PYROMETER.

Instruments for ascertaining the effects of a given change of temperature on the dimensions of solids are named pyrometers, from πυs, fire, and ∕zsrg=ω, 1 measure. The same name is also given to such instruments as are employed for the converse purpose of inferring from some of the various effects of heat, temperatures higher than those to which ordinary thermometers are applicable. Both classes of these instruments have been constructed in a variety of forms; but, unless where the temperature^was to be high, the most of them formerly acted on the principle of rendering the minute expansions sensible or appreciable by means of machinery. Accordingly, such an instrument generally consisted of an apparatus for producing the requisite change of temperature, coupled with machinery so contrived, that when to one part of it an imperceptibly small motion is given by the expansion of the substance under trial, a very sensible motion is thereby produced in another part. However, in almost no case can the machinery for increasing the sensibility be with safety or propriety exposed to any high temperature; and frequently the heat of a furnace is now inferred from or denoted by the fusing point of the particular metal, alloy, or other substance which it is just able to melt, such fusing points being supposed to be previously known. But the methods as yet employed to determine high temperatures, however useful some of them maybe for recording particular intensities of heat, and showing when the intensity in one case is equal to that in another, are insufficient to indicate their absolute values, or in what ratio unequal intensities differ among themselves. Nay, even their values in terms of the common scales of temperature are as yet but very imperfectly known in the higher part of the range.

In most of the earlier pyrometers the substance under trial was heated by the immediate contact of the flames of lamps; a method which not only produced an entirely unknown temperature, but probably gave to different bodies, or even to different parts of the same body, very different temperatures. This was greatly improved upon by applying the lamps to a metallic trough or boiler, containing some liquid, in which the bar under trial and a thermometer were immersed. Sometimes an inner case or trough has been used to keep the specimen dry; and when only a very moderate heat is required, steam has also been used to heat the specimen. This, though generally supposed to be a recent application of steam, had, according to Mr Nicholson (Journal for February 1805), been used by J. II. de Magellan in 1784.

To obtain an appreciable indication of the expansions of bodies, Muschenbroeck, to whom we owe the first instrument of this sort, as well as the name pyrometer, made the expansion of a rod of the substance under trial move a toothed rack, turning a pinion fixed on the axis of a wheel, which again turned a second pinion on the axis of the index, and the latter revolved over a graduated dial. Some have added more wheels and pinions, or have used a system of levers, or one consisting partly of levers and partly of wheels and pinions; and did the accuracy keep pace with the sensibility, such instruments might be correct enough. Other contrivances for increasing the sensibility are very numerous, but they are generally so readily referrible to similar principles as to render particular descriptions of them unnecessary, more especially since none of them is free from the objections about to be stated. Smeaton employed one lever, and observed how many turns and parts of a turn of a fine screw, whose end was just in contact with a piece touching the lever, would make it be again barely in contact with that piece, after the bar under trial, and acting near the fulcrum of the lever, had undergone the requisite heating. Lavoisier and Laplace made the expansion of the bar under trial act upon one lever, which again acted on a telescope hung as a second lever. This telèscope being directed to a large graduated scale placed at a known distance, the slightest deflection which the expansion of the bar under trial occasioned in the direction of the telescope was thus rendered very conspicuous. Had the accuracy of this mode of operating, therefore, been as great as the sensibility thereof, it would certainly have given the expansions to a great degree of exactness.

But the preceding kinds of pyrometers, however useful for exhibiting in a general way the expansions of bodies, or for illustrating the subject in a public lecture, are by no means entitled to much confidence; for, in using wheels and pinions, as well as levers, or any of these coupled with other machinery, there is always considerable uncertainty in the result, owing to the loose connection of the several parts, and their sometimes bending under the strain, as also to the friction and obliquity of action. Nay, an error of some consequence may even arise from the bar itself under trial being compressed by its giving motion to the machinery, more especially at the time when it is softened by heat; and those parts of the mechanism which touch the ends of the heated bar, and that in particular which is moved by its contact, will be apt to partake in its temperature, to an uncertain extent, and to occasion a corresponding uncertainty in the result.

