aureolin u Double nitrite of cobalt and potassium . Cadmium yellow ... 4 0 Sulphide of cadmium . Naples yellow 0 45 Cadmium yellow and zinc white . Indian yellow 4 0 Prepared " purree " from India . Olive green 1 5 Indian yellow , umber , and indigo . Indigo 0 40 Vegetable blue from indigo plant . French blue 3 30 Artificial ultramarine . Permanent blue 3 30 A pure variety of French blue . Payne 's grey 1 0 Indigo , crimson lake , and carbon black . Violet carmine 4 0 A lake obtained from the root of Anchusa tinctona . Purple madder 0 20 Lake from the madder root . Sepia 0 50 From the cuttlefish bags . Brown pink 0 30 Lake from quercitron bark . Vandyke brown 1 15 Native earth . Destroyed . Carmine 0 10 Lake prepared from cochineal . Crimson lake 0 30 55 55 55 A weak variety of Prussian blue containing alumina . Antwerp blue u Prussian blue u Ferrocyanide of iron . 1907 . ] The Action of Ozone on Water-colour Pigments . The table on p. 148 shows the results obtained . The first column is a list of colours exposed to light in moist air the order of stability . It is copied # from the report above mentioned . The second column shows the time taken to bleach or change the colours in a moist atmosphere of ozone , { u signifies that no change took place in the colours after prolonged exposure . ) The third column shows the composition of the different colours ( water ) according to Winsor and Newton 's catalogue . The following table shows the time of fading when certain mixtures were tested:\#151 ; - Mixtures submitted to damp ozone . Time of fading . Remarks . Carmine + Prussian blue Mins . 15 Blue left . " + Leitner 's blue 15 \gt ; 5 Both bleached . Indigo + gamboge 45 " + Venetian red 25 Red left . " + Indian red 25 " + burnt sienna 10 Sienna left . ,5 + Indian yellow 10 Blue gone . " + Vandyke brown 10 , , + yellow ochre Crimson lake + cobalt 10 \#187 ; 30 Cobalt left . 3 , + Antwerp blue ... 20 Blue left . 3 , + Prussian blue ... 3 5 ) It will be seen that the ozone had no effect on any of the colours which light failed to affect with the single exception of emerald green . From its composition it is not strange that some effect should take place in it . Again , it will be noticed that all the colours unchanged by the ozone are mineral colours . In the list of colours destroyed by light are Prussian and Antwerp blue , both of which are of the same composition . Ozone had no effect on either of them . In the report referred to it was mentioned that if bleached Prussian blue were placed in the dark its colour revived . Presumably there is some action caused by light which is absent when the exposure is to ozone Two other colours unchanged by ozone are aureolin and vermilion , ' ; both of which are high up in the " altered " list . In light , vermilion blackened and aureolin lost but little . In regard to the remaining colours the order of bleaching would be slightly altered . Beginning with those which took longer to bleach , we should have\#151 ; Rose madder . Cadmium yellow . Indian yellow . Violet carmine . French blue . Permanent blue . Vandyke brown . Olive green . Payne 's Grey . Gamboge . Sepia . Naples yellow . Carmine . Indigo . Brown pink . Crimson lake . Purple madder . L 2 150 The Action of Ozone on Water-colour Pigments . Those in the list as far as permanent blue took hours to be bleached and should be regarded as permanent so far as moist ozone is concerned . The remainder must be looked upon as fugitive , the five last being very fugitive . Another set of experiments was carried out in which dry ozone was introduced into the tubes , the oxygen bubbling through strong sulphuric acid and passing over phosphoric anhydride before it reached the ozone tube . The pigments were dried in an oven and then placed in the tubes . No change took place in any of the colours , though submitted to the dry ozone for a long period . As in the experiments with light , it is evident that moisture must be present in order that bleaching may take place . It is unnecessary to make any deductions from the experiments , except to point out that the life of the colours will be longer in an atmosphere free from an active oxidising agent . I have to thank Mr. C. E. Woods for the care he took in carrying out , under my direction , the various experiments .

rspa_1908_0010

0950-1207

Preliminary note on the operational invariants of a binary quantic.

151

161

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Major P. A. MacMahon, D. Sc., F. R. S.

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Formulae

Tables

Mathematics

]\gt ; Preliminary on the tional Iof By Major P. A. ) , F.R.S. ( Received October 8 , \mdash ; Read December 12 , 1907 . ) lfy object is to present a theory of operational invariants for the binary quantic of order . Many of the results that are here given have been explicitly or implicitly yiven in the works of Cayley , Clebsch , Gordan , and other writers , but not from the present point of view or in the conve1lient notation that will be adopted . Some quite new results are reached , will be found to throw much light upon the wolk of others . 1 . In the algebraic theory we take the quantic to be and , as alternative symbolic letters to We then have symbolic factol . S of two types , , the snffix type , , and the bracketed or determinant type ( ab ) . In fact , for the substitution ' . the detel'minant of which is have ; where ( AB ) . The real of is I write symbolically ; whence it is readily seen that 1 , are cogredient to ; and that are cogredient to ; 152 Majol P. A. MacMahon . On the [ Oct. 8 , and that thus we obtain the new invariant symbolic factors , To this clear , I write the symbolic letters in two rows\mdash ; that 1etters which acontragredient DeterminantreS eemark tetters iredi tandwhere dernative ltersAn invariant f invariant symbolic factol . S are obtalned from any two letters in the same row , and suffix lnvarlant symbolic factors from any two letters in different rows . different letters , there will be invariant symbolic As regards any two letters in the first , the substitution gives , the power of the modulus for transformation ' unity . For any two letters in the second row , the power of the modulus negative unity . For an two letters in different rows the invariance is absolute , In a symbolic product absolute invariance is secured when the number of determinant factors drawn from the first is equal to the number drawn from the second . The power of the modulus is always equal to the excess of the number of such factors drawn from the first row over the umber drawn from the second . We are now able to form a calculus of tional invariants . All the operational processes at present in existence , including those which produce evectants , provectants , and emanants , the Aronhold process , the process , and transvection , are included in the presenlt enlarged symbolism . An invariant operator may or may not involve the , and it may be , separable into two portions , one of which involves the variables , while the other does not . The differe1lt classes will present themselves for examination as the work proceeds . Those operators which do not involve and may be eneous in the variables , and are then analogous to algebraical 1907 . ] of . The leading coefficient will then be found to have semi-invariant properties , and , of course , the same also may be said of the end coefficients . 2 . First consider the covariant of the quantic . In unsymbolic form it is or a covariant of order ? and of in the coetticients . Operating upon any algebraical covariant , if , produces a covariant , it is easy to see that , in many cases , it causes the covariant to vanish . For , if the operand be of order ) , it is transformed into one of and vanishes for the cases Annihilation takes place when the number of determinant factors in the operand is or In particular , is annihilated and , so is the Hessian ; and so on . In general , the symbolic factor is concerned with the process known as evectiou . 3 . Next consider the covariant operator which is lineo-linear in the coefficients , where may be any one of the , 1 , 2 , It has order ) , and therefore converts any covariant of characters into one which has characters . It is obvious that it annihilates any covariant operand for which . It is merely necessary to observe that the coefficient of . vanishes , and this implies the vanishing of the form . Observe also that if , the form vanishes unless ? is even . The case oives the invariant operator which is lineo-linear in the coefficients , viz. , In order to exhibit to the best advantage the unsymbolic forms of these , I write , following as far as possible the notation adopted by other writers , Jado ) mJOJ a SB ? . os Jasqo suoo s qmXs a uodn uoIlBJsdo a 1907 . ] of Binary From the known properties of , and it is clear that it an nihilates every invariant of Also annihilates the leading coefficient of every covariant . Hence , when a covariant is the operand , the term involving is absent , and , as a result , the operator annihilates also every coval.iant of Next , in the operator , put . We see that the sum of the ients of an . covaria1lt satisfies tlJe equation The solutions of this equation are invariants . The symbolic form of this operator is ; it annihilates if be any covaliant . Any covarian has the property that any three consecutive coefficients , satisfy the relation wherein , with ] a negative suffix or with a suffix greater than , is to be put equal to zero . It will be noted that the operators from their positions in the covariant are themselves seminvariants . Next take the Hessian of the covariant operatol where the multiplications are purely algebraical and not at all operational . We have thus an invariant operator of the second order , which will come under view later on in connection with Cayley 's operators . I pass to the case , which has the unsymbolic form I-3 156 Major P. A. MacMahon . On tloe [ Oct. 8 , erformed merely uiteral coefficients ohand oerein tultiplications operators ahand operator : and not at all upon the differential inverses . . I note first that the operator always produces a covariant . and are seminvariants . , for example , either annihilates a leading senlinvaliant or converts it into another one . In the former case the operator ariant causes the operand covariant to vanish ; for and the altelnant of does in fact vanish . What seminvariants are caused to vanish by this operator ? The reply to this question is supplied by the theory of symmetric functions . For make the transformation so that the seminvariants are non-unitary symmetric metionS of the roots of the equation is equivalent to and this again to ) where Take a function\mdash ; ; then and annihilates every symmetric function whose partition contains no part Hence here is equivalent to and all symmetric functions which , when expressed in partitions , contain no part 2 are solutions of the equation B.g. , the riano is annihilated by the quamtic covariant operator , because when transformed , is the symmetric function or ( 3 ) , the number 2 not appearing in the partition . The covariant of and weight 5 in the 1907 . ] Operational riants of coefficient is not anuihilated because the corresponding partition is ( 32 ) : we learn , moreover , that the result of the operation is the covariant of weight which corresponds to the partition ( 3 ) . enerally the covariant is converted into The operator , for the quantic , is , on development , of which the symmetry does not escape attention . 6 . When we obtain an annihilator , which has the form erative for all quantics of order not less than 4 . 7 . The unsymbolic form of the operator is Major P. A. MacMahon . On the [ Oct. 8 , It will be observed that , reading the rows down the page , the signs are alternately positive and ative as far as the middle row ( involving ) inclusive ; after that row the signs are alternately negative and positive umtil the last row , which thus has the sign ( It is operative for all quantics of order not less than The jrators 8 . Cayley , in his introductory memoir upon Quantics , defined a covariant of 1907 . of . 159 as a form which is annihilated by each of these operators . the linear transformation are obtained the fornrulae , , from which it is clear that a third annihilator of all covariants , viz. , , should be added to the two of We derive at once the absolute invariant wherein the multiplications are algebraical and not at all operational . The symbolic form of this is where observe that the absencc of determinant factors shows that it is absolute . Observe also that we have already obtained the absolute invariant whose symbolic form is ) . This was obtained as the discriminant of the quadratic covariant It also have been obtained by taking the -discriminant of the second polar of this covariant\mdash ; and since the invariantive form has the unsymbolic expression \ldquo ; we find the covariant under examination by its discriminant . 160 Major P. A. MacMahon . On the [ Oct. 8 , The Operator 9 . This is of degree one and weight zelO in the coefficients and of order in the variables ; and may be any of the integers 1 , 2 , 3 , $ Writing , when ; and , the operand any , we obtain which is the Jacobian of and Similarly , if and be any two covariants of orders and in the variables , the operation of upon produces the Jacobian of and and the operation of upon roduces ; , the same Jacobian with negative In other words , the first transvectallt ( iiberschiebung ) of over is obtained by the operation of upon and interchange of the forms merely the of the result . We may write the theorem in the form Passing to the case , we find and thus , if be any two iants , the econd transvectant of over 1907 . ] Operational Invariants of Binary In general , it is clear that or , as it may be otherwise written , ; showing the transvectant of two forms is obtainable by a pure operation upon either of the forms . So far as the writer is aware , such a transvection has not hitherto been exhibited as the result of a pure operation . The importance of the operational invariant is thus evident . VOL. LXXX.\mdash ; A.

rspa_1908_0011

0950-1207

The absorption spectra of the vapours of benzene and its homologues at different temperatures and pressures, and likewise of solutions of benzene.

162

165

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Walter Noel Hartley, F. R. S., D. Sc.

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Atomic Physics

Thermodynamics

Atomic Physics

162 The Absorption Spectra of the Vapours of Benzene and its Homologues at Different Temperatures and Pressures , and likewise of Solutions of Benzene . By Walter Noel Hartley , F.RS . , D.Sc . , Royal College of Science , Dublin . ( Received August 15 , \#151 ; Read December 12 , 1907 . ) ( Abstract . ) The author having been engaged since the year 1877 in investigating and correlating the physical and chemical properties of aromatic substances in relation to their chemical structure or constitution , he has latterly found it desirable that several very definite compounds should be examined in a state of vapour , as well as in solution . The work of E. Pauer , * W. Friederichs , f and of L. Grebej is referred to in detail . The vapours of benzene and several of its derivatives have been examined ( 1 ) at different temperatures and constant pressure ; and ( 2 ) at different pressures , the temperature being constant . The previous measurements of Pauer , Friederichs , and Grebe have been confirmed , and reconciled where they do not show complete agreement with each other . The records of temperature and pressure , and the shortening of the exposure of the photographic plates , constitute important differences between the work of the former investigators and that of the author . Details of the following photographs are given :\#151 ; Absorption Bands in the Spectrum of Benzene Vapour at Different Temperatures and a Barometric Pressure of 755*5 mm. Temperatures ... ... ... ... ... ... ... ... ... ... 12'*5 25 ' 43 ' 53 ' Number of bands photographed and measured 55 84 82 56 Absorption Bands in the Spectrum of Benzene Vapour at 11'*5 and Different Pressures . Pressures in millimetres ... ... 778 483 253 21 Number of bands measured ... ... . 36 38 46 44 The same at 100 ' and Different Pressures . Pressures in millimetres ... ... ... 683 589 478 381 279 172 Number of bands measured ... ... . 9 13 14 16 17 18 The same at 100 ' . Pressures in millimetres ... . 767 591 484 332 206 Number of bands measured 5 9 9 12 13 142 99 88 11 14 15 The same at 100 ' . Pressures in millimetres ... ... . 92 69 43 Number of bands measured ... ... 25 36 50 * 'Annalen , ' 1897 , vol. 61 , p. 363 . t 4 Zeitschr . f. Wissenschaftliche Photographies 1905 , p. 633 . J Loc . cit. , 1905 , p. 363 . The Absorption Spectra of the Vapours of etc. 163 The same at 100 ' . Pressures in millimetres ... . 6T5 525 37 5 28'5 225 15 5 9 5 4 Number of bands measured 31 54 60 72 75 88 52 38 30 Absorption Bands in the Spectrum of Toluene Vapour at Different Temperatures and Constant Pressure . Temperatures ... ... ... ... 10 ' 30 ' 40 ' 50 ' 60 ? 70 ' 80= 80 ' 100 ' Number of bands measured 16 20 16 20 23 21 24 23 18 The Absorption Spectrum of Toluene Vapour at Different Pressures and Constant Temperature . Pressures in millimetres ... ... . . 763 563 371 174 43 Number of bands measured ... ... 18 16 18 15 15 The Absorption Bands of Ethylbenzene Vapour at Different Temperatures . Temperatures ... ... ... ... ... 16'*5 40 70 100 Number of bands measured ... 19 18 8^2 General absorption , occurs here* The same . Temperatures ... ... ... ... ... . . 20 ' 36 ' 52 71 100 Number of bands measured ... 17 15 5 3 Complete absorption . The Absorption Bands of o-Xylene Vapour at Different Temperatures . Temperatures ... ... ... ... ... . 20 ' 45 ' 72 ' 100 ' 12T Number of bands measured ... . . 23 21 No bands , general absorption . Absorption Bands of m-Xylene Vapour at Different Temperatures . Temperatures ... ... ... ... ... ... 11 ' 40 ' 70 ' 100 ' Number of bands measured ... ... . 26 41 6 5 V--------y------J General absorption occurs between 2652 and 2429 . The same , jp-Xylene Vapour . Temperatures ... ... ... ... 10 ' 40 ' 70 ' 100 ' Number of bands measured 30 25 5 7 v-------------- ' General absorption from The same , Cymene Vapour . 2790 to 2416 . Temperatures 17C*5 40 ' Number of bands measured 0 7 70 ' 9 100 ' 9 The same , Mesitylene Vapour . Temperatures 18c-5 45 ' 72 ' 100 ' 120 ' v 140 ' Number of bands measured 2 2 2 2 General absorption . The measurements are given of similar groups of bands which occur in the vapour-spectra of benzene , toluene , ethyl benzene , and the three isomeric xylenes ; benzene and toluene being compared at ordinary temperatures and also at 30 ' below their respective boiling points . A tabulated statement is also made of the heads of strong bands which appear to be common to benzene and its homologues . The intensities of the bands in the benzene vapour-spectrum at 100 ' , and different pressures , were compared with those at temperatures below its boiling point , and it was seen that the bands ah m 2 164 Prof. W. N. Hartley , Absorption Spectra of [ Aug. 15 , 100 ' are almost identical with those at lower temperatures , but with this difference , that , at lower temperatures , some of the bands at the less refrangible end of the spectrum are feeble and less well defined . The vapour-spectrum of benzene is divided into groups of bands which are caused by the overlapping of two or more similarly constituted spectra differing in intensity . The strong bands number 54 , there being 27 in each of two spectra . In addition , there are 30 feeble bands , which also fall into two series of similar groupings , but with less regularity . The entire number of bands observed between 12a7 and 25 ' , under a pressure of 759*5 mm. , are thus resolved into four spectra , of which two are composed of strong and two of weak bands . Summary and Conclusions . As regards the vapour-spectra , it is proved that benzene at 100 ' C. has the same molecular mass as at 25 ' or 12''7 . The absorption bands at 100 ' are almost identical with those at lower temperatures , with variations as to definition in the less refrangible rays . The important influence of the position of the substituted hydrogens in benzene , upon the number and position of the bands in the spectra of its homologues , is clearly demonstrated . Variations in the spectra of benzene at different temperatures and 'pressures are explained by the fact that there are two different kinds of absorption which are sharply defined and may be differentiated . First , there is the general absorption , which is broadened and extended towards the less refrangible rays by rise of temperature ; secondly , there is the selective absorption , which includes all the narrow individual bands and groups of bands ; they are not widened and displaced by rise of temperature , and such changes of this nature that they undergo are the effect of the overlying general absorption . The selective absorption is best studied by raising the general absorption to a maximum ( at 100 ' ) , and studying the spectra produced by reduction of pressure . In this manner , any changes due to general absorption are eliminated . From the fact that increased sharpness and \#166 ; definition of the narrow bands is easily produced by rise of temperature , and also by reduction of pressure , the general absorption is clearly shown to be caused by encounters between the molecules , and the numerous narrow* bands are to be ascribed to the vibrations of the atoms or atom-complexes within the molecules . This confirms the conclusion drawn from the study of solution-spectra published in 1881 , * in 1882 , f and 18854 * ' J. Cliem . Soc. , ' vol. 39 , pp. 153\#151 ; 165 . t Loc . cit. , vol. 47 , pp. 685\#151 ; 757 . + ' Phil. Mag. , ' 1885 , vol. 19 , 5th ser. , p. 35 . 1907 . ] the Vapours of Benzene and its etc. The similar groups of bands occurring in benzene and toluene , and the close similarity between the spectra of toluene and ethylbenzene , with the further resemblance between m-xylene and toluene and ethylbenzene , is evidence that the mode of vibration within the benzene nucleus or ring-structure is in a great measure unaffected by the side-chain substitution . A distinction is drawn between the absorption spectra of vapours , called vapour-spectra , and of solutions , called s , and the relationship of one to the other is explained . Previous investigations carried on by the author for many years are briefly referred to , and it is shown liow the views entertained have been confirmed by the investigation of the . Attention is drawn to the insufficiency of ordinary chemical formulae to represent the constitution of organic compounds , particularly of those like benzene which are of an endothermic character , since they do not take into account the distribution of energy in the molecule , and this obscures the view of the physical character of chemical structure or constitution . In short , whereas bonds and linkings in the formulae usually written belong to a conception of chemical structure which is statical , the molecular constitution of such substances as are under discussion , when based upon the evidence derived from their optical properties , is essentially dynamical.* The relation of solution-spectra to vapour-spectra is shown , by reference to the results obtained by Pauer , Hartley and Dobbie , and by Grebe . The view entertained by Baly and Collief that benzene has seven and no more than seven solution-bands , indicative of a definite making and breaking of a double linkage of the carbon atoms in the ring , has been carefully examined , and the author finds this to be incompatible with well-ascertained facts . Prom the measurements and numerical relations of the wave-lengths of bands in solution- and vapour- spectra it is explained how four , six , seven , eight , or nine bands may be recognised in solution-spectra , six of which are similarly constituted , and four of these are not only similarly constituted but very nearly of equal width , intensity , and persistency , that is to say , they have the same coefficient of extinction , and in all other respects an almost exact similarity . They correspond with four groups of vapour-bands which are formed by the four different series of bahds which overlap , and they occur where they overlap to the greatest extent . * " Single , double , or treble linkings are simply an incomplete method of representing the relation of the carbon-atoms to each other at some particular phase of their vibrations n ( ' Phil. Mag. , ' 1885 , vol. 19 , pp. 55\#151 ; 57 ) . t ' Chem. Soc. Trans. , " ' 1905 , vol. 87 , p. 1332 .

rspa_1908_0012

0950-1207

Further consideration of the stability of the pear-shaped figure of a rotating mass of liquid.

166

167

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir G. H. Darwin, K. C. B., F. R. S.

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10.1098/rspa.1908.0012

Biography

Fluid Dynamics

Biography

166 Further Consideration of the Stability of the Pear-shaped Figure of a Rotating Mass of Liquid . By Sir Gr . H. Darwin , K.C.B. , F.R.S. , Plumian Professor of Astronomy , and Fellow of Trinity College , Cambridge . ( Received October 29 , \#151 ; Read December 12 , 1907 . ) ( Abstract . ) In vol. 17 , No. 3 ( 1905 ) , of the ' Memoirs of the Imperial Academy of St. Petersburg/ M. Liapounofif has published an abstract of his work on figures of \#166 ; equilibrium of rotating liquid under the title " Sir un Probl\amp ; me de Tchebychef . " In this paper he explains how he has obtained a rigorous solution for the figure and stability of the pear-shaped figure , and he pronounces it to be unstable . In my paper in the ' Philosphical Transactions ' * I had arrived at an opposite conclusion . The stability or instability depends , in fact , on whether the sign of a certain function , which M. Liapounoff calls A , is negative or positive . M. Liapounoff tells us that , after having seen my conclusion , he repeated all his computations and confirmed his former result . He attributes the disagreement between us to the fact that I have only computed portion of an infinite series , and only used approximate forms for the elliptic integrals involved in the several terms . He believes that the inclusion of the neglected residue of the infinite series would lead to an opposite conclusion . In my computation the critical function is decisively negative , whilst M. Liapounoff is equally clear that it is positive . The inclusion of the neglected residue of the series , which forms part of the function , undoubtedly tends to make the whole function positive , but after making the revision , explained in the present paper , it remains incredible , to me at least , that the neglected residue should amount to the total needed to invert the sign . The analysis of my former investigation has been carefully re-examined throughout , and I have , besides , applied the same method to the investigation of Maclaurin 's spheroid , where the solution can be verified by the known exact result.f As a further check , the formulae of the former paper have been examined on the hypothesis that the ellipsoid of reference reduces to a sphere . The * A , Vol. 200 , pp. 251\#151 ; 314 . . + \#171 ; Amer . Math. Soc. Trans./ 1903 , vol. 4 , p. 113 , on " The Approximate Determination of the Form of Maclaurin 's Spheroid , " and a further note on the same subject , recently sent to the same society . Pear-shaped Figure of a Rotating Mass of Liquid . 167 several terms correctly reproduce the analogous terms in the paper on Maclaurin 's spheroid . Dissent from so distinguished a mathematician as M. Liapounoff is not to be undertaken lightly , and I have , as explained , taken especial pains to insure correctness Having made my revision , and completed the computations , I feel a conviction that the source of our disagreement will be found in some matter of principle , and not in the neglected residue of this series . I can now only express a hope that someone else will take up the question . In the revision of the computations , the methods now used are much better than the old ones . In as far as this paper is a mere repetition of the former work with improved methods , the results are only stated in outline , but I now show how any of the ellipsoidal harmonic functions may be computed without approximation , and also how the functions of the second kind may be found rigorously . The Cambridge University Press is engaged in bringing out a collection of my mathematical papers , and when we come to the paper on the " Stability of the Pear-shaped Figure , " the new methods of computation will be substituted for the old .

rspa_1908_0013

0950-1207

On kinetic stability.

168

177

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Horace Lamb, F. R. S.

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10.1098/rspa.1908.0013

Fluid Dynamics

Measurement

Fluid Dynamics

]\gt ; On Kinetic bility . By HORACE LAMB , F.RS . } ( Received November 21 , \mdash ; Read December 12 , \mdash ; Revised December 19 , 1907 . ) 1 . The object of this paper is to illustrate the theory of kinetic stability , so far as such a theory can be said to exist , by a few simple examples . As the theory itself appears to be by no means widely known , some preliminary recapitulation seems advisable . The difficulty of framing a definition of kinetic stability which shall be comprehensive and at the same time conform to natural prepossessions has been recognised . * Thus , according to one definition which has been proposed , the vertical fall of a particle under gravity would be unstable ; according to another the revolution of a particle in a circular orbit about a centre of force varying inversel . as the cube of the distance would be reckoned as stable , although the slightest disturbance would cause the particle either to fall ultimately.into the centre , or to recede to infinity , after describing in either case a spiral path with an infinite number of convolutions . There are , however , certain restricted classes of cases where a natural definition of stability is possible and the corresponding criterion can be formulated . Suppose , in the first ] , that we have a dynamical system which is the seat of cylic motions whose momenfa ( in the generalised are constant . Apart from the cyclic motions the configuration depends on a certain number of " " palpable\ldquo ; -ordinates , , , and an " " equilibrium\ldquo ; configuration is one in which these co-ordinates can remain constant when the system is left to itself . Such an equilibrium configuration is said to be stable when the . extreme variations of these co-ordinates , consequent on an arbitrary disturbance , are confined within limits which diminish indeiinitely with the energy of the disturbance . Any alrangement of frictionless gyrostats gives a system of this kind ; on a larger scale we have the problem of the free rotation of a liquid mass under its own gravitation . In a second class of cases we have ( again ) certain co-ordinates whose values do not affect the kinetic or the potential energy , and the corre- *Cf . F. Klein . A. Sommerfeld , ' Ueber die Theory des Kreisels , ' Leipzig , 1898 , p. 342 . Cf . Thomson and Tait , ' Natural Philosophy , ' S319 , example ( G ) ; Lamb , 'Hydromics , ' 1906 , SS140 , 141 . On Kinetic Stability . sponding vdocities are now supposed to be maintained constant by the application of suitable forces . * We have then to investigate the stability ( in the same sense as before ) of an " " equilibrium\ldquo ; configuration in which the remaining co-ordinates , , have constant values . As an example , the system may be attached to a rigid body which rotates with constant speed . The theory of the stability of an ocean a rotating globe also comes under this elass . It has been customary , in treatises on dyna mics , to discuss all such questions by the classical method of " " small oscillabions If the variations of the co-ordinates , be arded as infinitely small , the solution of the equations of disturbed motion is obtained in the form , ( 1 ) the values of being determined by an algebraical or ( in the case of an infinite number of degrees of freedom ) a transcendental equation . If these values of are found to be all real and ative , the undisturbed configuration is reckoned as stable , whilst if any of them are positive or complex , it is accounted as unstable . As familiar instances of problems discussed from this standpoint , we have the stability of the conical pendulum , of the steady precessional motion of a top , and so on . The general theol.y of the method , including the condivions of stability ( in this sense ) , has been investigated by Routh . M. PoincareS has , however , insisted on the fact that this method may , from a practical point of view , be misleading as to the ultimate behaviour of the system . If deviations from the equilibrium configuration be resisted ( as in practice they always are ) by forces of a viscous character affecting the co-ordinates , , , then in the case of absolute ( statical ) equilibrium the usual criterion of stability , , that the potential energy must be a minimum , is not affected . But in such cases of 1-inetic equilibrium as have been referred to , it may happen that the effect of the viscous forces is gradually to increase the deviation , even the equilibrium configul.ation is ( i.e. , from the\ldquo ; classical\ldquo ; standpoint ) thoroughly stable . A distinction is drawn between " " ordi1ln \ldquo ; or " " temporary\ldquo ; stability , i.e. , stability as by the method of small oscillations , and ' secular\ldquo ; or ' permanent\ldquo ; stability , , stability when regard is had to possible viscous forces the co-ordinates Thomson and Tait , S319 , example . HydrodyIlamics , ' 1906 , SS202 , 203 , 204 . Stability of Motion , ' 1877 ; 'Advanced Rigid Dynamics , 6th 1905 , chap . vi . S " " Sir l'Equilibre Mass Fluide animee d'un Mouvement de . Rotation , \ldquo ; ' Acta Math 1885 , vol. 7 , p. 269 . above referred to , and in particular to the question of stability of equilibrium relative to a rigid body which is maintained in constant rotation about a fixed axis . 2 . The trivial character of the first example may be excused on the ground that it shows almost intuitively the necessity for some qualification to the doctrine of ' ordinary\ldquo ; stability . We consider a particle movable on the inner surface of a spherical bowl which rotates with constant angular velocity about the vertical diameter . If the bowl be smooth the equilibrium of the particle when in the lowest position is " " ordinarily\ldquo ; stable , since the rotation of the bowl is quite irrelevant . But if we admit the existence of friction , , between the particle and the bowl , the lowest position is " " permanently\ldquo ; stable only so long as , where is the radius . This results immediately from the consideration of the formula for the kinetic potential , , ( 2 ) where is the mass of the particle , and is its angular distance from the lowest point . When the above value of is exceeded , the only permanently stable position is that in which ' ( 3 ) See Poincare , . cit. , or the author 's ' Hydrodynamics , ' . cit. latest edition ( 1905 ) of Routh 's ' Advanced Rigid Dynamics ' contains no reference to the matter . 1907 . ] On Kinetic Stability . when the particle rotates with the bowl like the bob of a conical pendulum . To examine in detail the initial stage when the particle is slightly disturbed from its lowest position we may ( for mathematical convenience ) adopt the hypothesis of a frictional force vary ing as the relative velocity . If we employ horizontal rectangular axes Ox , Oy passing through the lowest point , and rotating with the bowl , we have , when are small , ( 4 ) where is the frictional coefficient . These equations may be combined into where . If we assume , ( 6 ) we find , if the square of be neglected . be Cartesian co-ordinates referred to fixed axes throughO , the complete solution is , ( 8 ) where . ( 9 ) If this be put in real form we perceive that the motion is made up of two superposed circular vibrations , in opposite directions , of period ; moreover that , if is positive , so that that circular vibration whose sense agrees with continually increases in amplitude . The particle works its way outwards in an ever } spiral path , approximating to the stable position of relative equilibrium indicated by ( 3 ) . 3 . The next illustration is of a more practical character , and admits of being realised with considerable exactness . A pendulum symmetrical about a longitudinal axis hangs by a Hooke 's joint from a vertical spindle which is made to rotate with a constant angular velocity . The pendulum used by the writer FIG. 1 . was constructed originally without any reference to the ( 10 ) . where denote the principal monlents of inertia of the pendulum at the centre of the joint . Hence , if , we have provided denote the distance of the centre of gravity from the joint . This expression ceases to be a minimum for , if lfgh ' and the only stable positions are then those in which the makes an angle with the vertical , iven by To examine the motion about the vertical position we neglect , in ( 10 ) , terms in and of higher order than the second . Thus const . ( 14 ) . Hence 's equations give As in the case of ( 4 ) , we find that these satisfied by 1907 . ] On Kinetic Stability . provided or ( 19 ) The vertical position is therefore " " ordinarily\ldquo ; stable , whatever the value of It . is evident that are the rectangular co-ordinates , relative to rotating axes , of a point on the axis of the pendulum . For the corre- sponding co-ordinates relative to fixed axes we have , ( 20 ) where . ( 21 ) The motion is therefore made up of two superposed circular vibrations of different periods , the more rapid vibration being the one whose direction of revolution agrees with that of the spindle . To investigate the of permanent stability we introduce into the left-hand members of ( 16 ) terms to represent the viscous forces at the joint . The modified equations are satisfied by , ( 22 ) provided . ( 23 ) If be the two values of given by ( 19 ) , this may be written , ( 24 ) the roots of which are , if we neglect the square of When the two values of have opposite , and the real parts of are both ative . The ver.tical position is then permanently , as well as " " ordinarily\ldquo ; stable . But if both values of are negative , and if be the smaller in absolute magnitude , the real part of will be positive , and that of yative . If we pass to fixed axes , writing as before , ( 26 ) we find that the periods of the two circular vibrations are to a first approximation unaffected by a small degree of friction , but that the amplitude of one of these vibrations , viz. , the one whose direction of revolubion agrees with that of the spindle , increases exponentially with the time , whilst the amplitude of the other sinks asymptotically to zero . These points 174 Prof H. Lamb . [ Nov. 21 , are illustrated in a striking manner by the apparatus referred to.* Sub- * stantially the same experiment can be made in a simpler form by means of a heavy metal ball hanging by a stout string from a hook at the lower end of the spindle . If due precautions be taken to check the violent evolutions which the ball is sometimes apt in the first instance to perform , the torsion of the soon brings the latter into a state of steady rotation about a vertical diameter , with practically the angular velocity of the spindle . When the steady state has been attained the ball may be left to itself , with the string vertical . The friction of motion relative to the spindle is in this form of the experiment very slight , and a close observation may soon detect the tendency to a circular vibration of continually increasing amplitude in the direction of revolution of the spindle , some time may elapse before this becomes really conspicuous . The final result is , however , unmistakable . 4 . The question is not seriously modified by a slight amount of deyiation from the theoretical conditions , , in the problem of S 3 , by a slight defect of alignment between the axis of rotation of the spindle and the centre of the joint . The configuration of relative equilibrium about which the observed oscillations take place is only slightly altered , except in the case cf approximate agreement between the imposed period of rotation and what would be the natural period of vibration in the absence of rotation . The effects of a want of perfect alignment in S 3 can be studied in their simplest form if we the moment of inertia ( C ) about the axis of the pendulum . The case is then that of a particle suspended from the lower surface of a horizontal disc , which is made to rotate about a vertical axis . If be the length of the string , and the distance of the point of suspension from the axis of rotation , the inclination of the string to the vertical in a position of relative equilibrium is given b.y , ( 27 ) where . If this has three solutions , for two of which is negative ; in one of these , moreover , is numerically greater , and in the other numerically less , It may be worth while to give roughly the dimensions . The steel rod shown in fig. 1 had a length of 36 in . and a thickness of . The diameter of the iron disc which could be fixed in valious positions along the rod was 7 in . and its thickness*in . The spiudle was driven from a small electromotor , by means of the small pulley shown , at speeds ranging up to about 25 revolutions per second . a typical experiment the ball was 3 in . in diameter , and was suspended by a string 33 in . long ; and the speed was about 7 revolutions per second . The circular vibration took about 18 minutes to attain an amplitude of 1 inch . 1907 . ] On Kinetic Stability . than . These three positions are shown in fig. 3 . The position is found to be both " " ordinarily\ldquo ; and " " manently \ldquo ; stable , whilst the position III is on either reckoning unstable . Case II is " " permanently\ldquo ; unstable , but the question of " " ordinary\ldquo ; stability is less simple . For sufficiently great values of the equilibrium may become unstable from this point of view , but there is no difficulty in the conditions so that FIG. there may be " " ordinary\ldquo ; staDility with " " permanent\ldquo ; instability . This was illustrated by an experiment in which the excentricity lvas purposely made appreciable . The metal ball referred to was suspended by a stout string about 3 feet long from a point 1 inch out from the centre of the disc . If the ball be carefully steadied in the central position before left to itself , its subsequent demeanour differs in no essential way from what is observed when the suspension is made as nearly axial as possible . 5 . The next example is one in which the number of degrees of freedom is nite . For a reason to be given it is hardly a practical one , but it may serve to illustrate the limitations to which the application of the tbeory is subject . We consider a cylindrical shaft rotating in fixed beariugs placed at isolated points , and the question is at what speed the straight form becomes unstable . If the circumferential of the shaft be Prof. H. Lamb . [ Nov. 2 small compared with the elastic wave-velocities of the material , the ular momentum about the axis may be ignored . Under this condition it is obvious that the straight form is " " ordinarily\ldquo ; stable , the fact of the rotation being irrelevant . To investigate the " " permanent\ldquo ; stability , consider , for definiteness , a length between two bearings , B. If the axis of be taken along the length of the shaft , and if denote the lateral deviation , we have , by the usual theory of flexure , , ( 29 ) , ( 30 ) where is the cross-section , is the radius of gyration about a diameter , denotes Young 's modulus , and is the density of the material . Hence , , ( 31 ) where . ( 32 ) The integrated terms vanish if each end be either free , or 1nelely supported , or fixed also in direction . It is known from the ordinary theory of transversal that any arbitrary function which is subject to the given terminal conditions can be expanded , for , in a series of normal functions , . ( 33 ) Here , satisfy the differential equations , ( 34 ) .and the proper terminal conditions , , , the roots of a certain transcendental equation , arranged in ascending order of magnitude . If we substitute from ( 33 ) in ( 31 ) , and omit terms which vanish in consequence of the orthogonal property of different conjugate functions , we find . ( 35 ) *See Rayleigh , ' Theory of Sound , ' chap . viii . Thus , if the shaft be merely supported at the ends , the equation is ; if it be fixed in direction at one end and free at the other , we have 1907 . ] On Kinetic Stability . The frequencies of the various modes of natural vibration of the shaft are determined by the relation . . ( 36 ) Hence is a minimum , in the straight condition , or the equilibrium is permanently stable , only so long as , i.e. , so long as the period of rotation is greater than that of the ravest mode of transverse vibration . The incipient of the instability might be studied as in the previous problems . The motion can be analysed into circular vibrations , and it appears that the amplitude oi one at least of these , having the salve direction of revolution as the shaft , should increase exponentially with the time , provided exceed the smallest root of the transcendental equation which determines We conclude that a truly symmetrical shaft , rotating accurately about axis , in rigidly fixed , with any speed exceeding that of the ravest mode of transverse vibration , would be rendered viscous ; cting the motion , such as are , in fact , present owing to the , internal friction of the substance . The instability , indeed , take time to develop itself , but the result would be inevitable . The fact that shafts can be , and are , safely driven at speeds the critical limit thus indicated* must be ascribed to the operation of dissipative forces ( so far fnored ) affecting the absolute as well as the relative vibrabions . The seat of such forces is probably to be found in a of the bearings . For similar reason the " " permanent\ldquo ; instability illustrated by the experiments of SS 2 , 3 above might be wholly masked if the resistance , of the air much greater than it actually is , or if the whole apparatus were immersed in } a viscous liquid . * The observed " " whirling\ldquo ; of shafts at a series of critical speeds is due to of absolute symmetry , and is to be regarded as a forced oscillation of exaggerated amplitude , due to approximate synchronism . ( See Dunkerley , 'Phil . , vol. 185 , Stodola , ' Die Dampfturbinen , ' Berlin , 1904 , p. 157 . ) . LXXX.\mdash ; A.

rspa_1908_0014

0950-1207

Prominence and coronal structure.

178

183

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

William J. S. Lockyer, M. A., Ph. D., F. R. A. S.|Sir Norman Lockyer, K. C. B., LL. D., Sc. D., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0014

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0014

10.1098/rspa.1908.0014

Astronomy

Atomic Physics

Astronomy

178 Prominence and Coronal Structure . By William J. S. Lockyer , M.A. , Pli . D. , F.R.A.S. , Chief Assistant , Solar Physics Observatory , South Kensington . { Communicated by Sir Norman Lockyer , K.C.B. , LL. D. , Sc. D. , F.R.S. , Director of the Solar Physics Observatory . Received December 2 , 1907 , \#151 ; Read January 16 , 1908 . ) [ Plate 3 . ] The routine work with the spectroheliograph of the Solar Physics Observatory since the year 1904 has been to secure daily , if possible , not only photographs of the sun 's disc in the " K " light of calcium , but also of the prominences round the limb at the same wave-length . To obtain the limb photographs , much longer times of exposure are necessary , so that , in consequence of unfavourable weather conditions , the number obtained is not so great as that in the case of discs . Many and varied have been the shapes of the prominences recorded , and occasionally some have indicated a pronounced " arched " or " partially ^arched " form , as shown in a few examples here brought together in Plate 3 , figs. 1 to 6 . All the photographs on this plate , including figs. 7 and 8 , are on the same scale , and I am indebted to Mr. J. P. Wilkie , the photographer to this observatory , for enlarging them . It was not , however , until July 17 of the present year that a photograph was obtained which presented a magnificent series of " arches , " " envelopes , " or " half rings , " as they may be termed . This photograph was secured by Mr. W. Moss , computer in the observatory . The disturbed area was situated near the south pole of the sun in the eastern quadrant , and two exposures were successfully made , the first at 3 h. 14 m. P.M. , G.M.T. , and the second at 3 h. 50 m. P.M. , G.M.T. These photographs are reproduced in Plate 3 , figs. 7 and 8 , and both have been enlarged twice from the original negatives . The parallel lighter streaks in each of the reproductions are due to changes in the clearness of the sky as the original photographs were being secured ; they have , therefore , no connection with the prominence images recorded . In the first photograph ( Plate 3 , fig. 7 ) the arches are clearly visible and complete , but in the second ( Plate 3 , fig. 8 ) they are less visible and partially broken up , in spite of the fact that the second photograph had the better exposure . How long the arches had been in existence previous to the time of securing the first record it is , of course , impossible to say , Prominence and Coronal Structure . but the second photograph clearly shows that a striking alteration had taken place . A close examination and measurement of the first photograph gives the following results , and the accompanying sketch ( fig. 1 ) is here presented . Fig. 1.\#151 ; Diagram to illustrate the more coospienous features photographed at 3 h. 14 m. , July 17 , 1907 ( see Plate 3 , fig. 7 ) . This sketch has been made by enlarging the original and painting the markings in Chinese white to render them more apparent , as the fainter details may possibly be lost in the reproduction in Plate 3 , fig. 7 . The most conspicuous feature of the whole of this disturbed region of the sun is the series of three concentric arches numbered 1 , 2 , and 3 . Their concentric nature seems to suggest that they were produced at one point of initial disturbance , and then moved radially outwards . The distance between the extremities of number 1 is l'*2 ; number 2 , 3'*6 ; and of number 3 , 5'*8 . Their heights from the chromosphere are about l'*5 , 2'-9 , and 3''6 respectively . It will be noticed that the intensity of the arches along their lengths is not uniform ; thus , Arch 3 has five points of increased intensity , while Arch 2 has three such maximum points . The mean width of the matter composing the arches is about 0'*3 to 0'*4 . On the eastern side of these arches there is another distinct semi-oval , numbered 4 in the sketch . This intersects arches numbers 3 and 2 , and at the point of crossing 3 a more intense patch is indicated . This arch is much flatter than those previously mentioned , and measures 6'*6 between the extremities on the chromosphere , and has a height of 2'*2 . The eastern base of arch number 3 falls nearly midway between the bases of Arch 4 . Turning to the southern side of Arch 3 , there will be found two projections of different intensity , marked 7 and 8 , which seem with little doubt to be N 2 180 Dr. W. J. S. Lockyer . [ Dec. 2 , associated with this system of envelopes ; their curvature indicates this very strongly . These projections may have formed the stump or , perhaps , a remnant of another large arch , which possibly was concentric with the envelopes 2 and 3 , but which was too faint to show on the photograph , or had already , perhaps , disappeared . Two small filaments are indicated at positions marked 9 and 10 . The enormous extent of this disturbance on the solar limb , taken as a whole , may be gathered from the facts that the extreme photographed portions of it were separated by a distance of 12'*7 , while the highest part was 3'*6 . Converting these into miles , it is found that its breadth extended over about 353,000 miles , or more than three-quarters of the solar radius , and its height reached about 101,600 miles . Attention may be drawn here to the fact that there is apparently no large prominence underlying these envelopes which may have given rise to them . Whether there be one just on the near or far side of the limb at this position angle cannot be stated , but no trace of any portion can be seen in the original negative . Examining now the photograph taken at 3 h. 50 m. p.m. ( Plate 3 , fig. 8 ) , it will be seen that considerable changes have occurred . Arch number 3 is in evidence by broken portions only , and may not show in the reproduction , and these correspond approximately with those of greater intensity in the sketch ( fig. 1 ) . All these portions seem to have risen from the chromosphere , as measurements show that the uppermost part is 4'*4 instead of 3''6 . Arches numbers 2 and 1 are difficult to trace , but remnants of them go to make up the spiral or hook-like form in their positions . The upper portion of this is about 3'*7 , which is again further from the chromosphere than it was before ( 2'*9 ) . The small prominence numbered 5 is still apparent , but in this photograph it has no longer arch number 4 over it , but only a portion of it . The prominence at 6 is broader , but less definite . The prominences 7 and 8 are still about the same , but somewhat fainter , the filaments 9 and 10 have disappeared , and a small prominence close to the eastern side of 9 has become visible . So far as I am aware this is the first time that such a series of concentric envelopes has been photographed with the spectroheliograph . This indicates that either this form is a most uncommon feature of prominence material , or that the envelopes very seldom appear broadside-on on the limb , so as to display the arch system to the fullest advantage . In looking up the literature of the visual observations of prominences made by means of the spectroscope , the only reference approaching to an account of prominences taking a ring shape is that given by Sir Norman 1907 . ] Prominence and Coronal Structure . 181 Lockyer in his volume on ' Solar Physics/ * There he narrates his observation of the behaviour of the F line , and he was led to conclude that the character of the prominence action he was watching could be expressed in these terms:\#151 ; " They were really in this case , as already stated , smoke rings thrown up by enormous circumsolar action/ ' In a later publication ! he suggested , in the following words , that the probable origin of such forms might be violent explosions :\#151 ; " . . . this falling material is dissociated in its descent before or when it reaches the photosphere ; the particles which descend sparsely and gently will be vaporised gently , and those wdiich descend violently and in great masses will be exploded violently . " Prior to 1901 no such envelope system , so far as can be found , had been photographed or even observed during eclipses . In the eclipse of May 18 of that year , Professor Dyson secured some excellent photographs of the eclipsed sun from his observing station at Pulo Aoer Gavang , on the west coast of Sumatra . In his description of these photographs , ! he called attention to the following feature :\#151 ; " A very remarkable arch in the corona round the large prominence at position angle 145 ' ( measuring N.E. S.W. ) . Round this prominence three separate arches are shown , one inside the other , their radii being l/ #2 , 2''4 , and 3'*7 respectively . They have the appearance of layers of cloud over an eruption . " It is interesting to note that the radii here stated correspond very closely to the values of the heights of the arches measured on the spectroheliograph photograph , namely , l'*5 , 2'*9 , and 3'*6 , showing that the two phenomena are of about the same order of magnitude . In the eclipse of 1905 , arches of a similar nature were recorded , as will be gathered from the following extracts :\#151 ; Thus the Astronomer Royal , who observed , at Sfax , Tunisia , stated:\#151 ; S " The inner corona in this eclipse seems to be in a state of turmoil ( all round the sun 's limb ) , corresponding to the sun-spot and prominence activity of the sun , oval rings and arched structures above the prominences being a special feature ... . The very bright prominence on the east limb , extending over an arc of more than 30 ' , associated with oval rings and arches in the corona . . . . " * ' Solar Physics,5 p. 403 , 1874 . t ' The Chemistry of the Sun,5 p. 412 , 1887 . X 1 Roy . Soc. Proc,5 vol. 69 , No. 454 , p. 244 , 1902 . . S 'Roy . Soc. Proc.,5 A , vol. 77 , p. 35 , 1906 . 182 Dr. W. J. S. Lockyer . [ Dec. 2y Describing the photographs he obtained at Vinaroz , Spain , during the same eclipse , Father Cortie , S.J. , wrote* :\#151 ; " The lower corona in the neighbourhood of these groups of prominences is very much disturbed . A series of interlacing rings or arches surmounts the group , their mean height being very nearly 3 ' . The general appearance is that of rings seen more or less edgewise , intersected by dark spaces . There are four such distinct bright edges , almost bright rays , from P.A. +75 ' to P.A. + 85 ' over the three first prominences of the group . " At Souk-Ahras , in Algeria , the expedition from the Hamburg Observatory , under the direction of Professor R. Schorr , also secured a series of large-scale photographs of the corona at this eclipse . Professor Schorr also photographed*)- these cloud-like envelopes , as will be gathered from the following extract:\#151 ; " The form of the inner corona over the prominence region on the east limb shows a specially interesting appearance . Three to four oval ringshaped cloud-like envelopes are conspicuous , which are situated at a distance from 4 ' to 6 ' over the prominence and can be concluded to be distinctly connected with the eruption of the prominence . This is the first instance to-my knowledge in which such an influence of a prominence on the form of the corona has been indicated . " The above extracts demonstrate clearly the arch-like forms photographed and indicate the close association of these forms with the structure of the lower corona and with the proximity of prominences . One of the most prominent features of the lower portions of some coronal streamers is that they are made up of groups of in-curving structure , or , as Ranyard termed them , " synclinal " groups . It seems very probable , therefore , that we have in these " envelope " forms the origin of this particular structure . Although the " envelopes " have been associated with both the corona and prominences in the extracts given above , no statement has been made as to whether they were composed of coronal or prominence material . Such a differentiation is not easy to make by means of photographs taken with a coronagraph , because the images which fall on the sensitive plate are made up of integrated light . The case is different with regard to photographs taken with objective prism cameras , because in these instruments a series of monochromatic images is recorded . With the object of trying to find out whether these envelopes had been secured by the prismatic cameras in the eclipse of 1905 , I have closely examined the negatives which I obtained with a six-inch three-prism * 4 Roy . Irish Acad. Trans. , ' vol. 33 , section A , part 1 , p. 20 . t 4 Mitteilungen der Hamburger Sternwarte , ' No. 10 , Hamburg , 1905 , p. 29 . 1907 . ] Prominence and Coronal Structure . 183 prismatic camera at Palma , Majorca , where the Solar Physics Observatory 's Eclipse Expedition was stationed . In the region about the large group of prominences in the north-east quadrant no trace of any images resembling envelopes could be found in either the " H " or " K " radiations of calcium . A similar examination of the green coronal ring at \ 5303*7 , which in one of the photographs is quite strong all round the moon , fails also to show any indication of these envelopes . Their absence may possibly be due either to the small intensity of the envelopes themselves or to the shortness of the time available for exposure . The fact that " envelopes " similar in form to those described above have now been photographed in the " K " light of calcium by means of the spectroheliograph indicates that the material composing those recorded at the two eclipses contained calcium , like the prominences , as at any rate one constituent . Fortunately , the spectrum of the corona has no line at the wave-length of " K , " so the evidence that the envelopes are composed of prominence matter is very strong . It may be stated , in conclusion , that we have now another link in the chain of evidence to show the dependency of the form of the corona on prominence activity , and this strengthens the view I put forward in 1903 , * which was that the different forms of the corona seen and photographed during eclipses depended on prominence and not on sun-spot action . Addendum , December 11 , 1907 . Since the above paper was communicated to the Society , I find that an " arch " over a prominence was photographed during the eclipse of 1898 . It was situated over the flame-like prominence in the south-east quadrant and was photographed at Sahdol , India , with the Thompson coronagraph by the Astronomer Eoyal , who has kindly notified me of the fact . DESCRIPTION OF PLATE . Plate 3 illustrates some prominences photographed at the Solar Physics Observatory . Figs. 1\#151 ; 6 represent some u arched " or " partially arched 99 forms . Figs. 7 and 8 show the system of u envelopes 99 recently recorded . The following are the dates and times when each of the prominences were photographed :\#151 ; Fig. 1 . . 1905 , Sept. 8 , 12 h. 11 m. p.m. " 2 . . 1907 , July 15 , 10 30 A.M. " 3 . 1904 , July 14 , 12 9 P.M. J ? 4 , . 1904 , July 19 , 3 52 " 5 , . 1907 , July 17 , 3 14 " " 6 . . 1904 , Sept. 21 , 12 23 " " 7 . . 1907 , July 17 , 3 14 " " 8 . . 1907 , July 17 , 3 50 " * ' Monthly Notices RA . S. , ' vol. 63 , No. 8 , p. 481 .

rspa_1908_0015

0950-1207

The conversion of diamond into coke in high vacuum by cathode rays.

184

185

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

the Hon. Charles A. Parsons, C. B., F. R. S.|Alan A. Campbell Swinton.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0015

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rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0015

10.1098/rspa.1908.0015

Thermodynamics

Electricity

Thermodynamics

The Conversion of Diamond into Coke in High Vacuum by Cathode Rays . By the Hon. Charles A. Parsons , C.B. , F.R.S. , and Alan A. Campbell Swinton . ( Received December 10 , 1907 , \#151 ; Read January 16 , 1908 . ) The objects of the experiment were three-fold : firstly , to ascertain whether a diamond could be entirely converted into coke or graphite by heating in a vacuum by cathode rays ; secondly , in the event of this being found practicable , to make a determination by Fery 's optical pyrometer of the temperature at which the conversion takes place ; thirdly , to endeavour to ascertain if , during the conversion , any gas was emitted or absorbed by the carbon . The vacuum tube employed is shown in the illustration , where A and B are the two aluminium electrodes , C the diamond and D an air-tight ground-glass stopper joint , through which the diamonds were introduced . xHternating current was employed , each of A and B acting as cathode and anode in turn , while their concave curvature was such as to accurately focus the cathode rays on to the diamond . The latter was supported on a plate of iridium , which , in turn , rested in a platinum cup , this arrangement being designed to prevent any stray cathode rays which might miss the diamond from striking the glass walls of the tube and melting the latter . During the experiment the tube was connected to two mercury pumps of the Toepler type , and in connection with the tube there were also attached two spectrum analysis discharge tubes for the purpose of collecting and examining some of the residual gas in the tube , both before and after the conversion of the diamond into coke . The alternating current from the mains , which was of 85 periods per second , was passed through the primary of a 10-inch Rhumkorff coil , with the contact-breaker and condenser disconnected , with an adjustable choking 5calc d INCH ' Conversion of Diamond into Coke by Cathode Rays . 185 coil in series in the primary circuit , so that the secondary voltage could be varied from about 5000 to 12,000 volts . A reflecting milliampere-meter was employed to read the current through the tube , while the volts across the tube 's terminals were measured by an electrostatic voltmeter . Two diamonds , each about 0*2 inch in diameter , were experimented with . The first was entirely converted into coke without difficulty , while in the case of the second the process was stopped when most of it had been so converted , the residue being black throughout its mass . As the proper degree of vacuum was reached by working the mercury pumps , and as the volts were raised , the diamond in each case became red , and then intensely white hot , till , with about , 8000 volts and 44 milliamperes ( 352 watts ) passing through the tube , the diamond began to throw off small sparks . On the volts being increased to 9600 , and the current rising to 45*5 milliamperes ( 436 watts ) , the sparks thrown off became more numerous and the diamond commenced to become black . Finally , with 11,200 volts and 48 milliamperes ( 537 watts ) , a rapid disintegration of the diamond took place , with considerable increase in volume , the residue having much the appearance and consistency of coke . The temperature of the diamond , as given by the pyrometer during disintegration , was 1890 ' C. During the heating up of the diamond and of the tube , large amounts of gas were driven off , and had to be pumped out , but there was nothing to indicate that any of this gas originated from the diamond rather than from the metal parts and glass walls of the tube . Two experiments were made , and in the latter there was distinct indication of a rise in vacuum just about the time of the conversion . These rises in vacuum are , however , not unusual in tubes in which there is highly heated metal , and it was impossible to decide whether any of the absorption of gas took place in the diamond . In the experiment in question , one of the spectrum discharge tubes was sealed off just before the conversion , when the diamond was commencing to blacken on the surface , while the other was sealed off after the diamond had been converted into coke . These two tubes , therefore , respectively contained samples of the residual gas before and after the conversion . Their spectra have been photographed alongside of one another , but though they are not altogether the same , the differences do not appear sufficiently marked to determine with exactitude any variation in the nature of the gases present . The experiments were arranged and carried out by Mr. Swinton at his laboratory in London .

rspa_1908_0016

0950-1207

On the scattering of the \#x3B2;-rays from uranium by matter.