The celebrated artist Mr Ramsden invented a method of measuring 4 the expansions, as seen greatly magnified through microscopes, which is not only free from the uncertainties of the instruments just noticed, but is much [7:18:748]more manageable than they are. A particu!ar description of the pyrometer which Mr Ramsden constructed on this principle, for ascertaining the expansions of the rods employed in measuring a base on Hounslow Heath for the trigonometrical survey, is given by General Roy, in the Philosophical Transactions for 1785; though, owing to the scarcity of letters of reference, the engraving must be nearly unintelligible to those who are not versed in such subjects. This apparatus appears to be susceptible of acting with great accuracy under moderate heats; but neither it, nor indeed any other instrument of the sort, seems directly applicable under very high temperatures, though we shall afterwards see how the microscopes may be rendered equally available for appreciating or measuring the expansions marked by register pyrometers, or those which, even after they have again become cold, preserve an indication of the extent of the expansion which has occurred during their previous exposure to a great heat.

We can only give here a very general description of Mr Ramsden’s pyrometer, which consists of a strong deal frame, five feet in length, nearly twenty-eight inches in breadth, and about forty-two inches in height. The bar of the material whose expansion is to be measured, and which may be even two feet long, is placed with water in a copper trough or boiler fully five feet in length. Beneath this trough are set twelve spirit-lamps, whose flames may heat the water in the trough, and the bar placed therein for trial, to the boiling point, if required. But it is evident, that by filling the trough with a liquid having a higher boiling point, a still higher temperature might be attained. On each side of the copper trough, and’parallel to it, at a little distance, is placed a wooden trough filled with water, and each of these contains a cast-iron prismatic bar. For greater simplicity, we shall suppose that there are also two cross, pieces, which can be fixed anywhere on the cast-iron bars, and at right angles to them, and that each cross piece carries a microscope to look directly down upon each end of the bar under trial.^[1. In Ramsden’s machine, the microscopes look horizontally; but their connection with the other parts is so complex that we could scarcely pretend to make them intelligible, without diagrams and a very long detail. ] The one microscope has only a simple mark or point in its field of view; but the other is furnished with such a wire-micrometer as is described under the article Micrometer.

Whilst operating with this apparatus, it is of consequence that the temperature of the two cast-iron prisms in the wooden troughs should continue as steady as possible, which can be easily tested by placing thermometers beside them in the water; or a steady temperature may be insured by keeping the troughs filled with melting ice, as was done by General Roy. Suppose, now, the cross piece carrying the microscope which has the point in its field of view, to be so set over one end of the bar under trial, that this point or mark may appear directly coincident with the extremity of the bar to be examined, or with a point or mark near its extremity. In like manner, let the other microscope be fixed over the other extremity of the bar under trial, so that its moveable wire may be accurately coincident with the other extremity of the bar, or with a point or mark near it. These adjustments being made, suppose the temperature of the water and of the bar in the boiler to be exactly 32° Fahrenheit. By means of the spirit-lamps under the boiler gradually heat it to 140°, or any other required temperature, and look through the second microscope. As soon as the change of temperature begins to affect the length of the bar, the mark at its extremity will be seen to deviate from its previous coincidence with the wire of the micrometer, and to extend beyond it. On the bar, therefore, attaining any other temperature, we can measure the corresponding expansion which has occurred, by observing how many turns and parts of a turn of the micrometer-screw are necessary to bring the micrometer-wire into coincidence with the slowly shifting mark on the expanding bar; and as the value in parts of an inch of each turn of the micrometer-screw is accurately known, a direct measure of the expansion of the bar is thus obtained, free from the errors of a system of levers, or of a train of wheels and pinions.

A different form of microscopic pyrometer has been employed by Mr Alexander J. Adie;^[2. Transactions of the Royal Society of Edinburgh, vol. xiii. p. 354, where it is described at great length, with an account of experiments, which, however, were made chiefly on building materials, from the temperature of 50° Fahrenheit, up to 207°. Some of the results are also given under the article Heat. It is neither said, nor is it at all likely, that the expansion of any of the stones which had a laminar texture was ever tried in the direction perpendicular to the scales or plates composing them. For the specimens being long slender slips or rods, their parts could scarcely have stuck together had their component plates run across. At any rate, the expansion was only tried in one direction, namely, in that which happened to lie in the length of the rod. But there is reason to think that, with the exception of brick, perhaps, and a few other amorphous bodies, almost every building material is likely to expand at different rates in its different linear dimensions. Such is known to be the case with certain bodies, particularly calcareous spar, which is said to expand in one dimension whilst it contracts in another. Now, since some of the marbles winch had been heated in these experiments were found to have thereby acquired a permanent increase of length, we have been led to conjecture whether the caverns which abound in calcareous rocks may not be,'in a great measure, owing to their having expanded permanently, but at different rates in their different dimensions. ] in which, instead of the horizontal iron prisms of Ramsden, the microscopes are merely attached to an upright oaken post, which supports and holds nearly all the other parts, and which was made from such an old and thoroughly seasoned piece of timber, that it scarcely expands at all by heat. The bar or rod of the substance under trial is enclosed in a vertical tube, which again is surrounded by steam flowing in a continued current through an outer tube incasing the other. Both tubes are provided with small glass windows, for the purpose of viewing the ends of the included bar through the microscopes, and likewise for excluding the steam from the inner tube. By this means, the tendency which an accession of moisture has to increase the expansions of certain bodies is obviated. But although the inner tube may thus effectually protect the specimen under trial from the humifying influence of the steam, it by no means obviates the uncertainty of the effects of such humidity as that body may already contain. For it appears from Mr Adie’s experiments, that as the temperature increases, the moisture, as might be expected, gradually evaporates from the bar under trial into the air which is enclosed with it in the tube. On this account, if the humidity remaining in the bar were constant, it might add to the expansion, but the gradual drying or evaporation of it tends to a contraction. Indeed, with respect to bodies which have their dimensions affected by a change of humidity, it seems very doubtful if the experiments with slender rods, the humidity of which is so easily altered, can be regarded as determining the expansion by heat of such blocks of the same substance as are massy, and have the humidity comparatively constant.

It is further to be observed, that in heating with steam, it only occasions an unnecessary expenditure of heat to allow a continued current, or indeed any quantity, of the steam to run waste or escape from the pyrometer, except as much as is sufficient at first merely to expel, through proper apertures, the air from the apparatus; after which the closer everything can be kept so much the better. It seems to have been owing to the employment of a continually escaping current, that Mr Adie found it difficult to maintain a temperature higher than 207° Fahrenheit; whereas, [7:18:749]if sufficient care be taken to regulate the heat of the boiler, a single pipe connecting the boiler with a proper air-tight vessel in the pyrometer is all that is required, provided that pipe be sufficiently wide, and so inclined as readily to restore to the boiler all the water formed by the condensation of the steam. A regulating stop-cock may also be useful in the connecting pipe.

In order to ascertain the relative expansions of different ^ materials for the construction of compensating pendulums, or what length of one material would by its expansion accurately compensate a certain length of another, Deluc suspended the one bar from an arm projecting horizontally from an upright deal plank; and the other bar he supported by resting its lower end upon a small cock or stage projecting from the lower end of the former bar. Whilst the first or hanging bar, therefore, expanded downward þy heat, the second or standing bar expanded upward. A microscope was attached to the plank in such a manner that, while it was constantly supported by an horizontal arm, and directed horizontally to the standing bar, it could be shifted up or down the deal plank. When, therefore, heat was applied to the bars, and, by repeatedly shifting the microscope up or down the plank, a point was found in the standing bar which was neither raised nor depressed by the changes of temperature, the compensation was exact, or the respective lengths of the two bars (reckoning that of the standing bar from its base up to the immoveable'point) were inversely as the rates of their expansions. The plank would remain nearly at the same temperature during the experiments, or it might be kept so by such means as are pointed out by the ingenious author, in his account of these and other experiments, described in the Philosophical Transactions for 1777. This method, however, Deluc owed to a hint which had been previously given him by Ramsden. A similar process has frequently been employed for testing and adjusting the compensation of the gridiron and other pendulums, after the parts are put together; namely, by finding when the position of a point in the pendulum, situated as near as can be found to the centre of oscillation, is not affected by a change of temperature.