186

206

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

J. A. Crowther, B. A.|Professor J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0016

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0016

10.1098/rspa.1908.0016

Tables

Atomic Physics

Tables

]\gt ; On ttering of the from Uranium by Matter . By J. A. CROWTHER , , St. John 's College , Cambridge . ( Communicated by Professor J. J. Thomson , F.R.S. Received and Read December 12 , 1907 . ) Introduction . The absorption of the -rays from radio-active substances during their passage through matter has , at various times , attracted a considerable amount of attentionl from various ysicists . Strntt , * for example , made some observations on the absorption of the from radium by thi sheets of various substances , and , later , performed similar experiments , using the -rays from uranium . Subsequently the present author made an nrvey of the subject by the absorp- tion of the -rays from uranium for nearly all the procurable elements , and numerous compounds . The results obtained may be briefly summarised as follows:\mdash ; ( i ) The absorption for a given substance may be represented by the equation where is the initial intensity of the -radiation , I the intensity after traversing a plate of material of thickness , and the coefficient of absorption for the substance . ( ii ) If is the density of bsorbing substance , then for the chemical elements is a periodic function of the atomic weight , the periods corresponding strictly to those of the chemical pel.iodic classification . ( iii ) The value of the ratio is an additive atomic property , depending only on the nature of the atom , and not upon its state of chemical combination . The methods employed in all the above experiments were substantially the same . A uniform layer of the radio-active substance was prepared , and covered with a sufficient thickness of aluminium foil to cut off completely all the -radiation . Sheets of the different substances of different thicknesses were then placed directly over the plate of radio-active material , and the * Strutt , ' Nature , ' vol. 61 , p. 539 , 1900 . erford , ' Radio-activity , ' p. 114 , 1904 . Crowther , ' Phil. Mag October , 1906 , p. 379 . lllC Cb ' Ullb ' : llb Clbb : amount by which the ionisation in an ionisation chamber placed directly above was reduced was measured in some suitable The incident rays thus enter the absorbing plate over an entire solid angle of , while the emergent rays are measured ovel an which depended upon the shape and position of the ionisation chamber , but which was always . In the experiments of all the rays , over the whole solid angle of , entered the ionisation chamber . In those of the present author the angle included amounted about . The results obtained in the two cases were practically identical . This method may be correctly said to measure the absorption of the -rays by the absorbing plate , as it does in fact measure the energy lost by the stream of -corpuscles in passing through it , under the conditions of the experiment , assuming that the ionisation produced is a measul.e of the energy of the rays . If the rays alter appreciably in velocity in matter , this latter assumption is not correct , as the power of the rays depends upon their velocity as well as upon their energy . Schmidt , *however , wIlo has very recently some direct experiments upon this point , was unable to detect any alterat , ion in the velocity of the -rays after through thin sheet of aluminium , and his experiments are supported by those of Lenard , who obtained a similar for cathode rays . In addition to the absorption as ured by these methods , there is another quantity of importance in the theory of the of -rays through matter , namely , the of the primary beam during its passage through the substance . The -corpuscles of the incident beam , owing to their velocity , are able to penetrate the atom , and will thus come into collision with the negative electrons contained in it . At each collision the moving corpuscle will be more or less detlected from its original path , the amount depending upon its velocity and its distance from the deflecting electron . In this way , an incident beam , originally parallel , will become scattered or diffused , during its passage through matter . Some of the incident -corpuscles may , in fact , after one or more collisions , be deflected through more than a , and , on the side of the plate at which they entered , make their appearance as return radiation . The scattering may be defined and measured as follows:\mdash ; Let ABCD ( . 1 ) 1oe a narrow parallel of -rays , and let be the intensity of -radiation crossing the section CD of the pencil parallel to the beam . Suppose , now , a thin sheet of the substance is inserted in the path of the beam , at . Owing to the collisions of he * ' Physik . , June 1 , 1907 . Mr. J. A. Crowther . On the [ Dec. -corpuscles in the rays with the corpuscles in the absorbing medium , the rays will be more or less scattered and bent away from their original direction . Let I represent the intensity of the radiation parallel to the original beam passing through the same area , after the insertion of the absorbing plate at . Then will a measure of the amount of scattering undergone by the incident beam its passage through the absorbing plate . An optical may make the idea somewhat clearer . Suppose ABCD is a parallel beam of , and a plate of ground glass is inserted at in the place of the absorbing medium . The ground glass will diffuse or scatter the rays , and the ratio of the intensity of the light passing through the small cross section CD of the beam , to the original intensity of the beam at , will give a measure of the amount of scattering produced by the glass . If , however , instead of measuring the amount of passing through the small area , we measured the total of passing out through the upper face of the plate , we should get a measure of the amount of light absorbed in the glass , and the two results would be in general very different . The former corresponds to what we have called the " " scattering\ldquo ; of the -rays , the latter to the orption McClelland , *using the -rays from radium , has very recently measured the absorption of these rays , by letting a nearly parallel beam fall upon a metal plate at normal incidence and measuring the whole amount of radiation which emerges the further side of the plate . The results obtained are very nearly the same as obtained by the earlier methods . As the whole of emergent rays were measured , this method also measures the absorption and not the scattering of the rays . Bxperimentd . It was decided , therefore , to undertake a series of measurements on the scattering of the -rays by the method outlined above . It is , of course , impossible to obtain an absolutely parallel beam of -rays . If , however , the radio-active material forms a layer at AB ( fig. 1 ) we can , by limiting the rays by a metal tube ABXY , sufficiently thick-walled to be impenetrable to -rays , obtain an approximation to our theoretical beam , which becomes * McClelland , ' Roy . Dublin Soc. Trans vol. 9 , part , 1907 . 1907 . ] Scattering the -rays from Uranium by Matter . more nearly exact as we increase the ratio of the length ( AX ) to the diameter . In the actual experiments the diameter was rather less than cm . ; the length AX was 3 cm . , and the greatest possible divergence from the normal was thus about . The rays from the absorbing plate were limited by an exactly similar tube , so that the rays from the plate into the ionisation chamber over exactly the same angle as that at which the primary beam fell upon the plate . Uranium was chosen as the source of -radiation . The intense activity of radium would have rendered it extremely useful for the purposes of the present experiments , and would have enabled the measurements to have been made with the greatest ease . Unfortunately , the -rays from radium are extremely complex , consisting of rays ranging in velocity from nearly the velocity of light to less than one-tenth of that amount . As the absorption val.ies very rapidly with the velocity of the rays , it becomes a matter of reat difficulty , and much uncel.tainty , to interpret the results obtained with such a eneous beam . Uranium , on the other hand , gives a homogeneous beam of -rays , with a velocity , according to the measurements of Becquerel , of about cm . per second , or about 55 per cent. of the velocity of Thus the results obtained by the use of uranium rays correspond to -corpuscles moving with a definite speed , and are therefore theoretically much more simple than the measurements obtained from the radium rays . Unfortunately , the amount of racliation given off by uranium is by no means large , and the experimental difliculties involved in its use were therefore considerable . The theoretical adyantages of a eneous beam of rays are so great , however , that it was decided to employ uranium , and to overcome the smallness of the effects to be measured by increased experimental care . The amount of radiation entering the ionisation chamber could be increased in two ways : ( 1 ) By using a large number of tubes fastened side by side , to limit the beam , instead of a single tube , as in the theory . ( 2 ) By using uranium X , the active -ray constituent of uranium , as the source of radiation . In ordinary uranium salts , in radio-active equilibrium , a very large proportion of the -rays by the uranium X are absorbed by the rest of the uranium , which , as it emits only -radiation , may be regarded for our purposes as inactive . By removing this inactive material , we can greatly reduce the amount of absorption taking place in the radio-active layer , and thus increase the amount of radiation which leaves it . Mr. J. A. Crowther . On the [ Dec. 12 , Both these methods were employed . The grid ) was constructed as follows . A large number of brass tubes , each cm . in diameter and 6 cm . , were soldered together side by side , to form a buudle of parallel tubes , about 6 cm . in diameter . This bundle was then sawn in half , FIG. 2 . at right angles to its length , thus giving two exactly similar grids . These were then mounted , the one over the other , as shown in fig. 2 , in exact register , so that each tube in the upper grid was an exact prolongation of one in the lower , a space of . being left between the two grids for the insertion of the sheets of absorbing material . With this arrangement the 190 Scattering of the -rays Uramum by Matter . 191 maximum angle at which the rays could fall upon the absorbin substance , or at which the rays could leave the substance and enter the ionisation chamber above , was about with the normal . As a measure of the difficulties of making measurements by this method it may be mentioned that the insertion of these grids between the layer of radio-active substance and the ionisation chamber cut down the amount of radiation entering the latter to less than 5 per cent. of its original value . Various methods were tried for the preparation of uranium from the uranium compound , Levin 's method of a solution of uranium nitrate with animal charcoal , and . the latter after and washing , and Schlundt and Moore 's 1nethod* of from various organic solvents by means of ferric hydl.ate . The method which gave the most satisfactory results in my hands was an extension of the process by which Sir W. Crookes first isolated the substance . A considerable quantity ( about lb. ) of uranium nitrate crystals was dissolved in ether , in a stoppered separating funnel , and the solution yell shaken . On allowing to stand , the liquid separates into layers , aqueous layer and an upper ) layer . The former contains a very large proportion of the uranimn X , and is carefully run off into a dish . About 20 . or so of water are added to the ethereal solution and well shaken up with it to ensure complete mixing . The mixture is then allowed to stand , and the aqueous solution settles to the bottom and is drawn off as before . This ocess was repeated a third time . In order to check the progress of the separation , each successive washing evaporated and its -ray activity tested . It was found that after three extractions with water the uranium nitrate remaining behind in the ethereal solution was practically inactive as far as -radiation concerned . The three aqueous extracts were mixed together and cvaporated down with a few drops of nitric acid until crystallisation occurred . These crystals were redissolved in a small quantity of ether , the solution obtained placed in small separating funnel , and treated in ex ctly the same as the solution . The aqueous extracts were evaporated down and the nitrate converted into red oxide by heating over a bunsen flame . In this way from a large quantity of uranium nitrate there was finally obtained a few grammes of substance nearly the whole of the -ray activity of the uranium nitrate . The powdered oxide was spread in a uniform layer over the bottom of a aluminium tray ( li , fig. 2 ) the exact diameter of the lower 'Phil . Mag October , 1906 , p. 377 . Mr. J. A. Crowther . On the [ Dec. 12 , and covered with a lid of aluminium foil 0 mm. thick , in order to exclude any -radiation . By repeating the process the uranium X might have been obtained in a still purer form . As , however , the amount of oxide after the second purification was only just sufficient to form a thin uniform layer over the bottom of the aluminium tray , it was not considered desirable to carry the process any further . Even when increased in this way the amount of radiation coming through the two grids was so small that special deyices had to be employed to measure it with any degree of accuracy . The chief difficulty in the measurement of small amounts of -radiation lies not so much , perhaps , in the smallness of the ionisation produced , as in the fact that this ionisation is comparable in amount with the spontaneous . ionisation in the ionisation chamber employed . A Wilson inclined electroscope , when carefully adjusted , is an extraordinarily delicate instrument for the detection and measurement of very small currents , and can be made sufficiently sensitive to measure the spontaneous ionisation in a closed vessel of , say , 1 litre capacity to within a few per cent. with ease . However , on making such measurements , I have always found it difficult to get consistent results . Successive readings will often difler by 20 per cent. . or even more in smaller vessels , although to all appearances the apparatus is working perfectly . Whether this effect is really due to actual variations in the ionisation within the chamber , or whether it is due to some irregularities in the working of the apparatus for very small currents , it is always presentThe discrepancies between the different readings become less and less noticeable as the spontaneous ionisationl becomes a less and less important . part of the whole . When , however , as in the present experiments , the spontaneous ionisation is a very appreciable fraction of the total ionisation to be measured , they are a source of considerable difficulty and a possible cause of error . It was decided , therefore , to employ a compensation method of measurement , and the result was most satisfactory . Not only was greater sensitiveness attained , but the above trouble was almost completely eliminated . The two chambers were constructed of exactly the same size , shape , and materials , and the spontaneous ionisation in the two was very nearly the same . Moreover , the small difference between the ionisatffin in the two vessels remained practically constant ( except for a small diurnal variation , . studied recently by Campbell and Wood , *which was just perceptible ) , and balances could be obtained with accuracy and regularity . has described a compensation method which depends upon the * Phil. Mag February , 1907 . 'Camb . Phil. Soc. Proc vol. 13 , p. 132 . 1907 . ] Scattering of the -rays from Uranium by Matter . variation produced in the current through a vessel containing uranium oxide , when the pressure in it is altered . This method is very suitable , when used , as by Campbell , for the measurement of small variations in a fairly large ionisation current . It is , however , only sensitive over a small range . It was thus unsuitable for the present experiment . The principle finally adopted was as follows . A layer of uranium oxide was formed , about 2 mm. in thickness , and covered with sufficient aluminium foil to cut off the -rays . This was placed beneath a shutter , sufficiently thick to stop all the -radiation . The amount of radiation from the uranium layer which entered an ionisation chamber placed above could be regulated by opening or closing the shutter so as to expose a greater or smaller area of the radiating layer . This method was found to be not only easy to work , but also very accurate . It may be worth while , therefore , to describe the apparatus more fully . It is shown in section in fig. 2 . are the pair of grids which have been already described . uranium X forms a thin layer over the bottom of the shallow aluminiu11 tray , and is covered with a lid of aluminium foil , to cut off all -raya The sheets of absorbing substance are inserted at . The rays pass upwards through into the ionisation chamber B. two cylindrical chambers exactly the same construction . They are closed at the bottom with thin alunlinitlm foil . The central wire electrodes pass out through earthed uard r , from which they are insulated by sulphur . The guard rings themselves are insulated from the rest of the chamber , which is kept to a sufficiently high potential to produce saturation in the ionisation current , by ebonite stoppers , , S. is the ionisation chamber of the compensator ; the shutter arrangement is shown below . is the utter itself , constructed of brass of sufficient thickness to cut off all the -rays from the layer of uranium oxide placed )elow . This layer was contained in a shallow depression / , 2 mm. deep , in a brass plate and covered with sufficient aluminium foil to cut off all -radiation . The shutter could be moved backwards and forwards across the layer , by means of the screw . The screw was accurately cut with nlnl . pitch , and the wheel was graduated into 100 divisions . The shutter could therefore be set , if necessary , to mm. The shutter was screwed on to an insulating ring of ebonite , to which the ionisation chamber was also idly attached by means of a projecting flange The ionisation in , when the shutter was open to its full extent , was many times the maximum ionisation to be measured in B. The radiation VOL. LXXX.\mdash ; A. 194 Mr. J. A. Crowther . On the [ Dec. 12 , from the uranium oxide layer was therefore cut down by aluminium screens , until the radiation in was equal to in , when the shutter was open to a suitable extent , say about 3 cm . The compensator was , of course , carefully calibrated , by measuring the actual rate of leak through the chamber , with the shutter open to different . The rate of leak was , in fact , found to be very nearly proportional to the area of uranium oxide exposed . It seemed clear , from the construction of the compensator , that the shape of the calibration curve would depend only upon the arrangement of the shutter , and would be independent of the radiating power of the layer of uranium oxide below . It should thus have the same shape , whether the layer was covered by only thin foil , or whether it was screened by a considerable thickness of aluminium . This was found experimentally to be the case . This fact added greatly to the accuracy attainable with the compensator , as the latter could thus be calibrated , using the full amount of -radiation from the uranium oxide layer ( a process which , on account of the amount of ionisation produced , was both easy and accurate ) and the adiatio could then be screened down to an amount suitable for the purposes of the experiment . Had it been necessary to calibrate the compensator , under the actual conditions under which it was used , those same difficulties would have arisen in the calibration curve which it was the object of the compensation method to ayoid . The two ionisation chambers were kept charged to equal , and opposite , potentials , by means of a cabinet of LQmall storage cells , : 400 volts were found amply sufficient to produce saturation . The electrodes of the two ionisation chambers were connected to the same Wilson electroscope , by wires dipping into a metal cup containing calcium chloride solution , connected to the gold leaf system . The system could be earthed , charged to any required potential , or left insulated by means of the key , dipping into the cup , which could be operated from a distance . solution of calcium chloride has been found , in practice , to be preferable to mercury in electroscope koys , as the mercury very rapidly becomes contaminated , and , when not perfectly clean , is very apt to cause a " " kick or displacement of ths gold leaf , on breaking contact . Calcium chloride solution appears to be quite free from this objectionable property . The electroscope , of the ordinary Wilson inclined type , was made as sensitive as possible , by a careful adjustment of the potential of the plate , the position of the point of suspension of the gold leaf , and the tilt of the , instrument . These electroscopes are somewhat difficult to adjust to sensi1907 . ] Scattering of the Uranium by Matter . tiveness , but when once the proper adjustments have beeu made , they form very delicate detectors of small ionisation currents . The particular electroscope used in these experiments gave a deflection of from 5 to 10 divisions for 1/ 50 volt . The capacity of the electroscope and the two electrodes was less than 10 cm . , and , using the null method , a movement of the leaf of one division in 10 minutes could be easily detected . It follows , therefore , that a difference in the currents through the two cbambers of about 5 ampere would produce a noticeable disturbance in the balance . It was in practice possible to obtain a balance between the two chambers to an accuracy of about 1 or 2 per cent. , except in the case of the thicker sheets , where the radiation was very much reduced . The method of making an observation was as follows . The sheet whose scattering power was to be measured was placed at yeen the grids , and the shutter was opened out , until , when the system was insulated , there was no appreciable movement of the gold leaf in 10 minutes . The ionisations in the two chambers are then equal and the reading of the shutter is obtained from the scale and the aduated wheel The sheet was then removed from and a balance obtained . Finally , a thick sheet of lead , sufficient to stop all the -rays , was placed at and the adjustment . The spontaneous ionisation in was slightly freater than in , and hence a balance could be obtained by slightly opening the shutter . The elative amounts of ionisation corresponding to each of these three shutter could then be read off on the calibration curve . The final , giving the small excess of the spontaneous ionisation in over that in , was subtracted from each of the first two readings . The results when thus corrected gave the relative amounts of radiation entering the chamber , with and without the . sheet at . The ratio , where I is the of radiation when the absorbing sheet is at , and the intensity of radiation when there no substance between the grids , is plotted against the thickness of the sheet . The curves thus obtained are given in Various thicknesses of material were used in every case . It was found that the falling off in the intensity of the radiation was much more iu this method than in the case of the measurements of the absorption . In fact , the results showed that the scattering of the incident beam was practically complete after passing through a thickness of about 1/ 10 . of aluminium , and thus very thin foil had to be used for the measurements . The number of substances which could be utilised , therefore , was strictly limited . The thickness of any particular sheet of the material was determined by Mr. J. A. Crowther . On the [ Dec. 12 , finding the weight of a known area of it . The thickness is then given by the formula , where is the weight of a sheet of area , and is the density of the substance . In this way , using an accurate balance , the thickness of even the thinnest leaf could be determined with considerable accuracy . Mass FIG. 3 . It was thought just possible that the shape of the curves obtained might be due to the presence in the uranium rays of some very soft radiation . If the -rays used contained any considerable quantity of very soft radiation , tlJe absorption curve would very much resemble the curves which were actually obtained . It would , in fact , be the sum of two exponential curves , one of which had a considerably higher index than the other . If this was the cause , however , we should be able to eliminate the preliminary rapid decrease by placing over the uranium X , but underneath the bottom grid , a thickness of foil sutficienb to cut off all the softer rays . We can see from the curve for aluminium that , if the rapid decrease is due to the presence of soft rays , these rays must be all absorbed in a thickness of about mm. of aluminium . Accordingly a sheet of aluminium , mm. thick , was inserted between the uranium X and the bottom grid 1907 . ] Scattering of the -rays from Uran , ium by Watter . and the experiments repeated . It was found that the insertion of this thickness of aluminium did not make the slightest difference to the results obtained . The curves bad exactly the same shape , whether the aluminium plate was present below the grid or not . It is thus clear that the results are not due to any want of homogeneity in the -radiation employed . One possible source of error has yet to be mentioned , and is connected with the use of the grids . The -rays which come from the radio-active layer and fall upon the walls of the tubes of which the rids are composed produce a certain amount of secondary radiation , some of which may fall upon the plate at at a greater angle than that of the primary beam . This would tend to diffuse the beam falling upon and thus cause departure from the simple theory . unable to discover any method of eliminating this effect , without at the same time reducing the radiation to such an extent as to be quite unmeasurable . The effect is , however , in all probability extremely small . The total return radiation from a plate exposed to uranium -rays has been shown by the author*to be only a few per cent. of the primary beam for copper , of which the tubes were made . From the nature of the case , only a small fraction of this call fall upon the plate at ; while a large proportion of the secondary radiation which does fall upon the plate does so at an angle not greater than that of the primary beam . The effec . G , therefore , cannot be large . It was possible also that the air in the tubes composing the grid have some similar effect in scattering the incident beam . In order to investigate these effects , a second pair rids was constructed , as different as possible in these respects from the original rids . In order to reduce the secondary radiation to a minimum , aluminium was used as the material of the grids . Two aluminium plates , each cm . thick , were fastened together by screws , and a large number of holes , each . in diameter , were drilled through the two plates . The plates were then separated by about 3 mm. to allow of the introduction of the metal sheets between them . In this way the total length of the rids was reduced from cm . in the case of the first pair to cm . , while at the same time the secondary radiation from the walls was considerably reduced by aluminium for copper as the material of the grid . The angle of the was somewhat greater than that of the original , amounting to about It will thus be seen that the second grids differed in every possible way from the first . The results obtained with the second grid are iven in 'fable . It will be seen that they very closely with the results obtained with the first grids . * Crowther , ' Phil. Mag October , , p. 391 . Mr. J. A. Crowther . On the [ Dec. 12 , The difference between the two sets of values for , the coefficient of scattering , does not exceed about 10 per cent. Considering the difficulties of the experiment , and the fact that neither of the grids gives a truly parallel pencil of rays , the agreement is quite satisfactory . We may fairly assume , therefore , that the results obtained are not due to any peculiarities in the construction or materials of the grid . Results . Experiments have been made on various thicknesses mica , aluminium , copper , silver , and gold . It was found that in order to obtain the desired measurements it was necessary to use very thin foil or leaf . In gold , for example , the scattering of the -rays was found to be practically complete after passing through a thickness of only cm . The number of substances which could be investigated was therefore very limited . Attempts were made to obtain sufficiently thin sheets of other metals , but without success . The results obtained are plotted in fig. 3 . The ordinates give the values of the ratio , where I is the intensity of the -radiation entering the ionisation chamber after passing through a thickness of material , and the initial intensity of the radiation in the absence of the absorbing plate . In order conveniently to represent all the curves on the same diagram , the abscissae represent not the thickness directly , but the corresponding mass per unit area , of the absorbing foil . In order to obtain the thickness , it is merely necessary to divide these values by the density of the particular stance to which they refer . The curve for mica is not given , as it is almost indistinguishable from the curve for aluminium . All the curves are similar in type . We will consider the curve for aluminium as typical of the rest . On looking at the curve ( fig. 3 ) it will be seen that it consists of two portions . In the first part , the curve descends very steeply , showing that the amount of radiation entering the ionisation chamber falls off at first very rapidly as the thickness of the foil is increased . After a certain thickness is reached , however , this effect rapidly dies away , and the curve finally assumes a much more gentle slope . It can easily be shown , by plotting the logarithm of the ratio against the corresponding thickness , that the portion of the curve is exponential in form and may be represented by the equation where is the thickness of material traversed by the -rays , and and are constants . 1907 . ] of the -rays from by On the values of these constants for the curve , it is found that the coefficient is approximately the same as the " " coefficient of absorpbion as measured by the earlier methods . It seems clear , therefore , that this final portion of the curve represents a true absorption of the of the rays . The earlier , and much steeper portions of the CUlVe , equally clearly due to some other cause , and represent , according to the theory of this experiment , the " " scattering\ldquo ; of the rays . It is evident from the shape of the ctlrve that the " " scattering\ldquo ; takes place in a much less thickness of foil than the absorption . In order to the way in which it varies with the thickness , it is necessary to co1Tect the experime1ltal values for the loss of intensity due to the absorption of the of the rays in through the particular thickness of foil used . The amount of this absorption can easily be calculated from the later exponential portion of the curve , assuming that the absorption obeys this exponential law for the thinner sheets also . The scattering effect for an incident pencil of rays of given intensity I and for a tcriven substance , is a function only of the thickness of material passed through by the rays . Thus if I ' is the intensity of the transmitted beam which vould enter the ionisation chamber in the absence of loss due to absorption of energy , and considering only the loss due to the scattering , we should have I ' , where represents some function , at present undetermined , of the thickness of material passed by the rays . The intensity of the transmitted beam I ' in the absence of any loss due to scattering of the rays , and considering only the absorption of energy , is , as shown above , represented by the equation I ' The actual experimental curve in the presence of both and absorption is , therefore , given by the equation , where I represents the intensity of the beam transmitted through the apparatus , when both the scattering and the absorption of the rays are considered . Thus representing the experimental value of taken from the curve by we have , or Mr. J. A. Crowther . On the [ Dec. 12 , But is known , from the final exponential portion of the curve , and hence we can easily find the values of for any given value of , from a table of exponentials . Dividing the values of from the curve , by the values of the exponential so obtained , we can find the value of for different values of Table I.\mdash ; Aluminium . The results of these operations are given in full in Table I for the case of aluminium ; the value of for alumimultl , as obtained from the last portion of the curve , The first column ives the thickness of the absorbing foil in centimetres ; I , he second column the ondinrr e values of . The third column gives the values of for the thicknesses given in the first column , being the coefficient of absorption calculated from the final portions of the curve . The fourth column gives the values of , and thus , on the previous theory , shows the true scattering effect of the foil . corrected for the loss due to the absorption of the rays . It will } ) seen that the value of the ratio , where I ' has the same significance as before , diminishes rapidly at first , but finally , after passing through a thickness of about cm . , becomes constant at about , and is not further diminished by through additional thicknesses of the foil . The scattering , in fact , becomes complete . The magnitude of his constant , which we will call , has no theoretical importance , its value depending upon the construction of apparatus . If it were possible to work with an infinitely narrow , and accurately parallel , pencil of -rays , the value of the ratio would decrease practically to zero . Owing to the necessities of experiment , the construction of the grid allows the rays to emerge into the ionisation chamber , over a finite angle , and hence a finite , 1907 . ] Scattering of the from Uranium by but constant , proportion of the rays enter the ionisation chamber , even when the scattering is complete . The larger the angle over which the rays can emerge into the ionisation chamber , the larger will be the value of C. Thus in the case of the aluulinium grids the value of is nearly twice as great as in the case of the first rrid of copper tubes . In order to obtain an approximate idea of the way in which the scattering would vary , in the absence of the effects due to the finite angle of the grid , we may subtract the constant final value ( which yives the intensity of the radiation which would enter the ionisation chamber when the rays are completely scattered , the absence of any absorption of the rays ) from each of the values of in the table . The results so obtained are given in the fifth column of Table I. If the logarithms of these numbers are plotted against the corresponding thicknesses , as given in the first column of the table , the resulting curve is very approximately a straight line . The curves thus obtained for the substances are given in fig. 4 . It will be seen that in every case we approximately a straight line . It appears , therefore , that the scattering , like the absorption , is approximately an exponential function of the thickness , and that it may be expressed by the equation I ' is the initial intensity of the -radiation passing a small cross section of a parallel pencil of the rays , I ' is the intensity of the radiation passing the same small cross section , when a sheet metal of thickness is interposed in the path of the beam ( corrections been made for the diminution in the radiation due to the absorption of energy ) ; and is a constant which we may , by analogy , call the " " of scatte " " of the rays for the given metal . The departures of the curve from the exponential are possibly somewhat greater than the probable erl.ors of the . They are , however , not greater than might be accounted for by the inevitable departures of the apparatus from the theoretical form . Assuming that the scattering follows this exponential law , and taking the absorption into account , it is easy to show that the experimental curves should be represented by the equation For we have from the above , which , since where , leads directly to the above expression . The values of and for aluminium have already been obtained , and can Mr. J. A. Crowther . On the [ Dec. readily be calculated from the last column of Table I. It is about 270 . By substituting these values in equation 2 , we can calculate the values of for different thicknesses of aluminium . A comparison of the values so Mass per aoea FIG. 4 . calculated , with the actual experimental values , is given in Table II , and affords a test of the accuracy with which the eory fits the experimental results . It will be seen that the divergence does not amount at most to more than a few per cent. of the initial radiation . Considering the departures of the apparatus from the theoretical form , and the difficulties of the experiment , the agreement is very satisfactory . So far have been considering the case of aluminium . The curves for the other substances investigated are , however , exactly the same in form , with different constants , and may be resolved into the sum of two exponential curves in exactly the way as the curve for aluminium . It will not be necessary , therefore , to describe them in further detail . The 1907 . ] Scattering of the Uranium by . 203 Table Aluminium . values of , and , for the different substances investigated are given in Table III . It may be mentioned that the reement in all cases was at least as good as in that of aluminium . Table III . Table III gives the values of the coefficients and as calculated from the experimental results ; and also the of , where is the density of the absorbing medium . A further column gives the value of It will be seen at once that is much greater than in general about 13 times as great , the ratio being very nearly the same for all substances . As the determinations of have to be made from the last observations on the curve where the radiation is very much reduced , and the proportional experimental error , , considerably increased , the rences do not amount to much more than the probable error of experiment . In this case we should expect to variations the value of with atomic weight similar to those obtained for the ratio , that is to say , it should be a periodic function of the atomic weight . Sufficient elements have not been measured to test this very thoroughly . It may be pointed out that copper , silver , and gold , which to the same chemical group , give nearly the same value for the ratio 204 Mr. J. A. Crowther . On the [ Dec. 12 , It may be noticed in passing that the values given by this method for the coefficient of absorption are somewhat higher than those given by the earlier methods . It was shown in a former paper*that for the heavier elements , such as silver and gold , the absorption in thin sheets was greater than would be expected from the final exponential value calculated from sheets of greater thickness . As the foil used in these experiments was much thinner than that employed in the previous measurements , it seems possible that had it been possible to measure thicker sheets by the present method the values obtained for in the two cases might have been more nearly equal . Table \mdash ; Aluminium Plate Grids . It will be noticed , howevel\ldquo ; that the values obtained for with the aluminium grid are inctl lower than those obtained when the copper grid was used . It seems probable therefore that at any rate part of the difference is due to the different arrangement of the apparatus in the two series of experiments . The above results show that a pencil of -rays is completely scattered in a thickness of matter which is quite small compared with the thickness required to completely absorb them . Thus , taking gold as an example , the rays are practically completely scattered in a thickness of only cm . The absorption in a layer of this thickness only amounts to about 20 per cent. of the initial of the rays . It seems evident , therefore , that an appreciable portion of the primary -rays must emerge on the same side of the foil and reappear as return radiation . It seems possible that a large proportion , if not the whole , of the return -radiation ( neglecting that set up by -rays ) may arise from this effect , and may thus consist principally , if not entirely , of scattered primary radiation . The fact that the return radiation from a metal piate has practically the same velocity as the primary rays seems to lend some support to this conjecture . While it may thus be possible to explain the return -radiation from a metal plate , on the hypothesis that it is due to the scattering of the primary rays , it does not appear to be possible to explain the results of the present experiments on the theory that they are due to secondary radiation . McClelland , * Crowther , 'Phil . Mag October , 1906 . 1907 . ] Scattering of the -rays from Uranvum by Matter . who has worked out the theory of secondary -radiation very completely in various recent papers in the ' Transactions of the Royal Society of Dublin , ' has shown that the effect of secondary radiation would be to produce an increase in the slope of the curve for very thin sheets . On the amount , however , it is at once seen to be mnch too small to account for the results of the present experiments . } the case of lead , which gives the largest effect of any of the metals , and plotting the arithm of the ratio for differenb thicknesses , McClelland has shown that the effect of the secondary radiation would be to cause an increase in the slope of this curve in its initial portions to about times the final exponential value . * For aluminium the of the secondary radiation would be less . In the present experiments , however , the slope of the initial portions or Che logarithmic curve is at least 12 times its final vftlue . We must consider , therefore , that the present results are mainly due to the scatterin0 of the primary -rays , by collisions with the -corpuscles iu the atoms of the absorbing plate , and not to secondary radiation . In conclusion , we may mention that the results of the present experiments remove what was apparently a serious discrepancy between the absorption of the -rays of uranium and radio-active materials enerally , and the -rays . the cathode stream . has measured the absorption for various ases of very fast cathode rays , due to a fall of potential of about 35,000 volts , and having a velocity , therefore , of about cm . per second . The values he obtained for the ratio , where is the coefficient of absorption and the density , between 1000 and 3000 . values obtained for the same ratio , using uranium -rays , which according to Becqnerel have a velocity of about cm . per second , ranged from about 4 to 10 . The difference is thus considerably more than can be accounted for by the mere difference in velocity of the rays in the cases . The " " \ldquo ; of the cathode rays is always measured by the falling off in intensity of the rays a small fixed area ( namely , the aperture of the Faraday cylinder used in the nents ) various thicknesses of the substance are interposed in the path of the beam , the original beam , always a nearly parallel pencil of rays . will thus be seen that what is actually measured in these experiments corresponds not to the ' absorption\ldquo ; of the -rays , but to quantity which we have calJed scattering . Comparing the results of Becker for the cathode rays with the values * McClelland , ' Roy . Dublin Soc. Trans vol. 9 , part , p. 41 , 190 'Ann . der Phys , p. 381 , 1905 . Scattering of the -rays from by Matter . obtained in the present paper for , the coefficient of scattering of the -rays , the apparent discrepancy is at once removed . It can be shown on theoretical grounds*that the scattering should inversely as the fourth power of the velocity . The -rays from uranium have a velocity of about times that of the cathode rays of Becker . Multiplying the results obtained for in the present experiments , therefore , by , to allow for the difference on velocity of the two kinds of rays , we obtain results varying between 650 and 2100 . These numbers agree well with the values , ranging from 1000 to 3000 , obtained by Becker for the cathode rays . Summary . The results of the present experiments may be briefly summarised as follows:\mdash ; ( i ) A parallel pencil of -rays is scattered in its passage through matter , the scattering being practically complete after the rays have traversed a thickness of material which from cm . for aluminium to cm . for gold . scattering , after correction for the loss of , due to the absorption of the rays , may be represented by an equation of the form , where is the thickness of the material traversed by the rays , and is the coefficient of scattering for the rays , being the initial intensity of a narrow parallel pencil of -radiation , crossing a small fixed cross section of the pencil , and 1 the intensity crossing the same cross section , when a thickness of material is placed in the path of the beam at a considerable distance from the fixed cross section . ( iii ) The ratio , of the coefficient of scattering to the coefficient of absorption is approximately constant for all the substances its average value being about 13 . The value of the ratio , where is the density , shows similar variations to those for In conclusion , I wish to express my best thanks to Professor J. J. Thomson for his kindness in suggesting to me the subject of this research , and for his helpful and inspiring interest during the course of the experiments . * See J. J. Thomson , ' Phil. Mag vol. 11 , p. 781 ,

rspa_1908_0017

0950-1207

The charges on positive and negative ions in gases.

207

211

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

John S. Townsend, F. R. S.

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6.0.4

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10.1098/rspa.1908.0017

Electricity

Tables

Electricity

]\gt ; Tlve Charges By JOHN S. TOWNSEND , , Wykeham Professor of Physics , Oxford . ( Received January 20 , \mdash ; Read January 23 , 1908 . ) In a paper on the Diffusion of Ions in Gases , described a method of comparing the charges on the ions generated in gases with ) on an ion in a liquid electrolyte . If be the number of molecules in a cubic centimetre of a gas at standard pressure and temperature , aJJd e the on an ion , then N. , where is the velocity of an ion in a field of unit electric force and the coefficient of diffusion . Thus from separate determinations of the quantities and , the product N. can be obtained . If is the charge on a monovalent ion in a liquid electrolyte , N. , so that a comparison of the various may be made , and the calculations have shown that the charge on a positive or negative ion in a gas is equal to the charge E. There were , however , considerable discrepancies , particularly with positive ions , which gave of as great as in some cases . Some time ago , while examining these investigations , I found that , by a somewhat erent method , it would be possible to arrange an experiment for determining N. directly , and to arrive at much more accurate than have been obtained hitherto . In order to apply the principle , it is necessary to have the ions in a uniform field , and to find experimentally how they are ibuted in some particular case . For this purpose two horizontal plates , A and , were set at a distance apart , and circular holes of the same radius were cut the plates , the centres of the circles being in the same vertical line . of very fine wire was laid across the hole in the upper plate , and a metal disc on insulating support was fixed in the aperture of the lower plate , leaving a small air space between the disc and the plate , so that the should be insulated from each other . . ( / * John . Townsend , ' Phil. Trans , 1899 , vol. 193 . Prof. J. S. Townsend . The on [ Jan. 20 , The plate was maintained at a potential , and a third plate above was maintained at a potential greater than and of the same sign . The lower plate and the disc were connected alternately to a sensitive electrometer , and during the course of an experiment their potentials did nob differ appreciably from the zero . The ions were generated in the air space between and by rays , and positive or negative ions were driven to the grating according as the potential of was positive or negative . The electric force being in the same direction above and below the grating , some of the ions pass through and travel under a constant electric force towards the central disc D. At the same time the ions diffuse laterally , so that some arrive on the disc and some on the plate . The greater the force the less time there will be for the diffusion , so the proportion of the total number that arrive at the disc increases with the force between A and B. The ratio of the number arriving at the disc to the total number was determined accurately with the aid of the electrometer . The mathematical investigation of the distribution of the ions between the plates A and can easily be made by considering the equations for the variation of the partial pressure of the ions . The three equations corresponding to the three ular axes are of the form . X. where is the number of ions ) cubic centimetre ( which is proportional to , the velocity and X the electric force along the axis of Differentiating the three equations and in the equation of continuity for the steady state , the following equation for is obtained\mdash ; where is the pressure due to 760 mm. of mercury , at which pressure is reckoned . This latter equation that at any point is a function of The constants in the solution are functions of the position of the point and at the lower plate , where , the ratio may be obtained by integration . Thus , where is the distance from the centre of the disc , and being the radii of disc and the plate respectively . 1908 . ] Positive and Ions in Gases . Hence It is not necessary to know the form of the function in order to see how to colupare the charge on a positive ion with that on a negative ion , or to compare the charges on ions in difierent gases . Experiments made with positive and negative ions for the same intensity of force gave a value of for positive ions which was much greater than he value for ative ions . This shows that the charge on a posiGive ion is reater than the charge on a negative ion . The same value of , within 1 per cent. , was obtained for the two kinds of ions when the force used with ative ions was double that used with positive ions . Letting the charge on a positive ion and the charge on a ative ion , then for all values of Z. Hence the charge on the positive ion is exactly double the char , on the negative ion . This shows that when a molecule of air is ionised by Bontgen rays , one positive ion and two negative ions are produced , the charge on the former being double that on either of the latter . In order to find the absolute value of N. , it is necessary to solve the differential equation in . An exact solution can easily be obtained which satisfies all the surface conditions , since can be expanded in a series of Bessel 's functions . The distribution being symmetrical round the axis of joining the centre of the with the centre of the disc , the differential equation reduces to the form\mdash ; where the distance of a point from the axis . Letting the equation for is so that , and The values of and are determiued from the surface conditions and is positive root of the equation Hence can be found at any point of the lower plate , where , and VOL. LXXX.\mdash ; A. Prof J. S. Townsend . The on [ Jan. 20 , the integrations and can easily be obtained from the known properties of Bessel 's functions . The connection between and N. was thus found , and a curve was drawn to show the values of for a series of values of N. . When is found experimentally the corresponding value of N. ( : . can be found immediately from the curve . The expression for in terms of N. is very complicated and I have to acknowledge my indebtedness to Mr. C. E. Haselfoot in having assisted in making the necessary calculations from the tables of Bessel 's functions . I have made a number of determinations of with different forces , pressures , and intensities of ionisation , and they all agree in giving results in accurate accordance with the theory . The values found for Ne are for positive ions and for ative ions . Each of these numbers represents the mean result of several different experiments in which none of the determinations differ from the mean value by more than 4 or 5 per cent. , which shows that considerable accuracy can be obtained by this method . When the value of N. is deduced by the first method which I gave , numbers corresponding to the positive ions were about 10 or 20 per higher those for the negative ions . Thus , when the rates of diffusion are compared with the velocities given by Zeleny , the values of N. for positive ions in air , oxygen , and hydrogen are , and , and the numbers for the negative ions were These numbers taken alone would not justify the conclusion that the molecules are ionised in the way that I have just found , but a little consideration shows that the relative values are of the kind that should be expected . If the effect of recombination be considered , it will be seen that a positive ion would rapidly combine with a negative ion when the charge on the former is 2 , as the force between them is . After combining with one negative ion , the force between the positive ion and another negative ion would be , so that the second step towards complete recombination would not proceed so rapidly as the first . The result of this would be that after the ) ositive and negative ions have been in the gas together for a short time , a large proportion of the positiye ions would have one-half of their original charge . The determinations of the coefficients of diffusion were made with small ionisations that had been reduced by the process of recombination , and from a consideration of Zeleny 's method of finding the velocities it is evident * J. S. Townsend , . cit. 'Phil . Trans , 1900 , vol. 196 . 1908 . ] Positive and Negative that recombination must have been on in his experiments also . Under these circumstances the numbers obtained for N. by the method correspond to positive ions , of which some have a charge and others a charge . The discrepancies from the value obtained for the negative ions are not greater than what might have arisen from experimental errors . In the experiments I have just now made the ination must have been ] ible , so that no appreciable number of the positive could have been reduced from to A full description of the experimental methods used in these determinations will be given in a future paper , when the experiments which are in ress with different gases are completed .

rspa_1908_0018

0950-1207

On the generation of a luminous glow an exhausted receiver moving near an electrostatic field, and the action of a magnetic field on the glow so produced.

212

217

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Frederick John Jervis-Smith, M. A. Oxon, F. R. S.

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6.0.4

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10.1098/rspa.1908.0018

Electricity

Thermodynamics

Electricity

On the Generation of a Luminous Glow an Exhausted Receiver moving near an Electrostatic , and the Action of a Magnetic Field on the Glow so produced . By Frederick John Jervis-Smith , M.A. Oxon , F.E.S. , University Lecturer in Practical Mechanics and Experimental Physics , Oxford . ( Received January 20 , \#151 ; Read January 30 , 1908 . ) 1 . In 1896* I found that bulbs exhausted as a Crookes radiometer , when bombarded by a discharge from a Tesla inductor , produced X-rays , and X-ray photographs of the hand were then made , using only exhausted bulbs having no terminals . The bulbs had the following dimensions : 5 cm . diameter , stem 12 cm . long , 0'4 cm . diameter . I had from time to time noticed that when any of the exhausted bulbs were rubbed on the palm of the hand , they became luminous for a brief period while they were being rubbed . In December , 1907 , I returned to the subject , using these same exhausted bulbs in connection with certain apparatus in which plates of sulphur were employed as insulators . Happening to move an exhausted bulb near a sulphur plate in the dark , I noticed that it glowed for an instant . It then became evident that an exhausted vessel , moving in an electrostatic field , itself became electrified and consequently glowed . 2 . An exhausted bulb was mounted by its stem in a hollow mandrel running in a bearing ; it was rotated by means of a pulley , driven by a cord connecting it to a small motor . Under the bulb a plate of sulphur was placed in the horizontal plane at distances varying between 1 cm . and 13 cm . The glow was apparent at 13 cm . 3 . The bulb was rotated about 20 times per second . The sulphur was rubbed on the hand before being placed below the bulb . When the bulb was rotated it became instantly filled with a luminous glow , with a patch of greenish light brighter than the rest of the glow situated about 90 ' from the vertical . When rotation was reversed , the patch appeared on the opposite side of the bulb , also about 90 ' from the vertical . 4 . In the next experiment the statically charged body placed under the rotating bulb consisted of a brass disc supported on an insulated stem . The disc was connected to an electroscope , and charged to 1200 volts . The bulb was rotated as before ; the charged disc remained charged during the * ' Nature , ' vol. 54 , p. 594 . On a Luminous Glow in an Exhausted Receiver , etc. 213 t experiment , which lasted about six minutes , and showed no signs of being discharged . 5 . An electrostatic field of opposite sign was maintained on two opposite sides of the bulb ; the glow throughout the bulb was considerably increased , but when two similarly charged discs were placed at equal distances on the opposite sides of the bulb , tl , ie glow ceased , and when one was charged to a higher potential than the other the glow again appeared , apparently due to the difference of charge of the two discs . 6 . Touching the rotating bulb lightly with a finger did not affect the appearance of the glow in any perceptible way . 7 . The bulb was rotated in the electrostatic field due to the disc of sulphur which had been rubbed on the hand , placed above the bulb in the horizontal plane , and below the bulb an insulated metal disc was placed connected to the electroscope ; no transfer of electricity to the disc was . indicated . 8 . A disc of sulphur ( 10 cm . diameter ) was mounted on a face plate of wood rotated by a mandrel ( running in ball bearings ) as in a lathe ; the disc of sulphur was rubbed so as to establish an electrostatic field . When it was rotated near an exhausted bulb or exhausted tube , no glow was produced . 9 . The sulphur disc , while rotating if used as the inductor of an electro-phorus , acted in exactly the same manner as if at rest . The disc was rotated from one revolution per second up to 20 revolutions per second . 10 . Five bulbs were prepared and rotated in an electrostatic field of constant strength . Some were exhausted to the same condition of vacuum as the radiometer of Crookes ; some to the condition of a Rontgen X-ray tube . The glow in those exhausted to the Rontgen vacuum was far brighter than that in those not so exhausted . 11 . The electroscope used to measure the P.D. of the charges was designed by Professor Townsend , F.R.S. , of Oxford ; it is calibrated so that each division of the scale indicates 100 volts . It is capable of keeping its charge for many days.* 12 . The experiments show that when an exhausted glass vessel is rotated in an electrostatic field an electrical glow is created , the intensity of which varies in some way with the velocity of rotation , while the position of maximum glow changes its position with the direction of rotation . 13 . Since the bulbs were exhausted by means of a mercury pump ( used by the manufacturer of Rontgen tubes ) , there may possibly be a very thin coating of mercury on the inner wall of the bulbs . An exceedingly minute * ' Nature , ' vol. 77 , p. 149 , " Sulphur as an Insulator , " by F. J. J.-S . 214 Bev . F. J. Jervis-Smith . On Generation of a [ Jan. 20 , coating of mercury on vessels exhausted by the mercury pump has recently been suggested as the cause of the change of conductivity of selenium when placed in a vessel exhausted by a mercury pump.* The Action of a Magnetic Field on the Radiant Glow in an Exhausted Vessel rotated in an Electrostatic Field . Considering the conditions subject to which the glow is generated it seemed probable that it would be unidirectional in its nature , and would therefore be acted on by a magnetic field . This was found to be the case . In preliminary experiments on this point a permanent magnet was employed , but , for convenience of reversal of the poles , it was replaced by an electromagnet taken from a Morse instrument by Siemens and Halske . The poles of the electromagnet were placed within 0'5 cm . of the bulb , in several different positions . The conditions of the experiment were varied in six ways :\#151 ; ( 1 ) The static charge was either positive or negative . ( 2 ) The rotation of the bulb was either in the clock-hands sense or the reverse . ( 3 ) The magnetic pole , in different experiments , was north or south . Both a horseshoe electromagnet and a long cylindrical electromagnet were used in the different experiments : the current of electricity used to energise the electromagnet was supplied from accumulators , a reversing key being placed in the circuit . Effect of two magnetic poles on the glow . ( Fig. 1 . ) D , disc giving the electrostatic field , charged inductively by means of a disc of sulphur rubbed on the dry hand . Rotation of the bulb , clock-hands sense , to an eye at A. Revolutions 20 per second . No current on electromagnet . A greenish-blue glow filled the bulb . Electromagnet on , the glow took the form of an equatorial bright band , brightest between the poles of the electromagnet , where its shape was modified as shown . Fig. 2.\#151 ; Bulb exposed to south pole . Charge on D as in Fig. 1 . Rotation , clock-hands sense . The glow filled a hemisphere of the bulb P with an equatorial band a little more brilliant than the rest of the hemisphere . Fig. 3.\#151 ; Bulb exposed to south pole . Rotation contrary to clock-hands . The glow filled a hemisphere of the bulb Q with equatorial band a little more brilliant than the rest of the hemisphere . If , while the charge on D and the rotation of the bulb are kept the same , * 'Nature , ' vol. 77 , p. 222 . Luminous Glow in an Exhausted , etc. the magnetic pole is changed , the glow phenomenon is reversed . Also when the charge on D and the magnetic pole are kept the same , but the sense of rotation is reversed , the glow phenomenon is reversed . 216 Rev. F. J. Jervis-Smith . On Generation of a [ Jan. 20 , 14 . The experiments in which one pole of the horseshoe magnet was employed were all repeated with an electromagnet of cylindrical form , so that only one pole was near the bulb . Fig. 4.\#151 ; The electrostatic field was maintained by a brass disc D charged by induction from rubbed sulphur . The views of the apparatus and phenomena are as seen by an eye above looking vertically down on them . The axis of the electromagnet was placed in the horizontal plane through the centre of the bulb , at 45 ' from the axis of rotation of the bulb . Glow in hemisphere G. Reversal of the magnetic pole deflected the glow to the opposite hemisphere . Rotation , clock-hands sense . Fig. 5.\#151 ; The axis of the electromagnet was in the axis of rotation of the bulb . Magnetic pole south . Glow G in hemisphere nearest to the disc . This was exactly reversed when the north pole was used . Fig. 6.\#151 ; E , a sulphur disc which had been rubbed , was used to maintain the electrostatic field . Glow at G , away from sulphur disc . Magnet pole south . The glow illuminated the opposite hemisphere when the north pole was presented to the bulb . In each case the glow is most brilliant in a region the mid-point of which is about 90 ' from the axis of the electromagnet . Shifting the pole of the electromagnet shifts the equatorial plane separating the dark and glow-filled hemispheres . 15 . A summary of the relationship which exists between the direction of rotation of the bulb , the charge of the inductor D , and the name of the magnetic pole , may be stated thus . When the rotation of the bulb is in the clock-hands sense , to an eye looking along XO , the charge on the inductor positive , the magnet pole south , the deflection of the glow is to the right of the south pole as shown in fig. 7 . B , bulb with axis of stem lying in OX , magnet pole south , Pp direction of deflection of glow matter . If any one of the conditions , namely , sense of rotation , sign of charge on the inductor or magnet pole , be reversed , while the other two remain unchanged , the deflection of the glow is reversed . 16 . Experiments have been made and are now being continued with a view to discover whether the glow will affect a photographic plate . When placed in a light-tight case , only very slight traces of this action have as yet been found by me . 17 . In order that the phenomena might be seen under any climatic conditions , the whole of the inductional apparatus was enclosed in a box having a glass lid , fitted with an air-tight rubber joint , the interior being kept dry with sulphuric acid . The discs were charged from the outside of the box by means of conductors 1908 . ] Luminous Glow in an Exhausted , etc. led into it through sulphur plugs . The phenomena could then be observed for any required time . 18 . Many forms of exhausted vessels were employed ; of these an exhausted ring ( 10 cm . diameter , made from tube having an internal bore of 1 cm . ) Y revolving about a diameter , in an electrostatic field , gives a good and beautiful glow . 19 . In conclusion , I wish to offer my best thanks to the President of the Royal Society for comments on the phenomena described in this paper . The diagrams for the paper were prepared by Mr. E. J. Jervis-Smith , RF . A. , who has assisted me in carrying out the experiments .

rspa_1908_0019

0950-1207

The spectrum of magnesium and of the so-called magnesium hydride, as obtained by spark discharges under reduced pressure.