In the grand operation of measuring a base for determining the great meridian arc in France, Borda combined metallic measuring rods in such a manner, that they indicated directly of themselves, and with more certainty than could be done with thermometers, their own variations both of temperature and of length. A rule of platina twelve feet long was attached, by one of its extremities, to a rule of brass somewhat shorter, which rested freely on its surface, when placed horizontally. Towards the loose end of the brass rule there were traced on the platina rule very exact linear divisions, the parts of which were millionths of the total length of this rule. This end of the brass rule carried a vernier, whose coincidences with the platina graduations were observed with a microscope. Now the dilatations of the platina being much smaller than those of the brass for the same changes of temperature, the vernier of the brass rule behoved to be incessantly changing its coincidence from one division to another, according as the temperature varied. Borda availed himself of these changes to know at every instant the common temperature of these two bars, and also the ratio of the absolute expansions of the two metals. The values of the vernier divisions, in degrees of the thermometer, had∙been previously ascertained from noting the change which took place between first surrounding the compound bar with melting ice, and afterwards placing it in boiling water. It was therefore sufficient to read the indications of this metallic thermometer, in order to learn both the actual temperature of the bars in the atmosphere, and also what compensation was to be made in the measuring rods or chains, to reduce their lengths to what they should be at the standard temperature. But, after all, we suspect that if the upper of these rules was at any time more exposed than the lower to the aspect of the sky, it might be somewhat more cooled by radiation; and the sun, again, would have just the opposite effect of heating the upper more than the lower.

By means of a simple and ingenious process, Dulong and Petit compared the expansions of the volumes of several solid bodies with those of air and mercury. Having ascertained the absolute dilatation of mercury by heat in respect of the indications of an air-thermometer, from observing the unequal heights at which the mercury stood when at different temperatures in the two legs of an inverted glass syphon, they next measured the apparent dilatation of mercury in a glass tube. The difference gave them the absolute dilatation of the glass. Every kind of glass which they tried was found to dilate at the same rate; a result in which some are not disposed to acquiesce. The dilatation of iron, copper, and platina was determined by placing a rod of each metal of a known volume and weight in the axis of a glass tube shut at one end, and having only a capillary opening left at the other. The remaining space in the tube being then filled up with mercury, the tube was heated to different temperatures, and the quantity of the mercury noted which was in each case expelled from the tube. It is obvious that the volume of the mercury thus driven out is equal to the expansions of the mercury and of the solid metal, minus the expansion of the glass. With the exception of the groundless objections of Mr Crichton, which are noticed farther on, this method of Dulong and Petit is, so far as we know, universally acquiesced in; but since it merely gives the expansion of the volume, there is no reason to think that it can afford accurate data for estimating the linear dilatation of bodies; because it assumes that they expand at precisely the same rate in every direction, or in all their linear dimensions. Indeed, the greater part of the direct experiments on linear expansions which have been put on record, lose much of their value from involving this assumption; for it has been ascertained of certain bodies, that they expand very differently in their different dimensions; and probably something of the sort holds of most bodies. Nay, some are said to contract in one dimension, whilst they expand in another. Besides, every article which has been more or Jess compressed by having, whilst comparatively cold, undergone such operations as hammering, rolling, or wiredrawing, may, on after exposure to heat, be expected to acquire some permanent enlargement, and one too which, on account of the unequal compression, is likely to be very different in the different dimensions. Many fine astronomical and optical instruments we suspect to be liable to derangement from this source. Various cases of permanent expansions will be found noticed in the course of this article.

Amongst the earlier attempts at ascertaining high temperatures, Μ. Achard constructed a pyrometer which is quite in the form of a common thermometer. The ball and tube are of semi-transparent porcelain, highly baked. They contain a very fusible alloy, consisting of two parts of bismuth, one of lead, and one of tin, which, though solid at low temperatures, becomes liquid about 212° Fahrenheit; and then, as the heat increases from that upward, it expands in the liquid state similarly to mercury, and is seen through the semi-transparent tube, which is graduated. There seems scarcely any limit to the temperature to which this kind of instrument could be extended, provided only a material could be got for forming a ball and tube which would both bear the heat and also admit of the liquid metal being seen through it. There would be no difficulty of finding a less fusible alloy; and were there no risk of its oxidation or evaporation, it might be put [7:18:750]into an open though perfectly opaque tube, in which a float might indicate the extent of the expansion by its top rising above the open-end. But it would still be desirable to ascertain, if possible, the value of the degrees of this and every other pyrometer, in terms of the common thermometer.