218

228

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

E. E. Brooks, B. Sc., A. M. I. E. E.|Sir William Crookes, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1908.0019

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10.1098/rspa.1908.0019

Atomic Physics

Electricity

Atomic Physics

218 * The Spectrum of Magnesium and of the So-called Magnesium Hydride , as obtained by Spark Discharges under Reduced Pressure . By E. E. Brooks , B.Sc. , A.M.I.EE . ( Communicated by Sir William Crookes , F.R.S. Received October 14 , \#151 ; Read December 12 , 1907 . ) In 1878 Living and Dewar* examined the spark spectrum of magnesium in ' an atmosphere of hydrogen and noticed a bright line of wave-length about 5210 , occasionally accompanied by other fine lines on the more refrangible side . In later papersf they remark that this line is only visible in hydrogen or when the C and E lines are also visible , and describe more fully the " two sets of flutings and a pair of fainter bands " which accompany it , and which appear to have been independently discovered by Ciamician . J Living and Dewar inferred that some compound of the metal and hydrogen was formed , and since the time of their research these lines and flutings have been known provisionally as the " hydride " spectrum . The term will be retained , for convenience , but it must be understood that its correctness is not assumed . Numerous researches have since been made to elucidate the relations between the arc and spark spectra of magnesium , partly in connection with the mechanism of electric discharges in general and partly on account of the importance of the line 4481 in astrophysics and the question as to whether its intensity in stellar spectra can be taken as a criterion of temperature . Of especial interest are the observations of Crew , Basquin and others as to the effect of a hydrogen atmosphere on the arc spectrum of this and other metals . The results obtained cannot be briefly summarised , but references are appended to the more important work dealing with the subject . Very little attention , however , appears to have been given to the hydride spectrum , which is a highly complex system of bands and flutings extending over the whole range of the visible spectrum , from the hydrogen C line to the magnesium triplet at 3830 . The writer 's experiments were suggested by phenomena met with in the course of a research on the spectra produced when compound bodies are used as electrodes in vacuo . The discharge vessel was usually a lamp glass fitted * ' Roy . Soc. Proc. , ' vol. 27 , p. 494 . t ' Roy . Soc. Proc. , ' vol. 30 , p. 94 ; vol. 32 , p. 197 . J ' Sitzber . Akad . Wissenscli . , ' Wien , 1880 , p. 437 Spectrum of Magnesium and So-called Magnesium Hydride . 219 .with rubber stoppers carrying the electrodes , and the pressures employed varied from atmospheric to 1 or 2 mm. of mercury . A large number of observationsK extending over several years , were made in different gases and with different kinds of discharge , but in this paper only the results obtained in the two special cases of alternating currents of high and low frequency will be dealt with . For high frequencies a spark coil was shunted with two large Leyden jars of total capacity about 0004 microfarad , and an adjustable spark gap was put in series with the discharge vessel . The primary current was from 10 to 16 amperes as a rule , obtained from alternating mains at frequency 50 , no contact breaker being employed . The electrodes usually consisted of two long spirals made from single strips of thin commercial magnesium ribbon , .enclosed in glass jacketing tubes with from to f inch projecting at the ends and about ^ inch apart ; this form being adopted because a simple .device enabled them to be fed forwards or backwards as required without impairing the vacuum . Absolute gas-tightness was of course impossible , but the rate of leakage could be made quite small . At a pressure of from t to jr inch of mercury and with an auxiliary spark gap of from 1/ 16 to 1/ 8 inch in length , an oscillatory discharge passes through the apparatus whose RM . S. value ( as read on a hot wire ammeter ) is about 3 amperes , which implies a maximum value of the order of 100 or 200 amperes . The discharge then assumes one of two possible forms which are essentially the same in all gases tried . If the electrodes are too massive or too far apart , there is a luminous gas column between them and they are surrounded by green ragged haloes which do not tend to extend into the gas column . This state may persist indefinitely without any marked waste of the electrodes or deposit on the walls of the vessel , and the spectrum is a mixture of gaseous and magnesium lines . In the case of hydrogen , C and F are especially intense . Increasing the pressure to 3 or 4 inches of mercury does not much effect the metal lines , but makes the four chief hydrogen lines very broad and diffuse ( the C line , however , often being much sharper than the others ) . If the electrodes are not too massive , if they are the single spirals of ribbon already mentioned , this discharge quickly passes into a new and more interesting form . The green glow increases in size and brilliancy , and becomes a green flame enveloping the electrodes and bridging across the whole distance between them , under favourable conditions completely replacing the gas column . The magnesium ions have become the carriers of the discharge , and the arrangement is analogous to a mercury lamp in which the mercury is replaced by magnesium . This state is perhaps most readily 220 Mr. E. E. Brooks . The Spectrum of Magnesium [ Oct. 14 , obtained in hydrogen , and in this gas the phenomena are least complicated by secondary actions . At the instant it sets in , a fine black deposit of metallic magnesium begins to form on the walls of the vessel , and rapidly obscuring the view , although by various devices observations can be maintained as long as is necessary . Meanwhile , the thin electrodes waste quite slowly away , neither fusing nor softening , and a slow absorption of gas goes on , so that a few bubbles must be admitted now and then in order to keep the vacuum from becoming too good and interfering with the oscillations . This will be called the " high-frequency flame discharge . " It gives a brilliant spectrum of perfectly definite character , which can be recognised at a glance , and which differs in many respects from the spark spectrum at ordinary pressures , and also from the normal arc spectrum , but bears some resemblance to the arc spectrum under reduced pressure , as described by other investigators . The points of chief importance may be summarised as follows ( assuming at first hydrogen to be present):\#151 ; . ( 1 ) A good magnesium spectrum is obtained , in which the gas lines are not obtrusive , although the C and F lines are sharp and strong and the fine line hydrogen spectrum more or less visible at the red end . The metal line 4481 is very intense , but still sharp and clear . As regards the fainter magnesium lines , one at 3938 is always found on negatives taken with sufficient exposure , and there are two very faint lines near 3895 and 3900 , and another pair near 3848 and 3853 . These appear to correspond to some of the fainter lines of the spark spectrum at ordinary pressures ( excepting the stronger line 3938 , which seems to be only mentioned by Fowler and Payn).* Two other faint lines at 3944 and 3961 may be due to aluminium as impurity . ( These results were obtained with glass prisms , and observations have not as yet been extended into the ultra violet . ) ( 2 ) In hydrogen the hydride spectrum is always present in great intensity . This is , in fact , the most convenient method of obtaining it . It is usually present , often with almost equal intensity , in the case of other gases , unless very special precautions are taken to exclude water vapour , but disappears in the complete absence of hydrogen and water vapour . ( 3 ) A very prominent feature is the presence of two pairs of sharp lines at wave-lengths approximately 4433*6 , 4428'2 , 4390 , 4385 , the more refrangible pair being slightly the stronger . This is the only type of discharge which gives them readily . Three of these lines appear to have been first observed , but not identified , by E. A. Porter.f * ' Roy . Soc. Proc. , ' 1903 , vol. 72 , p. 253 . t ' Astropliysical Journal , ' 1902 , vol. 15 , p , 274 . 1907 . ] cmcZ of the So-called Magnesium Hydride . Fowler and Pain * observed both pairs in the spectrum of the magnesium arc in an air vacuum , and concluded that they were really enhanced lines of the metal . No other reference to them has been found , although they are visible in a reproduction of the magnesium arc spectrum in , accom- panying a paper by J. Barnes.f As these lines will be frequently mentioned , it will be convenient to term them the " F and P " lines . Their frequency difference is about 27 , a number bearing a simple relation to the frequency differences of 40*5 and 81 , which hold good respectively for two pairs and three pairs of magnesium lines in the ultra violet . J The high-frequency flame discharge can be produced in a coal gas , air , nitrogen , or carbon dioxide vacuum ( these being the only gases tried ) , providing the terminals are not too massive . A very great momentary current density appears to be an essential condition . The type of spectrum just described remains the same , and , under ordinary conditions , the hydride fiutings and the C and F lines of hydrogen are invariably present , often with intensity little inferior to that obtained in hydrogen , so that photographs of the discharge in air or in hydrogen are practically identical . As already stated , this is due to the presence of a trace of water-vapour , extremely difficult to get rid of . Eventually it was eliminated by placing phosphoric anhydride within the discharge vessel itself for each experiment , , and then , in the complete absence of hydrogen or water-vapour , no hydride spectrum appears . In a coal-gas vacuum the carbon fluting at 4315 comes out strongly . In an air vacuum the first effect is a rapid fusion and scattering of the electrodes , due to the oxygen present , but the action quickly subsides , and the true flame discharge sets in with slow subsequent waste . This effect is still more pronounced in carbon dioxide . In nitrogen the discharge presents the usual features , but it is difficult to keep it steady for any length of time , and there is a strong tendency for a red nitrogen glow to appear at one of the electrodes . In all gases absorption occurs during this kind of discharge . The low-frequency discharge ( i.e. , without jars ) is quite different in character and in spectrum . In this case it was desirable to have at command a stronger current than could be obtained from a spark coil , and hence a small 2000-volt transformer , fed from alternating mains at frequency 50 , and with an adjustable liquid resistance in the secondary circuit , was usually employed , also magnesium rods about 3/ 16 inch diameter were * ' Roy . Soc. Proc. , ' 1903 , vol. 72 , p. 253 . t ' Astrophysical Journal , ' 1905 , vol. 21 , p. 75 . X Baly , ' Spectroscopy , ' p. 502 . 222 Mr. E. E. Brooks . The Spectrum of Magnesium [ Oct. 14 , more convenient to manage than strip , for the electrodes fused with a current whose R.M.S. value was perhaps only one-tenth of that carried easily under the former conditions . For a long time the results obtained were very puzzling , the " F and P " lines and the hydride spectrum appearing or disappearing under apparently identical conditions , but whilst the latter was more often present than not , the former were very seldom found on the negatives . Eventually it became apparent that several distinct spectra were present , the facts observed being briefly as follows . When a current of , say , 03 or 04 ampere is passed through rod electrodes in a hydrogen vacuum at about 2 or 3 cm . pressure ( the vessel itself containing phosphoric anhydride ) , the first effect is a perfectly steady pale glow around each electrode , which gives a faint hydrogen spectrum , but there is no luminous gas column between them . If no special care has been taken with the electrodes , i.e. , if the surfaces are oxidised , vivid green points may keep flashing out on them , most numerous at first and gradually diminishing as time goes on . The spectrum of these points has been observed frequently , and also photographed . It is characterised by the presence of the hydride flutings and the " F and P " lines , and the great strength of the line 4481 , but differs from the high-frequency flame spectrum in the comparative weakness of the minor magnesium lines . If the electrodes be trued up in a lathe so that their whole surface is perfectly bright and clean , very few or no flickering green points are seen , and in any case they disappear more or less completely in a very short time , but when one does flash out , its characteristic spectrum flashes out with it . The subsequent course of events is practically the same whether the rods are clean or not . Gradually a pale green tint creeps into the perfectly steady halo surrounding each electrode . This gives the b triplet and the line 5528 on a background of the two hydrogen spectra , but there is not a trace of the hydride flutings or of the " F and P " lines , 4481 being very faint and the other magnesium lines practically invisible . This spectrum has been repeatedly photographed , but only the brighter lines are shown . The green tint steadily increases in intensity until finally , with the suddenness of switching on a lamp , the discharge lights up brilliantly , the glow around the electrodes becomes intense , producing a flame effect not unlike that already described ( but really quite different in structure and properties ) , and accompanied by a rapid and copious evolution of brownish-black fumes.* With equal suddenness the gaseous lines disappear completely , * This stage marks the fusing point of the electrodes . Later experiments with unidirectional current have shown that the green glow and subsequent phenomena occur only at the cathode . 1907 . ] and of the So-called Magnesium Hydride . leaving an intensely bright and sharp magnesium spectrum , but without the hydride flutings and without the " F and P " lines . The line 4481 is distinct and about equal in intensity to 4571 , and relatively much fainter than 4703 and 4352 . It is difficult to eliminate completely the hydride spectrum , but when it appears it is in flashes , and in any case its intensity is very small compared with its great strength in air or nitrogen not specially dried . Photographs show barely a trace of it . Hence the mere presence of dry hydrogen is not sufficient to bring out the hydride flutings . In one experiment , without disturbing the apparatus , the connections were then changed to the coil with jars and the high-frequency discharge passed . As is usual with such thick electrodes , the flame state was not obtained , and although the " F and P " lines were well seen the hydride flutings were invisible , except that after long running a faint trace of the line 5210 appeared . In another experiment of the same kind some approach to the true flame discharge was obtained for a few moments and then the hydride flutings appeared distinctly , but only during that time . The general inference is ( since abundantly confirmed ) that the " F and P " lines are not in any way related to the hydride spectrum ; they are probably true magnesium lines , but require the jars to bring them out well , whereas either at high or low frequency the hydride flutings require something more than the mere presence of hydrogen . Unless special precautions are taken to eliminate water-vapour , the low-frequency flame discharge in hydrogen always gives a strong hydride spectrum , but the " F and P " lines have never been observed in it , although carefully looked for . For instance , rod electrodes which had been used to demonstrate the absence of the hydride spectrum in dry hydrogen were directly afterwards placed in another vessel , but without phosphoric anhydride . This vessel was then well washed out with hydrogen ( passed through strong sulphuric acid and over phosphoric anhydride before entrance ) , but when the final state set in the hydride spectrum appeared steadily . Hence this spectrum can be seen in the presence of a trace of water-vapour under conditions in which it would be totally absent without that vapour , a hydrogen atmosphere being present in both cases . A larger quantity of water-vapour makes very little difference , merely bringing out the oxide fluting at 5007 . Such results made it a possible hypothesis that the hydride bands were ; always connected with the presence of oxide or water-vapour , in which 224 Mr. E. E. Brooks . The Spectrum of Magnesium [ Oct. 14 , event there would be no occasion to assume the existence of a " hydride " at all . It would simply be the spectrum of the metal in a peculiar and nascent state . Some important evidence in this direction had been obtained years previously in the case of other elements and compounds . For instance , in a similar way , but with more difficulty , a jet-like glow can be obtained from point sources on an aluminium electrode , and this always gives the characteristic fluting spectrum of that metal , by some writers attributed to the oxide ; but Hemsalech has supported Aron 's view that it is really due to the element itself . It was , however , found that the hydride spectrum appeared with great intensity in the .high-frequency flame discharge in hydrogen even when every effort was made to eliminate oxide and water-vapour . It is always difficult to estimate how far such efforts have been successful , but apparently there are two distinct methods of producing the state or substance which gives this spectrum , one dependent on a chemical change accompanying ionisation and the other on ionisation by a current of very high maximum value . The low-frequency discharge in dry air or nitrogen presents problems of more difficulty and is still under investigation . It is , however , perfectly certain that there are at least two quite different spectra to be seen in one and the same discharge , having distinct and recognisable sources . One of these is characterised by the intensity of the line 4481 ; 4703 is weak and 4571 invisible , and the hydride spectrum is absent . In air the oxide fluting at 5007 is strong at first , disappearing later , and in nitrogen it is absent . The other spectrum , which depends in some way on the presence of nitrogen , probably on the formation of nitride , is remarkable on account of the great intensity of the line 4571 , which , next to the b triplet , is by far the strongest line in it , 44S1 being usually invisible , 5711 faint , and 5528 and 4703 of only moderate strength . When the air or nitrogen has not been specially dried the hydride spectrum appears with great brilliancy . There is an initial stage in which the cathode gets hot and may fuse , even with small current , but if " nursed " through this , a current of from 1 to 2 amperes may be passed for an indefinite time without fusion . The " F and P " lines are faint , but in all cases are seen when discharge is sufficiently intense . It is hoped to deal more fully with this part of the work in a later paper . As regards the long-debated question as to whether the intensity of the line 4481 is a criterion of temperature , it may be pointed out that in the high-frequency flame discharge the single spiral of thin magnesium ribbon never fuses , although it is carrying a considerable current , its temperature probably being kept down by the free ionisation going on . Yet this is the discharge which gives the line 448.1 with the greatest intensity and sharp1907 . ] and of the So-called Magnesium Hydride . ness . In the low-frequency discharge the whole apparatus is much hotter and the electrodes readily fuse . In fact , this latter spectrum has been photographed when the thick electrodes have been in a molten state and liquid globules dropping from them , without any marked increase in the intensity of this line , which is relatively weak in this kind of discharge , and , under these conditions , the spectrum as a whole is not so good as when the flame state occurs without fusion . Observations were made in several different ways on the high-frequency discharge , in order to determine the relation of the various lines to the electrodes . In some experiments a three-way globe was arranged so that one of the electrodes could be seen " end on , " the other electrode being a ring of iron wire . An image of the former electrode was thrown on the slit of a spectroscope by means of a lens , and thus different parts of the glow examined . The line 4481 was only conspicuous quite close to the electrode , a slight displacement suddenly cutting it off , as was also the case with the hydride bands . The line 4703 remained visible a little longer than 4481 , whilst the b triplet was brilliantly visible long after the latter disappeared , and , in fact , could always be seen more or less clearly in any part of the globe . The line 5528 varied with the triplet\#151 ; a fact often noticed\#151 ; as if these lines have a common origin or are connected in -some way . The discharge was also photographed by means of an ordinary camera with a diffraction grating in front of the lens , but without a slit . The negatives showed the 4481 light locally strong at the electrodes , whilst an image of the whole lamp glass was formed by the light of the b triplet , and also , but more faintly , by the light of the violet triplet at 3830 . Hence this latter radiation pervades the whole space as does that of the b group\#151 ; due mainly perhaps to reflection\#151 ; but partly to a real luminescence at considerable distances from the discharge proper . Similar results were obtained by using an ordinary prism spectrograph without a slit , and the phenomena can be observed directly in a specially clear and interesting way by means of Dr. Marshall Watts ' " Binocular " spectroscope . The 4481 light can be seen flickering brightly close to each electrode , and with a small gap and a strong discharge extending faintly across it . The whole globe is seen in the light of the b group , and also in the light of the yellow line 5528 , these flickering in unison . These observations are merely given as confirmatory of results obtained by other investigators . It may , however , be remarked that the locus of the line 4481 is visible without any apparatus at all . In the true high-frequency flame discharge the green glow envelopes the electrodes and YOL . LXXX.\#151 ; A. Q 226 Mr. E. E. Brooks . The Spectrum of Magnesium [ Oct. 14 , bridges over the space between them , but the root of the discharge is distinctly blue , and it is this blue region which gives the 4481 line most strongly . ( The low-frequency flame has no such blue core . ) The " F and P " lines were not examined in the same way , but in all probability it will be found that their source lies even closer to the electrodes . Some useful information as to the relation between the various phenomena already described and the sign of the electrodes was obtained by separating the components of the current in a magnetic field . For this purpose a narrow lamp glass was generally used , placed horizontally between the poles of an electromagnet so that the discharge was at right angles to the field , the magnesium electrodes being bifurcated so that on each the locus of origin of a positive and negative discharge could be readily seen . Sometimes one of the electrodes was an iron ring . With the means available the experiments were somewhat troublesome , and it has not been possible to obtain a direct current of sufficient voltage to confirm the results , which all pointed to the same conclusion . The high-frequency discharge separated into two paths , equally pervaded by the green flame , and the faint bluish root which gives the 4481 line was found to be on the positive source only . Blackening took place by diffusion uniformly all round the tube , no localisation being noticed . When the low-frequency flame was used , each electrode showed a bright green glow , * also attached to the positive source , but without a blue core . In this case the blackening was markedly local ; the glows behaved much more like jets , and could be driven in any predetermined direction by the field , instant blackening occurring in exactly that direction . The experiments were decisive as to the positively charged character of the magnesium ions . When one electrode was of iron , this also possessed a green positive glow , and by the same method it was found that positively charged magnesium ions were returning from it . The pressure used was about 2 inches . These experiments were made in hydrogen , but a remark occurs in a notebook , made nearly three years since , to the effect that " the green glow , due to incipient combustion in an air vacuum , clearly and definitely follows the field , always being on the anode , and accompanied by brilliant whitish points . " ( These points are due to incandescent oxide . ) It was much more difficult to study the cathode by this method , and certain curious results obtained lack confirmation and are being investigated further . In one experiment , also made long ago , a three-way globe was * This refers to a particular stage in the discharge . The facts are somewhat complicated and are being examined further , but the gi'een jets always act like positively charged streams . 1907 . ] and of the So-called Magnesium Hydride . used , fitted with a third idle terminal , a small metal disc which could be kept charged positively or negatively by a Wimshurst machine whilst the discharge was passing . This was of the high-frequency flame type , and it was found that when the disc was kept positive , no black deposit formed on it , whereas when it was negative , such a deposit formed on it as well as on the walls of the globe . If the third terminal was quite close to the discharge column , the black deposit formed upon it in either case . Apart from the question of charge , there are certain well-marked peculiarities in the evolution of fumes and formation of deposits which seem worthy of brief mention . It has already been stated that when the high-frequency flame discharge occurs in the presence of a trace of oxygen , there is an initial stage of fusion during which small particles of metal may be projected in various directions . These strike the glass at various angles , either rebounding or adhering as small metallic spheres flattened by the impact , and would not have attracted attention except for a peculiar structure invariably present in the splash . The metal particle is surrounded by a dark ring , and outside this , at a greater distance , is another fainter ring , as if the flying particle was surrounded by an atmosphere much larger than itself . According to the direction of impact , these rings may be nearly circular or portions of ellipses . When a particle strikes at almost grazing incidence , it leaves a long trace broken up into a series of separate splashes , but on either side is always found the faint line which marks the boundary of this atmosphere . The particles themselves may average a millimetre or so in diameter , the largest met with being 5 mm. and its " atmosphere " 2 cm . in diameter . The fumes from the low-frequency flame discharge are usually lighter coloured , more distinctly visible , and form in a quite different manner . The projectile effect is very seldom met with , but instead one frequently obtains , especially in air or nitrogen , very large and remarkable spiral formations on the glass , which , under favourable conditions , may be seen to correspond to almost stationary whirls inside . Single instances of this kind would not be noteworthy , but it is remarkable that when such formations occur at all they are always of exactly the same type , and their probable appearance or otherwise can be predicted in advance . [ Note added January 2bth , 1908.\#151 ; Since this paper was written , Professor Fowler has shown that the hydride bands and flutings occur in the spectra of sun-spots ; a most interesting and important discovery ; and he remarks that " there need be no hesitation in attributing the flutings in question to the compound magnesium hydride."* It is , however , somewhat difficult to * 'Notices Roy . Astron. Soc./ vol. 67 , No. 8 , p. 530 . 228 Spectrum of Magnesium and So-called Magnesium . imagine a compound of the metallic hydride type existing as such in the sun , even at the relatively low temperature of a sun-spot ; but , assuming this to he the case , and also that it is really formed in the arc and spark , it is still more difficult to understand why it eludes isolation by chemical means . One would naturally expect magnesium hydride to he an unstable compound , and apparently the only chemical evidence for its existence is to be found in a paper by Winkler , * who obtained a non-homogeneous substance ( by heating a mixture of Mg and MgO to redness for four hours in an atmosphere of hydrogen ) , which certainly appears to have contained hydrogen , but whose exact composition seems somewhat doubtful . On the other hand , in the current number of ' Nature 'j* is a paragraph referring to an article in the ' Observatory , ' ] : by Father Cortie , who has many times recorded lines attributed to water-vapour in the spectra of sun-spots , and who suggests the possibility of the presence of superheated steam . Again , it may be noted that the metallic banded spectra of which the hydride flutings are merely one instance , are especially readily obtained in the oxyhydrogen flame , and Hartley and Ramage attribute these to the metal itself . Professor Fowler ( whom I find has also been working for some years at the hydride spectrum ) informs me that the most convenient way of producing such .spectra is in the " flame " of the electric arc , but from my own experience I have no difficulty in believing that amply sufficient water-vapour may be present in this case also , unless very special precautions are taken to ensure its absence . On the whole , it seems best to regard the objective existence of the hydride as an open question , awaiting further experimental evidence . ] REFERENCES TO PREVIOUS WORK BEARING ON THE MAGNESIUM SPECTRUM . Living and Dewar , ' Roy . Soc. Proc. , ' vol. 27 , p. 494 . " " " " vol. 30 , p. 94 . " " " " vol. 32 , p. 197 . Crew , ' Astrophysical Journal , ' 1900 , vol. 12 , p. 167 . Basquin " " vol. 14 , p. 1 . Schenck " " 1901 , vol. 14 , p. 116 . Hartley and Ramage , 'Roy . Soc. Dublin Trans. , ' 1901 , p. 339 . R. A. Porter , 'Astrophysical Journal , ' 1902 , vol. 15 , p. 274 . Fowler and Pain , 'Roy . Soc. Proc. , ' 1903 , vol. 72 , p. 253 . Hartmann , 'Astrophysical Journal , ' 1903 , vol. 17 , p. 271 . Crew , " " 1904 , vol. 20 , p. 274 . Barnes , " " 1905 , vol. 21 , p. 75 . Loving , " " 1905 , vol. 22 , p. 290 . * ' Ber . Deutsch . Chem. Gesell . , ' 1891 , vol. 24 , p. 1973 . t January 23 , 1908 , p. 281 . J January , No. 392 , p. 51 .

rspa_1908_0020

0950-1207

Notes on the application of low temperatures to some chemical problems: (1) Use of charcoal vapour density determination; (2) Rotatory power of organic substances.

229

238

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir James Dewar, M. A., Sc. D., LL. D., F. R. S. |Humphrey Owen Jones, M. A., D. Sc.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0020

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0020

10.1098/rspa.1908.0020

Thermodynamics

Biochemistry

Thermodynamics

229 Notes on the Application of Low Temperatures to some Chemical Problems : ( 1 ) Use of Charcoal in Vapour Density Determination ; ( 2 ) Rotatory Power of Organic Substances . By Sir James Dewar , M.A. , Sc. D. , LL. D. , F.R.S. , Jacksonian Professor in the University of Cambridge , and Humphrey Owen Jones , M.A. , D.Sc . , Fellow of Clare College and Jacksonian Demonstrator in the University of Cambridge . ( Received February 6 , \#151 ; Read February 20 , 1908 . ) ( 1 ) Use of Charcoal in Vapour Density Determination . In a recent paper* Barkla and Sadler describe the investigation of the penetrating power of the secondary Rontgen rays emitted by different elements , which they find to be dependent on the atomic weight of the element . The behaviour of nickel was found by those investigators to be abnormal , and could only be reconciled with the behaviour of other elements by assigning to nickel an atomic weight of 61*4 , a value considerably higher than the accepted value , 58*7 . We therefore considered it of interest to make some further determinations of the density of nickel carbonyl at low pressures ( when it would approximately obey the gas laws ) by the use of a new method of manipulation which enables greater volumes of vapour to be employed , while , at the same time , the accuracy of the weight of the nickel carbonyl used in each experiment was considerably improved . Previous determinations made by usf gave the value 83*3 at 63 ' C. and 760 mm. ( when slight dissociation had taken place ) and 85*6 at 17 ' C. and 67*7 rnm . , when no dissociation could be detected . These results show no indication that the accepted atomic weight of nickel is too low . The basis of the present method is the use of charcoal at low temperatures to absorb gases and vapours . As liquid air is the material used for cooling , easily condensable vapours would , at the low temperature , have such a small tension that even the charcoal might be dispensed with , so far as one of the operations is concerned ; but as its presence was not a disadvantage , it was retained in all the condensers . In the following experiments , the vapour or gas , of which the density had to be determined , occupied a definite known volume at 0 ' C. under a measured pressure , and was absorbed in a small bulb filled with charcoal cooled in * 'Phil . Mag./ 1907 , vol. 14 , p. 408 . t 'Roy . Soc. Proc.,5 1903 , vol. 71 , p. 427 . 230 Sir J. Dewar and Dr. H. O. Jones . Application of [ Feb. 6 , liquid air which was afterwards weighed . In the conduct of the several operations it was found most advantageous to use three charcoal reservoirs for the purposes of air exhaustion and condensation . The apparatus is sketched diagrammatically in fig. 1 , and the following brief general description of it , and the mode of procedure , will make clear the essential details of the method . A is a flask whose volume is about 2 litres , which is connected to a mercury manometer at B , and through a stopcock at C , to a weighed bulb F , with separate stopcock containing cocoanut charcoal . A stopcock at I ) enables communication to be made to a suitable reservoir containing the substance whose vapour density was to be determined , or to any gas generating mixture like that used for the production of carbonic acid . As all air has to be removed and a high vacuum reached in this part of the apparatus , it is convenient to seal on a special charcoal condenser , not shown in the drawing , instead of exhausting the whole apparatus by means of the one charcoal reservoir . During the charcoal exhaustion , liquid substances , like nickel carbonyl , ether , or sulphurous acid , were frozen at the temperature of liquid air . The usual preliminary washing out of the flask by the gas or vapour under examination made no detectable difference in the densities . The volume of the flask A and the connecting tubes enclosed between the stopcocks C , D , and a mark at B on the manometer tube , was ascertained from the weight of water at 0 ' C. , which filled the space and was found to be 2161*6 c.c. The contraction of the flask , when the internal pressure was reduced to 40 mm. , was found to be approximately 1 c.c. Taking the weight of air displaced by the flask as 2*58 grammes , we get the value 2163*2 c.c. as the volume of the exhausted flask . This gas or yapour receptacle , after charcoal exhaustion , was surrounded with melting ice , all except a small portion of the manometer tube at B , which had to be left uncovered in order to take readings of the level of the mercury . The volume of the exposed part was , however , not more than 2 c.c. , so that the error introduced by this , being at a temperature above 0 ' C. , is negligible . Beyond the tap C the apparatus is connected through a tube Gr to a bulb H containing cocoanut charcoal , and by a side tube to a Fleuss pump , also by another side tube with a stopcock J to a small bulb E containing charcoal . The weighted bulb F , also containing charcoal , was connected to the rest of the apparatus by a piece of thick rubber tubing , so that it could be detached and weighed . This rubber joint in refined experiments might be replaced by one of ground glass . The mercury reservoir below the manometer B was movable , so that the 1908 . ] Low Temperatures to some Chemical Problems . 231 upper surface of the mercury could always be brought approximately to the level of the mark on B and carefully adjusted by means of a plunger in the reservoir . The stopcocks were all carefully selected , and after proper lubrication were found to allow no appreciable leak into the exhausted apparatus on standing for many days . Fig. 1 . The arrangements for supplying the vapour were varied according to the substance used , and will be described in each case . The stopcock D being closed , C , J , and K open , the whole apparatus was exhausted through the side tube at G by means of a Fleuss pump , while the three charcoal bulbs were heated by means of a Bunsen burner . The side tube was then . sealed off at G , and the bulb H inversed in liquid air for several hours , usually over night , after which the tube at I was fused and the charcoal condenser removed . The vacuum left is less than a ten-millionth of an atmosphere . During the main period of the charcoal exhaustion of the whole apparatus the stopcocks J and K were closed . The flask being now shut off* by closing the stopcock C , the charcoal bulb F was detached , weighed with an equal volume counterpoise , and again connected to the 232 Sir J. Dewar and Dr. H. O. Jones . Application of [ Feb. 6 " apparatus . The small space in the connecting tubes between C and the taps J and K was now necessarily filled with air , which was removed by immersing the bulb E in liquid air for about 10 minutes , and then shutting stopcock J. Meanwhile the 2-litre flask A was surrounded with powdered ice , and the height of the mercury column in the manometer determined by means of a cathetometer . It is evident that the accuracy of the results will depend on the determination of pressure , since the errors here will be greater than those in the determination of the volume of A or of the weight of the vapour . The cathetometers used ( one of which was very kindly lent by the Cambridge Scientific Instrument Company ) were capable of reading to 0*02 mm. Four readings of each surface of the mercury were taken , the condition of lighting and background having previously been arranged so as to ensure the best result obtainable , and the mean of these to the nearest tenth of a millimetre taken , this being sufficiently accurate for the main object in view , namely , to see if the atomic weight of nickel was considerably higher than 58*7 . The gas or vapour was now introduced through the tap D to any desired pressure , D was closed , and after adjusting the level of the upper surface of the mercury to the mark on B , the pressure was again determined . Several determinations of the pressure were usually made , but it was found that equilibrium was very soon reached , and after about 10 minutes the pressure did not change . When the charcoal bulb F is immersed in liquid air , the taps C and K being open , the vapour in A is rapidly condensed in F. The exhaustion of the vapour from the flask was allowed to go on for about one hour , though in most cases no measurable diminution of pressure could be detected after about 10 minutes cooling . The taps C and K were then closed , F was detached and weighed against an exactly similar counterpoise after the expiration of a sufficient interval for it to acquire the atmospheric temperature . The flask is now left exhausted and ready to be recharged with vapour or gas , and another determination made . It was found advisable to exhaust and heat the charcoal in F after each experiment . The weight of vapour filling A at 0 ' C. and under a measured pressure is thus determined , from which the vapour density can be calculated . One difficulty with regard to the determination of the pressure must be noted . The pressure of the vapour is found from the difference in the readings of the mercury manometer taken at different times . During the interval between these readings the atmospheric pressure may change , and it was found in certain cases that owing to this cause the initial and final 1908 . ] Low Temperatures to some Chemical Problems . 233 readings of the manometer did not agree . When this is observed the pressure of the vapour is best obtained from the difference between the reading of the manometer before and after introducing the vapour , since the interval between these readings is not long , usually about half an hour . In order to test the method* some condensible gases , whose vapour densities are accurately known from the determinations of Rayleigh and Guye , were selected for experiment . For this purpose carbon dioxide and sulphur dioxide were chosen , and the results showed that the method worked satis* factorily , the variations being within the limits of accuracy aimed at . The pressure was corrected for temperature by the simple formula pt = jpb ( 1 + 0-0001818* ) where t is the temperature of the column of mercury . The manometer tube was 6 mm. wTide , so that the correction for capillarity may be neglected . The correcting factor ( 0*99971 ) for reducing the weights from the value of gravity at Cambridge to that at Paris , may also be neglected as the difference is not within the limits of accuracy aimed at . Carbon Dioxide.\#151 ; This gas was prepared by heating together an intimate mixture of fused boric acid and recently ignited sodium carbonate , and passing the gas through a tube containing some pure phosphorus pentoxide distilled in oxygen . The apparatus for the preparation of this gas was sealed on to the inlet tube D beyond the stopcock and was thoroughly exhausted by means of a special charcoal reservoir and then finally connection was made to the previously exhausted flask A. The apparatus was allowed to stand for some time , and the special charcoal bulb sealed off . The large flask A was then ready to be filled with carbon dioxide through the inlet tube D. The following results were obtained :\#151 ; Pressure corrected . Weight of gas . Weight of 1 litre of the gas . Vapour density of gas , taking 1 c.c. of H 0 *00009 gramme . mm. gramme . gramme . 115 *4 0 *6476 1-972 21 -91 206 *5 1 *1624 1 -978 21 -98 206 *0 1 *1600 1 *978 21 *98 Rayleigh* gives the value 1*52909 as the weight of a litre of carbon dioxide compared to air at 0 ' and 760 mm. , which is 1*9782 gramme per litre . Sulphur Dioxide.\#151 ; Some pure dry sulphur dioxide was liquefied in a glass bulb which , with a tube containing phosphorus pentoxide , was sealed on to D * ' Roy . Soc. Proc. , ' 1897 , vol. 62 , p. 206 . 234 Sir J. Dewar and Dr. H. 0 . Jones . Application of [ Feb. 6 , and the whole was then , while the sulphur dioxide was frozen in liquid air , exhausted by means of a pump followed by the use of charcoal in the manner described above . The vapour could now be changed into the previously exhausted flask A to any desired pressure . The following results were obtained:\#151 ; Pressure ( corrected ) . Weight of gas . Weight of 1 litre of gas . Yapour density . mm. gramme . grammes . 76 T 0 *6200 2*863 31 -81 198 *5 1 *6243 2-875 31 -94 Guye* takes 2*9266 as the most probable value for the weight of a litre of sulphur dioxide at 0 ' C. and 760 mm. The theoretical value of the vapour density is 31*79 . Ether.\#151 ; The experiments were carried out substantially as described for sulphur dioxide . The results obtained were as follows:\#151 ; Pressure . Weight of vapour . Vapour density . mm. gramme . 31 *4 0 *2968 36 *90 63 *9 0 -6024 36 -91 Theoretical value of the vapour density is 36*76 . Nickel Carbonyl.\#151 ; In this case a small bulb was sealed on to D , which was connected , by means of a constricted tube and a stopcock , with another bulb containing pure dry nickel carbonyl . The first bulb was exhausted with the whole apparatus , the tap at D was shut , nickel carbonyl was admitted into this small bulb , this was then cooled to \#151 ; 183 ' , the constricted tube sealed off , and the whole apparatus exhausted , wdiile the bulb containing nickel carbonyl was kept in liquid air . The following results were obtained :\#151 ; Pressure . Weight of vapour . Yapour density . mm. gramme . 16 6 0 *3600 84 -67 41 -7 0 -9046 84-69 46-8 1 *0164 84 -79 * 'Compt . Rend . , ' 1907 , vol. 144 , p. 1360 . 1908 . ] Low Temperatures to some Chemical Problems . 235 Taking the atomic weight of nickel as 58*3 ( H = 1).\#151 ; The theoretical vapour density is 84*73 , whereas on the assumption of the atomic weight suggested by Barkla and Sadler reduced to the same standard it would be 86*05 . A slight deposit of nickel , due to dissociation of the nickel carbonyl under low pressure , formed on the tube just inside the tap I ) , where the vapour entered the apparatus . This would , of course , tend to make the result obtained too low ' ; the amount of nickel deposited , even after several experiments , was so small , however , that its influence on the vapour density would be quite outside the limits of error . No correction was made for the presence of vapour of mercury . Taking into consideration the fact that the deviation of the vapour from the gas laws would tend to make the result too high , it is probable that the value found is not too low , and makes it impossible that the atomic weight of nickel should be as high as 61*4 relative to the oxygen standard , or 60*95 when hydrogen is taken as the fundamental unit of atomic weights . The accuracy of the method could be greatly improved by the use of a larger vessel and more delicate manometric measurement , so that good results might be obtained at very much lower pressures . Further , if the charcoal condenser F was made of metal instead of glass , any increase of pressure on heating the charcoal up to the ordinary temperature would be immaterial , and thus more volatile gases like oxygen and nitrogen could be equally well manipulated . ( 2 ) Rotatory Power of Organic Substances . The optically rotatory power of organic substances does not appear to have been examined at temperatures below 0 ' C. An attempt to determine the change which takes place in the rotatory power of some substances down to much lower temperatures is here recorded . With this object in view , solutions of various optically active substances in alcohol and in petroleum ether were cooled to a low temperature by means of liquid air , and it was found that solutions of a number of substances could be solidified without losing their transparency . A jacketed polarimeter , 10 cm . in length , was made entirely of metal , and surrounded with a thick covering of wool . Experiments were made to find out how best to avoid the deposition of hoar frost on the glass plates at the ends of the tube . This caused some trouble , and , after trying a number of devices , it was found that , when the glass plates used to close , the ends of the tube were about 1 cm . thick , and their outer surfaces were continually moistened with absolute alcohol , readings could be taken at quite low temperatures . 236 Sir J. Dewar and Dr. H. O. Jones . Application of [ Feb. 6 , Cooling was carried out by introducing liquid air , or other liquids of low boiling-point , into the cylindrical space between the actual tube and the outer jacket . Cooling caused distortion of the field of the polarimeter as seen through the liquid , and accurate determinations of the rotatory power soon became impossible ; however , by cooling slowly , and allowing a considerable time for inequalities in density to disappear , it was found that fairly consistent readings of the polarimeter could be obtained , and the-uncertainty in the result was usually not greater than 0'*3 . When the liquid in the tube solidified to a transparent glass , readings were no longer possible , as the field of the polarimeter became uniform in all positions of the analyser ; this effect is probably due to double refraction , caused by strain . In the case of some solutions , such as that of menthol in alcohol , , this effect appeared at \#151 ; 80 ' C. , while the solution was still liquid . The choice of solvents is practically limited to ethyl alcohol and petroleum ether of low boiling point , since these are among the few liquids which solidify below \#151 ; 100 ' C. to a transparent glass . It soon became clear also that very few active substances were suitable for examination , as it was necessary to get a sufficiently large rotation to observe , , and solutions of most substances , when concentrated enough to give a rotation as large as desirable , could not be cooled and still retain their transparency . Solutions of a number of substances have been examined , but two only need be mentioned here as it is hoped later to communicate the results of further experiments on the effect of temperature on rotatory power . These two substances are / -nicotine and " bitter orange oil , " consisting chiefly of cZ-limonene . These were chosen for several reasons : first , on account of their great rotatory power , [ a]D = \#151 ; 163 ' and +96 ' respectively ; secondly , they both formed mixtures with alcohol which could be solidified to transparent glasses , and , thirdly , on account of the difference in their behaviour within the limits of temperature hitherto examined . The rotatory power of nicotine increases with increase of temperature , while that of limonene decreases with increase of temperature . . The following observations are selected from those made and illustrate the kind of change observed . Nicotine.\#151 ; Solution in alcohol , 21*2 grammes in 100 c.c. at 20 ' C. Density , . 0*871 . Temperature . + 20 ' C. Observed rotation . \#151 ; 30'*0 C. - 50 - 70 - 90 - 120 -28 -7 -27 *3 -25 *3 -22 *0 1908 . ] Low Temperatures to some Chemical Problems . 237 At lower temperatures readings were impossible . Solutions of nicotine in petroleum ether on cooling soon deposit solid nicotine and are therefore useless . It is clear from the above results that the rotatory power of nicotine diminishes with decreasing temperature below 0 ' C. just as it does above this temperature . Moreover , the diminution appears to be quite regular ; since the curve showing the relation between the temperature and the observed rotation is approximately a straight line which , when produced , gives a rotation at the absolute zero of about 12 ' . The specific rotatory power cannot be calculated , since the densities of the solution at the different temperatures have not been determined . A rough estimate of the specific rotatory power can , however , be obtained by using the densities of alcohol calculated from a Waterston formula , V = 2-8911 \#151 ; 0-6938 log ( 243-6 \#151 ; 0- The density of alcohol at \#151 ; 90 ' C. would be , according to this formula , 0-877 . The density of the nicotine solution at 20 ' C. was 0-871 , and may be assumed to be about 0'95 at \#151 ; 90 ' C. , hence the specific rotatory power at this temperature would be approximately \#151 ; 109 ' . Taking the value of the observed rotation from the curve to be \#151 ; 23''5 at \#151 ; 115 ' C. , the density of alcohol to be 0'894 , and that of the solution to be 0'97 , we get the specific rotatory power at this temperature to be about \#151 ; 99 ' . Hence , by extrapolation of the linear law , the specific rotatory power at \#151 ; 273 ' C. would be about \#151 ; 54 ' . Bitter Orange Oil.\#151 ; Solution in alcohol , 20 grammes in 100 c.c. at 15 ' C. Density , 0'816 . Temperature . Observed rotation . + 8 ' C. + 18'-5 C. -35 20 -5 -65 22 -3 -85 24 -5 -95 25 -5 Further readings were impossible . The curve expressing the relation between temperature and observed rotation was found to be practically a straight line , and the value of the observed rotation at the absolute zero would be about 37 ' . The rotatory power , therefore , increases with diminishing temperature below 0 ' C. as it does above this temperature . On calculating the densities of the solution in the same rough way as in the case of the nicotine solution , we get the density of the solution at \#151 ; 90 ' C. to be 089 , and hence the specific rotatory power would be about +114 ' . By extrapolation , on the assumption of the linear 238 Application of Low Temperatures to Chemical Problems . law , the value of the specific rotatory power at \#151 ; 273 ' C. is found to be about 156 ' . Solution in petroleum ether ( B. P. 30'\#151 ; 35 ' C. ) , 20 grammes in 100 c.c. at Temperature . Observed rotation . + 5 ' C. +19'-2 C. -15 20 -5 -35 22 .2 -60 23 -7 -75 + 24 -2 -95 26 -0 Further readings were impossible . The results in this solvent are therefore just the same as those in alcohol , the rotatory power increases with diminution of temperature and would be about 40 ' at absolute zero , if the linear law be extended . Similar results have been obtained with a number of other substances such as menthol , camphor , ethyl tartrate , and pinene , but on account of the smaller rotations that were observed they were not so regular nor so conclusive . It would therefore appear from these preliminary observations that the rotatory power of optically active carbon compounds in solution changes in a regular manner with temperature down to \#151 ; 120 ' C. and that the molecules would , in all probability , still exhibit optical rotatory power at much lower temperatures .

rspa_1908_0021

0950-1207

Address of the President, Lord Rayleigh, O. M., D. C. L., at the Anniversary Meeting on November 30, 1907.

239

251

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Lord Rayleigh, O. M., D. C. L.