It is long since the expansion of air had been proposed by Μ. Schmidt as a measure of high temperatures. This was afterwards suggested by Dr Ure, and still later by Mr Mill, who proposed to employ for that purpose a differential thermometer having one ball and half the tube of platina, and the other ball and half tube of glass. The platina ball being put into the furnace, it is supposed that the instrument would indicate the excess of the heat within over that of the external air. Such might at first sight appear to be a very convenient pyrometer, but it stands greatly in need of improvement; because, unless for small differences'of temperature, a differential thermometer cannot continue to give the difference of two thermometers indicating the temperatures of the respective balls. Neither can this method afford data for computing the temperature of the platina ball, unless the temperatures of the other parts were first accurately known, which is far from being the case. For although, to ascertain the temperature of the glass ball with tolerable accuracy, it would only require to be immersed in a bath along with a thermometer, which however could not be so easily done if the whole tube were straight, as proposed by Mr Mill; yet since a large proportion of the included air would necessarily be contained in the tube, it would be next to impossible to allow for its temperature, because that would vary through all the degrees intermediate between the temperatures of the two balls. Perhaps the most correct apparatus yet employed on this principle, and in which precautions are used to avoid the errors now mentioned, is that of Mr Prinsep, described farther on, for ascertaining the melting points of his pyrometric alloys, in terms of the scale of the common air-thermometer. But Schmidt’s scheme, as described in Nicholson’s Journal (vol. xi. p. 141), comes nearer the mark than any of the other two. Schmidt and Mill seem to have taken it for granted that a bulb of platina could be as easily formed as one of'glass; but of this Dr Ure probably had some doubt; for he suggests that the platina might be formed into a hollow cylinder having the tube screwed inr, like that of a tobacco-pipe. Perhaps the ends, too, might be screwed in. Mr Prinsep’s bulb being of gold, could only be used at temperatures below the melting point of that metal.

The determination of the temperature of furnaces is an important question; but until nearly twenty years ago, when Professor Daniell took up the subject, the only instrument in repute for this purpose was Mr Wedgwood’s pyrometer; “the indications of which,” says Mr Prinsep, “are assumed in every chemical work as authority for some doctrines relative to the scale of temperature which savour of the marvellous, and for others which a slight practical acquaintance with metals and crucibles must at all times have proved to be fallacious.” The principle on which this pyrometer depends is vague and uncertain in the extreme, namely, the permanent contraction of certain aluminous clays, when exposed to an intense heat. For it has been found, that the amount of the contraction, even of the same clay, so far from being in exact proportion to the intensity of the heat, as assumed by Mr Wedgwood, depends very much on the duration of the process, so that long-continued exposure to an inferior temperature produces as great a contraction as if the clay had been sub mitted for a shorter time to a more intense heat. This instrument has of course served its day, and gone into disuse.

'There are many igneous operations, such as enamelling, assaying, those of the foundery, &c. which furnish tests, of themselves, on which the workman can generally place considerable confidence, though some of these require to be used with great caution. Thus, the colour which heat produces on the surfaces of metals furnishes a somewhat deceptive criterion of the temperature or temper; because the particular colour depends very much on the duration of the exposure to the heat. For example, a piece of hardened steel may become quite blue, if long enough exposed to a heat which is too low to produce the supposed corresponding effect in tempering or reducing the hardness.

In the Quarterly Journal of Science (vol. xi. p. 309), Professor Daniell has described an ingenious instrument, of his own invention, with which he has ascertained the fusing points of various metals, and which has served to overturn the catalogues of high temperatures deduced by means of Wedgwood’s pyrometer, and so long occupying a place, with standard authority, in every chemical work.^[3. Some of these extravagantly high numbers had been previously questioned by Morveau, in the papers which he published on his very imperfect platina pyrometer, in the Annales de Chimie for 1803, tomexlvi., and in the Mémoires de I’lnsíitut for 1808 and 1811. ] But from the journal just cited it has now become unnecessary to draw any further account of Mr Daniell’s pyrometer, because he has since made great improvements u])on it, as described by him in the Philosophical Transactions for 1830 and 1831, and in his revised version of the same in the Philosophical Magazine for 1831 and 1832.