speech

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0021

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0021

10.1098/rspa.1908.0021

Biography

Fluid Dynamics

Biography

239 Address of the President , Lord , O.M. , D.C.L. , at the Anniversary Meeting on November 30 , 1907 . Since the last Anniversary the Society has sustained the loss of twenty-five Fellows and three Foreign Members . The deceased Fellows are:\#151 ; Thomas Andrews , Sir Benjamin Baker , Sir Dietrich Brandis , Sir William Henry Broadbent , Dr. Alexander Buchan , Lord Davey , Dr. August Dupre , Sir Joseph Fairer , Sir Michael Foster , Sir William Tenant Gairdner , Lord Goschen , Sir James Hector , Prof. Alexander Stewart Herschel , The Foreign Members are:\#151 ; Marcellin Berthelot , Dmitri Ivanovitch Mendeleeff , Henri Moissan . From the length of this list it will be seen that death has been unusually busy during the year . It includes many names of great distinction , of whom I can refer only to a few . Sir B. Baker was a Councillor at the time of his death , and was well known among us as a frequent attendant at our meetings and as combining scientific interests with the highest degree of successful practice in his profession . The recent catastrophe in America will , perhaps , even enhance his reputation as the designer of the Forth Bridge . In Sir Michael Foster we have lost one , to whom probably more than to anyone else the present position of our Society is due . For 22 years he held the office of Secretary , during about half of which time I was his colleague . It would not be too much to say that the interests of the Society and a desire to extend its usefulness were never out of his mind . It was inevitable that his pronounced views and his energy in giving effect to them should occasionally arouse opposition , but he was impelled always by public spirit , sometimes to the detriment of his own private interests . His work for Cambridge , for the Government in commissions of inquiry , as well as for the . Society , constitute a lasting claim upon the gratitude of our generation . VOL. LXXX.\#151 ; A. R Bev . John Kerr , Sir Leopold McClintock , Dr. Maxwell Tylden Masters , Prof. Alfred Xewton , Cornelius O'Sullivan , Sir William Henry Perkin , Dr. William Henry Hansom , Sir Edward James Beed , Dr. Edward John Bouth , Henry Chamberlaine Bussell , Prof. Charles Stewart , Bobert Warington . 240 Anniversary Address by Lord Rayleigh . [ Nov. 30 , The name of Kerr will go down to posterity as the discoverer of two remarkable phenomena in Electro-Optics . His success is a good example of what may be accomplished under no small difficulties by courage and perseverance . The claims of Sir W. Perkin as the pioneer in the aniline industry and as a distinguished worker in scientific chemistry have recently been celebrated , and are recognised all over the world . It is satisfactory to reflect that , unlike many inventors , he met with full appreciation during his lifetime . Hr . Eouth 's name is one that I cannot allow to pass without a word . I was indebted to him for mathematical instruction and stimulus at Cambridge , and I can still vividly recall the amazement with which , as a freshman , I observed the extent and precision of his knowledge , and of the rapidity with which he could deal with any problem presented to him . His book on Dynamics is well known . In its earlier editions it illustrated , perhaps , rather the vices than the virtues of the Cambridge School , but it developed later into a work of first-rate importance . I have always been under the impression that Eouth 's scientific merits were underrated . It was erroneously assumed that so much devotion to tuition could leave scope for little else . On the foreign list we have to lament three chemists of high distinction , Berthelot and Mendeleeff , though still active , had attained old age ; but in Moissan we lose one from whom much more might have been expected . All three have been recipients of our medals . An important feature in the work of the Eoyal Society consists of various enquiries , undertaken for different Departments of Government , in regard to diseases which affect the tropical portions of our foreign possessions and dependencies . Among these diseases the attention of the civilised world has been for some years directed to the malady known as Sleeping Sickness . The first concerted action for the study and combating of this apailing scourge arose out of a representation made by the Eoyal Society to the Foreign Office in the spring of 1902 , in consequence of which , at the request of the Treasury , the Society 's Malaria Committee organised and despatched a small scientific commission to Uganda . In the course of a short time the source of the disease was traced by this Commission to the presence of a trypanosome in the blood and cerebro-spinal fluid of the victims , and the further discovery was also made by the same Commission that the trypanosomes are carried by a species of biting tsetse-fly . These important revelations w'ere followed up by detailed studies of the character and distribution both of the disease and of the fly . Besides sending out a succession of observers to prosecute the investigations of its Commission at Entebbe , the Eoyal Society urged upon the Colonial Office the necessity of organising , and under an increased 1907 , ] Anniversary Address by Lord Rayleigh . 241 medical staff , a more comprehensive enquiry into the local conditions under which the disease is propagated . This recommendation was carried out and some valuable information on the subject has been obtained , Meanwhile , though various drugs had been tried with at best only temporary success , no lasting remedy had been found for the malady , which has continued to be fatal and to spread steadily over Central and East Africa . The various European Governments which have possessions in those regions have at last determined to make a united effort to cope with Sleeping Sickness through the instrumentality of an International Conference having a separate bureau in each country concerned and a central bureau in London . The object of this co-operation will be to collect information bearing on the disease , to devise and carry out such scientific researches as may seem to be necessary and to concert measures for dealing with the disease and the populations- , affected or likely to be affected by it . The Boyal Society , having led the* way in this subject , has been invited to give the proposed combined international action its support . The Society welcomes the proposal and will be-prepared to render every assistance in its power . In the meantime our Tropical Diseases Committee is continuously and actively engaged in the endeavour to discover a drug that may prove effective in the treatment of the disease . Their investigations have been directed to the study of trypanosomiasis in rats and the latest results obtained are such as to encourage the hope that at least in this direction their labours have been successful . During the present year three parts of the Reports of the Society 's Mediterranean Fever Commission have been published , embodying the final observations and conclusions in this important enquiry , which was undertaken at the joint request of the Admiralty , War Office , and Colonial Office . It is not often that a difficult investigation of this kind can be brought to-a successful conclusion in so short a time as two years and a-half , and the various members of the Commission are deserving of the warmest commendation for the skill , zeal , and promptitude with which they have solved the problem submitted to them . They have shown how the scourge of fever^ which has been so long rife in Malta , and has so seriously reduced the strength of our garrison there , may be eventually banished from the island . Already their recommendations , so far as they have been followed , have reduced the amount of fever to trifling proportions . It now remains for the authorities to adopt the further precautions pointed out to them , which will probably banish the disease altogether . I have continued to preside at the Meetings of the Executive Committee of the National Physical Laboratory . 242 Anniversary Address by Lord Rayleigh . [ Nov. 30 , The work of the Laboratory has grown greatly during the year . The addition to the Engineering Building and the new building for Metallurgical Chemistry are completed and are now occupied , while the building for Metrology is very nearly finished . A new 100-ton testing machine , one of Messrs. Buckton 's latest patterns , has been installed , and the increased accommodation in the Engineering Laboratory enables the work there to proceed more easily and rapidly . Great progress has been made in the equipment of the Electro-technical Laboratory , and research and test-work can now go on there in a rapid and systematic manner . The question of the Commercial Testing undertaken by the Laboratory has been the subject of investigation by a Treasury Committee , before which I was summoned to give evidence . It is understood that the report of this Committee may be expected shortly . Progress has been made with the buildings at Eskdale Muir , some of which are now ready for occupation . It was hoped that the work might have begun this summer , and the Treasury have provided a sum of \#163 ; 750 for the expenses during three-quarters of the current financial year . Owing to the bad weather in the early summer this anticipation has not been realised , but a start will be made very shortly . The buildings are admirably adapted for their purpose , and will render possible the study of terrestrial magnetism under the undisturbed conditions which used to exist at Kew . A list of the more important researches is published in the Report of the Laboratory . Among these may be mentioned those by Dr. Harker on the Kew Scale of Temperature and its relation to the International Hydrogen Scale ; Mr. Paterson 's paper , read before the Institution of Electrical Engineers\#151 ; " Investigations of Flame Standards and the Present Performance of High-voltage Lamps " ; and the eighth report of the Alloys Research Committee , by Dr. Carpenter and Mr. Edwards , on the Properties of Alloys of Aluminium and Copper . Professor Ayrton , Mr. Mather , and Mr. Smith have finished their work on the Ampere Balance , and the paper is now being published in the ' Philosophical Transactions , ' while papers on the Silver Voltameter and the Weston Cell are also in the press . Dr. Stanton and Mr. Bairstow have completed a further research on the measurement of wind pressure , and are well advanced with the investigation into methods of impact-testing . Other researches in progress are those on the measurement of small inductances and capacities , with a view to the standardisation of the wavelengths used in wireless telegraphy , on alloys of copper , aluminium , and manganese , for the Alloys Research Committee , and on the properties of eutectics . Anniversary Address by Lord Rayleigh . The completion of the work on the electrical units will be satisfactory to those who have been interested in this question . At the time of my own researches about twenty-five years ago , the ohm and the ampere were uncertain to 2 or 3 per cent. , and I then scarcely hoped to get nearer than one part in a thousand . The recent work carried on at Bushey would seem to indicate that an accuracy of one part in ten thousand may have been attained . The possibility of such a refinement depends largely upon the use in the instruments of coils composed of a single layer of wire , the position of every turn of which is open to exact determination . The importance of this feature was insisted upon by the late Professor Jones . Accuracy of measurement appeals less to the lay and scientific public than discoveries promising to open up new fields ; but though its importance at any particular stage may be overrated , it promotes a much needed consolidation and security in the scientific edifice . A remarkable example of enhanced accuracy is afforded by modern measurements of luminous wave-lengths , for which we are mainly indebted to our Copley medallist . Not only did he introduce the vacuum tube charged with mercury or cadmium as the best source of homogeneous light , but by a most able use of an ingenious method he determined , with the highest precision , the values of the cadmium red , green , and blue wave-lengths in terms of one another , and of the metre . His work has been skilfully followed up by Fabry and Perot , and numerous wave-lengths are now known with a relative accuracy of one-millionth part . When we reflect upon the almost ultra microscopic magnitude of a wave-length of light , the possibility of such an achievement may well excite our astonishment . For the advancement of science the main requirement is , of course , original work of a high standard , adequately explained and published . But this is not enough . The advances so made must be secured , and this can hardly be , unless they are appreciated by the scientific public . In some branches of Pure Mathematics it is said that readers are scarcer than writers . At any rate the history of science shows that important original work is liable to be overlooked and is perhaps the more liable the higher the degree of originality . The names of T. Young , Mayer , Carnot , Waterston , and B. Stewart , will suggest themselves to the physicist ; and in other branches , doubtless , similar lists might be made of workers whose labours remained neglected for a shorter or a longer time . In looking into the more recent progress of Geometrical Optics , I have been astonished to find how little correlation there has been between the more important writings . That Coddington should have remained unknown in Germany and von Seidel in England need not greatly surprise us ; but in this subject it would appear that a man cannot succeed in 244 Anniversary Address by Lord .[Nov . 30 , making even his own countrymen attend to him . Coddington seems to have heard nothing of Cotes and Smith , and Hamilton nothing of Airy and Coddington . It is true that no two writers on theoretical subjects could differ more in taste and style than do Hamilton and Coddington . The latter addressed himself to special problems , the solution of which seemed to have practical importance . Among his achievements was the rule relating to the curvature of images , generally known as Petzval'S , although Petzval 's work was of much later date . Hamilton , on the other hand , allowed his love of generality and of analytical developments to run away with him . In his Memoir on Systems of Bays , with its elaborate and rambling supplements , there is little to interest the practical optician , though the mark of genius is throughout apparent . It was only in two or three pages of a later paper that he applied his powerful methods to the real problem of Optics . As Finsterwalder has remarked , his " six radical constants of aberration , " expressing the general properties of a symmetrical instrument , are at once an anticipation and a generalisation of von Seidel 's theorems . But the published work is the barest possible summary . If Hamilton had been endowed with any instinct for Optics proper , he could have developed these results into a treatise of first-class importance . In more recent times Hamilton 's footsteps have been followed by Maxwell as well as by Thiesen and Bruns , of whom the two latter do not seem to have realised that Hamilton ( or even Maxwell ) had concerned himself with the subject at all . The natural development of Hamilton 's ideas will be found in an able memoir by Schwarzschild ( 1905 ) . I have spoken of English work that lay neglected , but a scarcely less notable instance is the splendid discovery of the microscopic limit by Fraunhofer , a man who combined in the highest degree practical skill with scientific insight . Thanks to the researches of Abbe and Helmholtz , it is now well known that there is a world that lies for ever hidden from our vision , however optically aided ; but neither of these eminent men realised that the discovery had been anticipated by Fraunhofer . Some , perhaps , may doubt whether Fraunhofer 's argument , founded upon the disappearance of spectra from gratings of extreme fineness , is of adequate cogency , To this I may reply that I was myself convinced by it in 1870 , before either Abbe or Helmholtz had written a word upon the subject . Enough has probably been said to illustrate my contention that much loss has ensued from ignorance and neglect of work already done . But is there any remedy ? I think there ought to be . In all the principal countries of the world we have now a body of men professionally connected with science in its various departments . No doubt the attention of many of these is so 1907 . ] Anniversary Address by Lord Rayleigh . engrossed by teaching that it would be hard to expect much more from them , though we must remember that teaching itself takes on a new life when touched with the spirit of original enquiry . But in the older Universities , at any rate , the advancement of science is one of the first duties of Professors . Actual additions to knowledge occupy here the first place . But there must be many who , from advancing years or for other reasons , find themselves unable to do much more work of this kind . It is these I would exhort that they may fulfil their function in another way . If each man would mark out for himself a field\#151 ; it need not be more than a small one\#151 ; and make it his business to be thoroughly conversant with all things new and old that fall within it , the danger of which I have spoken would be largely obviated . A short paper , a letter to a scientific newspaper , or even conversation with friends and pupils , would rescue from oblivion writings that had been temporarily overlooked , thereby advancing knowledge generally and sometimes saving from discouragement an unknown worker capable of further achievements . Another service such experts might render would be to furnish advice to younger men desirous of pursuing their special subject . The readers of whom I have been speaking are experts capable of advancing science themselves and of helping others to do so . But there is another class of possible readers of scientific books on behalf of whom I wish to make an appeal . We who are dependent upon sight in almost everything that we do must specially sympathise with those unfortunates who are deprived of this most precious gift . A movement is on foot , and has already received valuable support , to promote the publication of standard scientific works in embossed type suitable for the use of the blind . Such publication is costly and can hardly be undertaken upon an adequate scale without external aid . My friend , Mr. H. M. Taylor , a Fellow of this Society , tells me that in the course of the last 12 months he has written out the whole of Mr. C. Smith 's Elementary Algebra in Braille type , lias afterwards read the copy with his fingers and again , later , read the whole in proof . There can be no doubt that books in embossed type on such subjects as Mechanics , Physics , Astronomy , Geology , not to mention the various Biological Sciences , would be an immense boon to many blind readers . I commend the proposal heartily to your notice . Another remedy for the confusion into which scientific literature is liable to fall may lie in the direction of restricting the amount of unessential detail that is sometimes prevalent in the publication of scientific results . In \#166 ; comparing the outputs of the present time , and of , say , 30 years ago , the most striking feature that appears is doubtless the increase of bulk , in recent 246 Anniversary Address by Lord Rayleigh . [ Nov. 30 , years coming especially from young workers stimulated by the healthy encouragement of direct research as a part of scientific education . But I think it may also be observed , and not alone in the case of such early dissertations , that there is , on the whole , less care taken for the concise presentation of results , and that the main principles are often submerged under a flood of experimental detail . When the author himself has not taken the trouble to digest his material or to prepare it properly for the press , the reader may be tempted to judge of the care taken in the work from the pains taken in its presentation . The tendency in some subjects ta submit for immediate publication the undigested contents of note-books is one that we hear much of at the present time . It is a matter that is difficult for publishing bodies to deal with , except by simple refusal of imperfectly prepared material , with its danger of giving offence to authors of recognised standing , but it seems not unlikely that at present public scientific opinion would endorse such a course of action . A related difficulty and one that contributes to this trouble , is the tendency , noticeable in some public scientific organisations , to imagine that their activity is estimated by the number of pages of printed matter they can produce in the year . Probably no consideration is further removed than this from the minds of the educated public , whose judgment is alone worth considering . MEDALLISTS , 1907 . * Copley Medal . The Copley Medal is awarded to Professor Albert Abraham Michelson , For . Mem. K.S. , on the ground of his experimental investigations in Optics . In 1879 , Michelson brought out a determination of the velocity of light by an improved method , based on Foucault 's , which gave 299,980 kilometres per second . Three years later , by means of a modification of the method , capable of even greater precision , he found for this constant , of fundamental importance for electric as well as optical science , the value of 299,853-kilometres . Michelson has been a pioneer in the construction of interferometers , which are now indispensable in Optics and Metrology . With his new instrument , at Paris , he determined the absolute wave-lengths of the red , green , and blue lines of cadmium by counting the number of fringes ( twice the number of wave-lengths ) corresponding to the length of the standard metre of the Bureau International des Poids et Mesures . He found the metre to be 1,553,164 times the wave-length of the red line of cadmium , a result 1907 . ] Anniversary Address by Lord Rayleigh . 247 which is almost in exact agreement with the redetermination last year by Perot and Fabry . Michelson thus proved the feasibility of an absolute standard of length , in wave-lengths , of such accuracy , that if the standard metre were lost or destroyed , it could be replaced by duplicates indistinguishable from the original . He had the greatest share in the elaboration of precise experiments on the relative motion of ether and matter . He repeated in an improved form Fresnel 's experiment of the speed of light in moving media , using water and sulphide of carbon . He found that the fraction of the velocity of the water by which the velocity of light is increased is 0434 , with a possible error of + 0-02 . The fact that the speed is less in water than in air shows experimentally that the corpuscular theory is erroneous ; but his results , moreover , established the correctness of Fresnel 's formula for the effect , the theory of which has since become well understood . In conjunction with E. W. Morley , he devised and carried out a very remarkable method by which , on the assumption of ether at rest , an effect depending on quantities of the order ( v/ Y)2 would appear to be appreciable . No displacement of the fringes was found . Of this result the simplest explanation would be that the ether near the earth partakes fully in its orbital motion ; but modern electric and optical science appears to demand a quiescent ether , and the existence of this and similar null results is fundamental for its theory . He has shown the possible application of the Interferometer method to Astronomy , by himself measuring the diameters of the four satellites of Jupiter , which are only about one second of arc . He suggests the further application of the instrument to such of the fixed stars as may not subtend less than one-hundredth of a second of arc . In 1898 , Michelson constructed a spectroscope which enables us to make use of the great resolving powers of the very high orders of spectra which are absent in the use of the ordinary grating , and with the added advantage of having most of the light in one spectrum . The echelon consists of a pile of glass plates of precisely equal thickness , which overlap by an equal amount ; with it spectral lines which appear single with the most powerful gratings can be resolved into components . This instrument has been especially useful for the direct observation of the important , because definite , influence of magnetism on light , discovered by Zeeman . With 30 plates , and using the 25,000th spectrum , the echelon has a resolving power of 750,000 , while the most powerful gratings do not exceed 100,000 . In connection with the analysis of radiations , he has constructed and used various machines for the analysis of periodic motions . For example , in 248 Anniversary Address by Lord Rayleigh . [ Nov. 30 , conjunction with Stratton , he perfected a remarkable machine which is based on the equilibrium of a rigid body under the action of springs . Professor Michelson has also investigated by his Interferometer the important subject , both theoretically and practically , of the breadth and the structure of spectral lines , including the effect of a magnetic field , and in various other ways his genius has opened up new ground in experimental Optics . Eoyal Medals . One of the Eoyal Medals has been awarded , with the approval of His Majesty , to Dr. Ernest William Hobson , F.E.S. During the last 20 years Dr. E. W. Hobson has been distinguished for the fundamental character of his contributions to Mathematics and Mathematical Physics . His earlier published work , from 1888 onwards , deals largely with the so-called Harmonic Analysis , which embraces many topics having for their common aim the solution of the Potential Equation in forms suitable for application to the problems of Physics . The exhaustive examination of the general types of Harmonic Functions contained in his paper in the ' Phil. Trans. , ' 1896 , has been found to be of high utility for this application . He was led by these researches , and particularly by the difficulty of describing in general terms the characteristics of a function capable of being represented by Fourier 's series , to take part in the revision of the logical basis of Differential and Integral Calculus which is now in progress ; his Presidential Address to the London Mathematical Society , in 1902 , on the questions here arising , aroused general interest among mathematicians ; and he has recently ( 1907 ) published an extensive volume , dealing with the whole matter and its applications to the theory of Fourier 's series , which is of great importance for the history and development of Mathematics . His Majesty has also approved the award of a Eoyal Medal to Dr. Eamsay H. Traquair , F.E.S. Dr. Traquair is honoured on the ground of his long continued researches on the fossil fishes of Palaeozoic strata , which have culminated , within the past 10 years , in his discovery of new groups of Silurian and Devonian fishes , and in his complete exposition of the structure of and other remarkable forms . For nearly forty years Dr. Traquair has been busy with the description of fossil fishes , mostly from the Palaeozoic rocks of Scotland , and he is deservedly held to be one of the most eminent palaeontologists of the day . He has been highly successful in the interpretation of the often very obscure and frag1907 . ] Anniversary Address by Lord Rayleigh . 249 mentary remains which he has had to elucidate , and his restorations of fishes have won such credit as to appear in all modern text-hooks of Palaeontology . It may be said that his work , notwithstanding the great difficulties of the subject , has well stood the test of time . Dr. Traquair has done much to advance our knowledge of the osteology of fishes generally . His earliest memoirs on the asymmetrical skull of flatfishes and on the skull of Polypterus remain models of exactness . His acquaintance with osteology enabled him to show how former superficial examination of the Palaeozoic fishes had led to wrong interpretations . He demonstrated that Chirolepis was not an Acanthodian , as previously supposed , but a true Pakeoniscid . In 1877 he satisfactorily defined the Palseonisckke and their genera for the first time , and conclusively proved them to be more nearly related to the Sturgeons than to any of the other modern Ganoids with which they had been associated . He thus made an entirely new departure in the interpretation of extinct fishes , replacing an artificial classification by one based on phylogenetic relationship . His later memoir on the Platysomidee was equally fundamental and of the same nature . All subsequent discoveries , many made by Traquair himself , have confirmed these conclusions , which are now universally accepted . In 1878 , Dr. Traquair demonstrated the Dipneustan nature of the Devonian Dipterus , and somewhat later he began the detailed study of the Devonian fishes . His latest researches on the Upper Silurian fishes of Scotland are equally important , and provide a mass of new knowledge for which we are indebted to his exceptional skill and judgment in unravelling the mysteries of early Vertebrate life . Davy Medal . The Davy Medal is awarded to Professor Edward Williams Morley . Professor Edward W. Morley is well known both to chemists and to physicists for his work in the application of optical interferences and other physical phenomena to increase the accuracy of measurement . Numerous valuable papers have appeared , either in collaboration with Professor Michelson and others , or in his own name , on such subjects . Special reference may be made to his experiments , in conjunction with Professor Michelson , on the fundamental question of the absence of effect of translatory motion of material bodies on luminous phenomena . Plis claim to the Davy Medal rests on grounds closely related to these researches ; for he has combined thorough mastery of accurate measurement with an intimate knowledge of modern chemistry , and has utilised them in his attempt to solve one of the most difficult and fundamental problems of Anniversary Address by Lord Rayleigh . [ Nov. 30 chemical science . The special problem to which he has consecrated many years of his life is the determination of the relative atomic weights of hydrogen and oxygen ; it has been attacked by him with rare insight and skill , and with indomitable perseverance , and he seems to have settled it for many years to come , if not permanently . All the recent work devoted to this problem , and there has been much , has tended to establish more firmly the ratio arrived at by Professor Morley . His determinations of the absolute weights of a litre of hydrogen and of oxygen , and his investigations of the amounts of moisture retained by gases dried by various desiccating agents , are of the very greatest importance for scientific progress . Sylvester Medal . Professor Wilhelm Wirtinger , of Vienna , is the recipient of the Sylvester Medal . He is distinguished for the importance and wide scope of his contributions to the general Theory of Functions . Our knowledge of the general properties and characteristics of functions of any number of independent variables , and our ideas for the further investigation of such functions are , , for the most part , at present bound up with the Theory of Multiply-periodic Functions , and this Theory is of as great importance for general Solid Geometry as the ideas of Abel have proved to be for the Theory of Plane Curves . Professor Wirtinger has applied himself for many years to the study of the general problems here involved . A general summary of his researches is given by him in the Abel Centenary volume ( xxvi , 1902 ) ' of the ' Acta Mathematical Two of his papers may be particularly referred to , both of 1895 . One of these deals with the reduction of the Theory of General Multiply-periodic Functions to the Theory of Algebraic Functions , with a view to their expression by Theta functions ; this was one of the life problems of Weierstrass , who did not , however , during his lifetime , , publish anything more than several brief indications of a method of solution . Professor Wirtinger 's memoir obtains a solution , and is , moreover , , characterised throughout by most stimulating depth and grasp of general principles . This paper was followed by two others , one continuing the-matter in detail , the other making an application of its principles to the general Theory of Automorpliie Functions . Another extensive paper , which obtained the Beneke Prize of the Poyal Society of Gottingen , deals with the general Theory of Theta Functions . In it he obtained results of far-reaching importance , for Geometry as well as for the Theory of Functions , the full development of which will require many years of work . 1907 . ] Anniversary Address by Lord Rayleigh . Hughes Medal . The Hughes Medal is awarded to Principal Ernest Howard Griffiths . Principal Griffiths lias conferred great benefit on physical science by his series of measurements of fundamental constants , mainly in the domain of thermal and electric energy . At a time when the equivalent of the thermal unit in mechanical energy stood urgently in need of revision , he devoted himself to the problem with all the refinements and patient manipulation that could be devised , the result being a value for Joule 's equivalent which at once acquired authority in the light of the evidence produced , and largely confirmed the corrections already advanced by Rowland and others . A main cause of discrepancy had been found to be the variation of the thermal capacity of water with the temperature ; and by an investigation in which this variation was determined , Griffiths elucidated and correlated fundamentally the work of previous observers , from Joule onward . Of special importance also , in the domain of chemical physics , was an investigation of the depression of the freezing point of water by very dilute admixture of dissolved substances , wherein he verified , with all the refinement of absolute physical determinations , that the change of freezing point ran exactly parallel to the electric conductivity when the dilution of the electrolysable salt was comparable to that of gases , being twice as much per molecule as the standard value of the depression for non-electrolytes . Buchanan Medal . The Buchanan Medal is awarded to Mr. William Henry Power , C.B. , F.R.S. Mr. Power 's services to Hygienic Science and Practice have extended over a period of more than thirty years , and have been of the most distinguished kind . He has himself personally conducted successful enquiries into the causes of the spread of various diseases , and has obtained results which have proved of the greatest benefit to mankind . Moreover , in his long connection with the medical department of the Local Government Board , he has planned and directed numerous general and local investigations whereby our knowledge of disease , and of the methods of coping with it , have been greatly increased . The medical reports issued by the Local Government Board , which are universally regarded as among the most important contributions of our time to this subject , have for many years past been either written by him or owe much to his editorial criticism and supervision . It is not too much to say that no living man in this country has advanced the cause of scientific hygiene more than Mr. Power , or is more worthy of the distinction of the Buchanan Medal .

rspa_1908_0022

0950-1207

On the non-periodic or residual motion of water moving in stationary waves.

252

260

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Mrs. Hertha Ayrton.|Professor J. H. Poynting, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0022

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0022

10.1098/rspa.1908.0022

Measurement

Fluid Dynamics

Measurement

252 i On the Non-Periodic or Residual Motion of Water Moving in Stationary Waves . By Mrs. Hertha Ayrton . ( Communicated by Professor J. H. Pointing , F.R.S. Received December 7 , 1907 , \#151 ; Read January 30 , 1908 . ) [ Plates 4\#151 ; 6 . ] It is well known that when water moves in stationary waves , the particles do not , like pendulums , simply swing to and fro , returning after each oscillation to the points from which they started ; but that each element takes up a new position after each oscillation , so that it traces out a path for itself , only returning after many oscillations to its starting point . Part of this non-periodic or residual motion , as I shall call it , in stationary waves , has been traced out mathematically by Lord Rayleigh . The object of the present paper is to show , experimentally , what it is , as completely as possible . In his classic paper " On the Circulation of Air observed in Kundt 's Tubes , and on some Allied Acoustical Problems , " Lord Rayleigh examined , among other things , the influence of the bottom of a horizontal vessel on the motion of water moving in it in stationary waves , and he came to the following conclusion : calling places of maximum horizontal motion loops , and places of maximum vertical motion nodes , " near the bottom the fluid rises from the bottom over the nodes , and falls back again over the loops , the horizontal motion near the bottom being thus directed towards the nodes and from the loops . " Quite close to the bottom , on the contrary , he found that the motion was in the opposite direction , from the nodes and towards the loops . Fig 1 shows these two sets of vortices diagrammatically . B A E D* F Mode Loop Node Loop Node Fig. 1.\#151 ; Diagram of Lord Rayleigh 's Residual Vortices in one complete stationary wave of water . In the course of some experiments on the motion of heavy particles under stationary waves , finding that it was necessary to trace out the complete Ayrton Roy . Soc. Proc. , A. vol. 80 , Plata P- Level of wAber aG rest Fig. 3 . Instantaneous Photograph of Water permeated with Bronze Powder , oscillating in half a stationary / 3 . Diagram of Residual Motion indicated by Bronze Powder in Water , oscillating in half a stationary we ABC , A'B'C ' , Lord Rayleigh 's upper vortices ; DEF , D'E'F ' , " end vortices . " ( Shallow water . ) a P- Level erf wAber Ab resG Node Fig. 4 . Instantaneous Photograph of Water permea/ ted with Bronze Powder , oscillating in half a stationary / j3 . Diagram of Residual Motion indicated by Bronze Powder in Water , oscillating in half a stationary ABC , A'B'C ' , Lord Rayleigh 's upper vortices ; DEF , D'E'F ' , " end vortices . " Depth of water nearly a wave-length . Non-Periodic or Residual Motion of Water , etc. 253 residual motion of the water , I tried to render this visible , oscillating the water in the simplest possible way , i.e. , in time with its natural swing , so that it formed half a stationary wave . The first attempts , which were made in a trough 3 feet long , were entirely unsuccessful : I found it impossible , with the help of any visualising agent I could think of , to disentangle , with the eye , the residual motion from the to-and-fro movement . In a trough only 10 cm . long , however , oscillated in the same way , the residual motion to within less than a millimetre of the bottom could easily be seen , even when pepper was the visualising agent ; but still better when this was replaced with bronze powder , rubbed down in a little gum with a stiff brush and then well washed . As a certain amount of residual motion continues for some time after the oscillations have ceased , a good way to observe , it is to oscillate the trough till plenty of bronze powder has been set in motion , and then to bring it to rest . When this was done with the little 10-cm . trough , Lord Rayleigh 's upper vortices , ABCD , etc. ( fig. 1 ) were clearly discernible ( inner vortices , fig. 2 , Plate 5 ) though the motion of the thin layer quite close to the bottom could not be detected in this particular way . What was plain , however , was that there was some residual motion , even quite near to the bottom , that could not be accounted for by either of Lord Rayleigh 's two sets of vortices ; for instead of his upper pair spreading horizontally along the whole length of the trough , as they should have done , they occupied a part of the length only\#151 ; at the middle\#151 ; and were flanked on either side by much more active vortices , that monopolised the whole of the ends of the trough from top to bottom . Moreover , the horizontal space occupied by each of the two sets of vortices varied with the depth of the water . When this was small compared with its length\#151 ; say 1 cm . deep to 10 cm . long\#151 ; Lord Rayleigh 's upper vortices ( ABC , A'B'C ' , ( 3 , fig. 3 ) , took up most of the length of the trough , and the end vortices ( DEF , D'E'F ' , / 3 , fig. 3 ) occupied very little room at the bottom , although they always met in the middle near the top of the water . As the water was deepened , however , the end vortices became longer and the middle ones shorter ( fig. 4 , Plate 4 ) till , with water as deep as half a wave-length , the middle vortices were practically squeezed out of existence by the expanded " end vortices " ( fig. 5 ) , while small corner vortices with a languid movement appeared at F and F ' ( fig. 5 ) . For these experiments with deep water I found aluminium powder better than bronze powder , on account of its lightness . This visual test , therefore , brings out one very important point , namely , that the complete residual motion of the water , even quite close to the bottom , is dependent on the depth of the water compared with the length of 254 Mi 's . H. Ayrton . Non-Periodic or Residual [ Dec. 7 , the stationary wave , and cannot be determined without taking that relation into account . Level of water cit rest Fig. 5.\#151 ; Diagram of Kesidual Motion indicated by Bronze Powder in half a stationary wave . Depth of water greater than half a wave-length . The foregoing experiments were , as I have mentioned , made with water moving in half a stationary wave , so that the loop was at the middle of the trough , and the two nodes were at the ends . It now seemed important to find out whether the " end vortices " would come into play at any node , or whether they only appeared at nodes at the ends of the vessel . Accordingly I oscillated the water\#151 ; still permeated with bronze powder\#151 ; in such a way as to obtain three loops and four nodes , i.e. , in one and a half stationary waves . Immediately double " end vortices " came into play at each of the two interior nodes , as well as the single ones at the end nodes , so that the residual vortices appeared as shown diagrammatically in fig. 6 . Thus , what I have called " end vortices " are not confined to the ends of the trough ; they come into play at each node of any series of stationary waves . The almost vertical light line down the middle of the trough in a ( fig. 4 ) is a good example of what is seen in all experiments with stationary waves in water permeated with visualising powder . At each vertical plane of Ayrton . Roy . Soc. Proc. , A. vol. 80 , Plate \#163 ; . _ _ Level _of_ water _ \amp ; 6 _ resb__ Fig. 7 . a. Instantaneous Photograph of Curves formed during first few Oscillations in Water moving m half a state wave , by water-colour stain placed along bottom of trough , ft. Diagram of Curves showing Residual Ma in Water moving in half a stationary wave during first few oscillations . Fig. 2.\#151 ; Instantaneous Photograph of Water permeated with Bronze Powder , just after it has ceased oscillating in half a stationary wave . i i M- Fig. 8\#151 ; Instantaneous Photograph of Curve formed , during first few Oscillations i Water moving in half a stationary wav by water-colour stain placed near middle o bottom of trough on one side , 1907 . ] Motion of Water Moving in Stationary Waves . demarcation between two residual vortices such a line is visible . These planes occur , as is clear from fig. 6 , at all the loops and at all the nodes , Level of water at rest Fig. 6.\#151 ; Diagram of Residual Yortices indicated by Bronze Powder in Water oscillating , in one and a half stationary waves . except the end ones , of any system of stationary waves . In a ( fig. 4 ) where* water oscillating in half a stationary wave is depicted , there is one singlevertical plane of demarcation only , viz. , at the loop , which is at the middle of the trough , hence the vertical line in the middle . I have said that the visualising powder only enables one to follow the residual motion of the water to within a millimetre or so of the bottom of the trough . That means that Lord Rayleigh 's thin vortices ( DAEF , etc. , fig. 1 ) cannot be detected by means of it . I noticed , however , that when the water was quite clear and only a thin layer of powder , or a small drop of water stained with water-colour paint , rested at the bottom , this rose , during the first few oscillations , in the shape shown in fig. 7 , moving in the directions indicated by the arrows in the diagram ( / 3 , fig. 7 ) . Here ABCD and A'B'C'D ' were clearly Lord Rayleigh 's upper vortices , and what went on close to the bottom could be inferred from the fact that a clear space of water devoid of powder quickly formed between AB , for instance , and the bottom , while the powder continued to be carried along AB and thence upwards to G and down again to D. The inference was that the powder at the bottom was being driven , by the residual current there , in the direction from E to A , so that it all gradually got carried away from the bottom back along AB , up BC , and so on . If this were so , then I had ocular proof of a part of Lord Rayleigh 's thin vortices ( DAEF , etc. , fig. 1 ) between AB and the bottom ( / ? , fig. 7 ) ; for the powder and , therefore , the residual current , went from the nodes E , E ' , towards the loop A along the bottom , and from the loop towards the nodes along AB , AB ' . VOL. LXXX.----A . s 256 Mrs. H. Ayrton . Non-Periodic or Residual [ Dec. 7 , To make sure that this inference was correct , I used clear water without powder , and squirted on to the bottom of the trough , with a pen-filler , a bright green solution near the left end , and a bright yellow one near the middle on the same side , holding the filler quite close to the bottom , so that the water should not be stained higher up . Having waited till the water had come to rest again , I then oscillated the trough as before , the idea being that the green colour would visibly travel along the bottom to the middle , while the yellow would move above it along AB and then up round CD \lt ; A fig- 7 ) . This actually happened . After a few oscillations the green stain was entirely in the middle of the trough at the bottom , while the yellow travelled towards the end of the trough and then rose , as shown in fig. 8 ( Plate 5 ) , leaving a clear space at the bottom between itself and the trough ; indeed , for an instant it was possible to see green travelling along the bottom towards the middle of the trough , and yellow along AB , above it , towards the end , the two colours passing one another , travelling in opposite directions ; after the green had reached the centre of the trough , it also moved back to the end , and the two colours became mixed . But the first effect was very striking , and proved beyond doubt , experimentally , the existence of the residual currents along the bottom from node to loop and return currents a little higher up , from the loop towards a node , that Lord Rayleigh had predicted . The question now arose , where does the downward flow in these thin vortices take place ? There is , of course , a downward flow at the nodes , but that current extends from top to bottom of the water and belongs to the " end vortices . " If Lord Rayleigh 's thin vortices were separate and distinct from the " end vortices , " there ought to be a downward flow at some such point as B ( 0 , fig. 7 ) . But the fact that the water under B always became clear so quickly after the oscillations were started , and thenceforward remained so , seemed to show that there could be no residual downward flow there , otherwise some of the stain or powder would be seen to move downwards from B to the bottom . This never happened , however ; on the contrary , stain squirted right , over B , even though it was , as usual , heavier than water , always travelled upwards along such a line as BC , but never downwards . It seemed to me , therefore , that the " end vortices " and Lord Rayleigh 's thin vortices must really form one vortex of the peculiar shape shown in ABCDEFA , AB'C'D'E'F'A ( 0 , fig. 9 , Plate 6 ) . To test this , I squirted a little green stain on to the bottom of the trough , quite at each end , and waited till it had fallen perfectly flat . I then oscillated the trough so that the water moved in half a stationary wave , and saw the stain spread itself as shown in a ( fig. 9 ) . It first crept along the bottom to Ayrton . Roy . Soc. Proc. , A. 80 , Plate 0- Level of water at rest Fig. 9 . a. Instantaneous Photograph after many Oscillations of Water moving in half a stationary wave . Besidual in shown by water-colour stain placed on bottom of trough when water was at rest . / 3 . Diagram of \gt ; of principal Besidual Vortices in Water oscillating in half a stationary wave . ABCDEFA , AB'C'D'F -outer vortices ; ABCG , AB'C'G ' , inner vortices . Depth of water less than a quarter of a wavedength . Fig. 10.\#151 ; Instantaneous Photograph of Water moving in half a stationary wave . Besidual motion shown by water-colour stain placed on bottom of trough when water was at rest . Depth of water more than a quarter of a wave-length . Fig. 11.\#151 ; Instantaneous Photograph of Wate permeated with Bronze Powder , oscillatin in half a stationary wave , after about si oscillations , 1907 . ] Motion of Water Moving in Stationary Waves . 257 the middle , A ( / ? , fig. 9 ) then rose up and travelled backwards in such a line as AB ( taking the left side only ) ( / ? , fig. 9 ) , then turn back again along BC , branching off at C , where part of it rose up CD and turned back along DE and down towards F , while part went down towards A and turned back towards G. The only interpretation that it seems possible to give to such a series of motions as this is that Lord Bayleigh 's thin residual vortices and the " end vortices " form part and parcel of one another and together make a vortex having an outer layer shaped like ABCDEFA ( / 3 , fig. 9 ) . Another layer of this odd vortex must have a shape like HKM , another like NOP , and so on . It seemed , at first , impossible to believe in the existence of even a residual vortex of such a form , but I have applied many tests , and each one has only shown more forcibly that this , and no other , is the real form of the vortex . I have , for instance , injected tiny drops of stain into the water at such points as N , B , H ( / 3 , fig. 9 ) , and oscillated the water in half a stationary wave before they had had time to fall , and whichever point they were placed at they always moved as if they were being carried along by such a vortex as ABCDEFA . I have placed drops of stain successively at various points along the same horizontal line a short distance from the bottom , and watched , while oscillating in the same way , to see whether there was any sign of a downward current anywhere except at an end of the vessel\#151 ; but there was none . There is , therefore , I consider , no room to doubt that , when the depth of water is less than half the wave-length , the residual motion does actually take the courses indicated in / 3 , fig. 9 . As the pair of vortices ABCDEFA , AB'C'D'E'F'A ( / 3 , fig. 9 ) entirely embrace the pair ABCG , AB'C'G ' , I propose to call the first pair the outer residual vortices , and the second the inner ones . In order to trace with more accuracy the exact way in which the height and length of the residual vortices altered as the water was deepened , and also to see what happened when the depth of the water was greater than half the length of the stationary wave , I used a trough 15 cm . high , 1 cm . wide , and 10 cm . long , with water-colour stain placed at the bottom while the water was still . Oscillating this so that the water formed the usual half stationary wave , I found that the inner vortices , which occupied practically the whole length of the trough when the water was very shallow " , e.g. , 5 mm. or so deep , diminished continually in length as the depth of the water increased , till they disappeared when this was half a wave-length . Their height , on the other hand , increased at first as the water wras deepened , and attained a maximum when the depth of water was about one-eighth of a wave-length . After this , the height of the inner vortices diminished again , s 2 258 Mrs. H. Ayrton . Non-Periodic or Residual [ Dec. 79 and became practically zero when their length became zero , i.e. , when the water depth was equal to half a wave-length . As for the outer vortices , they evidently consist of three parts ( / 3 , fig. 9 ) , REFQ occupying the whole depth of the water between a node and the nearest point to that node of the corresponding inner vortex ABCG ; BCDR extending over the inner vortex to the top of the water ; QAB lying between the inner vortex and the bottom . Deepening the water increases the length of REFQ and the height of BCDR , but diminishes the length of both BCDR and QAB , till , when the depth of the water is half a wave-length , REFQ extends the whole way from loop to node and from top to bottom of the water , except for the small place occupied by the ineffective little corner vortices already noticed , F , F ' ( fig. 5 ) . A comparison of a ( fig. 7 ) , a ( fig. 9 ) , and fig. 10 is very instructive in showing the way in which deepening the water , while retaining the same wave-length , alters the length and height of the inner residual vortices . In the shallow water in fig. 7 these are nearly as long as the trough , and reach nearly to the top of the water . In the deeper water in fig. 9 they do not extend so far along the trough nor to the top of the water , and yet they are about the same height as those in fig. 7 . In fig. 10 , where the water is still deeper , the inner vortices do not occupy more than about half the length of the trough , and are only about a third of the height of those in fig. 9 . It seemed just possible that , if the water were made considerably deeper than half a wave-length , such vortices as F and F ' ( fig. 5 ) might spread along to the middle of the trough\#151 ; to the loop\#151 ; and become important . No such thing happens , however ; it is difficult , even when the oscillations are very violent , to get any motion at all in the water lower down than half a wave-length , and the small corner residual vortices never spread under the outer ones ; they rise a little higher , perhaps , as the water is deepened , but they remain always feeble and always in the corner , with their lower boundaries on a level with those of the outer vortices , and below this there is no apparent residual motion at all . Practically , then , in water as deep as , or deeper than , half a wave-length , the residual vortices are reduced to a single pair , of which the upper portion moves from loop to node and the lower from node to loop , and this single pair always extends to the top of the water , but moves over a layer of still water at the bottom , when the depth of ihe water is much more than half a wave-length . It is interesting to notice that , whatever the depth of the water may be , in consequence of the way in which the outer residual vortices enclose the inner ones , the direction of the residual motion on top is always from loop 1907 . ] Motion of Water Moving in Stationary Waves . 259 to node , that at the bottom from node to loop , and that at the nodes downwards ( save for the small corner vortices ) . At the loops , on the contrary , although the residual motion of the upper part of the water is invariable , namely , vertically upwards , that of the lower part depends on the depth of the water , being downwards for any depth less than half a wave-length , and upwards\#151 ; moving in the same direction as the upper part\#151 ; when the depth is greater than this . Mathematically speaking , I suppose , there is always an infinitesimally small pair of inner vortices , and , therefore , a small downward current between the bottoms of the two outer vortices , however deep the water may be , but practically in water as deep as , or deeper than , half a wave-length these do not exist . Fig. 11 is a photograph of water , permeated with bronze powder , which had been oscillated in half a stationary wave some half dozen times only , it shows clearly where the residual motion first becomes perceptible , viz. , at the top of the water , at the nodes ; for there is no apparent disturbance anywhere else . The friction of the water against the front and back of the trough causes the residual motion to be slowest close to the glass and greatest half way between the front and back . This gives to the water-colour stain , that shows the residual motion in each quarter wave-length , a shape as of a sail bellying in a wind , which drives from the end of the trough towards the middle . The effect can be seen to a certain extent in a ( fig. 9 ) , but is much more clearly visible in the actual experiment . One final feature of residual motion , that is rather curious , must be mentioned . It has been said that , after the oscillations have been stopped , the residual motion continues , and is even more apparent , owing to the cessation of the to-and-fro movement . In a short time , however\#151 ; perhaps a minute after the oscillations have ceased\#151 ; a part of the water begins to move in the opposite direction to that which it had previously taken , and this tendency gradually spreads till the whole motion of the liquid is reversed , though it is more confused than it was before . Where originally there was upward movement , there is now downward , and vice versed ; motion from right to left has become motion from left to right , and so on . It is as if a set of water springs had been wound up , and now proceeded to unwind themselves . To sum up the results of this investigation ; the residual motion of water moving in stationary waves takes the form of two principal sets of vortices n each half stationary wave\#151 ; the outer ones extending from loop to node at top and bottom , but embracing the inner ones in the middle\#151 ; the inner pair , entirely surrounded by the outer pair , having their largest part at a loop , Profs . C. S. Myers and H. A. Wilson . [ Jan. 2 , and tapering to points near the bottom , between this loop and the corresponding nodes . Both the length and the height of the inner pair depend on the depth of the water , the length diminishing steadily as the depth of the water increases , and the height increasing till the depth of the water is about one-eighth the wave-length , and then diminishing till the water is as deep as half a wave-length , when they are practically reduced to nothing . The outer pair of vortices , since they entirely surround the inner ones , naturally grow as these diminish , until at last , when the depth of the water is half a wave-length and the inner vortices cease to exist , the whole length of the half wave is occupied by two oblong residual vortices moving from loop to node above and from node to loop below , the vertical motion being upwards at the loop and downwards at the node . On the Perception of the Direction of Sound . By Professor C. S\gt ; Myeks , M.A. , M.D. , and Professor H. A. Wilson , D.Sc . , F.R.S. , King 's College , London . ( Received January 2 , \#151 ; Read January 16 , 1908 . ) The following paper contains an account of a series of experiments on the perception of direction of sound which were undertaken with the object of investigating the nature of the influence of phase differences between the vibrations at the two ears . Lord Rayleigh* has shown that such differences help to determine the apparent direction of the sound , the sound appearing to be on the side at which the phase is the more advanced . Professor Moref arrived at a similar conclusion to Lord Rayleigh by experiments of a different character . The following paper also contains a theory of the influence of phase differences which appears to offer a possible explanation of the observed effects . Most of our experiments have been done with an apparatus similar in principle to Professor More 's , but permitting of a continuous variation of the difference of phase . The apparatus consisted of a brass tube , AB ( fig. 1 ) , about 250 cm . long and 2*5 cm . in diameter , with a short T-piece soldered on to it at its middle point . This tube could slide freely in two slightly larger brass tubes , CD and OF , which were supported horizontally a definite * 'Phil . Mag. , ' February , 1907 . t 'Phil . Mag. , ' April , 1907 .

rspa_1908_0023

0950-1207

On the perception of the direction of sound.

260

266

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Professor C. S. Myers, M. A., M. D.|Professor H. A. Wilson, D. Sc., F. R. S.

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http://dx.doi.org/10.1098/rspa.1908.0023

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0023

10.1098/rspa.1908.0023

Tables

Measurement

Tables

]\gt ; Profs . C. S. Myers and H. A. Wilson . [ Jan. 2 , and to points near the bottom , between this loop and the corresponding nodes . Both the length and the of the inner pair depend on the depth of water , the diminishing steadily as the depth of the water increases , and the height increasing till the depth of the water is about one-eighth the wave-length , and then diminishing till the water is as deep as half a , when they are practically reduced to The outer pair of vortices , since they entirely surround the inner ones , grow as these diminish , until at last , when the depth of the water is half a and the inIler vortices cease to exist , the whole length of the half wave is occupied by two . residual vortices moving from loop to node above and from node to loop below , the vertical motion upwards at the loop and downwards at the node . On the Perception of the Direction of Sound . Professor C. S. MYERS , M.A. , M.D. , and Professor H. A. WILSON , D.Sc . , F.lt . S. , King 's College , London . ( Received January 2 , \mdash ; Read January 16 , 1908 . ) The following paper contains an account of a series of experiments on the perception of direction of sound which were undertaken with the object of investigating the nature of the influence of phase differences between the vibrations at the two ears . Lord has shown that such diffelences help to deternline the apparent direction of the sound , the sound appearing to be on the side at which the phase is the more advanced . Professor More arrived at a similar conclusion to Lord Rayleigh by experiments of a different character . The paper also contains a theory of the influence of phase differences which appears to offer a possible explanation of the observed effects . Most of ollr experiments have been done with an apparatus similar in principle to 1rofessor More 's , but permitting of a continuous variation of the diffelence of phase . The apparatus consisted of a brass tube , AB , nbont 250 cm . long and cm . in diameter , with a short -piece soldered on to it at its middle point . ) tube could slide freely in two slightly larger brass tubes , CD snd , which , h were supported horizontally a definite 'Phi ] . Mag February , ] 'Phil . Mag April , 1907 . 1908 . ] On the Perception of the Direction of Sound . distance apart . From the ends of CD and OF wide tubes were led to caps fitting on to the ears of the observer . The tubes were made up of len ths of AB . Sliding tube . DE . Scale . T. -piece . K. Tuning fork . FIG. 1 . CA , . Fixed tubes . H. Observer 's head . . Screen on table . glass tubing joined together by pieces of wide indiarubber , and the two sides of the were made as symmetrical as possible . ear caps consisted of wooden discs with annular soft pads round them which could be pressed against the head . The caps were supported on retort stands clamped to a table , and were adjusted as symmetricalJy as possible . A graduated scale was fixed alongside the brass tube AB so that the position of the -piece could be read off on it . A wooden screen WtlS put up on the table between the observer and the -piece , so that } he was facing he could not see the position of the -piece . A vibrating tuming fork held near the mouth of the -piece so some of the sound from it entered the tubes and went along them to the observer 's ears . By the tube AB about , any desired difference couldbe produced between the paths to the two ears . Let the distance of th -piece fro1n the middle point scale of the scale be cm . , ond the waye-length of the sound given out by the for be , then the phase difference between the sounds at the observer 's is . If is the number of vibrations per second and the velocity of sound , then According to Lord 's results we should expect that for values of between and the sound would appear to bc in the ear on the cvht Profs . C. S. Myers and H. A Wilson . [ Jan. 2 , hand side of the middle point , while with between and it would appear to be on the left , and so on for other values of . If we denote the lateral effect by , and consider right effects positive and left effects negative , the connection between and should be , according to Lord 's results , , where A is a constant . It would , perhaps , be more correct to say that should be equal to a Fourier 's sine series , of which the above is the first term , but experiment shows that the other terms are unimportant , if they exist at all . One of us acted as observer while the other placed the -piece in a series of positions , in each of which the observer said on which side the sound of the fork appeared to him to be . A record of the results was kept , and the series of observations was usually repeated . The sensations were usually described as follows:\mdash ; " " Full right half right " " middle or half " " middle " " middle or half left half left " " full left " " Half right\ldquo ; meant that the perception of direction was only moderately while\ldquo ; middle or half left\ldquo ; meant that there was only a doubtful perception of direction . " " Middle\ldquo ; meant that the sound seemed to come from in front or behind , or that there was no lateral effect . The following is a typical series of observations:\mdash ; Fork 512 . Observer facing away from fork . Scale reading . 65 or or 135 Mor 145 or 1908 . ] On the . the The ntunbers in brackets indicate the order in which the observations were made . The results obtained can be conveniently represented by means of curves whose -ordinates are the scale readings the position of the -piece and the lateral effects . The lateral effect corresponding to any scale reading was calculated by the mean of the observations that point , counting ' fnll right\ldquo ; , a half " " middle or " " middle\ldquo ; , with equal negative ) to represent left effects . shows one of the curves obtained in this way with a fork of frequency 512 . The curve is also shown ( dotte(1 ) and it will be seen that the observations agree with it as well as could been expected . and 4 show similar curves obtained with forks freqnencies and 128 . Fig. 5 shows some of the results obtained frequency 20-C . It will be seen that with frequency 256 the observed and theoretical curves do not agree , in fact the lateral effect is just the reverse of that expected . A good deal of time was spent in the cause of this anomaly and it was finally found to be due to resonance urring in tube on one side or the othel , according to the position of the -piece . The ears were replaced by the thin indiarubber ) of ) nometric flames , which were observed in a ting mirror in the usual way . In this way it was possible to compare the amplitudes of vibration 011 the two sides of the apparatus . It was found that the two amplitudes were always ' equal with frequencies 512 and 384 , but with 256 there were differences between the two amplitudes in ) tain positions of the -piece . In fact , with this frequency , when the sound appeared to be on one side , } a greater intensity of sound on that side , which evidently completely the difference effect . These differences of intensity could ) detected , though not very certainly , by listening first at one tube and then the other . It was found that the same cause led to the discrepancy between the observed and calculated results with frequency 128 at ( see 4 ) . The lateral effects observed with frequency 256 were of ) recisely the same character as those ) served with frequency 512 , it pears t the effects were due to a difference between the sound intensities at the two ears , while those with frequency 512 were produced by a dilfel'ence , of phase without any difference intensity . Some experiments tried with the tube on one side partially block Profs . C. S. Myers and H. A. Wilson . [ Jan. 2 , fork FIG.3 . Faci n Gowd , FIG. 4 Gowards ) FIG.5 . with cotton wool so that the sound on that side was considerably weaker that on the other side . It was found that the observer , after a time , became accommodated , sc to speak , to the of intensities , and lateral effects in both directions could then be obtained , although the sound was all the time stronger on one side than on the other . Experiments were tried in hich one side of the tube was gradually closed 1908 . ] On the Perception of the Direction of Sound . ( by means of a screw pinch-cock ) , and it was found that the observer did not notice any change in the lateral effect until the tube was almost completely closed , when , of course , the sound always went over to the open side . The sensation of of direction produced in this was precisely similar to that obtained by the -piece along with both tubes open . Experiments were tried with tubes of different and with the observer facing towards the fork and then away from it , but no very interesting results were obtained . Experiments were also tried with the manometric flames to see if the phase differences calculated actually existed , and this was found to be the case frequency 256 as well as the others . The results obtained suggest that hile a difference of phase may be a primary cause of lateral effects , yet it acts by a difference between the intensities of the sound inside the ears . If we suppose that some of the sound entering an ear gets across the lead to the opposite internal ear , this enables a simple explanation of the phenon7ena to be iven . Let denote the vibration entering the right , and denote the vibration entering the left ear . resulting effect at the right internal ear will be , say , Here and are proper fractions , of which is much greater than , and is the retardation in phase due to the through the head . In the same way , the effect at the left internal ear will be . Hence and , where and are constants . Let denote the sound intensity at the internal ear , and that the left internal ear . Then is proportional to the differP , nce between the squares of the amplitudes in and ; hence , Thus , the difference between the intensities at the two internal ears is proportional to , and if we suppose tlJat , the laternl effect , is ) portional to , we get , where so is a constant for sound of a particular frequency . * We suppose that the displacements in the internal ear due to the two sets of waves are in opposite ections . It should be said that principal reason this assumption is that it enables an explanation of the lateral effects to be given . On the Perception of the Direction of Sound . Thus , provided is positive , if the phase at the right ear is ahead by an amount between and is positive , that is , , and the sound will appear to be on the side , whereas if is between and , and the sound will appear to be on the left side . Thus , the theory here proposed gives a complete explanation of the observed lateral effects due to phase differences . For very high-pitched notes would be veen and , and then the lateral effect would be reversed . The distance between the ears the is small , and the velocity of sound the bones probably very high , so that we should not expect a reversal of the effect due to this cause , unless the frequency were very reat . But with very frequencies the lateral effects cannot be obtained . The amount of sound which must the head to produce an appreciable difference between the intensities at the two internal ears is not large , because since the two amplitudes are added , an imperceptible amount getting through might produce an appreciable difference of intensity . It was found that an appreciable amount of sound could be sent a person 's head from one ear to the other . Ear caps with tubes attached were fitted to each ear , and a vibrating tuning fork was held near the end of one tube . An observer listened at the end of the other tube , and with a fork of frequency 512 a distinct sound was heard , which seemed to come along the tube . The amount of sound gettin through the head must , of course , be much smaller than the amount entering one ear and getting to the opposite internal ear . The experiments described were oarried out in the Physical Research Laboratory at King 's College , which has been fitted up with a grant of S500 from the Drapers ' Company , to whom , therefore , we wish to express our obligations . We also desire to express our best thanks to Lord Rayleigh for his kind interest in the experiments and for some valuable gestions .

rspa_1908_0024

0950-1207

On the intimate structure of crystals. Part VI. \#x2014;Titanic oxide, its polymorphs and isomorphs.

267

280

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. J. Sollas, Sc. D., F. R. S.

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10.1098/rspa.1908.0024

Atomic Physics

Fluid Dynamics

Atomic Physics

]\gt ; On the Structure of . Part VI . Titanic Oxide , its Isomorphs . By W. J. LLAS , Sc. D. , F.R.S. , Professor of in the University of Oxford . ( Received January 3 , \mdash ; Read January 23 , 1908 . ) key to crystalline structure is furnished by a study of molecular volumes , and one of the best criteria of its powers will be found in its application to polymorphous compounds . If it can explain consistently with our knowledge oi crystalline symmetry the change in volume which accompanies the passage of a substance from one crystalline system to another , this fact alone would seem to offer presumptive evidence in its favour . There are inherent difficulties in the subject which render progress laborious and slow , so we cannot at present offer an exhaustive account . of all cases of polymorphism , and on this occasion we collfine our attention to the single but remarkable instance of titanic oxide , which presents itself in the three -kncwn forms of anatase , brookite , and rutile . The chemical formula of the oxide , generally taken as , is bosed on analogy with zircon , , which is isomorphous with rutile . It may be represented graphically as ' and the simplest lyptic renderin of this gives at once the general uration of the crystal molecu ] , Haiiy 's " " molecule integrante out of which anatase , and , with slight modifications , brookite , and rutile also , are built up ( see , p. To obtain the molecule in its true relative nensions , we must first determine the relative sizes of its constituent atoms . The ross atomic volnme of metallic titanium is . This follows from the relation the molecular weight ( mw ) being , and the density ( d ) . On the assumption that the atoms in titanium are in open cubic order , this gives as the diameter of the atom , or radius The gross atomic volume of oxygen cannot be obtained from the free element , and it is difficult to arrive at a completely satisfactory result from its compounds ; in commencing this investigation , I selected the number as representing an of considerable probability ; this gives for the diameter , or radius . In an earlier part of Prof W. J. Sollas . [ Jan. 3 , this paper*I made use of a somewhat higher value ( 189 ) , but it is possible the dimensions of the oxygen atom are not absolutely constant throughout all its combinations . In any case , the number is that which harmonises with all the facts presented by the minerals we are about to consider . Anatase.\mdash ; The fundamental molecule of anatase consists of four atoms of arran ged in contact , with their centres situated at the corners of a square : one atom of titanium rests upon the four oxygen atoms , its centre the centre of the square ; the other atom is situated in a position below . On joining the ceutres of the titanium with those of the oxygen atoms , we obtain a pyramid of the tetragonal an resemblance to the primitive pyramid , which is the characteristic form of anatase . These molecular pyramids may be built up into a crystalline edifice by arranging them so that the oxygen atoms lie in square order in one sheet , taken as horizonfftl ; the titanium atoms form corresponding sheets Plan . The larger circles in all the figures represent titanium , the smaller , oxygen atoms . above and below . On this layer of molecules a second may be superposed in such a manner that the titanium atoms of its lowest sheet rest upon those sets of four oxygen atoms which are formed by the four corner atoms of four squares in contact below ( fig. 2 ) . The structure thus obtained is tetragonal and holohedral ; it may be regarded as a tetragonal lattice with the centres of the molecules situated on the nodes . The packing is fairly close : to determine the volume occupied by one molecule of titanic oxide ( taken for convenience as ) , we must now partition the space occupied by the configuration homogeneously . In plan 'Boy . Soc. Proc , 59 , p. 294 , 1902 . 1908 . ] On the Structure of ( fig. 1 ) the structure may be completely divided into equal square areas , such as a , ench including one atom of titanium and four -atoms of ; the of the side is , and this squared gives 8 , or .\mdash ; Elevation on a Plane passing through A of fig. 1 . Each square again is the base of a prism , which containls one atom of titanium and quarter-atolns of oxygen , in all one molecule of ; its height is shown by the line in fig. 2 , and is measured by , or ; the volume of the prism is . The best determinations of the specific gravity of anatase vary from to , and its molecular volume lies consequently between and , with a mean of . The accordance between the observed and calculated volumes is thus remarkably close . FIG. 3.\mdash ; Elev ation on a Plane passing through a , fig. 1 , but with the Oxygen Atoms separated as in fig. 4 . It is evident that the configuration we have described affords data for calculating the axial ratios or parameters of the crystal . For our horizontal axes we may select either or ; we take the latter and make the parameter equal to 2 the corresponding parameter on the vertical axis is given by the length of the elementary prism from which the volume was calculated ; we have , therefore , for the horizontal parameter a length of , and for the vertical of , and this gives a ratio of 1 : , while Prof W. J. Sollas . [ Jan. 3 , the ratio obtained by direct measurement of the mineral is 1 : . Ths agreement in this case is only roughly approximate . We may make it a little closer , however , by slightly modifying our original conception of the molecular configuration ; we have supposed the oxygen atoms to lie in contact with each other , let us now separate them by a short interval ; this ] allow the titanium atoms to approach one another , and the total effect will be to lengthen the horizontal parameters and shorten the vertical parameter , at the same time the volume will be increased ( figs. 4 and 5 ) . FIGS . 4 and ] to figs. 1 and 2 , but readjusted into a nearer approximation with the actual axial ratios of Anatase . In determining the amount of the change which can be produced without unduly the molecular volume , we shall make use of topic axes . horizontal axes we have already chosen do not correspond with the sides of the square which forms the base of our elementary prism ; we must compensate for this by the axial ratios from 1 : to or 1 : the volume we take the mean , Then , since , we have , and . Thus the parameters on the topic axes are and ; and from we obtain corresponding parameter on by dividing by , which gives ; but , and thus the interval between adjacent oxygen atoms amounts to With the data at our disposal , we can now calculate the length of the vertical pal.ameter as given by our tion when modified by the separation of the oxygen ; it is found to be , while the topical axes show it to be actually , a difference of 0.084 , or about per cent. * According to Schrauf 's measurements the axial ratio of anatase is 1 : ; this gives for , and our value deduced from the configuration becomes , or a difference of 2 per cent. 1908 . ] On the ucture of Our results , however , are based on the improbable assumption that all atoms possess a spherical form , and are thus first approximations only . It is extremely likely that the atoms of those elements which crystallise in other systems than the cubic are not true spheres . The of oxygen with sulphur and of titanium with tin gests that this may be the case with the atoms under consideration . Anatase cleaves readily along the planes of ( 111 ) and ( 001 ) . But it may be here that the form ( 111 ) does not correspond to the form of the inte rant molecule : the symbol for this , according to the have chosen , must be ( 101 ) . primitive pyramid of the rapher only rises when the molecules are built up into the edifice ; its basal section is given in the square of fig. 1 . The connection between and structure is thus not immediately obvious , but on referring to the ( fig. 1 ) it will be seen that alternate squares of four oxygen atoms exist over which titanium atoms are absent , both above and below , and these umoccupied spaces run in files parallel to the horizontal of the pyramid ( 111 ) , all the other squares covered with titanium atoms . It would seem probable that the structure should part along these lines in preference to any other . The basal cleavage ( 001 ) follows readily from the structure . The optical sign of is negative , , and ; hence the axis of greatest elasticity responds -with the axis of the crystal , or the titanium axis of the molecule . The coefficient of expansion is greatest the principal axis , least along the axes normal to it . According to Fizeau , it is parallel to , and in any direction normal to this ; according to Sehrauf , it is in the first direction , and in the second . To this relation we shall recur later . Butile.\mdash ; Although rutile crystallises in the same system as anatase , it presents very diHel.ent forms , and cannot be eferred to the same axes . Its mdamental molecule has the same constitution as that of anatase , there is no polymerism ; but it differs in two respects : first the titaninm atoms have approached each other the vertical axis so far as to come into contact ; and next , as a consequence , the atoms haave been pushed outwards as far as possible , so that they lie comparatively far ough still at the corners of a square , its plane at angles to the vertical axis ; which passes its centre and the centres of the titoninnl atoms above and below ( fig. 10 ) . The arrangement of these molecules differs completely from which obtains in the case of anatase . The first layer is formed by the molecules with the titanium axes horizontal and end to end , so that the VOL. LXXX.\mdash ; A. '1 ' Prof. W. J. Sollas . [ Jan. 3 , titanium atoms form continuous horizontal files ; on these together side by side they will be found to fit together , the molecules of adjacent files with each other . The titanium atoms are thus marshalled in square order in a single sheet , and the vgen atoms lie one over the centre of each square of four titanium atoms , forming two sheets , one above and one below ( fig. 6 ) . If the bonding of the atoms be disregarded , this configuration will be ; but when the bonds are taken into account it becomes rhombic ; consequently . to preserve the tetragonal character , the next layer of molecules , which is built up like the first , must be turned in a horizontal plane through an angle of , and then superposed so that the two titanium FIG. 6.\mdash ; Rutile\mdash ; Plan . atoms of one molecule lie immediately over the two oxygen atoms of the layer beneath , the centres of the two molecules on the same vertical axis ( figs. 7 and 8 ) . The structure so produced is and holohedral ; the . 7.\mdash ; Plan of Two Molecules stlperposed . FIG. 8.\mdash ; Elevation on 1908 . ] the Intimate Structure of gyrohedry , since it amounts to a erht atYle , no raphic effect . * We may partition the structure eneously into square prisms , having as a base the square of the figure with an area of , or ; the height is shown by the line ff ' , and nearly equals or . The volnme is , therefore , . The specific gravity of rutile lies between and , and its molecular volume between and 19 , but when heated in the speciiic ravity rises to , or the volnme diminishes to . The reenlent between theory and observation is thus as close as we can expect . If we take the height of the prism just determined ) as the vertical parameter of the crystal , then the horizontal parameter will be or , and the ratio 5 0831 : . The actual ratio found by angular measurement of the crystal is 1 : The most perfect of rutile is parallel to the prism faces ( 110 ) , fact consistent with the ration ; there is a parallel to the faces of the second prism ( 100 ) also , but this is less perfect than preceding , though there in the ruration which would have enabled us to predict this fact . Rutile exhibits a characteristic tendency to form reatly eated prisms , and this is quite in harmony with the tion , which a closer texture over the prism faces than at to them , that is to , the surface density is greater parallel to the axis than in any other direction . The optical of rutile is positiye , and consequently the clirection of reatest elasticity corresponds with the horizontal axes of the crystal , ) it is along these axes that the titanium of the molecules are disposed , so that we have in this case precisely the same relation as that which found to obtain in anatase . In agreement with the optical characters , the constant is at a parallel to the axis , its value in this dil'ection being 173 ; at to it only 89 , or about one-half . If the truth of our configuration should be confirnled , this ratio should afford some insi , ] into the difficult question of the connection between the optical ) erties i the molecular structure of a crystal . The thermal conductivity is at a maximum parallel to the principal axis . The thermal expansion , as determined ) Fizeau , ives a coefficient for the * Schrauf , however , has observed gyrohedry in some crystals of rutile : it would appear , therefore , that the rotation not always complete . The error oduced by this formula only affects the fifth place of decimals . Prof W. J. Sollas . [ Jan. 3 , vertical axis of the crystal of , and for the horizontal axis of ; if the volume of the oxygen atom expahds to a greater extent than that of the titanium atom for the same rise of temperature , this relation between the coefficients is such as the configuration lead us to expect . It not infrequently happens that prisms of rutile occur " " attached to plates of haematite in such a position that each prism lies with its face ( 100 ) upon the basal plane of the haematite , and with its prism edge perpendicular to the edge of the combination ( 111 ) : ( 100 ) of the haematite , fig. 220.\ldquo ; * Some seems to be thrown on this interesting phenomenon by the structure of the two minerals ; an attempt to formulate the structure of haematite shows that the atoms on the basal plane lie on the nodes of a hexagonal network ; and when the structure we have yned to rutile is observed as it presents itself on the side of the prism ( 100 ) , it also is found to exhibit a hexagonal arrangement , which , although not quite regular , may perhaps be sufficiently so to allow of the co-adjustment of the two crystalline structures ( fig. 9 ) . FIG. 9.\mdash ; Elevation on of the Prism ( 100 ) . Brookitc.\mdash ; This mineral crystallises in the rhombic system . Its molecule has the same chenlical formula as anatase and rutile , and there is no polymerism . The titanium atoms have approached each other and come nearly not quite into contact , and the atoms , though pushed out , are not equally separated , but lie at the corners of a rectangle having two sides longer than the others . Thus the molecule itself possesses a rhombic 'Mineralogy , ' by Professor Miers , 1902 , p. 86 . 1908 . ] On the lntimate of form , which is therefore inherent in the crystal from first ; in the same way the tetragonal form is already determined in the molecule in both anatase and rutile . The difference between the three molecules will be seen by inspection of fig. 10 , which represents them in plan . FIG. 10.\mdash ; Molecules of Anatase ( 1 ) , Brookite ( 2 ) , and Rutile 3 ) , shown in Plan . The first layer of molecules is constituted very much as in rutile , but with this difference that the adjacent files of titanium atoms are not in contact with each other , but separated by oxygen ; they a rectangular but not a square lattice . FIG. 11.\mdash ; Plan of First Sheet of Molecules . The second layer of molecules has the same constitution as the first , and is superposed with the same orientation , but with a horizontal displacement parallel with the axis , so as to bring the atoms of the upper Prof. W. J. Sollas . [ Jan. 3 , layer immediately over the interspaces between the most closely approximated titanium atoms of the layer below ( fig. 12 ) . The third layer is similarly superposed , but with a compensatory displacement in the opposite direction . FIG. 12.\mdash ; Plan of Two Sheets of Molecules . The structure so produced fulfils all the conditions of rhombic symmetry . The simplest means of ' this hypothetical configuration is furnished by the so-called topic axes . specific gravity of brookite ranges from to , but the most probable value lies near This ives for the molecular volume . The accepted ratios of the parameters are . The topic ratios are , therefore , as follows:\mdash ; In our construction ( fig. 11 ) we make the sides and of the rectangle equal to and , but we now proceed to deternline the vertical parameter means of diameters of our atoms , and we obtain as a result the number , while the observed value is , or a difference of , i.e. , about per cent. This is the sole difference which exists between the results obtained by hypothesis on the one hand and observation on the other . The volume is only slightly affected , still remaining well within the limits of its observed values . * Miers , 'Mineralogy , ' p. 365 . 1908 . ] On the of Crystals . The refractive indices for soditun The acute bisectrix coincides with the axis and is ; thus the direction of maximum elasticity coincides with the axis , or with the titanium axis of the molecule , recisely as it does in both anatase and rutile . The thermal expansion has been studied by Schrauf , who obtained the following coefficients at . : ) We may here return to the question of thermal expansion in connection with all the members of this polymorphous series . There are at least three ways in which changes of temperature may affect the relative dimensions of a crystal . our attention to a rise of temperature , this may act : ( 1 ) by the space dominated by one set of atoms , oxygell , for instance , to extent than that of the others . This willaccount for the relative iu the length of the axes in the case of rutile , where the question is not complicated by changes of uration ; but it is inapplicable to anatixse , the coefficients of which are in the iuverse order of magnitude to that which this change would pdce ; ( 2 ) In the next place , a of temperature cause the atonls of one kind , say the oxygen , to become more remote each other , the other titanium atoms to make a closer approach . This is what , by hypothesis , must happen in the case of the lnolecules of natase could but in this case also the change in the dimensions of the axes , at least in the as of anatase , is in the relation to that by observation . 3 ) There remains then the third factor : the rise in tenlperattlre m initiate those chan , in the configuration ) which ulti1nately one passes into another . The well be ) ) utthel.e would seem to be no good eason w ) not be set up long before the final change . Looked at from this point of view , the relative length of the topic in the several polymorphs be expected to throw the matter ; they give the efl'ect of the various changes definite directions . In the table the topic axes are , the axis of rutile homologised with the axis of tase : ookih . . . 2 . ookih . . . 2 . ookih . . . 2 . ookih . . . 2 . ookih . . . 2 . ookih . . . 2 . ookih . . . 2 . ookih . . . 2 . ookih . . . 2 . ookih . . . 2 . ookih . . . 2380 Prof W. J. Sollas . [ Jan. 3 , The corresponding thermal coefficients are as follows:\mdash ; It will be seen that the axis consistently diminishes throughout the series , this is in harmony with Schrauf 's observation of a negative coefficient , in the case of anatase . But the second axis of anatase ( in the table ) should a positive coefficient . It is barely possible that it does so , and in this might be found reconciliation between the apparently discordant obserservations of Schrauf and Fizeau . On the other hand , the complicated change which occurs in passing from anatase to brookite would seem to render it necessary to consider the axes and of brookite together , and to compare them with the second axis and the axis of anatase taken together . We then have for anatasc , and for brookite , a very ficant expansion . Turning next to relations between brookite and rutile , the topic axes gest a contraction along the axis , and an expansion along the axes and , but to a greater amount along than . In correspondence with this , we find that the expansion ( instead of contraction ) which takes place along , is represented by the minimum coefficient , and that the expansion along is greater than along Considering how many factors enter into the problem , this amount of agreement is as great as we can expect . It does not perhaps lend much confirmation to our hypothetical configuration , but relieves it from serious objections . Using constant dimensions for our atoms , we have been able to build them up according to the strict laws of crystalline symmetry into the three forms characteristic of the different polymorphs of titanium oxide , we have obtained for our hypothetical configurations similar volumes and similar parametral ratios to those determined by observation , and we have shown how the properties of these configurations are in harmony with what is known of the thermal and optical properties of the minerals they represent . If , however , our speculations possess any basis of truth , we should be able not only to explain the polymorphs , but also the isomorphs of titanium oxide , such as tinstone and zircon , which crystallise in similar forms to rutile . I have not as yet sufficiently studied the volumes of silicon and zirconium , and must therefore confine myself for the present to tinstone . 1908 . ] On the Intimate ucture of ystals . The metal tin crystallises in the tetragonal system , and consequently its utoms are probably not true spheres , or , what possibly comes to the same bhing , their poles are not of equal value . In the absence of information to the parametral ratio of the crystals , it is impossible to estimate what rmount of deviation from the spherical form exists ; but we may expect find some anomalies consequent upon it in studyiug the metal in its ompounds . We have already had occasion to refer to one of these compounds* when we took for the diameter of the atom of tin the numbel ) , which we will again adopt . The specific gravity of tinstone lies veen 6 and 71 , nd the molecular weightis the volume ranges , therefore , from We the crystal to be built up in precisely the same way as utile . The area of the base of our elementary prism is consequently eqnal or , i.e. , to ; the height is given approximately by the ormula , which is correct to the fourth place of decimals ; it amounts , and this multiplied into gives as the volume found the configuration : thus very nearly equal to the mean of the observed alues . The parametral ratio found from the configuration is 1 : by bservation it amounts to 1 : , a difference ) . This is more ccordant than might have been expected . It may be pointed out that if molecular volumes assist us to mderstand rystalline structure , the collverse is also true that crystalline structure throws ome on the anomalies presented by molecular volumcs . Taken in the ross the volumes of the three forms of titanium oxide can only wake istrust in the rnificance of atomic volumes ; thus , if we deduct the ooross , tomic volume of titanium from the volumes of the dioxide in its ] orms we have the results:\mdash ; Anatase volume of one atom Brookite , , Rutile , , , , , , by this method , the volume of one atom of oxygen is found to be inconstant and unduly low , but a study of the crystalline hows that the irregularity may be merely apparent , and restores us the xygen with a constant and normal volume . Before writing this account I was unaware that the subject already treated by previous writers ; a valuable literature , however , exists . 'Ro . Proc vol. 03 , On th , Intimate Structure of Crystals . Schrauf has published some yhly speculative views , attributes rutile the structure we have assigned to anatase . Prior has made estive remarks on the of titanium oxide , to which I hop to recul when treating further of the isomorphs of this substance . work which most nearly touches my own is by BaumhauerJ who , his attelllion to anatase , arrives at a si1nilar molecular and crystallin structure to that adyocated here , and he supports his conclusions by a variet of tant aeruments based on the crystalline form , and etch ures i in relation to a Bravais net ; but the atoms of the molecule are indicated their centres only , and no attempt is made to discuss the question of molecula volumes . echt Schrauf , " " Ueber die Trimorphie . die Ausdehnungscoefficienten vo Titandioxyd ' Zeits . . Kryst . , vol. 9 , p. 433 . . T. Prior , " " Molecular Volume and Chemical ition . Mag 190 vol. 1.3 , } ) . . Baumhauer , " " Die uctur des Anatas Zeits . 1895 , vol. 2 p. 555 .

rspa_1908_0025

0950-1207

Report on the eruptions of the soufri\#xE8;re in St. Vincent in 1902, and on a visit to Montagne Pel\#xE9;e in Martinique. Part II.\#x2014;The changes in the districts and the subsequent history of the volcanoes.

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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Dr. Tempest Anderson.|Professor T. G. Bonney, F. R. S.

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10.1098/rspa.1908.0025

Geography

Biography

Geography

281 Report on the Eruptions of the SoufSt . Vincent in 1902 , and on a Visit to Montague Pelee in Martinique . Part II.\#151 ; The Changes in the Districts and the Subsequent History of the Volcanoes . By Dr. Tempest Anderson . ( Communicated by Professor T. G. Bonney , F.E.S. Received January 11 , \#151 ; Read January 23 , 1908 . ) ( Abstract . ) This Report , and the accompanying Report by Dr. Plett on The Petrology of the Ejected Materials , form the sequel to the Report by Drs. Tempest Anderson and J. S. Elett on " The Eruptions of the Soufriere in St. Vincent in 1902 , and on a Visit to Montagne JPelee in Martinique , Part I. " At the time when that Report was published it was contemplated that an account should be given later on of the subsequent changes in the deposits of volcanic ejecta , and also on the petrology of the specimens collected in 1902 . In the spring of 1907 I visited the West Indies , but Dr. Elett was unfortunately detained in England by his official duties . I am therefore responsible for the field observations on the topography and geology , and on the return of vegetation , while Dr. Elett 's Report deals with the petrology of the ejected materials . A description of the topography of the Soufriere volcano and of the details of the immediate results of the eruption of 1902 are contained in the published Report , Part I. The principal points of interest in the observations made during my second visit lie in ( i ) the changes wrought by denudation on the deposits left by that eruption ; ( ii ) the light thrown by those changes on the operation of the forces which had moulded the features of this island in its earlier history ; ( iii ) the information I was able to collect with regard to the volcanic disturbances subsequent to the great eruption of May , 1902 ; and ( iv ) the return of vegetation to the devastated areas . In the 1902 eruption a certain amount of the ejecta overtopped the Somma ring , i.e. , the remains of the original great crater , and descended some of the valleys to the north of it ; but by far the greater portion was discharged into the transverse depression which extends right across the island and separates the Soufriere from the mountain known as Morn Garu , about three miles to the south . The water from the crater lake was discharged at the beginning of the eruption down the Rabaka and Wallibu rivers , while the solid and Dr. T. Anderson . Report on Eruptions of the [ Jan. 11 , gaseous ejecta , in the form of the incandescent avalanches and black clouds , descended to both sides of the island . The most important geological phenomena were observed in the Wallibu district . These phenomena have been fully described in the published Report ( Part I , p. 428 et seq. ) , as also the subsidence of part of the coast . To this district , therefore , attention was especially directed in 1907 , with the view of observing the further progress of the changes and the return of vegetation . A description of the Wallibu valley is given in the full paper . In that district the beds of newer date have been dissected into flat-topped plateaux by small rivers running in deep gorges , which have again been filled in places by ejecta of eruptions and re-excavated in different degrees , and sometimes on different lines , leaving plateaux and terraces of different ages and heights . This action is well exemplified in the lower Yalley of the Wallibu . In the 1902 eruption this part of the valley was filled by the incandescent avalanche to a depth of at least 100 feet in the upper part , and less towards the sea , and it was in this deposit of hot ash that the explosions of steam and hot ash , flows of boiling mud and other secondary phenomena took place . In 1907 almost the whole of this ash had been washed away , but a fragment remained in the shape of a terrace 60 to 80 feet high , situated on the north side of the valley . The ash of which it is formed is unstratified , and contains very few ejected blocks or fragments of any kind . The floor of the valley is all composed of water-sorted material , chiefly gravel and coarse sand , but with a good many blocks as big as a man 's head . They represent ejected blocks and fragments of lava derived partly from the ash of 1902 and partly from older beds , the fine ash in each case having been washed away . The surface of the gravel bed showed marks of quite recent running water , and during the last winter , 1906-7 , the river ran along the foot of the north bank of the valley . When examined in March , 1907 , it ran along the south side of the valley , and had already in those few months excavated a new channel about 30 feet in depth . The stratification , as exposed in the side of this new valley , is very distinct , and the sorting by water , mentioned above , is very evident . Further up the mountain the remains of the avalanche became more abundant in the valley bottoms , and here they were also often better preserved , so that traces of the feather pattern erosion , so noticeable in 1902 , were still visible on the surface . This was mainly due to the surface of these ash deposits , like those to be presently mentioned on the plateaux and on the ridges , having consolidated into a crust almost like a cement pavement which resists the action of the rain . Another interesting point was observed with regard to these massive ash deposits . Instead of one stream re-establishing itself along the centre of 1908 . ] Soufriere in St. Vincent 1902 , etc. the deposit , the tendency is for a new stream to form on each side at or near the junction of the new ash with the old valley slopes ; and , as these streams deepen themselves , two new valleys are formed where only one previously existed , and the walls of each are composed on the one side of the new ash and on the other of older tuff , with occasional terraces of new ash . It appears to be due to the fact that the water from the old slopes , in running down into the original valley , meets the soft new ash , and at once turns down along the valley and so starts the new stream , and it seems likely that the chief cause of its so turning is that the surface of the deposit tends to be higher along the middle of the valley than at the sides , as is usual with mud-streams or glaciers . A good example of the action above described is to be found in a wide valley to the north of and parallel with the lower Wallibu valley and bounded on the south by the Wallibu plateau . Before the 1812 eruption the Wallibu river flowed down this valley , but its course was changed after that eruption . The floor of the valley is now occupied by the gorges of two small rivers , divided by a very narrow ridge , formed of ash different from and less consolidated than that composing the walls of the main valley , and considerably lower than the Wallibu plateau . In 1902 both these gorges were iilled with new ash to the level of the main valley floor . One of these , the Trespe gorge , now emptied of the 1902 ash , shows its north wall to be much higher than the south , and also formed of older and more consolidated tuff . The same conditions , with sides reversed , are seen in the other gorge , the higher bank in that case being the Wallibu plateau to the south . The Wallibu plateau is composed of ash older than that dividing the above two small rivers , but still comparatively new , and its flat top and precipitous sides , both north and south , proclaim it to be in an early stage of denudation , while the south bank of the Wallibu river on the south of the plateau is composed of older tuff and lava , and shows a much more mature type of denudation , viz. , sloping hills with rounded or ridged tops , and a good deal weathered into valleys or gullies . The north face of the plateau , like the south , is precipitous and obviously much less advanced in weathering than the slopes of the Soufriere on the opposite side of the broad valley of the Wallibu Dry , and Trespe rivers to its north . The mass appears to be the remains of an avalanche , or succession of avalanches , of hot ash poured into the depression between the Soufriere and Morn Garu , on an enormously larger scale than anything formed by recent eruptions . It may be that the present bed of the Wallibu to the south and the broad valley to the north are enlarged and deeply-excavated developments of the valleys that were formed at the sides of this prehistoric avalanche . 284 Eruptions of the Soufriere in St. Vincent 1902 , etc. Descriptions of the changes in the fans and low plateaux subsequent to 1902 ; of the shore subsidence ; and of the upper slopes of the mountain , are given in the full Report , as well as a detailed description of the crater as seen in 1907 . This is best explained by reference to the plates accompanying the Report . The topography of the old crater is still correctly represented on the Admiralty Chart ( published with the Report , Part I ) . The whole of the interior of the crater is still quite bare , without any trace of returning vegetation ; small patches of moss appear about the rim and on the slopes outside , then grasses and herbaceous plants , and lastly , below a height of about 1500 feet , luxuriant tropical vegetation . The present condition of the devastated areas is described fully in the Report , which contains also a history of subsidiary eruptions which followed the great one of May , 1902 . The difference in character between the eruptions of the SoufrRre and Montagne Pelee , referred to in the Report of 1902 , appears to have continued since that year , the outbursts from the former volcano being generally less frequent but more violent than from the latter . The Report also contains an account of a subsequent visit to the volcano of Montagne Pelee , in Martinique , with a description of the crater as I then found it ; a discussion of the phenomena of the remarkable extrusion and subsequent destruction of the Dome and Spine , which have been described by Lacroix and others , and a comparison of the sequelae of the great eruptions in the two islands of Martinique and St. Vincent .

rspa_1908_0026

0950-1207

On the observation of sun and stars made in some British stone circles.

285

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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir Norman Lockyer, K. C. B., F. R. S., Hon. LL. D., Hon. Sc. D.

astronomical-observation

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10.1098/rspa.1908.0026

Astronomy

Meteorology

Astronomy

On the Observation of Sun and Stars made in some British Stone Circles . Third Note.\#151 ; The Aberdeenshire Circles . By Sir Norman Lockyer , K.C.B. , F.R.S. , Hon. LL. D. , Hon. Sc. ! ) . , Director Solar Physics Observatory . ( Received January 15 , \#151 ; Read January 30 , 1908 . ) In previous communications to the Royal Society , * I have shown that if we consider the sun 's declination at the quarter-days of the May year and at the solstices , and also the changes due to precession in the places of five or six of the more conspicuous stars visible , at any epoch , in these latitudes we are able to account for the alignments investigated in the stone monuments in Cornwall and Devon . The present paper deals with a special class of circles in Aberdeenshire in which the method of indicating alignments shows a striking difference-The Cornish method was that still set out in the instructions for the erection of the Gorsedd circle of the Welsh Eisteddfod , f the sighting , or directing , , stones were placed some distance outside the circle . In Aberdeenshire the method employed was to place a long , recumbent stone generally between two of the upright stones of the circle itself and to obtain the direction of the rising sun or star by sighting across the circle at right angles to the length of the recumbent stone . In every case yet investigated , with two exceptions where there had been disturbance , I have found this sight-line to have had apparently the same general direction , and therefore the same astronomical use as in Cornwall . In the tables , 1 give the name of the circle , followed by the magnetic ? azimuth of the direction of the longest surface of the recumbent stone towards E. , as determined with a Barker clino-compass . Deducting 18 ' 45'\#151 ; the westerly variation of the compass in Aberdeenshire at the present time\#151 ; from this , we obtain the true azimuth , which is given as reckoned from N. through E. On deducting 90 ' from this , we get the line at right-angles , which I believe to be the sight-line for which the circle was erected ; of this the true azimuth is also given . The local conditions often militate against the exact determination of the elevation of the horizon , but , where possible , I measured it approximately with the compass-clinometer and state the results . * 'Roy . Soc. Proc.,5 vol. 76 , A , p. 177 , March 15 , 1905 , and vol. 77 , A , p. 465 , March 19 , . 1906 . t See 'Nature,5 vol. 76 , p. 9 . Sir N. Lockyer . On Observation of Sun and [ Jan. 15 , The alignments are limited to four regions with about the following azimuths :\#151 ; N. 43 ' E. The sunrise at the summer solstice . N. 59 ' E. The sunrise in May . N. 5'\#151 ; 30 ' E. Clock-star observations . True north . I take them in this order . Summer Solstice . I found that three circles were probably erected to watch the summer-solstice sunrise . The following table ( I ) shows the results of the measures . With these circles accurate measurement is a difficult matter and , as the determination of the date of erection from the variation of the obliquity of the ecliptic entails very precise measures , I content myself with pointing out that the declinations are solstitial and that they agree , in the mean , with the values previously obtained for the English solstitial circles . Table I. Azimuths . Elevation of the horizon . Circle at\#151 ; Magnetic , mean of observations . True , from N. through E. True , at right-angles across circle . Declination N. Sunhoney o / # o / o / N.52 35E . o 4 o / 22 25 Midmar 155 15 136 30 46 30 2 23 15 Stonehead ( Insch ) ... 146 15 127 30 37 30 1 25 41 Mean of above ... ... ... ... 23 47 * At Sunhoney , as the recumbent stone was curved and irregular , it was simpler to measure directly across the circle at right-angles to the length of the recumbent stone ; the magnetic azimuth thus obtained was 71 ' 20 ' . Table II.\#151 ; English Monuments , for Comparison . Monument at\#151 ; Alignment . Azimuth ( true ) . Elevation of the horizon . Declina- tion N. Stonehenge Direction of avenue from circle o / N.49 34 E. o / 0 35 o t 23 54 Stanton Drew Great circle to N.E. circle 51 0 1 5 23 49 Boscawen-Un Centre of circle to fine menhir 53 30 1 15 22 58 Tregeseal Centre of circle to holed stones 53 20 1 15 23 2 Longstone ( Tregeseal ) To Men-an-Tol 50 30 0 34 24 7 Mean of above ... ... ... * * " ... 23 34 1908 . ] Stars made in some British Stone Circles . 287 . May-year . Suns Dedination 16 ' 20 ' N. ( May 6 , August 8 ) . Two of the circles , as shown in Table III , were apparently erected for the observation of sunrise at the commencement of the May-year . A comparison of the results given in this table with those given in Table IV shows how well they agree , in the mean , with the results obtained from the previous investigation of May-sun alignments in Cornwall and Devon . Table III . Circle at\#151 ; Azimuths . Elevation of the horizon . Declina- tion N. Dates . Magnetic mean of observations . True , from N. through E. True , at right-angles across circle . May . August . Berry Brae Hatton of Ardoyne ... Mean of above o 170 166 o / 151 15 147 15 o / N. 61 15 E. N. 57 15 E. 0 1 1 ( assumed ) O f 15 30 17 8 May 3 May 9 Aug. 11 Aug. 5 16 19 May 6 Aug. 8 Table IV.\#151 ; May-year Alignments in England , for Comparison . Monument at\#151 ; Alignment . Azimuth . Elevation of horizon . Declina- tion N. Dates . May . August . Boscawen-un Circle to two large menhirs 0 / N. 66 50E . 0 / 1 0 o / 14 55 May 1 Aug. 13 Merry Maidens Tregeseal Longstone ( Tregeseal ) Circle to Fougou Circle to Longstone To W. Lanyon Quoit N. 64 0E . N. 67 20 E. N. 67 0E . 0 30 1 18 0 0 16 21 15 3 14 3 May 6 May 2 April 29 Aug. 8 Aug. 13 Aug. 16 Down Tor Direction of avenue N. 67 0E . 0 30 14 23 April 30 May 6 Aug. 15 Aug. 8 St. Clear Holy well to Trevethy N. 64 0E . ( assumed ) 0 30 16 21 Lesquoit cromlech cromlech Orientation of cromlech ... N. 64 0E . ( assumed ) 1 30 16 55 May 8 Aug. 6 Druids ' Altar ( Pawton ) a ... N. 64 0E . 1 30 16 55 May 8 Aug. 6 Mean of above ... 15 38 May 4 Aug. 10 In addition to those given in Table IV , I have found* that Lukisf and BorlaseJ give plans of a number of cromlechs in Cornwall which appear to be oriented to the May sun . * See 'Nature , ' No. 1987 , vol. 77 , p. 84 , November 28 , 1907 . . t ' The Prehistoric Stone Monuments of Britain\#151 ; Cornwall . ' X ' Antiquities of Cornwall . ' VOL. LXXX.\#151 ; A. U 288 Sir N. Lockyer . On Observation of Sun and [ Jan. 15 , They are as follows :\#151 ; Cromlech . Authority . Azimuth . Lanyon Quoit Borlase ; plate xxi ... o N. 66 E. Mulfra Quoit Lukis ; plate xix N. 63 E. Chywoone Quoit Lukis ; plate xx N. 64 E. Zennor Quoit Lukis ; plate xxi N. 64 E. Three Brothers G-rugith ... Lukis ; plate xxiii ... N. 64 E. Mean of above ... ... ... N. 64 ' 12 ' E. Assuming an elevation of the horizon between \ ' and 1 ' , this mean value is the exact azimuth of the May sunrise in Cornwall . Clock-stars . Table Y contains the results for 15 circles , in each of which the observation of a clock-star* appears to be indicated . From the data in the table , the declinations of the stars were determined from a curve connecting azimuth and declination , for different elevations of the horizon , for the general latitude of 57 ' N. ; consequently they are not final , but are sufficiently accurate for a preliminary discussion . Between 2000 B.c. and 1 B.c. Arcturus and Capella were the only first-magnitude stars to come within the declination range shown in the table , and , as my results show that they were used as clock-stars in Cornwall and Devon , f I consider that the evidence in their favour warrants the assumption that one of them was used as a clock-star by the circle-builders of Aberdeenshire , therefore I give the dates for Arcturus and Capella respectively . . * See 4 Boy . Soc. Proc. , * vol. 77 , pp. 465\#151 ; 466 . t 4 Boy . Soc. Proc. , ' loc. cit. 1908 . ] Stars made in some British Stone Circles . Table Y. Circle at\#151 ; Azimuths . Elevation of the horizon . Declina- tion N. Dates B.c. Magnetic mean of observations . True , from N. through E. True , at right-angles across circle . Arcturus . Capella . O / o t o t o o / Braehead Leslie 132 20 113 35 N.23 35 E. lk 30 58 250 2000 Leylodge 123 0 104 15 N. 14 15 E. 0 31 18 330 1940 Loudon Wood 120 40 101 55 N. 11 55E . 0 31 38 370 1890 Tonmagorn 124 0 105 15 N. 15 15 E. k ? 31 42 390 1860 Wanton Wells 130 30 111 45 N.21 45 E. 2 31 52 420 1830 Old Keig 138 0 119 15 N. 29 15 E. 4 31 55 430 1820 South Fornet 116 48 98 3 N. 8 3 E. 0 32 4 450 1800 Nether Boddam 130 0 111 15 N. 21 15E . 2 32 8 460 1790 Aikey Brae 113 0 94 15 N. 4 15E . 0 32 18 500 1 1760 Castle Fraser 129 36 110 51 N.20 51 E. 2k 32 42 570 1680 New Craig 129 34 110 49 N.20 49 E. 2k 32 43 570 1680 Loanhead of Daviot ... 116 45 98 0 N. 8 0E . 1 33 14 660 1580 Kirkton of Bourtie 123 30 104 45 N. 14 45 E. 2 k 33 57 770 1460 Cothie Muir 127 40 108 55 N. 18 55E . 4 34 42 920 1300 Eslie the Greater 113 30 94 45 N. 4 45 E. 2k 35 5 980 1230 Comparing these results with those given for the English circles in the previous paper , * the similarity of the object in view , and the means of attaining it , are , I think , obvious . The mean date for Arcturus is about 600 B.c. , and for Capella about 1600 B.c. Collateral evidence suggests that Arcturus was the clock-star employed , but more observations and enquiries are necessary to determine finally this point . Due North Alignments . In addition to the circles mentioned above , there are four in Aberdeenshire in which the alignments are due north . They are respectively situated at Dice , Whitehill Wood , Eaes of Clune and Candle Hill ( Insch ) , and probably represent a later development when the observer 's knowledge was so far advanced that he needed only the cardinal point in order to recognise the clock-stars which it was necessary for him to observe . My best thanks are due to Dr. Angus Fraser , Aberdeen ; Mr. Eitchie , Port Elphinstone ; Mr. Braid , Durris ; Eev . D. Forest and Mr. Ainslie , Mintlaw ; and Colonel Smith and Mr. J. Graham , Callander , Insch , who assisted me in many ways in the different localities . Mr. W. E. Eolston , F.E.A.S. , one of my staff , has computed the declinations and assisted in the preparation of this paper ; the dates corresponding with the declinations involved have been taken from tables furnished by Mr. J. N. Stockwell , of Cleveland , U.S.A. * ' Boy . Soc. Proc. , ' vol. 77 , pp. 467\#151 ; 468 , March 19 , 1906 .

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On the determination of viscosity at high temperatures.

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Charles E. Fawsitt, D. Sc., Ph. D.|Professor Andrew Gray, F. R. S.

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Tables

Thermodynamics

Tables

]\gt ; On the Determination of Viscosity at High Temperatures . By E. FAWSITT , D.Sc . , Ph. D. , Lecturer on Metallurgical Chemistry in the University of Glasgow . ( Communicated by Professor Andrew Gray , F.R.S. Received January 22 , \mdash ; Read February 13 , 1908 . ) A large number of viscosity determinations have been carried out with liquids at temperatures near the ordinary room temperature , and some observations at lower and higher temperatures have also been made by similar methods to those adopted for working at the usual temperatures . easurements at temperatures higher than to C. present considerable difficulties , and until the present year this subject had not even been by experimenters . As I was anxious to determine the viscosity of substances which melt at temperatures up to a white heat , I lately set myself to work out a satisfactory method of determination . The present communication contains a description of the method used . The method is suitable for the measurement of the viscosity of liquids which are not very viscous\mdash ; not more than say times as viscous as water , and is especially designed for the determination of the viscosity of molten metals and salts . The determination of the viscosity of salts up to 1200o C. , or even higher , can be quite satisfactorily carried out by this method . Determinations of the viscosity of metals are much more difficult , owing to the impossibility of preventing a certain amount of face oxidation . The smallest trace of surface oxidation will completely spoil a series of observations , and the prevention of oxidation is really the chief difficulty in such determinations . Previous Work in this Branch . The usual method adopted for the determination of viscosity at ordinary temperatures depends on the rate of flow of the liquid through a capillary tube . The determination is easy to carry out , the calculation of the viscosity from the time of flow is simple , and the experimental results are in close agreement with the laws of flow deduced from theoretical considerations . The glass capillary has been used up to C. by Beck* for the determination of the of fused mercury salts . With a Jena glass tube the method has been used as high as 60 C. for the determination of 'Zeit . fiir Physikal . ' 1907 , vol. 58 , pp. 425\mdash ; 441 . On the Determ , of Viscosity at High Temperatures . 291 the viscosity of lead salts . * A platinum capillary has been used as high as C. by Goodwin and Mailey . It is probable that this is about the limit of temperature to which the capillary method may be used , and in any case it did not appear that this method was likely to be employed with good results for metals of even comparatively low melting point . A rough method of determining the viscosity of molten silicates , depending on the rate at which a platinum wire sinks in the liquid , has been used by Doelter . An advance on this is an interesting apparatus used by Arndt , S who measured the rate at which a platinum cylinder fell in the liquid . These methods of Doelter and Arndt can only be used for very viscous substances\mdash ; for liquids whose viscosity is more than 1000 times that of water . They are of no use for measurements on ordinary salts and metals , which appear , in general , to have a viscosity not more than 100 times that of water . Method . The method used is based on the method originally given by the modiiications introduced being due to the special nature of the determinations . In Coulomb 's method a horizontal disc is allowed to execute horizontal vibrations about a vertical suspeIjding wire attached to its centre . The viscosity of the liquid can be calculated from the rate of decay of amplitude . In recent years this method has not been used to reat extent for ordinary viscosity determinations , and this can probably be explained from the following facts:\mdash ; ( 1 ) The disc used has to be fairly large ( 15 to 20 cm . diameter is usual ) , and this involves the use of rather large quantities of liquid ; ( 2 ) the calculation of viscosity from the observations of experiment is much more involved than in the case of the capillary method ; ( 3 ) an error made in the observations produces a much greater error in the ( calculated ) value of the viscosity . While it is not possible to rid of these last two difficultieH , this method is nevertheless capable of good results , and the tinle necessary to carry out a determination is certainly less than that occupied by a determination according to the capillary tube method . The apparatus as employed by Coulomb consisted of a vertical rigid metal rod several inches in length , which was fixed at its upper end into the centre * Lorenz and Kalmus , ' Zeit . fur Physikal . Chem 1907 , vol. ) , pp. ) 'Amer . Chem. Soc. Trans 1907 , vol. 11 , pp. 211\mdash ; 223 . Sitz . der Kais . Akad . Wiss . Wien , ' 1905 , vol. 114 , p. 629 . S 'Zeit . fur Elektrochem , ' 1907 , vol. 13 , pp. 578\mdash ; 582 . 'Mem . de l'Institut Not . des Sciences et Arts , ' 1800 , vol. 111 , p. 246 . Dr. C. E. Fawsitt . On the nination of [ Jan. 22 , of a graduated metal disc , and at its lower end into another disc which was ungraduated . The centre of the upper disc was provided with a small screw arrangement for the reception of the suspension wire , the upper end of which was fixed to a rigid support . The apparatus was first of all made to oscillate in air , and the logarithmic decrement of the amplitude obtained . The lower disc was then submerged in a number of liquids , and the logarithmic decrements noted . After deducting the value for air from that obtained for each liquid , it was possible to compare the viscosities of liquids whose densities were known . The method has been considerably improved and made much more sensitive by Stokes , *Clerk Maxwell , and Meyer , and it has been shown that the viscosity of a liquid is given by the equation , ( 1 ) where and are the logalithmic decrements of the apparatus in the liquid and in air , , and are constants depending on the apparatus , and is the density of the liquid . This method is found to give results which agree well with eory except in the case of very viscous liquids . In adapting this method to high temperature work the following difficulties have to be encountered:\mdash ; ( 1 ) It is not practicable , when working on a laboratory scale , to keep large quantities of liquid at a high temperature ; it is desirable , therefore , to make the method work with an amount of liquid which will be taken by a crucible , say 3 inches deep and inches in diameter . The dimensions of the immersed solid must therefore be small . ( 2 ) The solid whose oscillations are to be damped , and other ompanying parts , cannot be made too small , as the sensibility of the apparatus is thereby decreased , and aJso as the molten salts or metals corrode the parts immersed too rapidly . ( 3 ) The liquids , especially the metals , havs a comparatively high density , and the apparatus must be made to sink in these to the proper depth . A consideration of the decay of amplitude in torsional oscillation , when applied to viscosity determinations , shows that it is made up of three parts : the first due to the defective elasticity of the wire , the second to the viscosity of the liquid , and the third due to the loss of energy consequent on a simple movement of translation being imparted to the liquid . If 'Camb . Phil. Soc. Trans 1850 , vol. 9 , II , p. 8 . 'Phil . Trans 1866 , vol. 156 , pp. 249\mdash ; 268 . 'Pogg . Ann 1866 , vol. 126 , p. 177 . 1908 . ] Viscosity High Temperatures . represent the amplitude and the time , the decrease in amplitude from these causes is iven as follows:\mdash ; - where , and are constants . Combining these we have . . ( 2 ) If A is small , and if is small , i.e. , if the translation movement communicated to the liquid is small , or ( ) where and are the values of A at the beginning and after time . In this case the logarithmic decrement for successive oscillations is constant . If the velocity of movement of the liquid is considerable , the last term cannot be neglected and the integral has the form . ( 4 ) In this case the arithmic decrement is not constant for any one series of observations , but varies with the amplitude . As it is necessary that the oscillations should conform to equation ( 3 ) , the of motion communicated to the liquid has to be kept to a . It follows that the body submerged must be of such a form that a horizontal section throu , point will be circular . A circular disc , a sphere or a cylinder are all quite suitable , but after some trials with these I have returned to the disc , it best suited to the present purpose . The diso used was 26 mm. in diameter and 1 to 3 mm. thick . For temperatures up to 40 C. the diameter of the stem ( which forms the axis of rotation ) was 1 to 3 mm. ; for higher temperatures it was to mm. It is very important that the disc should be an exact circle , and should rotate truly about its axis . It is not possible to obtain for the manufacture of the disc any material which is heavy enough to sink in metals , and at the same time resistant enough to stand the corrosion and heat of the liquid in which it is placed . The only way out of this difficulty seemed to be to weight the apparatus externally . The amount of this weight and its distance from the disc must be snch as to keep the centre of gravity of the rigid part of the apparatus low possible , otherwise the apparatus will not swing evenly of Dr. C. E. FawsitL On the of [ Jan. 22 , any particle of the disc becomes an ellipse instead of a circle , thus making the motion correspond to equation ( 4 ) instead of to equationl ( 3 ) . The wei , ht used was a small iron cylinder clamped on to the stem about to 2 inches above the disc . For temperatures up to C. iron is quite suitable as a material for the disc . For temperatures up to a white heat one may use either fireclay , or a mixture of fireclay and plumbago . In making a series of observations with this apparatus , the disc is allowed to sink about half an inch below the surface of the liquid . The amplitude of the oscillations is indicated by a pointer ( wire ) at right to the top of the iron rod which carries the disc , and the pointer moves above a circular scale divided periments varied betwee , and 9 seconds . The period of the oscillations in the liquids used hardly val.ied at all . The period in the case of mercury was only per cent. greater than in the case of water . 1908 . ] Viscosity at High The Calculation of the from an } of the Logarithmic Decrement . In obtaining the logarithmic decrement , Briggs ' logarithms have been used throughout . The constants , and in equation ( 1 ) are best determined empirically from determinations on three liquids of known viscosity and density . Knowing , and , the viscosity of any other liquid can be determined by solving the quadratic equation where The expansion of the disc at high temperatures is small , but a slight correction has to be made on account of the slightly larger surface in contact with the liquid . If . be the radius of the disc , the surface in contact with the liquid is approximately equal to The coefficient of expansion for the surface is to twice the coefficient of linear expansion for the material composing the disc . The coefficient of linear expansion for iron is , and for fireclay it is probably about . Each unit of face will therefore increase by per in the one case and in the other . The logarithmic decrenlent is proportional to the surface in contact with the liquid , and a slight correction must therefore be made on this according to the temperature of experiment . nentat . There has occasionally existed in the minds of previous workers with the oscillation method some doubt as to whether this was a real test of the internal friction of the liquid . If any slipping takes place at the surface of contact between the solid and the liquid , the method is really of very little use . This point was therefore tested first of all . The experiments show that slipping does not take place to any detectable extent ; this holds good even for liquids like mercury , which do not " " wet\ldquo ; the solid . We can therefore assume that the layer of liquid next the solid moves with the same velocity as the solid itself . If any slipping took place the amount of slip would be different for different liquids and for different solid surfaces . A number of different discs gave the following results:\mdash ; VOL. LXXX.\mdash ; A. Dr. C. E. Fawsitt : On the of [ Jan. 22 , Table I. Material of disc . rough , smooth , with smooth s Any differences in the results of Cases 1 , 2 , and 3 may be put down to experimental error . The somewhat higher figures obtained in the fourth case are due to the disc being thicker ; it will be noticed that the proportionate increase is practically the same for all the liquids . It is assumed from these results that there is no slipping at the surface of contact . The method was next tested with liquids of known cosity . Taking three of these as standards the viscosity of the others was calculated . The results are given in the next table . The values of density and viscosity in the table are taken from Landolt and Bornstein 's tables with the exception of some density values obtained from the researches of Patterson . * Table II.\mdash ; Iron Disc 26 mm. diameter . Period of oscillation , seconds . Using water , chloroform , and mercury to calculate the constants from , we have We may now use these values to calculate the viscosity of benzene and alcohol from the observed logarithmic decrements . The values obtained are 'Journal Chem. Soc for the last few years . 1908 . ] Viscosity at High and respectively , which compare well with the values given in Iable II . The same apparatus gave the following results for mercury at temperatures:\mdash ; Table III.\mdash ; Mercury at High Temperatures . ture . Logarithmicdecrement . Density . according to * ' Ann. de ] ' Physik 1881 , vol. 14 , pp. 1\mdash ; 12 . An example of a determination of viscosity at a somewhat higher temperature is given in Table . The values of the density and viscosity for sodium nitrate have already been determined by the ] method.* These values are given in the table with the values of viscosity calculated from the logarithmic decrements using the same density values . The disc used was one of fireclay , 27 mm. in diameter . The constants , and , as determined by oscillations in water , mercury , and chloroform , were Table \mdash ; Sodium Nitrate ( Melting Point The numbers in the last two columns agree within the experimental error . These results show the availability of this method for the determination * Goodwin and Mailey , . cit. VOL. LXXX.\mdash ; A. Dr. T. E. Thorpe . [ Mar. 5 , of viscosity up to the highest temperature at which a platinum capillary has been used . As the fireclay or graphite disc remains uncorroded at temperatures of 1000o C. and over , the method is quite well suited for high temperature work . I am now on viscosity measurements with a number of salts and metals , and hope before long to report on these . Any expenses connected with this ation have been defrayed by grants from the Chemical Society and from the Carnegie Trust for the Universities of Scotland . BAKERIAN LECTURE for 1907.\mdash ; On the Atomic Weight of By T. E. THORPE , C.B. , .D . , F.B.S. ( Delivered June 20 , 1907 ; MS . received in completed form , March 5 , 1908 . Although there has been a considerable amount of discussion , based upon spectroscopic considerations and on its supposed mode of genesis , respecting the place of radium in the system of the elements , and inferentially , therefore , concerning its atomic weight , we are indebted for the only direct experimental determinations of this value hitherto made known to the discoverer of the element , Mme . Curie . Her first observations , published in 1902 , were made on about 90 milligrammes of the chloride , and furnished the value 225 as the mean of three fairly concordant experiments . * In the autumn of last year Mme . Curie communicated to the French Academy the results of a second series of estimations . These were made upon much larger quantities of the careful]y purified chloride ( about 4 decigrammes ) and afforded the value as the mean of three closely concordant determinations In 1906 , at the instance of Sir William , then President of the Society , and by the aid of the kind interest shown by H.R.H. the Prince of Wales , the Austrian Government placed about 500 kilogrammes of pitchblende residues from the mine at Joachimsthal at the disposal of the Royal Society . These residues were sent to be worked up by M. Armet de Lisle at his factory at Nogent-sur-Marne , by the method employed by him in the case of the ' Ann. de Chim . et de Phys vol. 30 , 1903 . 'Comptes Rendus , ' 1907 , vol. 146 , p. 422 ; 'Le Radium , ' October , 1907 .

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Bakerian lecture for 1907.\#x2014;\lt;italic\gt;On the atomic weight of radium.\lt;/italic\gt;

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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