This instrument we regard as a very important one, but still labouring under several imperfections, and susceptible of great improvements, some of which will be particularly noticed, after giving a general description. It consists of two distinct parts: The register, which alone is to be exposed to the heat, and is also to preserve an indication of the expansion of the material under trial; and the scale, which is not so exposed to the heat, but only measures the expansion upon the register after, the latter has cooled. The former of these, represented in fig. 1, Plate CCCCXIX. consists of a bar of blacklead earthenware A A, eight inches long, seven tenths broad, and of the same thickness, cut out of a common blacklead crucible. In this is drilled a hole B B, three tenths of an inch in width, and seven and a half inches deep; and about six tenths of an inch in length of the substance of this bar is cut away from its side next the open end at C C, by a plane running along the axis of the bore. When this blacklead register is held upright, and a rod of any material 6 ’ 5 inches long is dropped into the bore, it rests against the solid end; and then upon the top of this rod is set a cylindrical piece of porcelain D D, about 1∙5 inch long, which Mr Daniell calls the index, and which, projecting into and beyond the open part, is firmly held to its place by a ring or hoop of platina, E E, which, passing round the blacklead bar, and over the piece of porcelain, is made to press upon the latter with any required degree of tension, by means of a small wedge of porcelain, F F, inserted between the bar and the platina ring. When the apparatus, so arranged, is exposed to a high temperature, the expansion of the rod under trial will obviously force the index D forward through a very small space, equal to the excess of its own expansion over that of the blacklead; and after the register has again cooled, the index will be left nearly at the point of greatest elongation. According to Mr Daniell, the exact indication of this amount is not in the least affected by any permanent contraction which the blacklead may undergo [7:18:751]at a high temperature, because he assumes any such contraction to occur-at the moment of the greatest expansion of the metal, and the index, in consequence, still to mark its point of farthest extension upon this contracted basis. We are not, however, so clear on this point; but admitting it at present, the problem would now consist in the accurate measurement of the distance through which the index has been shifted from its original position. For this purpose, the scale, fig. 2, is constructed of two rules of brass G G and H H, joined together at a right angle by their edges, and fitting square upon two sides of the blacklead bar A A, and of about half its length. From the end of this double rule a small bracket, I, of brass, projects at a right angle, and which, when the two sides of the rules are applied to the two sides of the register, is brought close to the shoulder formed by the notch cut away at its open end, and the whole may thus be steadily adjusted to the blacklead bar by three planes of contact. Upon the outside of this frame, another and much larger brass rule K K, is firmly attached to it by the screws L L. This rule, projecting beyond the frame, and being turned up at the end Μ, about half an inch, so as to bring that end opposite the cavity in the blacklead bar when applied to it, supports a moveable arm, N, exactly 5∙5 inches long, turning, at its fixed extremity, upon a centre near M, and at its other end carrying an arc of a circle 0 0, accurately divided into degrees and thirds of a degree, whose radius is exactly five inches. At P, the centre of this arc, upon the arm N, and, of course, at the distance of half an inch from the other centre Μ, turns another lighter arm Q, whose length being five inches, equals the radius of the circular arc 0 0, and one end of which carries with it a vernier a, which moves upon the face of the arc, and thereby subdivides the former graduation into minutes. The other end projects half an inch beyond the centre, P; and at the exact distance of one tenth of the radius Pa, and which equals the interval between the two centres of motion, it carries an obtuse steel point b, turned inwards at a right angle. This part of the apparatus may be regarded as a pair of proportional compasses attached to the end of the brass rule and frame, and whose longer legs N and Q, carrying the arc and vernier, are to the shorter, carrying the point b, as ten to one; and the opening of the shorter being regarded as a chord of a small circle, is enlarged in the same proportion by the longer, and measured upon a scale. A small steel spring m m, let into the larger arm N, is made to press upon a little pin n, in the smaller arm Q, so as to adjust the vernier α to the commencement of the graduation; and when forced back, it tends to restore it to its original position. A small lens i is represented as folded down, but may, by means of the joints k and I, be raised to be directly over the vernier, to facilitate the reading of the divisions which coincide.