T. E. Thorpe, C. B., LL. D., F. R. S.

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Chemistry 2

Thermodynamics

Chemistry

298 Dr. T. E. Thorpe . [ Mar. 5 , of viscosity up to the highest temperature at which a platinum capillary has been used . As the fireclay or graphite disc remains uncorroded at temperatures of 1000 ' C. and over , the method is quite well suited for high temperature work . I am now engaged on viscosity measurements with a number of salts and metals , and hope before long to report on these . Any expenses connected with this investigation have been defrayed by grants from the Chemical Society and from the Carnegie Trust for the Universities of Scotland . Bakerian Lecture for 1907.\#151 ; On the Atomic Weight of Radium . By T. E. Thorpe , C.B. , LL. D. , F.R.S. ( Delivered June 20 , 1907 ; MS . received in completed form , March 5 , 1908 . ) Although there has been a considerable amount of discussion , based upon spectroscopic considerations and on its supposed mode of genesis , respecting the place of radium in the system of the elements , and inferentially , therefore , concerning its atomic weight , we are indebted for the only direct experimental determinations of this value hitherto made known to the discoverer of the element , Mme . Curie . Her first observations , published in 1902 , were made on about 90 milligrammes of the chloride , and furnished the value 225 as the mean of three fairly concordant experiments.* In the autumn of last year Mme . Curie communicated to the French Academy the results of a second series of estimations . These were made upon much larger quantities of the carefully purified chloride ( about 4 decigrammes ) and afforded the value 226*2 as the mean of three closely concordant determinations ( Ag = 107*8 , Cl=35#4).f In 1906 , at the instance of Sir William Huggins , then President of the Society , and by the aid of the kind interest shown by H.RJEL the Prince of Wales , the Austrian Government placed about 500 kilogrammes of pitchblende residues from the mine at Joachimsthal at the disposal of the Royal Society . These residues were sent to be worked up by M. Armet de Lisle at his factory at Nogent-sur-Marne , by the method employed by him in the case of the * 'Ann . de Chim . et de Phys.,5 vol. 30 , 1903 . t 'Comptes Rendus,5 1907 , vol. 145 , p. 422 ; 'Le Radium,5 October , 1907 . 1908 . ] On the Atomic Weight of Radium . material which served M. and Mme . Curie for their researches . The funds for both these purposes were defrayed from a grant made by the Goldsmiths ' Company to the Royal Society in 1904 for the purpose of the investigation of radium . The residues , as received by M. Armet de Lisle , were stated to have a radio-activity of about 2| times that of uranium . The process of extraction employed by M. Armet de Lisle resulted in the production of about 413 grammes of practically anhydrous barium chloride , containing radium chloride sufficient to give the salt a radio-activity 560 times that of uranium . This salt was received by the Royal Society in the autumn of 1906 , and was handed to me in January , 1907 , with the request that I would extract the radium chloride from it , and undertake , if possible , a redetermination of the atomic weight of the element . This in view of the discussion , already referred to , which was then taking place as to the relation of radium to certain other elements , seemed at the time the most profitable use to which the radium salt , when extracted , could be put . When received by me the barium-radium chloride was distinctly cream-coloured , and the bottle in which it was contained was coloured violet . The method of extraction was substantially the same as that originally adopted by Mme . Curie , and described in her thesis , * namely , systematic fractional crystallisation , first from water and then from increasingly strong hydrochloric acid , until finally the acid used was the strongest that could be obtained by distillation . All the solvents employed were carefully purified , the acid being distilled in a platinum retort , and preserved in a platinum bottle . The crystallisations were made first in porcelain , subsequently in Jena glass , and finally , as the radio-active matter became more and more concentrated , in vessels of fused rock-crystal . Every precaution was taken to guard against loss and accidents , and to ensure the recovery of the radium should such occur . It is satisfactory to be able to state that the whole scheme of extraction , involving some 9400 recrystallisations , was carried through without a mishap . I have to thank Mme . Curie for her courtesy in affording me information concerning certain details of her method of isolating the radium salt . At the outset of our exchange of letters she informed me , of what at the time I was unaware , that she was then actually engaged on the same problem , and she has since , as already stated , published the results of her determinations . She was good enough , however , to express the hope that I would continue the work which I had been requested to undertake , in view of the desirability * Loc . cit. Y 2 t 300 Dr. T. E. Thorpe . [ Mar. 5 , of gaining all possible knowledge as to the true atomic weight of the element . . During the autumn of 1907 , whilst still engaged in the isolation of the radium chloride from the material furnished by M. Armet de Lisle , I received a further small supply of radium from the Royal Society . It was bought in Cambridge and was of German origin , and had been purchased through the instrumentality of Professor Liveing . It purported to be radium bromide , but on removing it from the metallic capsule in which it had been stored since 1903 , it was found to be wholly insoluble in water . On treatment with pure dilute hydrobromic acid it readily passed into solution . The salt obtained by evaporation was sent to Professor Rutherford , who had kindly undertaken to make any measurements of radio-activity which I needed . He estimated the amount of radium present as equivalent to 33 milligrammes of radium bromide . This salt was eventually converted into chloride , and was purified by repeated crystallisation from strong hydrochloric acid . Traces of lead cling persistently to the radium chloride thus separated by means of hydrochloric acid . Mme . Curie was so kind as to draw my special attention to this fact , and accordingly care was taken to remove this metal . When practically the whole of the radio-active matter had been concentrated into a few grammes of the material , this was dissolved in water acidulated with hydrochloric acid , and treated with sulphuretted hydrogen out of contact with air . A small precipitate of lead sulphide was formed . The liquid was further treated with sulphuretted hydrogen , the lead sulphide removed by filtration , the filtrate evaporated to dryness , the residue treated with strong hydrochloric acid , and the process of fractionation resumed . That the precipitate was lead sulphide was confirmed by its conversion into the yellow iodide . Determination of Atomic Weight . This was effected by ascertaining the amount of silver chloride yielded by a weighed quantity of the anhydrous radium chloride\#151 ; the principle of the method already employed by Mme . Curie . Since it was very improbable that the amount of the radium salt at my disposal would amount to as much as a decigramme , it was absolutely necessary so to arrange the process of carrying out the estimations as to minimise , to the greatest possible extent , the errors due to manipulation . Accordingly a method was devised whereby the whole of the operations of drying and weighing the radium chloride , precipitating , washing , drying and weighing the silver chloride , might be performed in one and the same vessel , thus 1908 . ] On the Atomic Weight of Radium . 301 obviating the necessity of transferring the silver salt , and of separating it by any of the ordinary processes of filtration . The vessel in which these operations were made consisted of a thin glass tube with a conical base furnished with a hollow well-ground stopper . It had a capacity of about 15 c.c. , and was as light as was consistent with the requisite strength , and could be suspended from the balance-arm by fine platinum wire . In all the weighings a precisely similar bottle of almost identical weight and capacity , suspended in like manner , was employed as a tare . The weighings were made on a very sensitive assay balance , with 4-inch arms , carrying a maximum load of 12 grammes and provided with light stirrup pans . I am indebted to Mr. Oertling for the loan of it . It was a beautifully finished instrument of great delicacy , and remarkably constant in its indications ( fig. 1 ) . 302 Dr. T. E. Thorpe . [ Mar. 5 , The weights were also of Oertling 's make , and were compared before use with a standard set belonging to the Government Laboratory . A room was specially set apart and arranged for the determinative work . It was a small apartment on one of the upper floors of the Government Laboratory and had a wooden block floor arranged " herring-bone " fashion . The walls of the building were subject to a very slight tremor , due to a small steam engine in the basement . The balance table , therefore , was not bolted to the walls , as is the usual practice , but was placed directly on the floor , which , by reason of its mode of construction , was less susceptible to tremor than the walls . The legs of the table stood on packets of filter paper , as did also the levelling screws of the balance case . Under these conditions the balance was found to be quite free from tremor and the levels remained absolutely constant throughout the entire course of the work . The weighings were made by the method of vibrations , the zero-point being determined before and after each determination . The course of the operations was as follows :\#151 ; The small glass vessel and its tare were first heated to about 150 ' in an air bath for an hour and allowed to stand overnight in a desiccator containing phosphoric oxide . They were then weighed one against the other in the manner described . The chloride , previously dried at 140 ' to 150 ' , was next transferred by means of a platinum spatula from the rock-crystal basin in which it was contained , to the glass vessel , and this and its tare were again heated to 150 ' for about an hour in the air bath , and , after standing overnight in the desiccator containing phosphoric oxide , were again weighed . The chloride was then dissolved in 2 c.c. of distilled water , the solution acidulated with two drops of dilute nitric acid ( 1 :4 ) , warmed and mixed with a slight excess of silver nitrate solution of known strength added drop by drop , with constant shaking , from a narrow burette capable of being read to 1/ 50 c.c. When clear , the liquid was again tested with the silver nitrate solution in order to ascertain that the precipitation was complete , and after standing for about 18 hours in a warm place when the silver chloride had wholly subsided into the bottom of the conical portion of the Vessel , the clear supernatant solution was drawn off by means of a capillary glass tube . This was conveniently effected in the manner illustrated by fig. 2 . The vessel ( a ) containing the silver chloride was placed on the small elevating table ( b ) , the height of which could be adjusted by means of the rack and pinion arrangement seen at ( c ) , so that the end of the drawn out capillary syphon ( \lt ; d ) , made of thermometer tubing , could be brought to within a millimetre or two of the deposit of silver chloride . By gentle aspiration at ( e ) the action of the syphon was started , and by far the greater quantity of the clear On the Atomic Weight of Radium . 1908 . ] liquid could be drawn over into the flask ( f ) without the slightest risk of disturbing the precipitate . The table was then lowered , and the end of the syphon as well as the internal sides of the vessel washed by a fine stream of hot distilled water . After clarification , the wash-water , which was about 4 or 5 c.c. in bulk , was drawn over as before , and the process repeated . After each addition of hot water the vessel containing the silver chloride was well shaken , and the d a \#151 ; Fig. 2 . precipitate broken up by means of a fine platinum wire , so as to bring the washing water in thorough contact with it . As is well known , silver chloride which has become granular by standing shows little or no tendency to occlude soluble matter and is readily washed . Both the end of the syphon and the platinum wire were always washed by a stream of hot water and were carefully examined by a lehs , but in no case was any silver chloride found to have become attached . The liquid drawn over was invariably perfectly clear . Assuming that we have 100 milligrammes of soluble matter in the 4 c.c. of the clear supernatant liquid and that we draw over 3*5 c.c. at each successive Dr , T. E. Thorpe . [ Mar. 5 , operation as above described , it is readily calculable that the amount of matter in solution , even after the third operation , is probably too small to be appreciated by the balance . The following table shows how rapidly the soluble matter is removed by systematic washing in the manner described . Milligrammes . Original solution contains ... ... ... ... ... . . 100 After first decantation , residual liquid ... 12*5 first washing " ... . . . 1-56 second " \gt ; \gt ; , , ... . . . 019 third " , , ... . . . 0-02 fourth " \#187 ; , , . . . . . . 0-003 fifth " \#187 ; jj ? ... . . 00004 As the precipitated silver haloid was always thus washed six times in succession , it may be assumed that it was practically freed from all soluble matter . Care was of course taken to protect the silver chloride from the action of light , and to the extent that was practicable all the operations were carried out in a photographic dark room which adjoined the small laboratory set aside for the work . No matter what precautions were taken to exclude ordinary white light , the silver chloride invariably became violet in contact with radium solutions . The washed silver chloride was first dried at 100 ' and then heated in the air bath to 160 ' for about a couple of hours , and , after standing in the desiccator over phosphoric oxide for about 18 hours , weighed in the manner described . In order to test the practicability of the method and to acquire experience of its working , as well as to gain some idea of its accuracy before actually making use of it in the case of the radium salt , a series of determinations of atomic weight was made with barium chloride , purified by systematic recrystallisation from water , according to the method already indicated , the same apparatus , reagents , and solutions being employed as were to be used subsequently in the radium determinations . The results were as follows:\#151 ; Ag = 107-93 . Cl = 35-45 . Barium chloride . Silver chloride . milligrammes . milligrammes . Atomic weight , Ba . 114*7 157-8 1375 172-1 236-8 . 137-5 57-1 78-8 136-9 62-6 86-1 137-6 681 93-7 137-5 \#151 ; : spnsoj SuiMopoj 9q^ oauS 'pojoaoooj snqi opuojqo umijuq uo paquosop jouuura oqj ui opuiu 'ranijuq jo p{8i0M oiuupu 9q^ jo suoipmiuua^op omj , .opijojqo oq^ ojui p0:pi9Auoo0j os puu piou oijojqoojp^q ojnd jo soipjuunb quuts qpM pojuJoduAO iCjpo^uadoj uoq^ sum onpisoj poijp oqj^ *su8-quoo uopuoq jo uoujsnquioo oqj Xq poonpojd jnqdpis jo sopixo oqj jo uoi(pu ojqissod Are pioxe oj duiej |oqooje ue qpM pojeoq q^eq-jopsM e joao ssouAp oj po^ejodexo pue mseq eoips e oj pojjojsuej^ uoipqos 9q^ pun 'poquosop Apeojje jouuuui 9q^ in poqsexv iqqgnojoqi opuojqo joajis oq^ 'uoqdis Aepideo oq^ , \#163 ; q jgo uA\ejp sua\ pmbij pie'jeujadns oq^ 'juojo iCpjoojJod p^un Suipuejs jopy .uopnjos pioe ouojqoojpifq oip jo dojp ojSuis e jo uoipppe 9q ; A(\ 'o^ojduioo suav uoiiepdioojd oip ( }eq^ uiejjoose oj 'poqsoj sua\ p jeop ^uoioigns sum pmbq oqj uoqM pun 'guiqeqs ( }uejsuoo qpM 'dojp iq dojp 'poppe ijsnopineo noqj sum 'q'jguojis uMouq jo uoi^rqos opqip e ui pouie^uoo 'pioe ouopjoojp^q jo ; unoiue siqx *p ojepdioojd 04 pojinboj pioe ouoppojpiq jo ip^uenb oqj ouiuijo^op os pue uopnjos ui Suiuiuuioj ^unorae oq ; ojejnopso 0^ Aeo sum p 'iiMOuq ojom 'optjopjo JOAps poqSiOM 9q^ in geq^ se p9M se 'posn ipeuiSuo JOAps oqj jo ^unoiue oq'j sy .uoippos in pioe ouopjoojpXq jo SS99X9 ojqejopisuoo Xue guiAuoj ^noqpM JOAps oq ; jo iioiiepdtoojd oq ' } p)9jj9 oj se pioe oijojqoojpiq oq^ uoipiodde o^ os Ajussooou ^ppionbosuoo suay p 'opuojqo uinipui jo suoi^njos ui 'ojojojoq ; 'ijquumsoid puu 'sq^juo 9iiquqju oqj jo sopijojqo 9q^ jo pnu piou ouojqoojpiq jo suopnjos in ojqnjosui ipoqM ^ou si 9pijojqo J9A|ig 'jjasp p9 ; ii9S0jd 00110 c[u jC(qnoqjip y 'piou otiojqoojpiq jo suu9in A(\ p9^O9j[j0 9q ^qSiiu snpp -uoipijos ni joajis jo SS90X9 9qj 0Aom9i o^ suav d9^s ( jsiq 9q^ .uoi^miiiiu9^9p ( }u0nb9sqns v ui ^qSi9M oimo^u 01^ jo 9UJBA 9q^ oouonqiii ^ou pjnoM siqj ^0050 0^ ifjuss099ii suoi^ui9do 0q ; ^uq^ puu S 0puojqo o^ui p9jJ9AU009i pnu p9J9A009J 0q pjnoo 'opiiojqo j9Aps su ouuojqo 01^ jo not^ujidioojd 01^ J0jju piou oijpu qpM noi^moossu ui uoipijos 9qi in ^six9 ppiOAV qoiqM ^U9IU9J9 9q^ ^uq ; 9A0^d 0^ 9[qujiS9p sua\ p 'suoi^uuiuLm^p ^n9pu9d9pui jupuixs 9quin 0^ 9ui 9jquu9 0^ 90q}ns ^ou ifjuiuji0O ^souqu p^noM uiu^qo 0^ 9doq pjnoo j pus mnipuj jo jfp^uunb oip sy quiJ9^um jo sjunoinu ; u9pu9d9pui no 0puui 010M suopuniinj9^0p 0saqx T-Z8I si '80\#151 ; Z06I 'smSiQAi '\#153 ; '1Y no aa^irauioo juiiopunj9pij 9qj iCq p9^dopu mnuuq joj 9iquA 9qx 'p0ifo{diu9 Xpun^ou 0.10M su puras os soipprunb jo osuo oq^ in ojqiSqSou ^CpoqM osjiioo jo oju ioq^ fX[0Apo0ds9J oiiiuiu.iS jod 5000-0 puu ^0000-0 A\uo opijojqo imiiiuq oq^ joj puu opuojqo joajis oq^ joj .nu p0OU[dsip joj siioi^oojjoo oq^ sy 508 luntpng fo 1 ']m'W uO [ '8061 Dr. T. E. Thorpe . [ Mar. 5 , Barium chloride , milligrammes . 139*5 78-8 Silver chloride , milligrammes . 191-4 108-3 Atomic weight , Ba . 138-1 137*7 In the hope that I might be able to employ the bromide of radium in the determination of the atomic weight of this element , I also made a similar preliminary series of determinations of the atomic weight of barium by means of barium bromide prepared from the pure chloride , and repeatedly recrystallised from alcohol . The results were as follows :\#151 ; Ag Barium bromide , milligrammes . 89*9 96*0 111*0 107-93 . Br = 79*96 . Silver bromide , milligrammes . 113*6 121*4 140*3 Atomic weight , Ba . 137*5 137*3 137*4 Two determinations were made on the recovered barium bromide , with the following results :\#151 ; \#166 ; Barium bromide . Silver bromide . milligrammes . milligrammes . Atomic weight , Ba . 91-0 114-9 137-7 80-8 102-1 137-5 It will be seen from these numbers that a very close approximation to the true atomic weight of barium can be obtained by the method described , the maximum error being about half a unit , or less than 0*5 per cent. Considering that the atomic weight of radium is probably nearly double that of barium , the same fortuitous errors would affect its value to about a unit . There is , however , one circumstance which , whilst not without influence in raising the value of barium , when determined on the recovered chloride , hardly affects the value of radium . In the case of radium , the effect of any minute quantity of retained silver haloid in the recovered salt , provided it is weighed with the precipitated silver chloride , is practically negligible , since radium chloride gives approximately its own weight of silver chloride . As the work of isolating and purifying the radium chloride proceeded , determinations of the amount of chlorine were made as described from time to time , and as soon as approximately constant values were obtained it was assumed that any barium or other impurity present was too small 1908 . ] On the Atomic Weight of Radium . in amount to affect the results when regard was had to the unavoidable experimental errors . The resulting chloride was then repeatedly and carefully recrystallised from pure , strong , hydrochloric acid , the " tails , " which were comparatively rich in radium , being specially set apart . The purified salt finally extracted from the material supplied by M. Armet de Lisle weighed , when anhydrous , 64 milligrammes . I regard this salt as substantially radium chloride . I am not , however , in a position to say that it was absolutely free from barium . At the same time , I have reason to believe that the amount still present was probably too small to materially influence the result , considering the limited quantity of the salt I had to work with , and the consequent relatively large experimental errors . With the aid of Sir William Huggins , who kindly made the spectroscopic trials for me , I was able to carry out Mme . Curie 's test of comparing the relative intensity of the lines of barium and radium in the spark spectrum of the separated radium chloride . Mme . Curie compared the relative strengths of lines 4554*2 of Ba and 4533*3 of ltd . Although these have the advantage of being close together , they are of dissimilar intensity . Sir William Huggins advised that a more stringent test would be to take the line 5536*2 of Ba of intensity 10 , and compare it with the Ed lines 5813*8 and 5560*8 , which are also of intensity 10 . On actually making the trials , which were repeated several times , the green Ba line 5536*2 , although visible , was seen to be relatively very feeble\#151 ; less intense , indeed , than that afforded by the most dilute solution of barium chloride that we were able to employ . With this material , therefore , I attempted to make the determination of atomic weight . Accordingly , the greater portion was transferred to the vessel already described , and the amount of chlorine in the anhydrous salt determined with all possible care . The result was :\#151 ; Radium chloride . Silver chloride , milligrammes . milligrammes . Atomic weight , Rd . 62*7 60*4 226*8 The radium was recovered from the solution , reconverted into chloride , added to what remained of the original quantity , and the amount of chlorine again determined in the anhydrous salt . The second result was:\#151 ; Radium chloride . Silver chloride , milligrammes . milligrammes . Atomic weight , Rd . 63*9 61*8 225*7 The purified chloride obtained from the Cambridge material amounted to 308 Dr. T. E. Thorpe . [ Mar. 5 , 24 milligrammes . A chlorine determination on a portion gave a number exceeding 230 for the atomic weight . No more importance can be attached to this value , considering the very small amount employed , than as showing that the salt was of the same order of purity as that obtained from the French material . It was accordingly added to the main bulk , and the whole was repeatedly crystallised from strong hydrochloric acid , about 6 milligrammes being thus removed in the mother liquors . The resulting chloride , after being dried at 150 ' , was again analysed , with the following results:\#151 ; Radium chloride . Silver chloride , milligrammes . milligrammes . Atomic weight , Rd . 78*4 75*3 227*7 The mean value is 226*7 , or , to the nearest unit , 227 . This , it will be observed , is in very close accord with Mme . Curie 's latest number . I think , therefore , it is reasonably well established that the atomic weight of radium is now known to within a unit which , considering the relatively high number , is , under the present circumstances , as fair a degree of exactitude as could be anticipated . There are , however , one or two facts connected with the behaviour of radium chloride which , as they may possibly affect the determination of its atomic weight , may here be mentioned . If a quantity of the salt be kept in perfectly dry air , it will be noticed that it very slowly increases in weight . The increase is very small , but it is plainly perceptible on a sufficiently delicate balance , and in the course of three or four days may amount to 0*3 per cent. On opening the vessel a marked smell of ozone is perceived , and on aspirating the air from above the chloride by means of a capillary tube passing into a freshly-prepared solution of potassium iodide and starch , iodine is found to be liberated , as seen from its action on the starch . Moreover , on dissolving radium chloride which has stood for some time in contact with the air in warm water , and acidulating the solution with dilute nitric acid , a smell recalling that of hypochlorous acid is perceived . The observed increase in weight may be due , therefore , to a portion of the air in the vessel becoming ozonised , or to a slight oxidation of the chloride , or to both these causes combined . Their joint effect would tend to increase the atomic weight of radium . Another remarkable circumstance connected with radium chloride is its action on colourless rock-crystal , which is gradually turned a deep purplish black . Berthelot has already drawn attention to the action of radium on quartz . The silica vessels which I employed in connection with the foregoing work were thus strongly coloured in the course of a few months . 1908 . ] On the Atomic Weight of Radium . Moreover , these vessels , as well as those of porcelain and glass , are slightly attacked by radium chloride , with the formation , apparently , of insoluble silicates . A similar observation has been made by Mine . Curie . It occasionally happened that a sample of radium chloride , after standing for some considerable time in contact with glass , gave a faintly turbid solution , although when the salt was newly crystallised from hydrochloric acid its aqueous solution was perfectly clear . I had hoped , as stated , to have obtained an additional series of values for the atomic weight of radium by the analysis of the bromide . As already mentioned , I reconverted the Cambridge material into this salt ; but my experience with it leads me to infer that it is not sufficiently stable to afford trustworthy values for the atomic weight of the element . It appears to lose bromine and eventually becomes insoluble in water . I hope to be able to study this change more minutely , as well as to throw some additional light on the action of radium salts on glass . In conclusion , I desire to acknowledge my indebtedness to my assistant , Mr. Arthur G. Francis , B.Sc. , for the assiduity , conscientiousness , and skill with which he has carried through what has proved to be the most irksome and tedious part of the work , namely , the isolation and purification of the radium chloride . I am also indebted to Professor Rutherford for the measurements of radioactivity which he made for me in the course of the fractionation of my material .

rspa_1908_0029

0950-1207

Alternate current measurement.

310

352

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. E. Sumpner, D. Sc., M. I. E. E.|Professor J. Perry, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0029

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0029

10.1098/rspa.1908.0029

Electricity

Tables

Electricity

]\gt ; Current Measurement . By W. E. SUMPNER , D.Sc . , M.I.E.E. ( Communicated by Professor J. Perry , F.R.S. Received October 5 , 1907 , \mdash ; Read January 16 , 1908 , \mdash ; Received in revised form January 21 , 1908 . ) Part I.\mdash ; The Mathematical Relationships of Cyclic Quantities 311 II.\mdash ; The Action of a Cyclic Magnetic Field on a Movable Coil conveying a Current of the same Frequency 316 III.\mdash ; The Theory of Shunt Magnet Instruments 320 \mdash ; Expcrimental Verification 327 The lack of precision of measurements with alternate currents , as compaled with those using direc6 currents , is mainly due to the relative sensitiveness of the instruments available for such tests . The fact that the turning moment acting on the moving system depends in one case on the square of the current and in the other on the first power of the current , readily explains the high ratio between the currents needed to cause the minimum measurable deflection in the two cases , but this ratio is , nevertheless , most when a numerical comparison is actually made on some fair basis . The only likely way at present of improving alternate current instruments is to use iron cored electromagnets to increase the strength of the magnetic field . I have found that the difficulties due varying permeability and hysteresis of the iron can be avoided by exciting the in shunt . It proves possible , with careful design , construct an electromagnet whose flux is connected with the exciting voltage by a strict mathematical law involving no variable physical properties like permeability , etc. Such an electromagnet is eminently suited for purposes . The theoretical and experimental study of instruments constructed on this principle has brought out certain novel points which are set forth in the present paper . The first part discusses the mathematical relations of cyclic quantities having a common fundamental period , and constitutes a development of a method already published . * This method is the only one known to me which is independent of assumptions in regard to the wave form of the quantities dealt with . The usual methods , which are based on the erroneous assumptions of sine law wave form , are not any simpler in working , and are most ) when the accuracy of new results has to be critically examined . All alternate current measurements refer to mean squares or to mean products , and the natural method of obtaining the connections between 'Roy . Soc. Proc vol. 61 , 1897 . Alternate Measurement . such squares and products is to study the properties of quadratic functions of the variables . The earliest instance of this in alternate current theory was in connection with the " " three voltmeter method * Such processes lead to a very simple form of calculus appropriate to cyclic quantities . The theory of the action of an alternating magnetic field on a movable coil conveying a current of the same frequency is discussed in the second part of the paper ; and the application of such theory to shunt magnet instruments is given in the third part . The final portion deals with experimental verification . Part I.\mdash ; THE MATHEMATICAL BELATIONSHIPS OF CYCLIC QUANTITIES . We shall use heavy letters such as , to denote single valued cyclic functions of the variable , and the corresponding letters in lighter type , , to denote the square root of mean square values of respectively . A we define as the agnitude of , and will be a constant as regards . The mean value of the product of two quantities such as will be represented by , so that Any cyclic quantity A must either have its mean value zero , when it may be described as alternating , or it must consist of the sum of two parts , one of which is stendy and the other alternating . With few exceptions the quantities occurring in actual alternate current problems are alternating in the above sense . The differential coefficient of any cyclic quantity is necessarily . The integral of a cyclic quantity is not met with unless its mean or steady value is zero . and as this integral will in most actual cases also have zero mean value it will be as nite quantity as that of a differential coefficient . The product of two cyclic quantities such as a and a current A consists in general of two portions , one of which is steady and the other alternating . These parts correspond precisely with the scalar and vector products of two vectors . Whatever cyclic quantities A and may be if we consider the meaIl values of the two identical expressions we see that these mean values can only be zero when A is proportional to for each instant of the cycle , and also that we can always find a such that ( 1 ) The value of determined from this equation may be defined as the ph * . Soc. Proc vol. 49 , March , 1891 . Dr. W. E. Sumpner . [ Jan. 21 , differ of the quantities A and B. These quantities will be said to be in phase when is zero , and this can only happen when the ratio of A to is independent of the time . They will be said to be in quadrature when is zero , that is , when the mean product of A and is zero . For any two quantities A and it is always possible to consider either of them , say , as the sum of two quantities the first of which is in phase with A and the second in quadrature with it , for we can so define that ( 2 ) where is a quantity , independent of time , which we can so choose that and A are in .quadrature . It ] follows that the nitudes of the three quantities in ( 2 ) can be denoted by the fths of the three sides of a triangle , and that the angle between any two sides of this triangle is the phase difference of the corresponding quantities . The mode of proof merely involves the process of multiplying the equation by some cyclic quantity and taking means . By successive application of this process , it is possible to establish the following theorem:\mdash ; one of a ' of known cyclic quantities , however differcnt these be in cravj form ? , can be expressed as linear function of an equal number other cydic quantities , these latter bein , such that the melxn square of each is unity and the product of any two is zero . Thus , if there are cyclic quantities , we can always find other cyclic quanties , , each of which is of unit magnitude , each two of which are in quadrature , and which are sucl ] as to satisfy the identities ( 3 ) where is the magnitude of , and where ( 4 ) for every value of from 1 to The quantities are perfectly determined by the magnitudes and phase differences of the quantities A. Indeed , is the phase difference between and , so that if the system of equations ( 3 ) has been established as far as , say , , the quantities are known ; the differences between and can be calculated , determining ; the equation for , constituting the definition of , can then be used to show that is in quadrature with each of the quantities ; equation ( 4 ) determines ; and so on . 1908 . ] Alternate Currenb If three quantities , , A2 , , of different wave form , together with linear functions of these quantities , comprise all the cyclic functions which have to be considered , it is possible , as previously show represent the nitudes and phase relationships of all such quantities by a vector drawn in three dimensions . This is not possible when four independent wave forms are involved , but in all cases it is possible to establish the system of equations ( 3 ) and ( 4 ) . Important alternate current problems involve so many quantities , and the relationship between these is so complicated by the effects of varying permeability , hysteresis , egular wave , etc. , that mathematically accurate representation is impossible with a simpler system of equations than is indicated in ( 3 ) . In practice , however , great simplification results from two considerations . In the first place , the quantities involved may be very numerous , it is only necessary , as a rule , to consider the mutual relations of two or three of them at any one time , and it is in general possible to construct the vector . actually needed for this purpose . In the second place , the figure can in all cases be reduced to a two-dimensioned figure by projection , as illustrated by figs. 1 , 2 , and 3 below . quantity involved can be reduced to one of the forms where and are cyclic quantities in quadrature , the same for the quantities , and where each quantity is in quadrature both with and . The projection of , denoted by , is It is possible to represent all the quantities , by vectors in a plane , and it is always true that ( 5 ) The plane figure so constructed will in most cases meet all requirements . It is frequently necessary to consider quantities like and , such that one is the differential coefficient of the other . Newton 's notation may be conveniently used , not only for the instantaneous values , but also for the corresponding magnitudes , since the latter are constants as regards time , so that no ambiguity can arise . If A and are any two cyclic quantities , it will be readily seen that ( 6 ) ' Roy . Soc. Proc vol. 6 ] , p. 465 . VOL. LXXX.\mdash ; A. Dr. W. E. Sumpner . [ Jan. 21 , It follows from ( 2 ) , that for any two quantities and A we can so choose that a right-angled vector triangle is denoted by the equation ( i ) From this we have ( ii ) and ( ui ) The represented by ( iii ) is the projection of that denoted by ( ii ) on the piane determined by ( i ) or by , and . By making use of ( 5 ) , it can be seen that the plane vectors involved in the ve equations are represented , as in fig. 1 , by two similar right-angled triangles with corresponding sides perpendicular . It follows ( 7 ) If and A are any two cyclic quantities represented by vectors in a plane , the vector projections of and on the same plane will be obtained by turning each of the vectors and A through a right angle in the same sense , and by increasing their magnitudes in proportion . We might similarly represent , , and by vectors in a plane , and project on to this plane vectors denoting , and , and also those denoting , and epresenting the projected vectors by the suffix mity , we have fig. 2 , consisting of three similar righ - will be represented by a vector in the same direction as , but drawn in the opposite sense to , that which lepresents will also be true of the vectors and , etc. Of course , the actual nitude of will bear to that of a ratio which is dependent on the wave form of , and this ratio will not necessarily be the same as that of the magnitudes of and , two other 1908 . ] Alternate quantities related in the same way . Indeed , this ratio is not the same for and as it is for and , except in the special case in which each follows the simple sine law denoted by In other cases it can easily be established by aid of the theorems denoted and ( 6 ) that 8 ) It is also easy to show that and where is in quadrature with both and , and the ) rojection of on the plane containing and Part \mdash ; THE ACTION or A CYCLIC NETIC FIELD ] CONVEYING A OF THE If be the current a coil , flux through which is ( the flux per turn multiplied by the number of turns ) , and if be an } displacement , the corresponding torque will be given by ( 10 ) If the current and the flux are steady , the torque due to their lnteraction convenient rule Maxwell , will be so directed as to tend to increase , provided we consider as positive threading ) coil in the anle direction as the flux due to the curl.ent C. If we choose a particular direction round the coil as positive for , this fixes the positive direction of , and the direction of , which is to be conDr . W. E. Sumpner . [ Jan. 21 , sidered positive , is that corresponding with such a displacement that increases with the displacement . If the current and the flux are alternating , the above statements are still true at any instant , but it does not follow that the average or steady value of is such as to turn the coil so as to increase the magnitude of , that is to say , so as to increase the square root of the time average of . The mean value of the product determining will be zero when and are in quadrature , and will as the phase difference alters from just below , to just above , right angle . If is entirely due to , that is , if , where is the selfinductance of the coi ] , we have ( 11 ) and is positive , that is , is so directed that the displacement it tends to produce is such as to increase L This torque always exists whatever may be the cause of the current , but , in the cases we shall have to consider , it is so small as to be negligible . We shall in all cases assume that the magnetic field , though varying with the time , has a fixed mode of distribution in space , or that the induction density at any point is the product of a vector function determined by the position of the point and not dependent on the time , and a scalar metion of the time , the same for all points in the field . In other words , we shall assume that the fluxes through any two coils placed anywhere in the field are always in the same phase , though the of each flux depends on the configuration of the coil , and on the co-ordinates determining its position . Alternate currents of commercial frequencies vary so slowly that this assump- tion justifiable , except in a few cases in which the variable permeability and hysteresis of iron prevent the medium from having a fixed magnetic character , and cause the flux distribution to alter for different netising currents . If the position of the coil is completely determined by , we have , on the above assumptions , where depends solely on and depends solely on the time . Thus or ( 12 ) CF . 1908 . ] Alternate Current surement . Thus the mean value , or the steady part , of , which we shall denote by , is given by ( 13 ) ; and this equation must be true in all cases . Now if the current is , due to the electromotive force induced by the time rate of change of the coil flux , the torque which results will depend on the nature of the circuit this coil . Suppose this circuit to be metallically closed , and to have a resistance and self-inductance , we then have ( 14 ) Multiply this by and take means . We get ; but if we multiply the same equation by and take means , we get or , using ( 6 ) , By these two derived equations , we get , on dividing by Hence , substituting in ( 13 ) , we get ( 15 ) From this it follows is negative , or ( 16 ) A dosed conducting circnit having placed in magnetic field noill to set itself so as to decrease to a ) the magnitude of the flux it rrocmds . The forces tending to displace the coil vanish if is zero or igible , but they are not simply proportional to , since is inversely proportional to the impedance of the coil . Suppose in the next place that the circuit of the coil is closed through a condenser of capacity K. If the resistance of the circuit is , the current induced by the field will , under ordinary circumstances , be so small that is negligible in comparison with . Under these conditions , if is the of the condenser we find , after paying due regard to , that , and whence Dr. W. E. Sumpner . [ Jan. 21 , so that , using ( 13 ) , we have in this case ( 17 ) where is the voltage induced in the circuit by the field ; thus T. is necessarily positive , or we have ( 18 ) If a coil whose circuit is closed through a condenser be placed in rnating mqnetic field , it wilt tend to move so as to increase to a maximum the magnitude of the flnx it snrrocmds . It can be shown that ( 17 ) is accurate , even allowing for the resistance of the coil , though in this case the voltage of the condenser is not the same as the electromotive force induced by the field . Allowing for the resistallceR , it will be found that From these equations we obtain as in the previous case , while the power supplied to the circuit is and so that if is less than one cent. of , the values of and will differ by less than 1 in 10,000 . Now let us suppose we have constructed an instrument for alternate current measurements , consisting of a movable coil placed in the intense alternating magnetic field due to an iron-cored electromagnet , and let us assume that the circuit of the coil includes a portion , external to the instru- ment , on which an alternating electromotive force is impressed . The torque acting on the coil will still be given by ( 13 ) , where is the flux through the coil due to the electromagnet , and where is the resultant current through the coil , due to all the impressed and reactive electromotive forces in the circuit . Let us assume iu the first place that the moving coil circuit is metallically closed , and that its resistance is and its self-inductance L. We then have for the moving coil current ( 19 ) Ihe solution of this is where 1908 . ] A lternate so that the torque is , or where is the torque already calculated which depends on , and is independent of , while T2 is a torque due to the interaction of with current calculated from alone , without reference to , or to its reactive influence on the circuit . A similar argument applies to the case in which the coil is ] osed through a condenser . In this case we have the equations ( 20 ) and and we can pnt and , etc. , where the quantities the first suffix satisfy the equations ) is zero , and those with the second suffix satisfy the equations when is put equal to zero . As in the previous case , the torque on the moving coil will consist of two independent parts , one of which is solely due to , and the other of which is due to snd , where is solely due to E. In each case the importance or otherwise of can easily be tested in an actual instrument by simply arranging for to be zero . As shown later , can also be easily calculated from the formula . The method of superposition can be conveniently applied to alternate current problems provided , ( 1 ) the differential equations colmecting the and voltages are linear , and ( 2 ) the resistances , induction coefficients , capacities and other factors are independent , not only of the time , but also of the physical variables , such as current , , etc. Under these conditions it is easy to prove the following theorem:\mdash ; ( 21 ) If , etc. , be any impressed electromotive forces distributed in any manner the branches of any network of conductors , the current in any selected branch will be given at each instant by the equation where is the current calculated on the assumption that all the impressed electromotive forces are zero except , and similarly for , etc. The current in any branch is at every instant the sum of the currents which would be produced in that branch by each impressed elecCromotive force alone . Since the current in any branch can theoretically always be reduced to zero by inserting a suitable electromotive force into the branch , the above theorem may readily be used to prove that . Dr. W. E. Sumpner . [ Jan. 2 ] , ( 22 ) If the electromotive forces impressed on a network cause a difference of potential V between two given points of the network , and if these two points be afterwards joined by a wire possessing resistance and self ( but not mutual ) inductance , the current which will flow through the wire will be exactly what an electromotive force V would produce in a circuit consisting of the wire , and the network to which the wire is joined , assuming the other impressed electromotive forces removed from the network . The above theorems I have found serviceable in reasoning out the behaviour of conducting networks used for a number of tests made in connection with the present paper . The complete mathematical solution of the problems presented by such networks is , as a rule , impossible , owing to the unknown wave forms of the variables . For the purpose of an actual test the complete solution is not , as a rule , needed , while the particular relationship required can often be readily seen with the aid of the above theorems*without making any assumptions about wave form . Part III.\mdash ; THE OF SHUNT MAGNET INSTRUMENTS . Let be the resistance of the coil of an electromagnet subjected to a periodic voltage V , and let be the total number of lines of force enclosed by the winding , that is let be the product of the number of turns of the coil and the flux of lines through the core . Let be the current through the coil . We then have 23 ) For the cores of large transformers with closed magnetic circuits it is in some cases the fact that the magnitude of V is over one hundred thousand times as great as that of . For small magnetic circuits suitable for instruments of ordinary size the ratio will be much less , especially if an air gap is introduced to allow a coil to move across the field , but even in such cases I have found it possible with careful design to make this ratio exceed 250 for alternate currents having a frequency of 50 cycles per second . Let us for the present assume to be so small is ] ible compared with , or that the ratio of the resistance to the impedance of the coil is negligible . The relationship between the field and the exciting is then independent of the permeability of the core . Suppose the electromagnet to have a narrow air gap in which a coil can move , * The truth of ( 21 ) and ( 22 ) for direct urrent circuits has been long known . The latter theorem ( 22 ) is due to Thevenin , 'Comptes Rendus , ' 1888 , vol. 97 , p. 159 , and is often convenient . Theorem ( 21 ) for alternate current circuits , though not precisely stated , seems more or less indicated in one of Heaviside 's ' Electrical Papers , ' vol. 2 , pp. 294\mdash ; 296 . 1908 . ] Alternate Curren\ldquo ; Measurement . aeo as to turn about an axis , its position being completely specified by a deflection . Let be the flux enclosed by this coil for the deflection We assume strictly in phase with , so that 24 ) where depends on , but is independent of time . Hence , in ( 24 ) negligible , we have so that is the ratio of the voltage of the coil ( on open circuit ) to the applied voltage , and is a quantity which for any deflection can be measured , provided suitable voltmeters are available . Suppose the moving coil circuit be closed a condenser of capacity , and to have an electromotive force impressed upon it , or suppose the [ moving coil in series with the condenser K ) be applied to mains at potential , we then have , from ( 20 ) , assuming and ible , , where so that Hence ; and by ( 25 ) this is equal to For a voltmeter we can make the same as V , but we can apply it to the coil in either of two ways . Thus for a voltmeter This quantity is proportional to the torque , and hence this torque for a given value of and of simply depends on , so that the instrument can be calibrabed as a voltmeter . It is easily possible to make igible compared with unity , but in any case the factor only affects the 'calibration , and not the accuracy of the voltmeter . It readily follows from , remembering that is independent of , that 27 ) and so that the general expression ( 13 ) for the steady torque is the same as Dr. W. E. Sumpner . which in the case of the above voltmeter ( with negligible compared with unity ) becomes 29 ) Next assume moving coil circuit to be metallically closed through the secondary of a transformer the coils of which have a constant mutual inductance M. Suppose the primary coil of this ormer to be traversed by a current A. Let be the resistance of the moving ] circuit , but the present let us assume the self-inductance of this circuit ible . We then have RC , where Also by ( 25 ) and by ( 13 ) and ( 28 ) But so that 30 ) or is a measure of the power in watts associated the current A and the voltage V. The uity of sign merely implies that the secondary of the transformer can be connected up in two ways . Certain assumptions have been made in establishing the formulae ( 29 ) and ( 30 ) , and it remains to show what influence any error in these assumptions , has on the action of the instrument . I have already discussed the theory and construction of iron cored shunt magnet instruments , and described a rather long experimental investigation of theirbehaviour , in two papers published by the Institution of Electrical ( vols . 34 and 36 ) . In one of these papers the theory of the voltmeter , and of its error , were very fully dealt with , and it will suffice to add here that these voltmeters are most satisfactory instruments . They need but a negligibly small current to work them , and are very sensitive , especially when constructed so as to have a weak control , and for use with an optical pointer . The theory of the wattmeter nlerits much fuller consideration . The properties of magnetic fields due to shunt excited electromagnets have a wider interest than that arising from the use of these magnets for a particular purpose , such as that of a voltmeter or a wattmeter . If a magnetic field can be caused and controlled by an applied voltage in accord1908 . ] A lternate Current Measurement . ance with a strict mathematical law [ by which is meant a law which in essence involves no factors dependent upon the magnetic or other variable physical properties of the medium , and which , therefore , is independent of in these physical properties ] , such a field must be found sooner or later , for a variety of measuring purposes . more searching test can well be applied to such a field than an investigation of its action in connection with a wattmeter , for no other electrical instrumenb is required to work under such severe conditions . Its indications must be correct for all values of no than five variables , viz. , , volts , power frequency , and wave form . Moreover , while the deflecting forces corresponding with the power to be measured diminish with the power factor of the load , this is not the case with those corresponding . with the error of the instrument . The true power for a given current and voltage is proportional to , while the most important part of the error is to so that this actually increases as , and becomes relatively very important for low power factors . Now to determine we have , besides ( 28 ) , the equations ( 31 ) is the electrolmotive force in the secondary of transformer the primary of which is trave1sed by the main current A. For an air core transformer will be strictly proportional to . If the netic circuit of the transformer contains iron , the flux enclosed by the secondary coil will not be strictly proportional to , but we can always put ( see ( 2 ) ) ( 32 ) where is in quadrature with A and From the above equations ( 31 ) we can omit , since , as already ] lown ( 19 and 15 ) , we can calculate the part of due to separately . Its value will be where is calculated from or since and are in quadrature and the ratio of the magnitudes of and is very small , with sufficient accuracy . Hence the torque due to is ( 33 ) Dr. W. E Sumpner . [ Jan. 21 , a quantity determined by alone . It is not dependent on A or on the power factor of the load , nor is it dependent upou the frequency or wave form of , assuming is negligible . If we omit from equations ( 31 ) , these become 34 ) The above may be regarded as equations between vectors , and remembering ( 7 ) and the quadrature relationship of vectors like and , the complete figure can be easily indicated as in , where is the phase difference of the current A and the main , and the small phase errors of the instrument , which for the sake of clearness are greatly exaggerated in the figure , are denoted as follows:\mdash ; 30 ) , the angle between and V due to the resistance of the magnet coil . , , , , and , , self-inductance of the moving coil circuit . , , , , and , , hysteresis of the transformer core . These angles must each be made very small if the wattmeter is to be even approximately correct , so that we shall regard them as small quantities of the first order , and neglect their squares and products compared with unity . Hence it follows , with the aid of ( 34 ) , that to this degree of approximation or and that these magnitudes are the same as if , were all zero . Now the torque depends upon , that is upon FC where is the phase difference between and C. The nitudes and are the same as if the phase errors were zero . It will be seen from fig. 3 , assuming as a first approximation that all the vectors lie in one plane , that is the complement of the separating and , since is in quadrature with and F. Hence and , since all the phase errors are small , 36 ) where Hence , by 28 ) , ( 31 ) , and ( 33 ) , the complete expression for is 1908 . ] Alternate Cnrrent where is given by the preceding equation and where , the true power in watts . In establishing the above , we have assumed that all the vectors of lie in one plane . This , in general , will not be the case , nor , indeed , as a rule , will a three-dimensioned figure suffice . But if all the angles are small quantities of the first order , it will be seen that the of any projected vector will bear to the of the corresponding vmprojected FIG. 3 . vector a ratio , where is a smaH quantity of the second order . Moreover , this will also be true of the projected values of the phase errors . Neglecting such quantities , the formula ( 37 ) is still accurate , as also ( 36 ) , the equation for , provided the latter is regarded as a vector equation , so that can never exceed , and must , in } eneral , be less than , the numerical sum of the separate phase errors . The full analytical investigation quite bears out these statements , but as its working involves much detail , and does not bring out any new point , it will be sufficient to Dr. W. E. Sumpner . [ Jan. 21 , indicate a shorter proof in which advantage is taken of the smallness of the fractions the phase errors . The value of must evidently be a function of , and the phase errors , and , hence , if we can neglect squares and products of the latter , we can , by Taylor 's theorem , expand and put where is the value of , assuming all the phase errors to be zero , and where do not involve these quantities . It only remains to determine the values of these coefficients , and it is clear that we find any one of them by assuming two of the quantities equal to zero , and solving the equations ( 34 ) so modified . It is easy to show that each coefficient can be expressed by the formula where is a positive quantity , which may be zero , which is always very small , and which , in fact , can nearly always be neglected . Thus , to find , the coefficient of , we put and each to zero in ( 34 ) , and have the equations ; ; and Thus . NA where is the between the vectors A and N. Referring to , it will be seen that though the vectors , V , and A may not lie in one plane , they can be properly represented in a three-dimensioned figure , and that cannot exceed , and must , in general , be less , or the ratio of to must be less than unity . Also the magnitudes and must be equal , since is small and is approximate]y perpendicular to . In other words , is independent of , and it readily follows that T. tall so that By a similar process the coefficients and may be obtained , and their values will be found to satisfy a formula . The result is to completely establish ( 36 ) and ( 37 ) with the limitation already stated in regard to the former equation ; that it be regarded as a vector 1908 . ] Alternate Current ) ) equation , so that can never be greater , and nnust , in general , be less than Ghe numerical sum of , and Part A moving coil instrument , the istics already described , may be constructed of thin sheet iron stampings , as illustrated , in which shaded areas denote the in section . The magnetic circuit contains one air gap . To reduce the reluctance of bhis as much as possible , its section is increased ) the poles , that one almost surrounds the other as . The ] distance across [ he gap is reduced to the smallest value consistent with the free motion the moving coil . This coil is ular in shape , and turns about one FIG. 4 . FIG. 5 . of its long sides as an axis ( shown at O ) , the opposite side in the arc-shaped gap between the poles . A pointer OP is attached to the coil and reads on a suitable scale PS . The netic joints , indicated at , needed for constructional purposes , are made as as possible by building up successive stamp n , so as to overlap at the joints . The resistance of the netising coil of two dings , one on each limb ) is reduced by using as much metal in the coil as the available space allows . Such constructional features ensure two desirable results . The ratio of the resistance of the coil to its impedance is made small , and the ratio of the magnetic to the total magnetic flux is dinlinished as much as possible . The latter ratio cannot be assumed to be quite constant for different currents , so that , unless it is a small fraction , the Dr. W. E. Sumpner . [ Jan. flux density at a particular part of the air gaP may not always be sufficiently proportional to the total flux enclosed by the coil . The umenta actually made have been constructed to several designs , the earliest of which is indicated in fig. 4 . In none of these instruments has any adverse effect . due to variation of magnetic leakage been observed . But the instrument illustrated in is more likely to show such an effect than that illustrated in fig. 5 . The magnet of fig. 4 consists of two blocks of stampings with butt joints at , and measurement shows that while most of the netic flux through the centre limb crosses the narrow circular air gap in which the moving coil turns , an appreciable portion of the total flux leaks to the side limbs by longer air paths . In the magnet of } this leakage must bear a much smaller ratio to the total flux . The Inductance of the Moving Covl . If the field coil of such an be excited by an alternating voltage , and the coil be closed through a small resistance , this coil will be found to turn ( in accordance with ( 16 ) ) till the flux it encloses is as small as possible . Thus , in each of the cases represented in and 5 , the coil will turn towards the position Oa . By increasing the resistance of the moving coil circuit the force can be easily made negligible , since , very approximately , the torque is inversely proportional to the square of this resistance ( see ( 15 ) ) . If the moving coil is connected with ] the terminals of a condenser and the field magnet coil be excited , the moving coil will be found to turn so as enclose the greatest possible flux ( see ( 18 ) ) . For the case represented by fig. 5 the coil will turn to the position Oc , while for that represented by fig. 4 the coil will turn to the nearer of the two positions Oc , Oc ' . These effects are quite in accordance with the theory previously given , but do not indicate any special facts about the self-inductance of the moving coil . More information is obtainable on this point by testing the formula ( 11 ) where is the moving coil current and is the self-inductance of the coil . In order to test this formula , it is necessary to ] iminate the torque , due the interaction of the moving coil current , and the flux due to the current in the magnetising coil . This can be done by using currents of two different frequencies for the moving and field coils . Under these circumstances the only torque acting on the moving coil that given by the above formula , 1908 . ] Alternate Current and by the movement of the coil we can thus find in which direction increases . Such tests were made upon an instrument constructed like fig. 5 . The urning moment was found to be so minute that the springs had -o bs removed , the current passed into the by means of fine vires exerting no appreciable contlol . The system had also to be )arefully balanced . The nl0yin3 coil contained 20 turns , and the maximum )urrent that could be safely passed through it was about ampere . The nagnetic force due to this current feeble ( the length of the iletic ircuit was about in ches , aIJd the force was spent mostly the ooap ) , so that the permeability of the iron was first test n-as made with the field unexcited and with the field coil open circuited . tn alternate current of ampere through the coil caused it to ttUin to a osition between Ob and Oc , about from Ob as actually in [ he position of maximum self-inductance would , theoretically , ) Oc the only magnetic circuit comprised the iron path from pole to pole the single between the poles . The self-inductance is , er , due to the local magnetic circuit crossing the air twice , once on side of the mov ing coil , and tlJis portion of the self-in ductance be 'reatest when the coil lies along Ob . Hence , umder the actual conditions , he position of maximum self-inductance must lie } Ob and ; as ndicated by the test . The field coil 2000 turns and a esistance of ohms ) was then electrically closed , either by a short circuit , by a small resistance , this latter consisting , in one case , of a ccumulator producing the field coil a current of about a quarter of amlaere , and , in another case , of the low resistance armature of au excited lternator applied direct to the field coil . An alternate current of ampere produced by a second alternator ) when passed through the coil caused latter in each of these cases to to the position Ob . That is to sa whenever the field magnet coil was electrically closed ( the total of -he circuit being in all cases small ) the position of maximum of he moving coil was Ob , whether the electromotive force impressed the field coil circuit was steady , alternating , or zero . Thus the -inductance of the coil was dependent upon the resistance of the ield coil circuit . To explain this , it must be remembered that a closed coil low resistance has , approximately , the effect of a perfectl conlucting sheet . If we assume the resistance of the field coil to , and the coil to be short circuited ( or what is mathematically equivalent if a be applied to it , the value of which is independent of current ) , it is theoretically impossible for the numl ) of lines of force enclosed by the coil to be in VOL. LXXX.\mdash ; A. 2 Dr. W. E. Sumpner . [ Jan. 21 , any way altered , unless there is an unbalanced electromotive force in the circuit , iu which case the rate of change of the flux must be such as to cause a reactive electromotive force exactly balancing that which is impressed . In such case the closure of the field coil circuit would perfectly control the flux the core , and this flux would be uninfluenced by the currents in a neighbouring circuit such as that of the moving coil . The theory of the instrument already given shows that it is necessary to carefully consider the inductance of the moving coil circuit . It is found possible to construct the instruments so that this inductance has no appreciable influence on the deflections . Such a result may , at first , seem unlikely . The inductance , directly or indirectly , affects the deflection in three ways . In the first place , the reactance causes a shift of phase of the moving coil current , and a resultant error similar to that which arises in a wattmeter of the ordinary dynamometer type . Next there is the torque fiven by the formula where is the moving coil current , and is the deflection . Fintdly , there is the torque due to inductive action given by ( 15 ) and ( 33 ) and or where is the electromagnet flux , travel.sing the coil , the value 04 which increases with the number of turns , and , therefore , with the selfinductance of this moving coil . Moreover , it is necessary to consider whether the moving coil can even said to have a true , i.e. , constant , self-inductance , for the coil is always in the close neighbourhood of iron masses whose induction density , and , therefore permeability , continually varying throughout the period . It must be borne in mind that the self-inductance of a coil is merely a coefficient , convenient when constant , for connecting the magnetising current with the magnetic flux resudting from it , and that what is necessarily associated with a nagnetising current is not a magnetic flux but a magnetising force . The current causes no flux if the circumstances are such that the force due to the current merely calls into existence , by reaction , an equal and opposite netising force . The case is analogous to that of the weight of a body which causes no acceleration in it when at rest on a table . If there is no extra flux due to the current in the coil , this coil be L908 . ] A lternate Current as devoid of self-inductance . Such result is , in the } , true of he coils of a potential msformer . The variation of the secondary culrent not alter the flux th.ough the core , since this flux is essentially ontrolled by the primary voltage ; all that happens is a in the rimary current of such a character and amount as to exactly the hang in the magnetising force due to the ration of the secondary curl.ent . flux through the core , as ramnlatically in fig. 6 , consists of a lain portion threading both the prinnary and secondary coils and nd the best circuit , and also of two local , or uxes and , each of hich threads the of one coil only , and ach of which traverses a bad magnetic circuit the reluctance of hich is most entirely due to that of an air path and , therefore , esselltially constant . flux is determined by the primary , and is independent of the urrents in the coils and , but the flux is ictly proportional to the urrent in , while the flux is similarly proportional to the curlent in 4 one of the coils , say , is on open circuit , the of the other orresponds with a small flux strictly to the current , ether with a flux which , to the variable pel.meability of the iron , is lot proportional to the current . Under these conditions the self-inductance large but not constant . If , howevel , one of the coils , say , is ited b alternating voltage , the self-inductance of the coil is solely due to tlJe mall flux . This flux is proportional to the current , so )hateIlergy is not dissipated when the flux alternates , nnd the coil ] a colttant self-inductance in or ' the presence of iron masses . But nductance is vely lall , it is possible that under some circumstances it may be actually less than would be the case if the iron masses were relnovel . iron , with its controlled flux , dimini hes the flux resulting from the current in the secondary coil , since it } ) available for this flux . For instance , if the ) coil is wound in Dr. W. E. Sumpner . [ Jan. 21 , fig. 5 , so as to well cover the core , and the secondary consists of a few turns round the primary coil , the reluctance of the leakage path will , in such case , be so great that the secondary coil will be essentially devoid of selfinductance . By those accustomed to transformers , and similar apparatus , it is recognised* that the self-inductance of the coil arises from the leakage flux , and not from the main flux ; but I know of only one set of experimental tests in which the matter has been investigated . These tests were carried out at 's College , London , in 1892 , and are described in a report written by the late Dr. John Hopkinson for the house Company . The description in question is much more than an ordinary commercial report . It is a record of a searching experimental investigation on two transformers . the points examined was the instantaneous relationship of the fluxes and the coil currents . Unfortunately this investiryation has only been published in the technical so that it may be useful to state briefly the experimental result of interest here . Referring to fig. 6 , if VI and are the and the currents , and and the resistances of the primary and the secondary coils , we have with a similar equation for . The experiments showed that the leakage flux was proportional to the current AL for every instant of the period and for different nitudes of the current . This was proved by determining the values and wave-forms of the different quantities required by means of Joubert 's instantaneous contact lnethod , using a quadrant electrometer as indicator . The curves for and were separately determined in the usual manner . The curve for was obtained with the aid of an open circuit coil surrounding the flux , or by an equivalent method , and the curve for was obtained from the others by using the above equation . The curve for was then differentiated to get the lrve , and the latter was finally compared with the curve for . The two curves were found to coincide , and the comparison made was the more convincing because of the irregular and complicated shape of the curves . The tests were carried out As , for instance , in the much used ' ' short-circuit ' ' methods of testing alternate current machinery . The first of these short-circuit methods was pointed out by myself in 1892 in reference to the efficiency testing of transformers . See 'Proc . Inst. Elec . Engineers , ' vol. 21 , p. 741 . ' Electrician , ' vol. 29 , June 24 July 1 , 1892 . I understand that most of the tests were actually carried out by ofessor E. Wilson , who has since published in the ' Electrician ' for February 15 and February 22 , 1895 , an account of some additional experiments which constitute furLher verification of some of the points here referred to . 1908 . Alternate jIeasttrement . not only with the secondary coil open circuited , but also with different load currents taken from this coil . The value of was found proportional to , and that of was found proportional to A2 , at each instant , and under all circumstances , assuming constant voltage excitation of one of the coils . It follows that the self-inductance of the moving coil is due to the part of the flux through it , but not traversing the core surrounded by the field coil . In the case of the self-inductance will be greatest when the coil lies along Ob , and in that of fig. 4 the corresponding position will be but the self-inductance will be larger in the latter case owing to the leakage flux which passes through the moving coil , and traverses the closed iron magnetic circuit formed by the outer limbs of the magnet , without traversing the central core whose flux is controlled by the field coil circuit . In several cases the impedance ( and hence reactance ) of the field coil was tested experimentally and found to compare satisfactorily with that calculated from the dimensions of the boap , the reluctance of the iron part of the magnetic circuit being for the induction densities used in the tests . It was hence possible to deduce the reactance of a field coil the same number of turns as the moving coil . A quarter of this value will be the working reactance of the coil in the position Ob of fig. 5 , since the two halves of the air will be in parallel for one magnetic circuit and in series for the other . It was thus possible to calculate the approximate value of the inductance of the coil for diffel'ent values of , and to show that the values of , and of , were too small to aHect the accuracy of the instruments actually constructed . In some cases the value of was measured directly . This was not a simple matter . It was necessary to use an alternate current method . It was useless to attempt to compare the impedance of the coil with its ance , for these two quantities only differed by about one part in 5000 , since the reactance was only about 2 per cent. of the resistance . A bridge method was actually used , the coil to be tested forming one arm , the other three consisting of non-inductive resistances , two of which measured about 1000 ohms each . All the resistances were suitable for , and were used with , currents of about ampere . A pressure of 100 volts , at a frequency of , was applied to the bridge . The cross conductor was arranged to have a resistance of about 200 ohms to reduce errors , and contained an instrument capable of pressures as low as volt applied to this conductor . So far as I am aware , no instrument for alternating curl.ents is obtainable which is at all suitable for such a measurement . The voltage was measured after rectification by a suitable Dr. W. E. Sumpner [ Jan. 21 , commutator , *with the aid of a delicate galvanometer . To measure the minimum cross voltage it was necessary to make an extremely fine adjustment of the . This was obtained by means of a sliding contact on a potentiometer metres and of about 9 ohms resistance . The minimum cross voltage , divided by the current through the coil under test , gay the reactance of this coil . An instrument of the type indicated in fig. 5 was examined by the above method . The moving coil contained 20 and had a resistance ( including leads ) of 11 ohms . It was fixed in the position Ob and its reactance was tested when the field coil was ( i ) on open circuit , and ( ii ) on short circuit . The values measured were respectively and ohm a frequency of 50 cycles per second . The difference between these numbers is the part of bhe reactance due to the main magnetic circuit of the magnet , and its small value is attributable to the low permeability of the iron under the feeble fnetic forces to the coil current . A coil of 15 turns , wound round the yoke of the magnet , was also tested with currents of the same frequency . The resistance of this coil was ohm , and its reactance was found to be ohm with the field coil open circuited , and ohm with the field coil short circuited . The two coils were afterwards put in series ( opposing ) , and the reactance of the combination was found to be ohm for the field coil short circuited , and ohm for the field coil open circuited . The coils so connected were essentially non-inductive as ards their mutual magnetic circuit , so that the two above values should be equal to each other , and also to the sum of the numbers and found for the coils separately . This auxiliary coil was originally wound round the magnet for another purpose , being intended for use in series with the moving coil , and to be so connected that the voltages induced by the magnet in these coils opposed each other and balanced for a certain position of the moving coil . In this way the small error ( see ) and ( 33 ) ) due to the voltage induced in the moving coil circuit could be elinlinated or made negligible . The device was , however , found to be ] to the nificant amount of the error in question . A fixed auxiliary coil wound round the inner pole ( near the line Ob in fig. 5 ) might in special cases prove useful , since essentially it would serve to remove from the circuit of the moving coil not only the induced by the electromagnet , but also the self-inductance of the moving coil . * For the commutator and voltmeter methods here referred to , see " " The Measurement of Small Differences of Phase ' Phil. Mag Janualy , 1905 . They have been much used in connection with the present investigation for the determination of minute alternating voltages . 1908 . ] Measurement . S35 of Deflecting The residualmagnetism properties of an such as is indicated in fig. 4 or fig. 5 are most striking , but the distribution of the magnetism in the air gap must be the same , whatever current may be passing through the field coil . All the instruments were calibrated by direct current methods . steady current passed through the field coil and maintained constant , while observations were made of the deflections in rees due to various measured steady currents through the coil . The scale was made proportional to the current producing the corresponding deflection . The scale so obtained has been found in all cases accurate for alternate current use , being directly proportional for wattmeters , and proportional to the square of the volts for yoltmeters . The air gap is bounded by two sets of , those of each set circular edges of the LQame radius , so that with construction the air gap can be made very approximatel of the same radial distance everywhere , and the wattmeter scale almost exactly equally diyided . Tests have proved this to be the case . For the purpose of the formulae given above for the torque acting on the moving coil , tests were also made of the voltage induced in this coil by the alternating . For this purpose the alternating voltage on the coil kept constant , and the of the moving coil measured for differeIlt values of the deflection . The ratio of the latter voltage to the former is . The relation between and was foumd in all cases to be very approximately linear . the case of an instrument like 5 , increased as altered from Ooe to Oc , while , for an instrument like fig. 4 , passed through zero for some deflection denoted by Oa . The relation between and was so nearly linear that it was found sufficiently accurate for the purpose of an verification of the formulae for to take as the value of the alteration in for a in of ont ) radian , or . The formulae given are in absolute umits , so that the unit torque is one erg per radian . It is convenient to measure the rical quantities in commercial units , and the torque in " " gramlne centimetres so that the for must be multiplied by or approximately by 10,200 . One instrument tested had a field coil of 990 turns . The moving coil turns , and its working range was . This coil fixed at deflections of , and , and the measured values of expressed as were respectively , and . These values will be found to plot very well on a straight line , the slope of which corresponds with a rate of per cent. radian . Dr. W. E. Sumpner . [ Jan. 21 , Using for shortness to denote 10,200 , the above tests imply that is . Formulae ( 28 ) , ( 29 ) , and ( 30 ) for expressed in gramme-centimetres become respectively ( i ) ; ( ii ) ; ( iii ) W. The strength of the spring was first tested mechanically by acing a wire rider , weighing about 20 milligrammes , on the pointer at a measured distance from the axis , and carefully adjusting the instrument till the pointer and the axis were each horizontal , first with and then without , the rider . In this way the torque for deflection was measured as . cm . , corresponding with . cm . for . The instrument was then tested as a voltmeter with a standard condenser of microfarad for the moving coil circuit . A number of tests made for deflections near yielded as a mean result ) volts produced a deflection of . Substituting in the formula , we get gr. cm . for or . cm . for . A test on the instrument as a wattmeter on a noninduct.ive load , measuring the current and voltage with hot wire instruments , resulted in a deflection of for 94 volts and 18 amperes , or for 1692 watts , when the transformer was such that was approximately millihenry , and , the total resistance of the moving coil circuit , was ohm . These numbers , when substituted in the above formula , give . cm . for , or . cm . for . Thus the mechanical tests and those using formulae ( ii ) and ( iii ) yield values respectively and . cm . for a deflection of This instrument was afterwards altered . A moving coil of 44 turns replaced the original one of 20 turns and stronger controlling were used , the torque for measurin approximately . cm . The value of was not again measured , but it may be assumed to increase in proportion to tloe number of turns on the moving coil , and hence may be taken as 44/ 20 , or . Two transformers were successively used with this instrument , the resistance of the moving coil circuit being adjusted in each case till the instrument gave a deflection of exactly for 1000 watts . The values of for the two transformers were measured approximately as and millihenry . The corresponding resistances for the moving coil circuit were and ohms . On substituting in formula ( iii ) above the two values of the torque for work out to be and . cm . , or , for and . cm . When used as a voltmeter with a condenser of , the instrument gave a deflection of for a pressure of 97 volts . On in formula ( ii ) these . numbers will be found to correspond with a torque of . cm . for 1908 . ] Alternate Current easurement . A test was also made using formula ( i ) in connection with an instrument referred to in subsequent tests ( see Table II ) . It was found that when 107 volts at a frequency of 52 were applied to the fixed coil and moving coil in series , the resultant deflection was . The value of found for this instrument was approximately 56 , and the torque required to deflect the spring was . cm . The field coil was such as to take : 90 milliamperes for a voltage of 200 when the frequency was 50 cycles per second , hence for 107 volts and 52 cycles per second the value of in ( i ) is ampere . The value of is such that , or is . Hence , is . cm . for , or . cm . for This result would have been nearer , the value found from the mechanical test , if allowance had been made for the phase difference between the magnetising current , and the resultant flux N. The angle , judging from measurements made on other instruments , is about , and though large enough to be fatal for a wattmeter having an electromagnet of the ordinary series , or current controlled type , is not such as to make differ more than 3 or 4 per cent. from unity . No attempt was made to prove exact coincidence between the mechanically and electrically measured values of the torque . The tests in question really constituted absolute measurements , and in order to carry them out properly it would have been necessary to most carefully check all the and subsidiary measurements , made use of . This was not done , since only an approximate verification was aimed at . Iany such tests were made on the various instruments constructed . The results above given are taken from the more concordant tests . The indications of the commercial instruments used were accepted without verification . Condenser The most serious error arising in the action of the wattmeter on circuits of low frequency and low power factor is that due to the resistance of the field coil . The self-inductance of the coil circuit tends to increase the effect of this error , not to compensate it . The voltage V applied to the field coil of resistance produces a current which magnetises the core and causes a reactive voltage or . These quantities are elated by the equation and in fig. 7 are represented respectively by the vectors , BO , and OP . If the number of turns on the field coil is the product can be represented to some other by BA drawn along BO , and is the number of ampere turns round the core needed to magnetise it to the extent represented by ) : Dr. W. E. Sumpner . [ Jan. 21 , reactive voltage U. The error of the instrument arises from the phase difference between and V , not from the fact that the magnitude of is less than that of V. The ratio between and independent of the current and the power factor , and is essentially the same for all voltages . In all cases it differs inappreciably unity , and any difference that exists is taken of in the standardisation of the instrument . For a given frequency the relationship between the total uetising ampere turns BA round core , and the reactive voltage OP is quite fixed by the netic circuit , even if there are several coils round the core traversed by independent currents . Suppose that in addition to the primary exciting coil already referred to there is a second winding of turns round the core , and that the terminals of this coil are joine to a condenser . The on the primary necessary to produce a ctive voltage due to the core , will now be given by where is the new current in the primary . Since is the total number of ampere turns necessary to produce the core , we have where is the condenser current . The current will necessal.ily be in quadrature with the core , since it in phase with , and hence 1908 . ] A .339 will be represented by a vector , perpendicular to OP , lvl]ile its magnitude will be proportional to the capacity of the condenser applied to the secondary winding . Since the vectors BA and represent espectiyely , it follows that will represent and that if be drawn parallel to to meet in BI this vector will denote , while the vector will represent . By the capacity of the condenser attached to the secondary winding , the point may be made to reach the line OP at and even to cross it to , so that the phase difference between and can be ednced to zero and can be reyel.sed in until an of " " \ldquo ; it becomes an of " " lead It is thus possible by the use of a condenser of the capacity to compensate the phase error of the , but also the extra phase error due to the inductance of the coil circuit . The adjustmeJ ) lvill hold for different volt , but will only be exact for one frequency . is chase is needed in most cases , since one of the most stant properties of an nate crren t system of distribution is its frequency . In the case considered the of the line OP is from 100 to 200 the of OB , so that to a close approximation the lines , OP , etc. , are all of equal . Also the BOP does not mnch exceed right angle , and hence BA and are essentially equal . The angle is about , while the angle BPO is on about a quarter of a . If the fiekl coil of the be excited at constant voltage and frequency , the reactive can thus be arded as fixed , } the capacity 1 of the condenser applied to the secondary winding . For a zero value of the primary current will have a certain value represented by BA . For a particular value of the capacity , the primary current will be a minimum represented by , the line to some other scale the capacity . For any other capacity , represented by , the sponding primary current will be represented . Thus , if the be excited at constant voltage and frequency , rtnd measurements of the primary current be taken for various values of , the curve obtained by plotting the primary current or turns as ordinates , and the corresponding values of as bscissae , will be catenary-shaped with a minimunl ordinate for the capacity needed to compensate the phase error of the . Such curves are well known in connection with alternate current measurements . When suitable scales are chosen the curve must also be such that the ordinate is equal to when the abscissa is equal to in The value of obtained will be inversely proportional to the square of the current frequency used , since the ampere turns BA needed to produce a iverl reactive voltage will vary inyersely as the frequency , while the ampere Dr. W. E. Sumpner . [ Jan. .turns due to a capacity will be directly proportionaI to the frequency. . For a similar reason the capacity needed will be inversely proportional to the square of the number of turns used on the secondary winding . All these points have been fully verified by actual tests . The results given below in Table I and fig. 9 are taken from a set of testg made on an electromagnet provided with a moving coil , and connected up as a voltmeter of the magnetostatic type previously described . The connections of the coils are shown diagrammatically in . The field coil oonsisted of two coils of 500 turns each , the two coils being twin wound rouud the core so as to ensure that each coil enclosed the same flux . Ihese coils were permanently connected in series . The moving coil , , was connected to the terminals of one of the windings of 500 turns a condenser of microfarad capacity . core of the magnet was wound with an extra coil of 50 turns . The pointer was found to deflect to a certain mark on the scale when 80 volts were applied to 1000 turns ( or 40 volts turns ) . The deflection for a given voltage was the same for ordinary frequency of the used for the test . This deflection was utilised in the tests to adjust the reactive voltage of the core to a constant , value . Experiments were then made by passing an alternating current A amperes through the 50-turn coil . The current frequency was kept , constant at 80 cycles per second , and A was adjusted by means of suitable resistances until the pointer was steady at the mark on the scale , the curl'ent , being read by a hot wire ammeter . The values found for A for different . capacities of microfarads applied to the field coil of 1000 turns are given in the first two columns of Table I. A tbird column gives the corresponding values of or the ampere turns associated with the 50-turn coil . The value of was known with fair accuracy , and was due to various parallel combinations of condensers which had been tested by ballistic methods some months previously . The half microfarad condenser used with the : 1908 . ] Alternate 500-turn coil for the moving coil circuit used a small netising c round the ] . The values eoiven represent the capacities actually connected with the 1000-turn coil , and these should be each increased by or microfarad to numbers proportional to the ampere turns due to the condenser currents . Table I. . 8 FIG. 9 . Dr. W. E. Sumpner . S [ Jan. 21 , The results are shown plotted in fig. 9 . When the current A has its minimum value , reference to fig. 7 will show that A is in phase with the reactive . Hence the power wasted in the core may be obtained by multipJying the minimum number of ampere turns , 35 . by the voltage per turl } round the core . This power works out to be watts for 80-cycle circuits for the induction density corresponding with this frequency and volt per turn . The loss thus obtained agrees closely with other meastlrenlents which have been made ) the core losses of the electromagnet in question . A more convenient method of testing one of these instruments for the capacity needed for compensation is ( see fig. 10 ) simply to put the field coil . in series with the moving coil ? . and to apply various condensers to the ninals of the field coil only , when a constant voltage is lied to the two coils in series , the frequency being kept constant . The impedance of the moving coil is quite negligible compared with that of the field coil . Hence for constant and the reactive voltage ( fig. 7 ) is constant . The magnetic field , is in quadrature with is represented by a vector drawn along the line BK and is fixed both in phase and magnitude . The vector BA represents the field coil current , which in this case includes the condensel current , but the moving coil current is represented by , for a capacity ] to the field coil . Since the field is represented by a vector of constant length drawn along , the acting on the nloving coil will be represented by the projection of on or by . It will thus reverse in as the capncit increases through ] 1leeded for compensation , and , moreover , there will be a lineal connection betweell the capacity used and the coil torque as indicated the deflection on the calibrated wattmeter scale . The results given in , and plotted in fig. 11 , illustrate ono of many tests made on a number of instruments ) this method . 1908 . ] Table II . The voltage was kept constant at 107 volts and the frequency was vays adjusted approximately to 52 cycles per second , by means of a resonance frequency meter . is the capacity in microfarads shunted to the field magnet coil , and is the deflection of the in strument . The ative FIG. 11 . readings were obtained by reversing the connections of the coil . The instrument was the same as that referred to later in the tests on compensated wattmeters , the field winding consisting of foul coils in each coil containing 2000 turns . the plotted results it ) pears that is microfarads for a frequency of 52 , with Inicrof.arads for circuits of freqnency 50 . The ampere turns due to the condenser winding if the frequency is ) is 200 , and . will be This is approximately the value of for this frequency and , since tests showed that for 200 volts at 50 cycles per second alue of was Dr. W. E. Sumpner . : [ Jan. 21 , 90 milliamperes , corresponding with 180 ampere turns . The eement is satisfactory in view of the fact that the frequency was not adjusted with any special care . C'ompensated Wattmeters . The foregoing theory shows that a wattmeter of the type here considered , if correctly calibrated on non-inductive loads , will , when used on inductive loads , of power factor , give a reading denoting where is the true power in watts , and is the phase error of the instrument given by ( 36 ) . The wattmeter reads low for currents , and for leading currents in direct contrast to the behaviour of a wattmeter of the ordinary dynamometer type . When an additional coil is wound round the core and connected to the terminals of a condenser , the value of is given by the formula where is the phase angle corresponding with the condenser winding and which is proportional to the capacity of the condenser attached to this winding . The ratio of to will approximatel . be that of the ampere turns due to the condenser to the alnpere turns needed to magnetise the core . By using a suitable condenser it is possible to reduce to zero and even to reverse its sign , that is to make the wattmeter read high for lagging currents and low for leading currents , like an ordinary dynamometer wattmeter . This has been experimentally verified on several wattmeters the electromagnets of which differed rreatly in shape . The following results were obtained on a wattmeter having an shaped like that represented in fig. 5 . This instrument had been wound for use as a voltmeter . The onet was wound with four coils each of 2000 turns . Two of these coils were wound on each limb , one coil being completely wound on the bobbin before the of the other was commenced . The resistances of the four coils are 745 , , 715 , and ohms , the two lower resistances corresponding with the inner coils , and the others with the outer coils . With all four coils in parallel it was found that 200 volts produced a current of ampere when the current frequency was 50 , so that 180 ampere turns were needed to produce a flux density in the core corresponding with 10 turns per volt at 50 cycles per second , follows that the impedance of the winding is 2222 ohms at this frequency . The parallel resista1lce of all four coils is ohms . The two inner coils when in parallel measure ohms and the two outer coils puooas a Xq JDuI SWA aq$ sasvo amos pur i,1$s1Jt[0 ) uassa 8 pasn } epuoi ) aonpoJ ) Jo$ Jtio a Aq fxnpuooas oeauI p sa1Jas mIJd o passvd : ot JsmJoJsutJl axoo ue ? 11aaq } ) auuoo 8 S$1 U0J1 ) J9mJojsut ? J$ eJnooti 1o ou mo5 ouIsnQ . [ T00 @utom sq os U0J1 puooas po auff OT dn SUJnt ? smqo uIaq 1 -uou } JJno So dn uuoo SatII dnooo edmoo rdnoi ) aq$ os suoo ) QmpuTA @ . ; qmoo III SI JO Dr. W. E. Sumpner . ; [ Jan. 21 , in parallel for the field coil , the values of , and are respectively , and per cent. The sum of these numbers is per cent. If the field coil consists only of the two outer coils in parallel , this number , owing to the increase of , becomes per cent. Tests of the uncompensated wattmeter on circuits of frequency 80 and for loads of power factor , have shown percentage errors given by the formula for values of in close agreement with the above numbers . An approximate value of the reactance of the moving coil can be obtained from the impedance of the 2000 turns of the field winding . This , for a frequency of 50 , is 2222 . The moving coil consisted of 40 turns . If the field coil contained only40 turns , the impedance would be or ohm . The moving coil , when in the central part of the gap , will have its reactance a maximum , and approximately equal to a quarter of the above value . It will thus be ohm for a frequency of 50 , or ohm for a frequency of 80 . Since the resistance of the moving-coil circuit is 118 ohms , the phase error due to the coil 's reacta1lce will be per cent. for 80 cycle circuits , and this will be its maximum value . As already stated , the total phase error is the vector sum , and is less than the numerical sum , of the different phase errors . I have generally found that the value of , experimentally deduced from tests of the wattmeter on inductive loads , agrees well with that calculated from adding the separate phase errors , when that due to the reactance of the moving coil is neglected . In order to test the iron-cored instrument as a compensated wattmeter , the outer coils were put in parallel , and used as the field winding , to which the voltage was applied , while the inner coils , also in parallel , were applied to the terminals of a condenser . The tests were made , using as a standard wattmeter a Mather Duddell instrument ( M.D.W. ) , constructed by Messrs. Paul . In order that the tests on ging current loads could be immediately succeeded by tests on leading current loads , and vice , the circuits were arranged as shown in fig. 12 . Two similar -phase , rigidly coupled so as to run together , generated two voltages and of the same frequency and approximately in quadrature . The magnitudes of and could be varied independently by adjusting the exciting currents of the two machines . The current A was produced by the voltage , and passed through ( i ) the primary of the current transformer of the I.C.W. ; ( ii ) the current coils of the M.D.W. ; ( iii ) a large non-inductive resistance of glow lamps ; and ( iv ) small adjustable carbon resistance . This current was approximately in 1908 . ] Alternate Current Measnrement . phase with the voltage , but there was a slight angle of lag owing to the inductance of the coils in the circuit . The voltage V for the pressure coils of the two wattmeters was obtained from the mains , which were connected up to the two alternators with the aid of a reversing switch , B.S. , so arranged that , for one position of the switch , , and for the other position , . The vector figure is indicated in fig. 13 . The current A was in each case approximately out of phase with the voltage , leading for one position of the switch and for the other position . Its magnitude in the various tests varied from 7 to 9 amperes , in all cases adjusted by the carbon resistance CR till the M.D.W. was balanced . The voltage for one position of the switch was about 230 volts , and for the other about 200 volts . The frequency was in all cases adjusted to 80 cycles per second . The pressure circuit of the FIG. 12 . FIG. 13 . . contained a non-inductive resistance of 9000 ohms , which was sufficient to make this circuit essentially non-inductive for a frequency of 80 . One terminal of this resistance was connected to the main , so that the pressure coil of the M.D.W. had one of its ends joined directly to the main , and was thus at essentially the same potential as the current coil C. This precaution was found necessary to make negligible any electrostatic forces acting on the moving system of the M.D.W. , this moving system and delicately suspended . The constant of the M.D.W. had been carefully determined on a non-inductive load , using the same hot wire instruments to measure the and current as were afterwards employed to measure the same quantities for the inductive tests . The power factor of the load was determined in each case from the readings of the volts , amperes , and of the watts , as indicated by the hot wire instruments and the M.D.W. From the power factor the value of was deduced , this value Dr. W. E. Sumpner . [ Jan. 21 , being considered positive for ging currents and negative for ones . In Table , below , the first column shows the capacity in microfarads joined up to the two parallel connected inner coils wound round the electromagnet core . The reduced readings of the M.D.W. for a deflection of exactly on the I.C.W. are next given , arranged in three columns , in order to separate the lesults obtained with the three kinds of load corresponding with the voltage used . The last two columns show the value of the power factor as deduced from the readings of voltmeter , ammeter , and wattmeter , and the corresponding value of Table The results show that ( i ) the uncompensated instrument is moresensitive for leading currents than for lagging ones ; ( ii ) when a capacity of 2 microfarads is used the reverse is the case ; and that ( iii ) when a capacity of microfarad is used , the instrument is perfectly compensated for circuits of frequency 80 . It was easy to test the effect on the reading due to suddenly switching on the condenser ] , and there was no doubt , that for lagging currents switching on the condenser caused an increase of the deflection of the I.C.W. , while for leading currents the reverse effect took place . When the load was essentially non-inductive no effect due to. . switching on a condenser could be observed . This is only natural , since 1908 . ] Alternate Current Measurement . when the error vanishes , whatever the value of . But though the nature of the effect due to the condenser current could thus be easily demonstrated , it needed a set of tests such as those indicated in Table to actually measure its amount . The numbers given are in each case the means of several observations , and only a few of the tests taken are iven . This more especially applies to the observation with microfarad . These were repeated many times , with the result that it was impossible to say under the actual conditions of test whether the I.C.W. was more , or was less , sensitive with load currents lagging than with load currents leading . It now only remains to show that the differences actually observed are in accordance with the error mula . FIG. 14 . The results given in Table are plotted in fig. 14 , abscissae representing values of and ordinates the corresponding wattmeter readings for the standard deflection of the I.C.W. These results are found to plot fairly closely on three lines , each having the ordinate for the zero value of . The resultant phase errors calculated from the slopes of the lines in fig. 15 will be found to be , and per cent. for values of respectively , equal to , 2 , and microfarads . Owing to the nature of the error formula , the mean value of can be best obtained numerically by taking the mean wattmeter reading and the corresponding mean value of for each set of tests , and , the results as indicated in Table denotes the ratio of the difference between the wattmeter readings to the corresponding difference between the tangents , while the ratio of to is the phase error . Now , as already shown , the calculated values of , and add up to Dr. W. E. Sumpner . [ Jan. 21 , Table per cent. , disregarding the self-inductance of the moving coil , which will increase the number by an amount less than per cent. This figure agrees closely with the phase error of per cent. as actually measured for The value of , or the shift in the value of , caused by applying condensers of and 2 microfarads to the secondary winding , will be seen from the tests to be per cent. and per cent. respectively . These numbers can readily be compared with the values calculable from the capacities . The value of alone , as shown by Table TII , is per cent. for an exciting winding of the two outer coils in parallel and for the frequency of 80 . Also , it was found that 180 ampere turns round the field winding produced a magnetic flux corresponding with volt per turn at a frequency of , and , therefore , with volt per turn at a frequency of 80 . The alternation of such a flux would induce in 2000 turns a pressure of 320 volts at the latter frequency . Assuming the wave form of the voltage approximately sinuous , as was the case in the actual a condenser of 1 microfarad applied to the 2000 turns under the conditions assumed would take a current of ampere , or ampere , corresponding with .332 ampere turns for the coil of 2000 turns . The value of for a condenser of 1 microfarad is , therefore , very approximately given by per cent. per cent. Hence , condensers of and 2 microfarads would , at the frequency of 80 assumed , produce values of , respectively equal to per cent. and per cent. , which are essentially the same as the values actually found . The testing conditions were such that the closeness of the agreement is of no special significance , but it will be apparent that within the limits of experimental error the action of the wattmeter corresponds exactly with the formula given for it . 1908 . ] Alternate Current Measurement . Conclusion . The foregoing tests were all made with alternate currents of the low frequencies usual in commerce , on instruments of the non-reflecting type , each having a moving system subject to the control of a strong spring . Few tests yet been made on reflecting instruments in which a weak control is used for the moving coil . Under such conditions much ) crreater sensitiyeness can naturally be secured , but , to causes already mentioned , the sensitiveness reached will not even then be comparable with that obtainable with the best direct current galvanometers . To measure very minute alternate currents or voltages it must ultimately prove necessary to use instruments of the heterostatic type . such purposes the shunt-excited elecCromagnet see1ns specially suited , and additional interest in consequence attaches to the foregoing examination of the behaviour of voltage-controlled letic fields . The precision of direct current measurements is mainly due to the use of null methods . Analogous methods have been ested , or can easily be devised , for alternate current testing . But such methods are not used . The advantage of a null method arises from the possibility of fully utilising the sensitiveness of an for the purpose of measuring or a small difference between two nearly equal quantities . It follows that when , as with alternate currents , instruments sufficiently sensitive to indicate such a difference do not exist , null methods are really of little value . In fact , when the testing voltmeter is such tlJat the deflection depends on the square of the voltage , a direct deflection method is sensitive than a balance method , the voltage tested is not large enough to over-deflect the instrument . By making use of bhe properties of separately excited -controlled fields it seems ible to construct voltmeters for alternate current working which are quite as sensitive as the corresponding direct current instruments , and which are also such tlJat the deflecting forces are proportional to the first power of the voltage tested . The special difficulties due to phase can be readily overcome , since it is easy to apply in succession to the field ccil two cves of known relative magnitude and phase . For the purpose of null methods the nitudcs of these need only be very roughly determined . The instruments yet made have been suitable only for low-frequency circuits . -frequency working special difficulties will arise , while others will disappear . For low frequencies the chief difficulty is to make igible the phase error , represented approximately by the ratio of resistance to impedance . For frequencies will become quite Current Measurement . negligible , but on the other hand , the phase error due to the inductance of the moving coil circuit , will become serious , as also possibly will eddy current effects in the core of the . Eddy currents in the core only affect the accuracy of the magnet in so far as they affect the value of , provided the core is so well laminated that the distribution of the magnetic field is the same for direct as for alternate currents . With very frequency currents the value of will be negligible , and , possibly , in some cases , there will be no need to use iron in the core , so that eddy currents will not occur . The increase of the inductance phase error for high frequencies is more serious , but on the other hand it is possible to compensate it , not only for one but for all frequencies , by means of the condenser winding . It can readily be shown that while varies inversely as the frequency , the ratio of to varies directly as the square of the frequency , so that is directly proportional to the frequency like Hence , it should prove possible by using a suitable condenser in conjunction with a special winding to neutralise the phase error of the instrument for all frequencies for which is negligible .

rspa_1908_0030

0950-1207

The decomposition of ozone by heat.

353

369

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Edgar Philip Perman|Richard Henry Greaves.|E. H. Griffiths, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0030

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0030

10.1098/rspa.1908.0030

Thermodynamics

Chemistry 2

Thermodynamics

The Decomposition of Ozone hy Heat . By Edgar Philip Perman , Assistant Professor of Chemistry , University College , Cardiff , and Richard Henry Greaves . { Communicated by E. H. Griffiths , F.R.S. Received December 24 , 1907 , \#151 ; Read February 13 , 1908 . ) Much doubt has recently existed as to the interpretation which may be put upon measurements of the velocity of chemical change in gas reactions . Va n't Hoff deduced the " order of the reaction " in certain cases from considerations of the law of mass action . Bone and Wheeler* have shown that the combination of hydrogen and oxygen at temperatures below that necessary to explode the mixture takes place mostly ( if not entirely ) at the surfaces with which the gases are in contact , and that no conclusion as to the order of the reaction can be drawn from pressure measurements . Ozone was chosen for further work on the subject , as it affords one of the simplest possible cases . The decomposition by heat furnishes only one substance , and the reaction is irreversible ( at least for all practical purposes ) . Production of the Ozone.\#151 ; The ozone was made by means of the usual Siemens ' induction tube . Oxygen was obtained by heating potassium chlorate , and was stored over caustic potash solution . The ozonised oxygen was collected over sulphuric acid in a small gas-holder , consisting of two glass bulbs , each of about 350 c.c. capacity , and connected below by a U-tube . One of the bulbs was connected above with a three-w^ay stop-cock , while the other bulb was open to the air through a calcium chloride tube . The ozone was admitted from the induction tube to the gas-holder through one limb of the three-way stop-cock by means of a ground-glass joint . It was transferred by another ground-glass joint to the decomposition globe through the other limb of the stop-cock . Apparatus for heating the Ozone.\#151 ; The ozone was heated in a globe A , of about 350 c.c. capacity , by means of a bath of calcium chloride solution . The globe A was connected with the gauge C , and a similar globe B was connected with the gauge on the other side . The ozone was admitted through the ground-glass joint made at D , and the stop-cock E. The large globe F and the pressure gauge G were used only for experiments under less than atmospheric pressure . H , K , L , and M represent two-way 4L * ' Phil. Trans. , ' A , vol. 206 , p. 1 . Messrs. E. P. Perman and II . H. Greaves . [ Dec. 24 , diagonal stop-cocks , and N was a small ordinary stop-cock through which sulphuric acid was admitted to the gauge . The bath was heated by an Ostwald burner ; it was thoroughly stirred , and the temperature maintained constant to 0''l . Method of conducting an Experiment.\#151 ; The apparatus being in position ( as in diagram ) and the temperature steady , the globe A was exhausted by means of a Fleuss pump , the globe B being left open to the air . Ozonised oxygen was then transferred from the gas-holder to the globe A. Great care was taken to prevent any moist air from entering . The pressure was regulated so that A was filled at a pressure slightly greater than atmospheric . The excess was allowed to escape through D , the globe A was connected with the gauge , and readings of the pressure were taken at suitable intervals . In order to find the total amount of ozone present , the two globes and gauge were removed from the bath , and the globe A heated for 10 minutes with a Bunsen burner to about 300 ' ( at the lowest part of the globe ) . In a trial experiment it was found that the ozone remaining after this treatment could be neglected . The apparatus was then replaced in the bath , and after the temperature had become steady , the pressure was read again . Method of Calculation.\#151 ; The pressure of the ozone at each reading was calculated as follows :\#151 ; The actual pressure , as shown by the gauge , at each reading was subtracted from the final reading ( when all the ozone was decomposed ) ; double the number obtained gave the pressure of the ozone in millimetres of sulphuric acid . A correction was then applied for the change of volume of the gases in A and B caused by the movement of the acid in the gauge . The correction was a small one , as the gauge tube was only 2 mm. in diameter . The first or second order " constants " were then calculated in the usual way . Great difficulty was experienced in obtaining concordant results , especially with a new globe , which usually gave a greater rate of decomposition than it did after some use . The following results ( p. 356 , etc. ) were obtained at various temperatures ; where t = time in minutes , x = amount of ozone decomposed ( mm. of H2SO4 ) , a = initial pressure of ozone , Ki is the first order constant ^-log \#151 ; , and K2 the constant of the second order , X :\#151 ; t \amp ; a\#151 ; x t(a\#151 ; x)a 1907 . ] The Decomposition of Ozone by Heat . Fig. 1 . Messrs. E. P. Perman and R. H. Greaves . [ Dec. 24 Temperature 119''9 . Globe IT . t. a \#151 ; x. X. K2 X 106 . K. x 104 . 0 2 190 *2 152 *7 37 *5 646 477 3 137 *4 52 -8 673 471 4 124 -3 65 *9 697 462 6 105 *4 84 *8 705 427 8 89 -2 101 -o 744 411 13 64 *5 125 *7 788 361 18 49 *5 140 -7 830 325 28 33 *3 156 *9 885 270 Mean ... 746 Temperature 120 ' . Globe II . t. a \#151 ; x. X . K2 X 10* . Ki x 104 . 0 227 *2 1 199 *5 27 *7 611 564 2 178 *7 48 -5 597 521 3 159 *0 68 *2 629 517 5 130 *5 96 7 652 482 7 108 *0 119 *2 694 461 12 74 -0 153 *2 760 406 17 54 *8 172 -4 815 363 27 34 *3 192 *9 917 304 Mean ... 709 Temperature 100 ' . Globe II . t. a \#151 ; x. X. K2 X 10 ? . Ki x 10* . 0 405 *1 2 388 *8 16 *3 518 90 4 372 *5 32 6 540 91 6 358 *2 46 *9 539 89 11 326 *2 78 *9 543 85 16 299 *3 105 *8 545 82 26 255 *4 149 *7 557 77 41 210 *2 194 *9 558 69 61 168 *1 237 *0 570 63 96 121 *9 283 *2 597 54 Mean ... 552 1907 . ] The Decomposition of Ozone by Heat . 357 Temperature 80 ' . Globe II . t. a \#151 ; x* x. K2 X 108 . K , x 105 . 0 15 322 *9 311 *4 11 -5 762 105 30 301 -1 21 *8 748 101 45 289 '9 33 *0 783 104 60 280 *2 42 *7 786 103 90 262 *9 60-0 785 99 120 247 *0 75 *9 793 97 180 220 -3 102 *6 801 92 240 198 -7 124 *2 806 88 300 180 -0 142 *9 819 85 360 164 *5 158 *4 829 81 420 151 *1 171 '8 838 79 508 135 *4 187 *5 844 74 568 125 *2 197 *7 857 72 Mean ... 804 Temperature 60'T5 . Globe II . t. a \#151 ; x. X. K2 x 109 . Ki x 10B . 0 382 *5 180 361 *2 21 3 856 139 330 344 -2 38 3 881 139 1320 264 *9 117 6 879 121 1533 251 *9 130 -6 884 118 1780 237 *8 144-7 894 116 2046 224 *8 157 -7 897 113 2745 195 *1 187-4 915 107 Mean ... 887 Temperature 40 ' . Globe II . t. a\#151 ; x. X. K2 X 1010 . x lO ? . 0 376 *3 675 368 *4 7*9 844 136 1420 361 *9 14 4 745 119 2055 356 *2 20 *1 730 116 2730 350 *5 25 *8 716 113 4170 338 -6 37*7 710 110 5600 327 *2 49 *1 712 108 7040 317 *4 58 *9 700 105 Mean ... 722 No correction has been applied for change of barometric pressure , or for the change of pressure of the oxygen during the decomposition ; for , as will be seen later , the variations thus caused are within the limits of experimental error . 358 Messrs. E. P. Perman and R. H. Greaves . [ Dec. 24 , It will be noted that the results are not in close accordance with either a first or second order reaction ; they are , however , considerably nearer the second than the first.* With one exception ( at 40 ' ) the value of _x . t(a\#151 ; x)a rises steadily throughout the experiment . In the experiment at 40 ' the amount of ozone decomposed is very small and the measurements extend over several days , so that the decrease in the " constant " may be due to experimental error . The rate of decomposition increases roughly 10 times for a rise of temperature of 20 ' at the lower temperatures , and somewhat less rapidly at the higher temperatures . Effect of varying the Extent of the Glass Surface.\#151 ; Globe I was packed with short pieces of glass tube of a total area of about 1120 sq . cm . The internal area of the globe was about 240 cm . , so that the area of the glass with which the ozone was in contact was nearly six times as large as before . Temperature 1190,9 . t. a\#151 ; x. X. K , x 106 . t. a x. X. K , x 106 . 0 272 -5 4 176 *2 96 *3 501 1 240-3 32 *2 492 6 149 -4 123 *1 504 2 213 -5 59 -0 507 11 109 *3 163 *2 498 3 193-7 78 *8 498 Mean ... 500 The corresponding mean value for the globe with the tubes is 117xl0"6 ; thus the rate of decomposition was 4*27 as fast . Both the bulb and the tubes were made of soft soda glass . It will be noted that the rate appears much more constant owing to the increased glass surface , but this may be due simply to the increased rate and consequent shortening of the time intervals . A similar experiment at about 80 ' gave the following result:\#151 ; Temperature 790,9 . Globe II . t. a \#151 ; x. X. K2x106 . 1 t. a \#151 ; x. X. K2 X 106 . 0 308 *0 6 166 -0 142 0 463 1 268 *8 39 *2 473 8 144 -3 163 *7 460 2 238 *2 69 -8 476 13 107 *5 200-5 466 3 215 *2 92 *8 467 23 68 -1 239 *9 497 4 196 2 111-8 462 * Cf . Warburg , ' Sitzungsberichte der Konig . Preuss . Akad . Wiss . Berlin , ' 1901 , vol. 48 , p. 1126 . 1907 . ] The Decomposition of Ozone by Heat . The mean rate with the same globe at 80 ' is 8*04 x 10~6 , so that at this temperature the rate was increased nearly 60 times by the glass tubes . In another experiment the globe was loosely packed with glass wool , with the following result:\#151 ; Temperature 40 ' . Globe III . t. a\#151 ; x. X. K2 X 10 ' . t. a \#151 ; x. X. K2 x 107 . 0 283 *4 55 213 *1 70 *3 212 5 275 *1 8*3 213 70 199 *4 84 *0 212 10 266 '8 16 *6 220 90 181 1 102 *3 221 20 252*2 31 *2 218 120 158 *8 124 *6 231 30 239 *2 44 *2 217 150 140*7 142 *7 239 40 228 *6 54 *8 211 210 109 *8 173 *6 266 Mean ... 224 The normal rate for the globe was not determined at this temperature , but at 100 ' it was 000013 . Calculating from the ratio of the rates observed with Globe II , this gives a rate T74 x 10~7 at 40 ' , so that the presence of the glass wool increased the rate of decomposition 129 times . The effect of a porous substance was next tried , the globe being filled with pieces of clay-pipe stem . The rate of decomposition was then so rapid ( no doubt owing to the very large surface ) that it was found impossible to measure it , even at the ordinary temperature . In order to obtain a rate that would be measurable , six pieces of pipe stem of about 2 inches in length were placed at the bottom of the globe . The following numbers were then obtained :\#151 ; Temperature 99'*7 . t. a \#151 ; x. Kx x 104 . t. a \#151 ; x. Kj x 104 . 0 188 *2 5 85 *6 684 1 *25 155 *6 661 7 63 *3 676 2 138 *1 672 9 46 *6 674 3 117 *8 678 14 22 *0 666 4 100 *0 687 24 5*1 653 Temperature 60'T . t. a \#151 ; x. Kx x 104 . t. a \#151 ; x. K , x10V i 0 302 *7 7 150 *1 435 1 273 *8 435 9 123 0 435 2 247 *0 442 15 70 *6 421 3 222 *0 449 26 27 *3 402 4 200 *4 448 36 11 *2 398 5 181 *3 445 360 Messrs. E. P. Perman and R. H. Greaves . [ Dec. 24 These numbers extend over a wide range and clearly indicate a reaction " of the first order . " The effect of certain metallic oxides was then tried ; a few grammes of the oxide were placed at the bottom of the globe . For each change of material the globe was cut at the neck and resealed after the introduction of the substance . Temperature 99'*7 . About 20 grammes granulated CuO in Globe . t. a \#151 ; x. X. K2 X 105 . Ki x 104 . 0 1 257*3 208 *3 49 -0 91 917 2 173 *5 83 -8 94 856 3 147*6 109 -7 96 804 4 126-6 130 7 100 770 5 109 -4 147*9 105 743 6 95 -0 162 -3 110 721 hr 83 -2 174 -1 116 700 9 63 -3 194 -0 132 677 11 47 *4 209 -9 156 668 16 23 -2 234 -1 245 653 21 10 *7 246 *6 427 657 The numbers show that the reaction is in this case much nearer first order than second , but is not in close agreement with either . In another experiment at a lower temperature , a good first order constant was obtained :\#151 ; Temperature 40o#5 . About 20 grammes granulated CuO in Globe . t. a\#151 ; x. Ki x 104 . t. a \#151 ; x. Kj x 104 . 0 342-6 7 196 -0 346 1 314-8 368 8 181 *3 345 2 289 -9 362 10 155 -2 344 3 266-6 363 12 134 -7 338 4 247*5 353 17 93 -3 332 5 227 *6 355 28 38 -6 339 6 211 -0 351 38 15 -2 356 A similar result was obtained with magnesia , but the rate was so fast that it was very difficult to measure . Temperature 40 ' . About 10 grammes MgO . t. a\#151 ; x. x 103 . t. a \#151 ; x. Ki x 103 . 0 34 -1 3 7-7 215 1 20 -9 213 4 5-0 208 2 12 -4 220 7 1 -9 179 1907 . ] The Decomposition of Ozone by Heat . Manganese peroxide also decomposes ozone at an extremely rapid rate , as shown by the following results :\#151 ; Temperature 40 ' . 10 grammes Mn02 , in small lumps , in Globe . t. a\#151 ; x. K , x 103 . t. a \#151 ; x. Kj x 103 . 00 151-8 2 0 27 '8 367 0*5 102-0 345 2*5 17 *6 372 1 O 67 -0 354 3*5 6 6 386 1*5 42-7 367 Temperature 15''4 . 10 grammes MnC\gt ; 2 . t. a \#151 ; x. K , x 103 . t. a \#151 ; x. Kj x 103 . 0*0 149 -7 3*5 32 *2 190 0-5 119 *4 195 4*5 21 *0 189 1*0 94 -8 198 5*5 13 *6 189 1-5 75 -7 197 7*5 6*3 183 2*5 49 *2 193 9*5 2 1 195 Lead peroxide , on the other hand , was found to have comparatively little effect on the rate of decomposition . Commercial lead peroxide was found to absorb ozone , no doubt owing to the presence of lower oxides . The following numbers were obtained with specially purified peroxide , which had been allowed to stand in the presence of ozone:\#151 ; Temperature 60 ' . 1 gramme PbC\gt ; 2 , in Powder . t. a \#151 ; x. X. K2 x 108 . Kj x 105 . 0 421 -4 17 396 *7 24 -7 869 154 37 371 -2 50 -2 867 149 57 347 *4 74-0 887 147 87 316 0 105 -4 910 144 167 248 *6 172-8 987 137 207 221 *7 199-7 1033 135 The normal rate at 60 ' , calculated in the same way as for 40 ' , is 209 x 10-8 . Effect of Metallic Surfaces.\#151 ; Consistent results were not obtained unless the metal had been previously heated in the presence of ozone . The normal rate for the globe is 1220 x 10~7 , so that the presence of the platinum appears actually to diminish the rate . It is probable that the VOL. LXXX.\#151 ; A. 2 O 362 Messrs. E. P. Perman and R. H. Greaves . [ Ded . 24 , normal rate for the globe had changed owing to the alteration in the neck during the opening and resealing . Temperature 99''7 . Total Area of Surface of Platinum Foil , 19'5 sq . cm . t. a\#151 ; x. x. K2 X t. a\#151 ; x. X. K2 x 107 . 0 435 *0 9 360 *0 75 *0 532 1 425 *6 9 *4 508 14 328 *8 106 *2 530 2 417 *2 17 *8 490 19 300*5 134 *5 541 3 407*9 27 *1 509 24 275 *7 159*3 554 5 391*2 43 *8 515 34 236 *6 198 *4 567 7 375 *7 59 *3 518 56 178 *8 256 *2 588 Similar results were obtained in the case of nickel:\#151 ; Temperature 99''8 . Total Area of Surface of Nickel Foil , 71'5 sq . cm . t. a\#151 ; x. X. K2 x 107 . K , x 104 . 0 365 *8 2 350 *7 15 *1 588 92 4 336 *0 29 *8 606 93 10 295 *0 70 *8 656 93 18 254 *0 111 *8 668 88 30 207 *4 158 *4 696 82 52 155 *6 210 *2 710 71 72 124 *6 241 *2 735 65 112 86 *0 279 *8 794 56 Some experiments were carried out with silver foil , but the rate of decomposition could not be measured owing to the gradual oxidation of the silver to peroxide by the action of the ozone . An experiment with platinum black showed an acceleration of the rate of decomposition , though not a large one , and a " second order " constant was obtained . Temperature 99''7 . Globe VI . About 2 grammes Platinum Black . t. a\#151 ; x. X. K2 X 10t t. a \#151 ; x. X. K2xl06 . 0 98-8 23 59 *0 39 *8 297 3 89 -8 9*0 338 33 50 *6 48 *2 292 8 79 '2 19 *6 313 53 38 *0 60 *8 305 13 70-6 28 *2 311 88 26 *5 72 *3 314 The normal rate for this globe was 8P9 x 10~6 . Influence of Moisture.\#151 ; A trace of moisture is known to be held by a glass surface , even at temperatures above 100 ' . An experiment was therefore 1907 . ] The Decomposition of Ozone by Heat . ; . 363 made to discover whether the moisture so held , ,was sufficient to have an appreciable effect on the rate of decomposition . The globe was heated in an air bath at about 400 ' , and pumped out several times . It was then placed in the calcium chloride bath , and an experiment conducted as usual . The mean rate was 0*000055 , while the rate found without the previous heating was 0*000053 , a difference which may be ascribed to experimental error . A series of experiments was made with varying quantities of moisture in the globe . The water vapour was introduced from a nitrometer containing water . This was well shaken to ensure the saturation of the air with water vapour ; it was then connected with the exhausted globe , and the required quantity of moist air quickly admitted , the pressure of the air being maintained constant . In one experiment air was passed from the nitrometer through a series of four bulbs containing water , placed in a water bath , and thence into the decomposition globe . In this way , 2*77 milligrammes of water vapour were introduced . The general effect of the moisture is to quicken the rate of decomposition , and the numbers are in much better accord with a second order constant than those obtained with dry ozone . The following is a good example:\#151 ; Temperature 119'*5 . Globe I. 0*69 milligramme Water in Globe . t. a\#151 ; x. X. K2 X 106 . t. a\#151 ; x. X. Ko x 106 . 0 329 *0 8 225 *3 103 -7 175 1 311*3 17 -7 173 13 188-7 140 *3 174 2 294 -0 35 0 181 23 142-9 186-1 172 3 279 -9 49-1 178 33 114-0 215 -0 174 4 266 -1 62 -9 180 53 80 -8 248 *2 176 6 244 -2 84-8 176 Mean 176 The increase in the rate of decomposition is ( within the limits of experimental error ) proportional to the mass of water vapour present . The mean values of the constants are here given , together with the corresponding quantities of water admitted in milligrammes ( m ) , and the constants calculated from the formula : h = 122-f 135Tm . The normal rate for the globe was 0*000122 . m. K2 X 106 . Ic . 771 . K2 X 10 ' . Jc . o-o 122 0-58 209 200 0-75 214 223 1 -40 310 324 0-69 176 215 2-77 515 496 2 c 2 364 Messrs. E. P. Perman and B. H. Greaves . [ Dee . 24 , Effect of Nitric Oxide.\#151 ; An attempt was made to measure the rate of decomposition of ozone after the addition of a small quantity of nitric oxide . Several trials were necessary in order to find a suitable temperature , and how much nitric oxide could be added without decomposing the ozone too quickly . Finally , measurements were made at 119'*1 after the addition of 0*2 c.c. nitric oxide ( at 15 ' and 800 mm. ) . The nitric oxide was made in a nitrometer from potassium nitrate and sulphuric acid over mercury , and was forced into the globe , which already contained ozonised oxygen at a constant temperature . The following is the result:\#151 ; t. ! a\#151 ; x. X. K2 X 105 . Kj x 103 . 0 58 *5 1 43 *4 15 *1 595 130 2 30-5 28 *0 785 141 3 21 *5 37 *0 981 145 4 13 *7 44*8 1397 158 The rate of decomposition was thus extremely fast , and , so far as it could be followed , appeared to be roughly of the first order . In a similar experiment with 1 c.c. of nitric oxide , the decomposition was too rapid for measurements to be made . Attempts were made to 'follow the change completely at a lower temperature ; 0*8 c.c. nitric oxide , contained in a tube between two stop-cocks , was allowed to diffuse into a bulb containing 150 c.c. ozonised oxygen , the whole being placed in a water bath at 10 ' . The change of pressure was measured by a sulphuric acid gauge connected with the upper part of the bulb . It was found that a decrease of pressure of 47 mm. of sulphuric acid took place , the pressure then remaining constant . This represents a decrease of about 1 per cent , in the volume , and is more than would be accounted for by the combination of nitric oxide either with oxygen or ozone to form nitrogen peroxide . Probably this is due to condensation of nitrogen tetroxide in the liquid state . At 50 ' no rapid decomposition of the ozone was observed after introducing 1 c.c. of nitric oxide , while at 100 ' the rate was accelerated but very irregularly . Effect of Varying the Pressure of the Oxygen.\#151 ; A series of experiments was made at various pressures with the complete apparatus as shown in fig. 1 . The large globe F was connected with B , and brought down to the required pressure by means of a Fleuss pump . A was exhausted and the ozone admitted in the usual way , until the pressure in A was known to be 1907 . ] The Decomposition of Ozone by Heat . 365 in excess of that required . The globe A was connected with F until the pressure was equalised ; it was then connected with the gauge , the stopcock H was closed , and readings were taken as usual . The total amount of ozone was also determined as before . Some manganese peroxide was placed at the bottom of the globe F in order to decompose the ozone admitted . The general character of the results is the same as those at atmospheric pressure , i.e. , they are approximately of the second order , but the rate increases towards the end of the experiment . The mean results are given in the following table , together with two at ordinary pressure for comparison :\#151 ; Temperature 99a7 . Pressure . K2 X 107 . Pressure . K , x 10 ? . Pressure . K2 x 107 . 755 531 583 788 449 776 758 550 550 720 375 888 638 631 482 737 304 916 593 763 468 851 276 1070 Effect of Diluting with Air.\#151 ; A few experiments were made in which the pressure of the oxygen was diminished by the addition of air . The large globe F was exhausted to approximately \#163 ; an atmosphere ; the globe A was then filled as usual and allowed to blow off into F. The following are the results:\#151 ; Temperature 99a8 . Pressure of oxygen . K2 X 10s . mm. 467 155 458 165 462 152 Normal rate for the globe ( YI ) , 81*9 x 10"6 . Discussion of Results . Effect of Temperature.\#151 ; The relation between rate of decomposition and temperature may be expressed by the formula log k = a + bt\gt ; a formula found by one of us to express the connection between the rate of evaporation of ammonia from aqueous solution and temperature* and used also by Va n't Hoff.f * i Chem. Soc. Trans. , ' 1898 , p. 524 . t ' Yorlesungen liber theoretische und physikalische Chemie , ' 1901 , vol. 1 , p. 224 . 366 Messrs ! B ; P. P^rman and E ; t H. Greaves . [ D$cX 24 , Putting a = 2*86 and ft \#177 ; i\gt ; 0*05^ the following numbers are obtained:_ : : : : ri i V:^Uv . : j Temperature . \#166 ; f log Jc ( found ) . . . . : i " y . . . . ... . ^ log Jc ( calculated ) . :\#166 ; \gt ; 2o i d i 40 60 . . 80 100 ; 'i . ! V : . p \#166 ; \#166 ; : \#166 ; ff \#166 ; '* 2-86 -1 3-95 : . ' 4 -91 5 74 : , ; M 6'8(5 2 -86 3*86 4-86 5 *86 6*86 ; V/ \#166 ; : ! T ' It occurred to us , that the decomposition might take place instantaneously at the surface of the glass ( or other substance ) , and that the rate measured ; was simply the rate of diffusion of the gas towards the surface . These results , however , show that the idea is untenable , for the rate would in that case vary as the'square root of the absolute temperature . Effect of Varying Extent of Surface.\#151 ; It has been shown that the rate depends on the extent of the surface , but it could not be shown that it is proportional to the surface . ' It must be remembered , however , that it is impossible to vary the extent of the surface and yet ensure its uniformity . With a very large surface a much better second order constant is obtained ; this may be due to the almost entire prevention of any effect of diffusion , but we are inclined to think that it is caused simply by the increased rapidity and shorter range of the reaction . Effect of Oxides.\#151 ; From the results given it is impossible to conclude that the peroxides used act as carriers of oxygen , for lead peroxide has but little effect , whereas manganese peroxide accelerates the reaction enormously . Moreover , copper oxide and magnesium oxide have a great effect in increasing the rate of decomposition . Neither can the effect be due entirely to the extent of the surface of the oxide . Manganese peroxide in lumps had more effect than magnesia in powder , but lead peroxide in powder had very little influence . With these oxides a good first order constant was obtained , i.e.3 the rate of decomposition was proportional to the pressure of the ozone , and it seems to us that the only conclusion to be drawn is that the real factor is the rate of absorption or condensation of ozone on the surface of the oxide . Effect of Metallic Surfaces.\#151 ; Of the metals tried , the effect in each case was small , and appeared to be a diminution of the rate of decomposition . This is entirely different from the effect of metals on the combination of hydrogen and oxygen as found by Bone and Wheeler ; * the latter was attributed , however , to the occlusion of hydrogen . . ; ] Effect of Certain Vapours.\#151 ; It has been shown that water vapour * Loc . cit. 1907 . ] The Decomposition 367 ' , accelerates the rate of decomposition , and that the effect is roughly proportional to the quantity of water present . Ozone is not known to have any action on water vapour , and it appears probable that this effect is due to the deposition of moisture on the surface of the glass , owing to which the ozone would be more rapidly condensed ... ..These , results , appear to be directly in opposition to those of Shenstone , who found that ozone was more stable in the presence of moisture ( this was , however , at a much lower temperature ) . The action of nitric oxide is much greater than that of water if a sufficiently high temperature is employed ( 100'\#151 ; 120 ' ) , and it would seem a reasonable explanation that the nitric oxide acts as a carrier of oxygen , being continually oxidised to the peroxide , and reduced again by the action of the ozone until the latter is entirely decomposed . Effect of Variation of the Oxygen Pressure.\#151 ; The rate of decomposition has been shown to be a linear function of the pressure of the oxygen ; this cannot be caused by the reversibility of the reaction , for it has been shown to be irreversible for all practical purposes . S. Jahn* made somewhat similar experiments , varying the pressure of the oxygen by dilution with air , and found that the rate varies approximately inversely as the oxygen pressure , a result confirmed by experiments of our own . From these results Jahn deduces that a secondary reaction takes place , 03 + 0 = 202 . We find that on varying the pressure without the intervention of another gas , the rate is not affected to the same extent , e.g. , a variation of the pressure from 600 mm. to 300 mm. caused the rate to vary from 00000685 to 0'000097 . We are inclined to think that Jahn 's conclusion is not justifiable , and that the variation of the oxygen pressure produces a difference in the gas-film on the surface and so alters the rate . It can only be said at present that the mechanism of the process is not understood . Reversibility of the Reaction.\#151 ; Attempts were made to synthesise ozone by passing a slow stream of oxygen through a combustion tube heated in a gas furnace . The tube was bent at the outlet and dipped in a solution of potassium iodide and starch . No ozone could be detected . The experiment was then repeated with the following substances in the tube respectively:\#151 ; pipe stems , iron nails , platinised asbestos , manganese peroxide : traces of ozone were formed with the last named , but none could be detected with the others The solution became brown , and on letting it stand a blue colour was developed . No ozone was found unless the temperature was high ( a low red heat ) , and the oxygen was passed through quickly . With a slow stream probably the ozone formed was decomposed before leaving the tube . * ' Zeit . anorg . Chem. , ' 1906 , vol. 48 , p. 260 . The Decomposition of Ozone hy Heat . In the following experiments oxygen was heated in a globe for many hours in order to discover whether any ozone could be formed in this way :\#151 ; Temperature . Time of heating , etc. Result . o 130 24 hours Nil 100 17 " \#187 ; 100 4 days with Pt black \#187 ; 100 4 days with Mn02 a 100 7 days Trace of 03 ( ? ) 100 14 " a a It is somewhat doubtful whether any ozone was detected , for a blank experiment with oxygen ( not heated ) gave nearly as much colour , is . , a brownish tint , developing into blue on standing some hours . Experiments were also made to ascertain whether ozone could be completely decomposed by heat ; the following are the results :\#151 ; Temperature . Time of heating . Result . o 100 18 hours 1'7 milligrammes 03 remained . 100 5 days 0-07 " " 100 14 " Trace " " ? In the last experiment there was no doubt that a trace of ozone remained after a fortnight 's heating ; it seems probable that it had come into equilibrium . We conclude from these experiments that the decomposition of ozone by heat is not completely irreversible at 100 ' , but that the reverse reaction is so small that it is difficult to detect . Summary.\#151 ; The rate of decomposition of ozone has been measured under various conditions with the following results:\#151 ; 1 . In a glass vessel the reaction is approximately of the second order . 2 . The relation between the rate of decomposition and temperature may be expressed by the formula log k = a -b it . 3 . The rate of decomposition is very largely influenced by the extent of the surface with which the ozone is in contact . 4 . The reaction is of the first order when the ozone is in contact with a porous substance ( clay-pipe stems ) or some oxides . 5 . Metallic surfaces have but little effect on the decomposition . 6 . Water vapour accelerates the decomposition , and the acceleration is proportional to the amount present . Effects of Self induction in an Iron Cylinder , etc. 369 7 . Nitric oxide greatly accelerates the decomposition . 8 . The rate of decomposition is a linear function of the oxygen pressure . A greater effect is produced by diluting with nitrogen than by simply reducing the pressure of the oxygen . 9 . At 100 ' the reaction appears to be very slightly reversible . 10 . Finally , the decomposition appears to take place mainly ( if not entirely ) at the surfaces with which the ozone is in contact , and pressure measurements give no indication of the number of molecules reacting . The expense incurred in this investigation has been defrayed by a grant from the Royal Society . Effects of Self induction in an Iron Cylinder when traversed by Alternating Currents* By Ernest Wilson , Professor of Electrical Engineering at Kings College , London . ( Communicated by Sir William Preece , F.R.S. Received January 23 , \#151 ; Read February 20 , 1908 . ) In a previous paperf the effects of self-induction in an iron cylinder were studied when a continuous current flowing through the cylinder in a direction parallel with its axis of figure was suddenly reversed and again maintained steady . In the experiments reported in the present paper the currents in the cylinder were made to alternate in the following manner . A continuous current dynamo , capable of giving currents up to 2000 amperes or more , was weakly excited and its brushes were short-circuited by the cylinder to be experimented upon in series with the shunt of a moving-coil ampere-meter . The brushes were moved round the commutator by aid of a worm and worm-wheel from the position of maximum to that of zero current . The field was then reversed and the brushes moved back to their initial position . By continuing these operations an alternating current was caused to flow through the cylinder , and its periodic time was controlled by the speed at which the brushes were moved . The worm axle was uniformly rotated by hand at a speed determined by the operator listening to a seconds clock . * In connection with this research , I wish to acknowledge a grant voted to me by the Council of the Royal Society out of the Government Grant Fund . t ' Roy . Soc. Proc. , ' A , vol. 78 , p. 22 , 1906 .

rspa_1908_0031

0950-1207

Effects of self-induction in an Iron cylinder when traversed by alternating currents.

369

378

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Ernest Wilson|Sir William Preece, F. R. S.

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10.1098/rspa.1908.0031

Electricity

Tables

Electricity

Effects of Self induction in an Iron Cylinder , etc. 7 . Nitric oxide greatly accelerates the decomposition . 8 . The rate of decomposition is a linear function of the oxygen pressure . A greater effect is produced by diluting with nitrogen than by simply reducing the pressure of the oxygen . 9 . At 100 ' the reaction appears to be very slightly reversible . 10 . Finally , the decomposition appears to take place mainly ( if not entirely ) at the surfaces with which the ozone is in contact , and pressure measurements give no indication of the number of molecules reacting . The expense incurred in this investigation has been defrayed by a grant from the Eoyal Society . Effects of Self induction in an Iron Cylinder when traversed by Alternating Currents* By Ernest Wilson , Professor of Electrical Engineering at King 's College , London . ( Communicated by Sir William Preece , F.R.S. Received January 23 , \#151 ; Read February 20 , 1908 . ) In a previous paperf the effects of self-induction in an iron cylinder were studied when a continuous current flowing through the cylinder in a direction parallel with its axis of figure was suddenly reversed and again maintained steady . In the experiments reported in the present paper the currents in the cylinder were made to alternate in the following manner . A continuous current dynamo , capable of giving currents up to 2000 amperes or more , was weakly excited and its brushes were short-circuited by the cylinder to be experimented upon in series with the shunt of a moving-coil ampere-meter . The brushes were moved round the commutator by aid of a worm and worm-wheel from the position of maximum to that of zero current . The field was then reversed and the brushes moved back to their initial position . By continuing these operations an alternating current was caused to flow through the cylinder , and its periodic time was controlled by the speed at which the brushes were moved . The worm axle was uniformly rotated by hand at a speed determined by the operator listening to a seconds clock . * In connection with this research , I wish to acknowledge a grant voted to me by the Council of the Royal Society out of the Government Grant Fund . t ' Roy . Soc. Proc. , ' A , vol. 78 , p. 22 , 1906 . \gt ; \#166 ; ' ; Prof. E. Wilson . Effects of [ Jan. 23 , Simultaneously readings were taken at known epochs on ( a ) each of ' three dead-beat galvanometers connected to exploring coils threaded through holes in the mass of the cylinder for the purpose of obtaining the E.M.F. 's at different depths due to the rate of change of the magnetic induction , and on ( b ) the moving-coil ampere-meter . The cylinder is of mild steel and has a diameter and length each equal to 10 inches ( 25-4 cm . ) . It is provided with holes drilled in a plane containing its axis of figure in such manner that exploring coils could be threaded to enclose certain portions of that plane . The coils are referred to respectively as 1 , 2 , 3 , and are each 2 inches wide in a direction parallel with the axis of figure and mid-way between the ends of the cylinder . Their depths in a radial direction are respectively 1 , 2 , and 2 inches and therefore their average radii are 0-5 , 2 , and 4 inches respectively . The current was passed into the cylinder by aid of the massive gunmetal castings used in the experiments previously described.* The deflections of the galvanometers have been reduced to volts per turn per square centimetre and are plotted in the ease of two of the experiments in figs. 1 and 2 . The curves are numbered 1 , 2 , 3 to correspond with the particular coils from which they were obtained . Time progresses from left to right of each figure . Magnetic Induction ( B ) as affected by Variation of Periodic Time and Total Current.\#151 ; Oh integrating the E.M.F. curves the magnetic induction ( B ) has been obtained . In Table 1 , where the results are summarised , the maximum average values of the magnetic induction are set forth . Looking at the values of the maximum induction for periodic time O'75 minute , and maximum , total currents of 1000 and 2000 amperes , we notice how great is the shielding , effect in the former ease as compared with the latter . This effect is intimately connected with the average permeability of the iron , which , as will be shown , is higher with a maximum total current of 1000 amperes . A comparison of the maximum values of the magnetic induction for periodic time 0'75 minute and maximum total current of 500 and 1000 amperes shows that in those two cases the innermost coil is equally affected . For a maximum total current of 1000 amperes the percentage diminution of maximum B for coil 1 as the periodic time is varied from 6 to 0-75 minute is much greater than in the case of maximum total currents of 500 and 2000 amperes . It should be noted that in Table I the total amperes are given approximately , their accurate values are given in Table II . Wave-form and Phase Displacement as affected by Variation of Periodic Time and Total Current.\#151 ; Figs. 1 and 2 are given as showing two extreme cases . In each diagram ci , c2 ) c3 are the currents interior to the radii 2 , and 4 inches * See ' Boy . Soc. Proc. , ' vol. 69 , p. 440 , fig. 1 . 1908 . ] \gt ; ' *j Self-induction in an Iron , etc. Sfifc respectively . In fig. 1 the periodic time is \#163 ; minutes and the total 'current ; 1000 amperes , and the shielding effect is comparatively small . In fig. 2 the periodic time is 0'75 minute and the total current 1000 amperes , and this ' ------------------------------ ' . " 1 ' ' ' " .1 a r is one case in which the centre of the cylinder is practically devoid of current . It may be generally remarked that , referring the phase displacement of the E.M.F. curves to the maximum of current for a given frequency , the maximum E.M.F. occurs earlier as the current is increased . For a given total current Prof. E. Wilson . Effects of [ Jan. 23 , the maximum of E.M.F. occurs later as the frequency is increased . The wave-forms of the E.M.F. 's are very much more peaked for the higher currents and the longer periodic times . The peaks of the E.M.F. curves cease to be so prominent at the high frequencies , but they are retained more with the large total currents than with the small ones . UJ \lt ; 0$ \#163 ; Energy dissipated by Electric Current in overcoming Resistance and by Magnetic Hysteresis.\#151 ; For the varying conditions of frequency and total current the C2R watts per centimetre length of the cylinder have been calculated and compared with the C2R watts which would be found , if a continuous current equal in value to the root-mean-square value of the 1908 . ] Self-induction in an Iron , etc. 373 Table I.\#151 ; Maximum Average Induction B and Average Permeability . Maximum total amperes.* Periodic time in 1 minutes . J Frequency 0-75 . 1/ 45 . 1 -5 . 1/ 90 . 3 . 1/ 180 . 6 . 1/ 360 . 2000 fCoil 1 3,460 4,440 4,720 8,960 B\lt ; Coil 2 6,050 12,000 12,640 12,040 [ Coil 3 12,600 14,080 14,160 13,560 B at surface of cylinder 14,240 14,380 14,380 14,340 Permeability 2,520 2,800 2,140 1,260 1500 fCoil 1 206 B^ Coil 2 4,460 LCoil 3 8,940 B at surface of cylinder 13,780 Permeability 3,050 . 1000 fCoil 1 1281 680 2,040 3,1301 Coil 2 2,150 U 6,200 8,200 9,240 L Coil 3 8,325 J 10,620 11,100 11,360 J B at surface of cylinder 12,550 12,480 12,150 12,270 Permeability 3,080 3,060 2,690 1,990 500 fCoil 1 128 215 294 576 B\lt ; Coil 2 880 2,070 3,240 4,736 LCoil 3 4,580 5,500 6,620 6,940 B at surface of cylinder 8,400 7,300 7,250 7,000 Permeability 2,010 2,260 2,310 2.130 * These are approximate values . For accurate values , see Table II . t Fig. 2 . t Fig. 1 . alternating current were allowed to traverse the cylinder : ( a ) on the assumption of constant current density ; ( b ) having regard to the variation of current density which was found actually to exist , owing to end effect . An attempt is made to compare the ratios obtained with the average permeability of the material under the conditions of test . The watts due to magnetic hysteresis have also been calculated , and a comparison made between them and the watts which would be found if the distribution of magnetic induction under continuous current were assumed to persist at the particular frequency . By a different application of the same principles , an attempt has been made to check the values of the total watts due to C2K and magnetic hysteresis found separately . Finally , the ratios of the watts due to C2B , and to magnetic hysteresis are given . The results are set forth in Table II . ( 1 ) The C2K watts have been calculated as follows . The E.M.F. curves previously integrated have been used to give the average value of the magnetic induction ( B ) over the three annuli at any instant of time . From the hysteresis loops for the material , obtained by the ballistic galvanometer , the corresponding values of H have been obtained . In finding the currents from Prof. E. Wilson . Effects of [ Jan. 23 , Table II . Frequency . . . Total current in amperes . C2R loss per cm . length of cylinder in watts . Average permeability . Watts lost by magnetic hysteresis per cm . length , in 10~5 . Total watts per cm . length , in icr5 . II .M | | B \#163 ; o .J 03 \#171 ; Max. value . R.M.S. value . Alternate current , in 10-5 . Continuous current , uniform distribution , in 10-5 . Ratio A/ B. Continuous current , actual distribution , in 10~5 . Ratio A/ C. A. B. C. D. 1/ 45 1860 1200 4700 3390 1*39 3790 1*24 2520 824 5520 5*74 ( 0 -0222 ) 1520 915 2970 1985 1*50 2220 1*34 3050 663 3630 4*48 1000* 598 1490 847 1 *76 947 1*57 3080 381 1870 3*90 500 299 325 212 1 -53 237 1*37 2010 169 494 1*92 1/ 90 2000 1270 4770 3830 1-25 4280 1*12 2800 540 5310 8*85 ( 0 -0111 ) 980 627 1230 930 1 *32 1040 1-18 3060 298 1530 4*12 430 269 238 171 1 *39 191 1 *24 2260 97 335 2*46 1/ 180 2000 1260 4680 3730 1*25 4160 1-12 2140 286 4960 16 *4 ( 0 -00556 ) 900 588 1030 819 1 *25 915 1*12 2690 175 1200 5*88 435 267 226 169 1*34 189 1 *20 2310 69 295 3-28 1/ 360 1950 1270 4290 3810 1*13 4250 1*01 1260 140 4430 30 *6 ( 0 -00278 ) 930f 591 987 831 1 *18 929 1*06 1990 94 1080 10 *5 420 269 212 172 1 *23 192 1*10 2130 36 248 5*89 * Fig. 2 . f Fig. 1 . these values of H , it is assumed that the average value of B in each annulus occurs at the average radius of the annulus . The error thus introduced is not very serious . The total interior currents thus found have been plotted for each instant of time in terms of the radius of the cylinder . From these curves the current over each of five annuli , each having 1 inch radial depth , has been estimated . Its squared value has been multiplied by the resistance of the annulus , and hence the total C2R watts at any instant of time have been found . The time-average of the total values has then been taken over a half period of the alternating current . Referring to Table II , it will be seen that at frequency 1/ 45 ( 0*0222 ) the ratio of the watts with alternating to those with continuous current rises to a maximum for a total current of 1000 amperes . In attempting to connect these results with the average permeability of the material , the latter has been found as follows.* * The time-average of dB/ dH . has been chosen in preference to the time-average of B/ H , because the latter takes no account of the previous history of the material , which is vital when the effects of magnetic hysteresis have to be considered . For example , when the iron is subjected to a periodic magnetising force of fixed direction relative to the iron , 1908 . ] Self-induction in an Iron Cylinder , etc. 375 At equal intervals of time the values of the magnetic induction ( B ) have been taken , and from the hysteresis loops the ratio dB/ dK has been found . The time average of dB/ dH per coil was then multiplied by the volume of the annulus , and the sum of the averages of the three annuli was divided by the total volume of the cylinder . It will be seen that at frequency 1/ 45 the maximum value of this average permeability also occurs with a total current of 1000 amperes . Unfortunately , the ratio of the watts with alternating to those with continuous current at the other frequencies in Table II is not sufficiently large to justify an accurate comparison . All through it is striking how small is the variation of the average permeability . Its value is greatly affected by variation of wave-form . For instance , in fig. 1 , where the change of magnetic induction B is rapidly made , the average permeability depends largely upon the maximum value of B. In fig. 2 the change of magnetic induction B gradually takes place over the half period , in which case the average permeability is more dependent upon the intermediate values of B. ( 2 ) The watts due to magnetic hysteresis have been calculated from the area of the hysteresis loops as follows . The maximum values of the magnetic induction ( B ) over each of the five annuli , corresponding to the maximum values of H obtained from the distribution curves of current have been found . The ergs per cycle per cubic centimetre given by the hysteresis loop corresponding to the maximum value of B have been multiplied by the frequency and the volume of the annulus and by 10-7 to reduce to watts . These values have then been added , and the sums are given in Table II . Beferring to the experiment at frequency 1/ 45 , in which the hysteresis watts are 824 , the watts which would be dissipated if the distribution under continuous current ( rendered non-uniform through end effect ) persisted at this frequency are 1170 , and if the distribution under continuous current of constant density obtained the watts would have been 1040 . This bears out the statement that the watts due to hysteresis for a given total current are diminished by the effect of internal self-induction , commonly referred to as " skin effect . " ( 3 ) Using the equation E = where E is the impressed potential Ctb difference , R is the ohmic resistance , x the current , and I the total magnetic field external to the annulus considered , it was thought possible to check the values above found by a different process . The value of dljdt was found the ratio B/ H becomes infinitely great when H = 0 ; whereas the magnetic induction ( B ) at that moment depends entirely upon the previously applied magnetising forces . This is taken account of in the differential dB/ dH . , as this is the slope of the curve at the point . 376 Prof. E. Wilson . Effects off [ Jan. 23 , between the surface of the cylinder and the radii 1 , 2 , 3 , and 4 inches respectively , as follows . From the distribution curves of current , and the hysteresis loops , the wave-forms of B were plotted for average radii 1^ , 2\#163 ; , 3^ and 4\ inches . These were then differentiated to find E.M.F. 's , which were multiplied by the area of the annulus considered , and the values for the respective annuli were added together ; this gave the value dljdt . The effect of the magnetic field in the surrounding air space was proved to be negligible . The watts taken by five annuli each \ inch deep and having average radii of 1 , 2 , 3 , 4 , and 4$ inches were found as follows . From the distribution curves the current over each annulus was obtained and thence C2R ; also the product of the E.M.F. { dljdt ) external to each annulus and the current ( a ? ) was found . The sum of these gave at any instant the total watts . The average over a period then followed . Dividing this average by the volume of the annulus the watts per cubic centimetre were obtained at its average radius . A distribution curve was then plotted giving the watts per cubic centimetre in terms of radius , and from this the average watts at radii J , 1\#163 ; , 2| , 3J , and 4\ inches were obtained . Multiplying these values respectively by the volume of the annulus and adding them together , the total watts were obtained . The hysteresis loss xdljdt could also be found separately in a similar manner . Three cases have been worked out , and the results are given in Table III , together with the corresponding figures from Table II . This latter method could not be expected to yield such accurate results so far as hysteresis is concerned , since it depends upon the product of an E.M.F. and current largely displaced in phase . Table III . Frequency . Total maximum current in amperes . Total watts taken from Table II . Total watts obtained by alternative method . 1/ 45 ( 0 -0222 ) 1860 5520 6110 1/ 360 ( 0 -00278 ) 1950 4430 4460 1/ 45 ( 0 -0222 ) 500 494 480 ( 4 ) Referring to the ratio of the C2R and hysteresis watts , it is interesting to note that for a given total current the ratio diminishes as the frequency increases , the increase in the hysteresis watts due to increased frequency much more than counterbalances the decrease , owing to the greater skin 1908 . ] Self-induction in an Iron Cylinder , etc. 377 effect . At frequency 1/ 45 ( 0*0222 ) and maximum total current of 1000 amperes the skin effect is , however , so great ( see Table I ) as to give a ratio 3*9 , not much less than that given by practically the same total current at half the frequency . Experiments at High Frequency.\#151 ; The cylinder was transferred to the secondary circuit of a transformer , and various currents up to 1000 amperes were passed through it at a frequency of about 11 periods per second . A dead-beat galvanometer was employed in conjunction with a commutator driven by spur gearing at a speed differing from that of the alternator by 1 part in 10,000 , for the purpose of giving the integrals of the curves of E.M.F. of the exploring coils 1 , 2 , 3 . Large E.M.F. s were , of course , obtained in the case of coil 3 , but none in the case of coils 2 and 1 . The sensibility of the galvanometer was such that a terminal voltage of 7 x 10-6 could be detected . Table IV summarises the results obtained . It must be borne in mind that , as in the foregoing experiments , the average magnetic induction B is assumed to be effective at the average radius of the coil . On this assumption the total current interior to the radius 4 inches is only from 3 to 5 per cent , of the total current in the cylinder . The actual skin effect is much greater than these figures indicate . Table IV . Frequency . Total j current in amperes . Maximum induction B at surface . Maximum of average induction B through Coil 3 . Current in amperes interior to radius 4 ins . ( maximum value ) . R.M.S. Maximum . 11 *66 987 1800 14,250 625 56 *4 10 0 640 1090 12,800 490 47 ' 2 10 *93 371 691 10,200 268 30 *3 Application of Results to other Sections.\#151 ; Comparing two cylinders of the same material whose diameters are as 1 : n , it was shown* that , provided the total currents are as 1 : n and the frequencies as n2 : 1 , the magnetic forces at similar radii will be the same . It follows also that the total watts due to C2B and magnetic hysteresis will be the same . Thus , for example , the watts given in Table II refer also to a wire 1 cm . long and 0*1 inch diameter , provided the respective frequencies are 222 , 111 , 55 , and 28 , for each of which the total amperes are 5 , 10 , and 20 . The curves in figs. 1 and 2 can also refer to a cylinder 0*1 inch diameter , provided the respective frequencies are 28 and 222 , and the total current is 10 amperes , having the VOL. lxxx.\#151 ; A. 378 Effects of Self-induction in an Iron Cylinder , etc. same wave-form . Cylinders having other diameters could be dealt with in the same way . [ Note added February 22 , 1908.\#151 ; Lord Rayleigh , * experimenting upon a hard Swedish iron wire 0*16 cm . diameter , found that the ratio of the resistance with alternating to that with continuous currents was about 1*2 when the frequency of the alternating currents was 1050 . On the above assumptions this would correspond with a frequency of 0*04 in the case of the cylinder 10 inches in diameter . Table II shows that at frequency 0*022 and 299 R.M.S. amperes the ratio of the resistances is 1*37 . Having regard to the fact that the specific resistances and the magnetic qualities of the* materials of the two cylinders may have been different , and to the probability that the current in Lord Rayleigh 's experiments was less than 1*9 amperes , which is the current corresponding to 299 amperes in the 10-inch cylinder ( thereby giving rise to a smaller average permeability ) , the difference in the ratio of resistances corresponding to given frequencies may be accounted for . ] In conclusion , I wish to thank Mr. Alexander Siemens for the loan of the dynamo used in these experiments . I also wish to acknowledge the help I have received from Mr. A. E. O'dell and Mr. G. F. O'dell . Mr. Robertson , Mr. Franks , and some of my senior students gave me valuable assistance in the experimental part of the work , for which I wish to express my thanks . * 4 Phil. Mag. , ' 1886 .

rspa_1908_0032

0950-1207

The effect of hydrogen on the discharge of negative electricity from hot platinum.

379

382

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Professor H. A. Wilson, F. R. S.

abstract

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10.1098/rspa.1908.0032

Thermodynamics

Tables

Thermodynamics

]\gt ; The Effect of of ectricity Hot By Professor H. A. ILSON , , Londoli . ( Received Jannary 23 , \mdash ; Read February 13 , 1908 . ) ( Abstract . ) The effect of hydrogen on the discharge of ative electricity from hot Dlatinum was examined by the writer in it was found to produce a large increase in the current . The uents were all done with nearly new platinum wires which had not been heated in for any reat length of time , because it was known that long-continued auses the wire to rate . The present paper contains an of a eries of experiments in which wires were heated for long periods in , so that any changes in the effect of the ] could be )bserved . It appears that continued in hydrogen Cers the Jharacter of the effects observed so that tlJe behaviour of an old wire may ) different from that of a new one . The gies a short abstl.act of each section of the paper:\mdash ; 1 . that x , where denotes the current per square centimetre of platinum at constant temperature , is the pressure of the hydrogen , and are quantities depending only on the temperature , and also bhat , where denotes the absolute temperature and A and lepend only on the pressure ; it is proved that : ( 1 ) , where and are consCants ; ( 2 ) ; and ( 3 ) . These tions are hown to with the observations . from ( 2 ) and ives A. It is lown that all the values of A and for new wires satisfy this relation , those for wires in air . The equation ( 3 ) is therefore modified to , where , equal to , is the value of A in air or when . Thi equation represents all the values of A. With ( 4 ) this giveS The equation may now be written If , then , so that the effect of hydrogen can be represented by supposing that it without altering A. 'Phil . Trans , vol. 202 , 1903 , p. ) . LXXX.\mdash ; A. Prof. H. A. Wilson . Effect of drogen on the [ Jan. 23 , If , then , so that the effect of hydrogen can be presented by supposing that it changes A without altering Q. These formulae are shown to be in reement with observations by rent observers over a very wide of temperature and pressure . Assuming that the effect of the is due to its presence in the surface layer of the platinum , the concIusion is drawn that the hydrogen in new wires is dissolved in the platinum . The agreement between the formula obtained and the vations shows that the equation which was assumed at start is correct . 2 . It is shown that the leak from a wire which has been heated in hydrogen at a pressure for some time is nearly independent of the pressure at constant temperature between and 200 mm. of mercury . The conclusion is drawn that the wire in a state of stable chemical combination , and some experiments are described which seem to support this view . 3 . The variation of the leak with the temperature , from a wire giving a leak independent of the pressure , is measured , and is found to be 135,000 and A to be . These values do not satisfy the relation which agrees with all the values of A and for new wires . On heating the wire in air , and then rain in hydrogen at a small pressure , it is found to give the same leak as a new wire in hydrogen , but the leak takes longer time than before to get to its final value after the pressure has been changed . The conclusion is drawn that heating in hydrogen at a pressure produces a permanent change in the state of the platinum , which is not removed by heating in air , and which causes the hydrogen to dissolve more slowly in the platinum , but does not affect the final value of the leak . The leak in . is about the same at high temperatures as with a new wire . 4 . It is shown that a wire which has been heated in hydrogen at a high , and then in air , on heating in hydrogen at 1600o C. gives the same leak as in air . But at lower temperatures the leak after a time rises to the usual value in hydrogen , and is then large at 160 C. also . The conclusion is drawn that the wire does not absorb hydrogen above 1600o C. If the temperature is raised when the leak has only partially recovered from its initial very small value , then it falls on raising the temperature and rises fain on lowering it . 5 . It is shown that the resistance of the wire is slightly increased when it absorbs hydrogen . A wire ivin a large leak independent of the pressure was heated for some hours in a good vacuum , and then on heating in air the esistance fell slightly . The conclusion is drawn that the wire still contained 1908 . ] Discha ' of Negatire Hot hydrogen . Reasons are ) eriven for . that the stable compound only exists in the face laycl of the platinnm . 6 . In this section it is shown that the recovel.y of the leak described in Section 4 can be accelerated by passing an ordinary through ths from the wire to a nei , , electrode . 7 . The tive leak in is the positive leak in oxygen , and it is that there is a close between them . The conclusion is drawn that the ative leak is by in the same way that the positive leak is produced by In the absence of hydrogen there is , , a small ative leak due to the platinum alone . 8 . In this section it is shown that if the true value of A in the is denoted ) , and if is supposed to be umaffected by the , then the true value of is iveu by the equatlon . It is shown that the variation of the ative leak from lime with the temperature , as measured by Dr. Horton , is not really inconsistent with the view that is proportional to the number of free electrons per cubic centimetre of lime . 9 . This section contains a theory of the variation of , with the It is assumed that there is an electrical double layer at the surface of platinum , and that the electric force in this layer is increased by the presence of electl'ons in it between the two layers . The increase due to this cause is shown to be greater at higher temperatures . It is where is is charge per unit area in the layers , and is distance between the layers . This gives It is found that a value for can be obtained which makes ) nearly constant . is explained by supposing that the hydrogen } in the platinum positively charged , and act by ) of the negative in the double layer without altering Adopting this value of as the true value , is foumd to ) cn which agrees with the thickness of the double layer on hydrogen in dilute sulphuric acid . The carried by the in 1 . of the platinum is found to be electrostatic unitc which shows that there are eight free electrons to each atonl of platinum . 382 Effect of Hydrogen on of Electricity . This agrees with the fact that platinum is an octovalent element . The values found for are the following:\mdash ; The value of adopted is , but this may be in error by a factor of 10 or more . C'onclusion . The view taken in this paper is that the effect of the on the leak is due to its presence in surface layer of the platinum . To explain this it is supposed that the hydrogen atoms in the layer are positively , so that they diminish the charge per unit area in the electrical double layer covering the surface of the platinum . The hydrogen appears to dissolve in the platinum at first , but at high pressures in time forms a stable combination with the platinum , having a very small dissociation pressure . Before this compound has been formed , the leak is proportional to a power of the pressure of the hydrogen .

rspa_1908_0033

0950-1207

Comparison of the Board of Trade ampere-standard balance with the Ayrton-Jones current-weigher; with an appendix on the electromotive forces of standard cells.

383

389

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

T. Mather, F. R. S.|F. E. Smith, A. R. C. S.

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10.1098/rspa.1908.0033

Electricity

Tables

Electricity

]\gt ; Comparison of the of -Standard the Ayrton-Joncs an pendix on the Electromotire Forces of Cells . By T. MATHEB , , Central Technical College , London , and F. E. IITH , , National Physical Laboratory , Received Iarch Read March When the Board of Trade ampere balance was set up and verified in 1894 , the platinum veight ( marked A ) used with the instrument was adjusted so that a current which deposited silver from a 15-per-cent . solution of silver nitrate at the rate of rammes per second produced , on reversal , a of force equal to the weight of A. At thab period such a current was believed to represent of a C.G.S. unit , with a fair degree of accuracy . last few years a new rent w at the Central Technical College , been constructed at the National Physical with a precision preyiously not obtained in any instrument for the absolute determination of current strength , and by means of it the electrochemical equivalent of silver has been determined to a very high of acculacy . We therefore considered it of lnterest to determine the difference between the units of current as measured by the two balttllces , and at the same time ascertain how nearly the ampere , measured by the Board of balance , deposits silver at the rate of ] milligrammes The comparison of the two ) alances was carlie out by of cells and resistances used as secondary standards of CUl'rent ; for , if a current be passed through a resistance , and the of adjusted until the potential difference between the ternlinals of the is equal to the } . of a standard cell , , when the cell coil firt1 , iven temperaturcs , a ) crfcctly drent must bc coil . If this current be ined in absolute ] of current such described paper previously mention " " A New Current Weigher and a Determination of the of the Normal ) ' by rofeRbor W. L. ton , , T. ; F. F. E. Smith , , Phil. , vol. ) , pp. " " The Silver ] , by . E. mith , , T. Islatber , T. M. Lowry , D. Phil. Trans , . We may here rema1k tl1at the official of accuracy plied to the } of current ( not to the instrument ) is one-tenth part of 1 per cent. Council , 1894 . Messrs. T. Mather and F. E. Smith . [ Mar. 10 , combination of cell and coil is standardised , and can be used subsequently as a secondary standard of current . Knowing the relations between E.M.F. and temperature for the cell , and between resistance and temperatme for the coil , the current required to produce equality of P.D. and E.M.F. at any given temperatures can be found . The combination of cell and resistance can , therefore , be used as a secondary standard of current , at temperatures other than those at which they were standardised . A set of cadmium cells set up at the National Physical Laboratory was connected in parallel and used as one cell in the measurements , a sixth cell in the same oil bath being employed in making the preliminary adjustments of current principal resistance coil used in the tests was a 1-ohm standard , marked L. 87 , which was employed in the determination of the E.M.F. of the Normal Weston Cadmium Cell . other coils , each ohm ( nominal ) , were also made use of in some of the comparisons . All three coils have potential terminals . The resistances were measured to a high of accuracy at the National Physical Laboratory ; their values in international ohms , and those of their current leads and copper blocks with mercury cups for connecting the coils in series , are given in Table I. Table alues of Resistances employed ( International Ohms at Coil No. L. 87 ( between potential terminals ) CulTent leads of L. half blocks ( mcrcury cups ) One current lead of No. half block ( mercury cups ) , Sum of the above coefficient C. ) of coil L. No. 2200 No. 2492 After standardising the combination of cells and resistance by means of the Ayrton-Jones current weigher at Bushy , they were taken by hand to the Board of Trade Laboratory at Whitehall , and set up in a circuit the Board of Trade balance . Previous to making any measurements the insulation of the apparatus from earth , and that between the stranded wires connecting the loalances and resistances , were tested , and found to be qnite satisfactory . 'Phil . Trans , vol. 207 , p. 520 . 1908 . ] Board of Ampere-Standard , etc. Two methods of comparison were made use of . In one of these , represented by fig. 1 , a current about amperes ) sufficient a P.I ) . between the end indicates the Board of Trade , A the auxiliary Kelvin balance used ustable carbon ebistnnces , I iron wire ballast resistances , a of 64 accumulators , a standard 1-ohm resistance coil L. 87 , a set of 5 cadmium cells in parallel , an auxiliary cell , for connecting either or in circuit , a and a key , and are the potential terminals of of the -ohnl coil , L. , equal to the E.M.F. of the cadmium cell , passed through the circuit . Additional weights , calculated approximately from the known value of this current , and the mass of the platinum-iridium weight , used with the balance , were added to the standard eights , so that the suspended coil would come near the sighted position when the correct current was flowing . The current was then adjusted so as to exact balance on the galvanometer , fig. 1 , and the rest-point of the balance dete1mined by the vibration method . The current through fixed coils of the balance was then reversed , ljusted , and the rest-point of the balance determined . From the two rest-points thus found , the known sensibility of the instrument , the mass required to balance the of force on reversal was calculated . square root of th . ratio the value of the current in Board of Trade amperes . In the other method of } ) al'ison the Board of ance was used in the normal way , without any additional , the current adjusted to 1 Board of Trade ampere approximately , as in ordinary velification tests . This currexlb passed the resistances arl.anged as shown in resistance the * The value used in ) the combination of cells and The masses of weights were determined to a ordel of accuracy by the Office of Standard Weights and Measures , tender ou . best Messrs. T. Mather and F. E. Smith . [ Mar. 10 , terminals of , was adjusted until the P.D. between the points and equalled the E.M.F. of the standard cell S. When this condition exists , the FIG. 2 . The letters have the same meaning as in . In addition , and are the outer potential of two coils , and , of ohm each , and indicates a box of manganin resistance coils shunting current hrough the circuit , in terms of the Ayrton-Jones balance , is given by the formula , which , since , very nearly , may be written , where is the known E.M.F. of the cell , and the resistance of the three coils and the contact blocks and current leads included between the points and J. To obtain checks on the constancy of the cells and coils the combination was standardised by the Ayrton-Jones balance at Bushy on each of the three , January 6 , , and 8 , on which comparisons were made at Whitehall ; this procedure , in effect , made it unnecessary to know either . or resistance in absolute measure , as the ratio only is required , and this was determined directly by the current weigher . The results of the tests are iven in Table II . From this it will be seen that the currents , as measul.ed by the Board of Trade balance , are approximately per cent. than their values in terms of the Ayrton-Jones balance . The Board of Trade is about 1/ 30 ccnt . smaller of the of as rton-Jo/ xes weigher . A difference of this order of nitude was anticipated authors , for the new determination of the electrochemical equivalent of silver , previously refe1red t gives 1yrammes of silver per ' Phil. Trans , vol. 207 , 1908 . ] of Trade , etc. coulomb , whereas the Board of Trade ampere was intended to be such as would deposit milligrammes per second . Table II . Average of 1 3 , 4 , 5 , and The percentage ence between the two numbers and is , and this differs from per . by per cent. , or less than 1 part in 10,000 . We , conchlde equal to ( \ldquo ; defimd by silver part in 10,000 , i.e. , ? within 1/ 100 )per cmt . This result is satisfactory , that the meant was set } ) years . It credit on ] responsible for the adjustment , and shows that the care and skill which or was carried out was of a very order . very close reenlent also supplies evidence in favour of the constancy of instruments of this and confirms the decision arrived at the onnnitcee of the principle of the balance the best o1le It als support to the opinions of Professor the authors , an extensive experience with the Ayrtou-Jones ) constructed are of currcnt . It is interesting to notice according to these } ) .iments the of Trade ampere osit silver at the late of ) , . , tmInes per second , a value which } is nearly identical the This Committee consisted of . Courtenay Boyle , J. . Hopwood , Major P. Cardew , representing the Board of Trade ; Mr. reece and Mr , Graves , sentiug the Postal Telegrnph Department ; Lord Kclvin Lord , the Society ; Professor Carey Foster and Mr. B. T. azebrook , the BIitish Association ; and Dr. J. Hopkinson and Professor Ayl.ton , the Institution of EIectrical eers . Messrs. T. Mather and F. E. Smith . number , by Lord Rayleigh and Mrs. Sidgwick in their classical : memoir of 1884 . We desire to express our hearty thanks to Mr. A. P. Trotter , Electrical Adviser to the Board of Trade , for permitting us to make the comparisons , and also for the valuable help he and . Bennie rendered during the experiments . We are also indebted to Professor Ayrton and Dr. Glazebrook for the kind interest they have taken in the work , and the facilities afforded for carrying it out . , received March 20 , 1908 . In the above communication we have sbated the relation between the Board of Trade ampere and the ampere as determined by the Ayrton-Jones balance . This relation , together with the results given in a previous paper on " " A New CuIrent Weigher , Professor Ayrton and ourselves , enable us to deduce the E.M.F. 's of the nor1nal Weston and Clark cells in terms of the Board of Trade ampere and the Board of Trade ohm . In the last-mentioned paper we have shown that the E.M.F. of the normal cadmium cell , in terms of the ampere as given by the -Jones balance and the international ohm as realised at the Natiollal Physical Laboratory , is at C. , and for the normal Clark cell the value is at C. Now , a comparison of resistances made by one of us ( F. in 1903 , gave the following ] ation : 1 N.P.L. international ohm Board of Trade ohms ; and , as above , 1 Ayrton-Jones Board of Trade amperes . The ratio between the values of is therefore 1 : i.e. , 1 : ; hence we find that the E.M.F. of the normal Weston cell is Board of Trade Board of Trade volts at C. 'Phil . Trans , vol. 207 , p. Ibid. , ) ; also B.A. Report , , pp. 43\mdash ; 4 . The Board of Trade volt being defined as the P.D. between the terminals of a resistance of 1 Board of Trade ohm when a current of 1 Board of Trade ampere is passing through it . , @t11Xes } ! ? ? , : ( -00t eJqo Solo aquIlII a 81t1l\ldquo ; S ] S1 CoilIIonpag 688 jjlj ) vpuvIS y

rspa_1908_0034

0950-1207

The refractive index and dispersion of light in argon and helium.

390

405

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. Burton, B. A., B. Sc.|Professor J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0034

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0034

10.1098/rspa.1908.0034

Thermodynamics

Optics

Thermodynamics

]\gt ; The Index Dispersion of Light in Argon Helium . By W. , B.Sc. , Research Student , formerly Scholar , of Emmanuel College , Cambridge . ( Communicated by Professor J. J. Thomson , F.R.S. Received January 14 , \mdash ; Read January 30 , 1908 . ) The initial object of this research was to find the dispersion of light in the monatomic gases argon and helium , but as it was to know absolute value of the refractive index with considerable accuracy , determina . tions of the active index have also been made . Their relative powers ( air ) have been found by Rayleigh , amsay and Travers , I . coloured interference eres , but no determinations of the absolut refractive index for light of given wave-length have hitherto been made . The interferometer method due to Jamin was used . A horizontal beam : parallel white light was incident on the first Jamin plate . The two beams traversed two brass tubes of equal length closed by equal thickness of worked plane glass . Each brass tube had a small side tube attache which led to apparatus for the density in the tube and measuring . After reflection at the second Jamin plate , the recombined bean was focussed on the slit of a r$pectrometer , the spectrum obtained with a plane diffraction grating was examined through the telescope of spectrometer and was seen clossed by bands of maximum and minimum intensity . At the same time , by means of a small reflecting prism , a portio1 of the slit was illuminated the light from a Plucker tube hydrogen , helium , and mercury vapour . Thus one observed the interference bands and certain standard lines of known wave-length with any one of which the cross wire of the telescope could be brought coincidence . \mdash ; The active index of a at C. and 760 mm of leno t is iven b . C. is the temperature , is the coefficient of expansion , is nulilber of bands which move oyer the standard line of as th ' cm . , and is the length of path in the tube . The values of and are determined once for all , and those of ltayleigh , 'Boy . Soc. Proc vol. 59 , p. 203 . Ramsay and Travers , ' Roy . Soc. , vol. 64 , , and vol. 6 p. 331 . Index of 39 ] . bserved in each experiment described below . gas laws are assumed hold for argon and helium over the limited of pressure and emperature used , is taken as equal to Let and be the wave-lengths of two standard lines , and the corresponding refractive indices under pressure the corresponding refractive indices under pressure the diminution in number of fringes between the standard lines when the pressure changes from to a less pressure If be the nunaber of hands , then the number of bands rossing , so that the difference of path introduced is nd lso , from Gladstone and Dale 's law , Substituting for and , we } , from Cauchy 's , ve obtain Equating these values , we get The quantities to be determined are and The two former are known , and the latter are observed as described below . If the absolute value of the refractive index be known for wavelength , then by for and , we determine in Cauchy 's equation . in . The straight filament of a Nernst lamp was used as a source of . The lamp was mounted in a collimator tube so that the filament was vertical and at the focus of the collimating lens . The portion of the filament nsed was limited by a small circular of about 2 mm. diameter placed close to it . The tube was supported on an adjustable stand , so that one could thus a parallel horizontal beam of white light . The brass tube in which the Nernst lamp was perforated in the neighbourhood of the filament with a ring of holes about 1 cm . in diameter , so that the collimator tube should not get too hot : and radiation from it was prevented from reaching the optical tubes by screens of tin . 1908 . ] Dispersion of Light in and Heliu Intcrferometer.\mdash ; The dimensions of the Jamin plates were the reflecting surfaces being 6 cm . After silvering the back reflecting surface of each plate , each was placed on ( an adjustable screw stand at a convenient distance apart , so that two horizontal parallel beams of white passed between them . The brass tubes to contain the gases were mounted in shallow on an adjustable wooden support , and so placed that one of the reflected beams passed each tube . The tubes were wrapped in cotton , and a hermometer reading to tenths of a lay between them . The tubes Nere 1 cm . long and about cm . internal diameter . They were closed each end by worked pieces of plane glass , 1 cm . thick , attache by means cement . These glass ends were held in place by perforated screw caps cemented in position , so that the tubes were capable of a coniderable internal pressul.e . Into each tube a smaller side tube was screwed soldered , for attachment to the apparatus for altering the pressure . The ubes and plane lass ends were obtained from Messrs. Adam Hilger and Co. recombined beam was focussed on the slit of a spectrometer by means of lens of short focal length . The stancis supporting the above , and the source light , were all on a heavy slate slab built upon brick supports on the round floor of the laboratory . The apparatus was thus free from vibration md consequent displacement of ) ' The \mdash ; The image of the filament produced by the -focus lens on the slit of the spectrometer covers only about 1 mm. of , he central portion of the length of the slit , so that the spectrum observed , asing a plane grating in the usual way , is narrow in a vertical direction and is crossed by bands . By adjusting one of the Jamiu plates bhese bands can be obtained vertical and at a convenient distance apart . This adjustment is most conveniently made in the first place with a sodium flame source . By width of the slit , the minima can be made more less black , there is a cross wire in the eye-piece of the telescope which can be brought into coincidence with the middle of any one of these bands . Standard liines in Spectrum . These vere obtained from a small Plucker tube containing hydrogen , helium , and mercury } ) . By the use of a small reflecting prism a portion of the slit was illuminated by the from the narrow part of the Plucker tube , when certain well-defined lines of known wave-length could be observed . The lines used were five in nber , fairly distributed across the visible spectrum . That there was no measurable error introduced by this means of illumination was shown by , at the same time another similar tube placed directly in front of the slit , when the Mr. W. Burton . Refractire Index [ Jan. 14 , lines seen were continuous . The standard lines used were the hydrogen red ( cm helium yellow cm mercury green ( cm helium green cm and hydrogen blue cm In determining the absolute refractive index , the sodium line was used , the slit being illuminated directly by a sodium flame , whilst the cross wire was fixed in coincidence with the line . Pressure \mdash ; With the tubes used , a change of pressure of 1 atmosphere may cause the transit of about 500 bands in the case of argon , and of about 60 bands in the case of helium . Hence if one wishes to get 300 bands by in the latter case there must be a pressure range of 5 atmospheres , whilst in the former case a range of of an atmosphere will suffice . It was necessary therefore to adopt different methods for altering the pressure in the two tubes . Argon.\mdash ; The apparatus used in the case of argon was essentially the same as that adopted by Rayleigh , comparing refractivities . It is shown diagrammatically in fig. 2 , and the method of and the FIG. 2 . FIG. 3 . pressure is obvious . The reservoir is of about 500 . capacity , and the manometer limbs of 5 mm. diameter . The reservoir is joined to the optical tubes by compo tubing of 4 mm. bore . This tubing is soldered to the side * Rayleigh , ' Roy . Soc. Proc vol. 59 , p. 203 . 1908 . ] Dispersion of Light in Argon Helium . bube of the optical tube , and fastened by sealing wax to the glass tubing from the reservoir . Except for the gauge tubin . and the end into which the compo tubing is sealed , all the lass tubing is of capillary bore . , of course , is used to the maximum pressure change from a given olume ( of gas . The reservoir and optical tube could be xhausted from the side tube , and this side tube also the could be ntroduced . After the gas is put in , the side tube is sealed off at a onstricted part . The pressure was read on a cardboard millimetre scale laced behind the manometer tubes . This scale was lued on to the wooden upport and was afterwards tested against a standard brass scale . Over the ange of pressure that was to be used , the scale readings were accurate to vell within 1/ 10 mm. were taken on the scale ) eye to 1/ 10 mm. bfter a rise in both limbs of the manometer had been caused by he pressure tubing below the gauge . Three at least were aken , and the mean value used . Helium.\mdash ; The method of changing and measuring the pressule will be from an inspection of fig. 3 . The longer reservoir , about 105 cm . long and 1 sq . cm . cross section , is connected above with the pressure and indicator rauges , and through compo tubing with the optical tube . Below it is onnected t a steel tap with a shorter cylindrical reservoir about 55 cm . ong and . cm . in cross section . As much mercury is introduced as will fill the longer reseryoir , and about 10 cm . in of the shorter eservoir . This leaves about 660 . in the longer reservoir to be occupied the at atmospheric pressure . The cylindrical reservoirs were made rom ordinary iron steam piping , and the smaller tubing with which nercury would come in contact was of steel ; all connections were made screw-in joints and sCaling wax , the latter bein melted into the hot 'hread before screwing the tubes into position . Above , where the mercury lid not extend , brass -pieces and tubing were used , and the connections were made by screw-in joints and solder . The glass for gauges of capillary bore , about 2 mm. diameter , and fastened in position with ealing wax . The internal diameter of the brass or steel tubing into which he glass tubes were fitted was widened for the last 2 or inches , so that 'he glass tube could just fit in , and so that the end could press up against 'he ledge formed by the difference in internal diameter . pressure was produced by forcing mercury from the shorter reservoir into the longer one . This was done by pumping air into the former . To do bhe valve from a motor tyre was soldered on the top of the shorter reservoir , and a foot pump used for motor tyres enabled a pressure up to 10 atmospheres to be obtained if necessary . The steel tap was then closed VOL. LXXX . 396 Mr. W. Burton . Refractive Index [ Jan. 14 and the valve opened . By turning the steel tap now , and slowly reducin the pressure , it was quite easy to count the bands as they moved as as desired over the cross wire . Whilst taking observations for the refractiv index , one limb of the manometer gauge was open . The pressure rang then measured was about 1300 mm. Readings were taken by eye on millimetre cardboard scale placed behind the manometer . It wa endeavoured to read to 1/ 10 mm. , but as the tubing was of capillary bor and the considerable , this was not always possible , especially at lower part of the scale . This degree of accuracy is , however , not necessar ! for there was only a transit of 100 bands , and if these were read to twentieth of the distance between two bands , the error may be 1 in and , therefore , the pressure need only be taken to 12 mm. to obtai a corresponding accuracy . When experiments for the dispersio were made over a wide pressure range , the open limb of the manometer sealed . The gas laws were assumed to hold for helium , and the pressu1 change was not measured , the assumption being that for a range of pressu1 from 1 to 6 atmospheres the same laws held as from 1 to 3 atmosphere Before any into the apparatus , air was pumped in ti the pressure was about 10 atmospheres , and the whole was placed water , when no leaks could be discoyered . , after putting mercul into the reservoirs and manometer , it was pumped up , and readings of th pressure taken on successive days . By this method any leaks coul usually be detected , but very snlall leaks might be obscured by the due to temperature . The sealing wax joints were satisfactory , and leaks were observed from them . On one occasion a leak was found from solder joint , and on another from the compo tubing which led to the tube . Refractive Index and of Argon.\mdash ; The gas was prepared by Wm. Ramsay and obtained from Messrs. Tyrer and Co. It was introduce directly into the apparatus , after the latter had stood exhausted overnig } with a phosphorus pentoxide drying bulb and a small Plucker tube the latter showing that there had been no leak . The reservoir being seale off , the refractive index and dispersion were determined as below . A set of readings taken is given in each case , and later the results of all th other readings made are tabulated and the mean is taken . Refractive Index.\mdash ; Pressures were read to 1/ 10 mm. after causing a ris in both limbs of the manometer , the mean of three such readings at leas being taken . The number of hands crossing the standard line was read one-twentieth of the distance between two bands when possible . As pressure range used was about 450 mm. , and the number of bands abou smouem J ssqn$ am1Ji 'oe I ? JOJ xapu ) SI eJadmaiL aqn$ ' ' ' ' ' ' aJnssaJd StItOUtm J ssqnr amIJ : san ; } } \mdash ; : xadxa j nssaJd 5sqns P UILURf aq9 50 SI SJnoo 50 oUBJ ssod SR SB ssod JOU SI ? ( suo i ) ) JO sy aua } ) Sl ? At I xapur SB UITt UIBS pu St ? At S0 aq$ 50 uo ; I O$ SUOI ) 50 oauuoo o OS A OJ UIomJaqB ; pun Al dmoo uasq Jadmat 9 OT paJSB [ aSJnOO a@u[0 sseo ou } SI SJUa ? JOJJS [ 8061 Mr. W. Burton . Refractive Index and [ Jan. 14 , Pressure . Initial . Final . Difference . Number of bands crossing red and direction to left . Number of , Bands between Standard Lines and red . Finally green . blue . Time , 4.30 . femperature of tubes , C. Temperature of manometer , C. This gives for the red line at and 760 mm. ; also for the diminu tion in the number of fringes between the red and the standard lines above , ) bands cross the red , we get whence Results . Refractive Index of Are at and 760 mm. for line . 1908 . ] Dispersion of Light in Argon Helium . Befractive Index of ArgoIl at and 760 mm. for red . Date . . Dispersion in Argon , Date . He yellow . Hg green . He green . bluc . Mean To find we reduce as below , where refers to the red line cm to the other standard lines . Mean Mr. W. Burton . Refractive Index and [ Jan. 14 , Taking , and for line , cm . , we get ) ; therefore . \mdash ; This was prepared from thorianite . The thorianite was placed in one half of a porcelain tube , the other half containing copper oxide . The tube was attached to a mercury pump , and through a tube containing solid caustic potash to a gas collector full of boiled caustic potash solution There was also a mercury gauge to indicate the pressure in the apparatus After exhausting and shutting off the pump , the porcelain tube heated in a combustion furnace until the pressure indicated by manometer was just above atmospheric pressure . Connection with collecting reservoir was then made , and the gas slowly accumulated in it In this manner about llitre of helium was collected . The thorianite heated at atmospheric pressure , the helium comes off slowly , but present should , under these conditions , be removed by the red hot copper oxide . The gas was introduced about 200 . at a time into exhausted reservoir attached to the optical tube . Before entering reservoir , the gas was passed through a drying tube of calcium chloride a tube of charcoal surrounded by liquid air , each portion of the gas kept in contact with the charcoal for half an hour before being passed on the reservoir . A Plucker tube attached to the mercury pump , and arrangec before the slit of the spectrometer , enabled one to test the gas from time to time . No trace of foreign gases could be observed . Afte ] sufficient gas had been introduced to give ) required pressure range , reservoir containing it was sealed off , and the experimental results givel ] below were obtained . Index.\mdash ; The pressure range being 1300 mm. , it is not necessary , as stated before , to read to more than mm. to get an accuracy ol 1 in 2000 , though readings were attempted to 1/ 10 mm. The number of crossing the standard line used was about 100 , so that to get the same degree of accuracy it is necessary to read to one-twentieth of the distance between two bands . As it was possible in the case of helium always to start and end with the cross wire coincident with a standard line and with the middle of a black band , I consider this accuracy was obtainable . It may be remarked 1908 . ] Dispersion of Light Helium . here that with ases of small refractive like helium the accuracy of the value for the refractive index depends largely on the accuracy with which the number of bands that cross the standard line be estinlated ; for with the same pressure in helium only ohth the number bands will cross the standard line as in the cRse of air or rrgon . It will be observed belo that the value of the refi a index increase from day to day , hilsC the values well on any single Jay . This slight increase was , I think , due to a small air leak . If , in the ourse of the three days over which the experiments made , an air leak of 1 in had occurred , the variation observed would be accounted . The ; am increase is observed in the value for the red line , and the saule agreenent on any one day . That the inclease was less from Tuesday to ] fternoon is accounted for by the fact that the ooas was put in I the leyel of the in the leservoir so that after sealing off the tap connecting the reservoirs the gas should be un ressure shtly greater than attlospheric . The barometer rose on Tuesday light and the temperature fell , so that the fall in pressure on Wednesday possibly have been due to these changes ; that this was } ' the case is shown by the results obtained on Wednesday afternoon . The gas , however , left on Wednesday afternoon mder slightly less than atmospheric pressure , and subsequent taken night showed on reduction a decided but small increase in the refractive ndex . on Thursday an increase observable . The alues , herefore obtained on Tuesday , soon after the gas was put in , and on Wedlesday afternoon , are probably most correct . It will be seen that the extreme ralues for the refractive index obtained the three days do not differ more than 1 in , so that the for the dispersion not neasurably altered by the change in the refractive index . As in the case of rgon , measurements of the refractive index for the line and the red were made , and a summary of the is oive below . Dispersion.\mdash ; In some of the experiments the opeu ) of the was sealed off , and the pressure rranged so that about bands rossed the red line . As in the case of , the bands were estimated to one-twentieth when possible , and the used when the bands as far apart as possible over this pressure range . There is no great in having a larger number of than . the standard line , for the bands get so close ether in the blue and green that it is difficult to measure them accurately , and is ained in accuracy in the measul'ement of is lost in the measurement of Refractive Index at . for \mdash ; The ations were Mr. W. Burton . Refractive Index and [ Jan. 14 , taken and reduced in a similar manner to those of argon , except that the scale reading of the manometer used was the result of one observation only and not the mean of several . Refractive Index of Helium at and 760 mm. for line . As explained above , the value most probably correct is , the mean of the first three observations . Befractive Index of Helium at and 760 mm. for red . Dispersion in Helium , Where the number of bands crossing the red line was greater than 100 , the open limb of the manometer was sealed off and the pressure was not read . 1908 . ] Dispersion of Lighi in Argon Hetium . To find b.\mdash ; Reducing these values as for referring to the red line cm we Mean Taking , and substituting for line , cm . , we get ; therefore Mr. W. Burton . Index [ Jan. 14 , Discussion of Argon.\mdash ; The value obtained for the refractive index for line is Ramsay and give the refractive power ( air ) as for the hGest part of the spectrum . If air be taken for the mean line ( Kayser and ) , this makes to be . Ramsay and Trayers used a pressure range of about 500 mm. , corresponding to a transit of between 30 and 40 bands . The pressure used above is about the same , but corresponds to a transit of nearly 300 bands . The results agree to 1 in 300 , and closer agreement can hardly be expected , for if the refractive index of air for the brightest part of the spectrum be taken as , the results are practically identical . The dispersion of is htly less than that of air , if the coefficient for air be as found by Mascart . Hetium.\mdash ; The value of the refractive index for the line is Ramsay and Travers give the refractive power ( air ) as , and if air be taken as , this gives a value for helium of which is considerably larger than that obtained above . Assuming that Balnsay and Travers used the same apparatus as for argon , the same pressure range would correspond to a transit of between 4 and 5 bands only in the case of helium . Hence the accuracy of the value of the refractive power will depend largely on the accuracy with which , after a change of pressure , the middle of the movable band can be brought back into continuation with the middle of the fixed band used as a fiducial line . amsay and Travers considered that they could estimate to 1/ 25 of a band , so that the error of the may be 1 in 100 . The accuracy of their pressure measurements was increased by comparing the refractive power of helium with that of hydrogen , and then that of the latter with air . By this means the bands were kept in position in the field of view over a wider range of pressure than was possible when helium was compared directly with air . The diffel'ence in the value obtained by Ramsay and Travers and that obtained above may perhaps be attributed to the fact that the pressure changes in the experiments of the former compensate for the transit of so small a number of bands , though a diff'erence of 3 per cent. in the refractive power is more than one might expect . The dispersion is , as will be seen , much smaller than that of any other boas so far examined , the coefficient being almost exactly half that found by Mascart in the case of hydrogen . * Ramsay and Travers , ' Roy . Soc. Proc , p. 331 . Kayser and Rung , 'Abh . . Berl . Akad . ' ( 1893 ) . Mascart , ' Ann. de l'Ecole Normale ' ( 1877 ) . 1908 . ] Dispersion of in and Helium . The results for argon and helium are tabulated below , and , for comparison , Mascart 's values for hydrogen are also given . Refractive Index , reduced to C. and 760 mm. pressure for line . Argon , Helium Hydrogen scart ) Dispersion : equation , or ? A. B. Argou Helium 000003478 ( Mascart)f It may be noted that the values of for these substances are approximately in the ratio 3 : 1 : 2 . I wish to thank Professor J. J. Thomson for suggesting this work to me and for the interest he has taken in it . My thanks are also due to Mr. C. T. R. Wilson , to whom I am much indebted for advice in all that pertains to the optical part of this work .

rspa_1908_0035

0950-1207

On the refractive indices of gaseous nitric oxide, sulphur dioxide, and sulphur trioxide.

406

410

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

C. Cuthbertson|E. Parr Metcalfe, B.Sc.|Professor F. T. Trouton, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1908.0035

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rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0035

10.1098/rspa.1908.0035

Thermodynamics

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