In fig. 3, A is an iron tube about two inches in diameter, and closed at the bottom. B is a blacklead tube, closed at the top, and fitted into the mouth of the former one by grinding. C is a smaller blacklead tube projecting from the side of the latter, and likewise fitted in by grinding. The whole forms a kind of alembic, in which mercury may be easily boiled, without either loss, or annoyance to the operator, by the escape of the vapour. When the register containing a rod of some substance under trial was put within the iron tube, and the remaining space filled with mercury, the boiling of the latter served the purpose of a thermometer, showing when the temperature reached about 662° Fahrenheit.

When the expansion of any substance is to be ascertained, a rod of it is to be provided, of such dimensions as will suit the cavity of the blacklead register; and being placed therein, the porcelain index D is to be pressed down upon it, and secured in its place by the platina’ring E and porcelain wedge F. The scale part is then to be applied by carefully adjusting the brass rules GG, HH, to the sides of the blacklead, and pressing the cross piece I upon the shoulder. Holding the whole together steadily in the left hand, the moveable arm Q should be so placed that the steel point b of the short arm may rest upon the end of the porcelain index D, against which it will be pressed with some force by the spring m ; then, moving the arm gently forward with the right hand, the point b will slide upon the end of the index till it drops into a small cavity formed for its reception, and which is in a line with the axis of the rod under trial in the register and the centre Μ on the brass rule. The minute of the degree must then be noted, which the vernier a indicates upon the graduated arc. A similar measurement must be made after the register has been exposed to an increased temperature and has cooled again; and the number of degrees or minutes which the vernier may then mark, will, by a simple calculation from the known length of the radii and angle, give the length of the chord comprised between the original position of the point b and the point to which it has been shifted, namely, the distance over which the index has been moved by the expansion.

But the preceding description, which contains the substance of Mr Daniell’s view of the matter, is by no means even theoretically correct in the mode of computing the extent of the expansion. For Mr Daniell assumes that the above-mentioned chord of the small arc intercepted between the two positions of the point b, is always accurately in the same direction with the axis of the bore in the blacklead; whereas nothing can be more evident than that it must be owing to mere chance if it is ever so at all. Nor do we know any direct method of insuring that the chord shall have that direction. The problem obviously requires that chord to be reduced to the direction of the bore; and its length so reduced may, in every case, be obtained from considering that it is equal to the sum or difference of the sines of the two arcs which measure the angular deviations of the short arm (or rather of the straight line joining the centre of motion and the point b) from being perpendicular to the direction of the bore. But it is obviously by mere chance if the two arcs happen to be equal, so as to have the sum of their sines the same with the chord of their sum, as they are always assumed to be by Mr Daniell. If the graduated arc had its zero placed so as to correspond to the perpendicular position of the shorter arm, the two required arcs could then be more conveniently read off. When these lie on opposite sides of the zero, it is the sum of their sines that is to be used; but should they happen to be both on one side, the difference of their sines is to be taken. But in place of using either sines or chords, it would be preferable greatly to increase the lengths of both arms; and then if sufficient care were taken to have the shorter arm as nearly perpendicular as possible to the direction of the bore, the arc itself comprised between the two positions of the point ó, from its now subtending a much smaller angle, might generally be taken as the measure of the expansion.

Mr Daniell, as we have seen, though he admits that during an experiment a permanent change may occur in the length of the blacklead, yet alleges that his results are not affected thereby. But since it is in respect of the shoulder at the mouth of the bore as bearing against the bracket I that his measures of expansions are taken, it is evident that the position of the bottom of the bore in respect of that bracket, and consequently the position of the index D in respect of the steel point b, must be affected by the full amount of any permanent change in the length of the bore of the register. However, it is equally clear that, were the rules G and H made of sufficient length to admit [7:18:752]of the bracket I being placed at their other end, and so as to hold against the closed extremity of the blacklead bar, any permanent change which may have occurred in the length of the latter at the highest temperature, except in the mere thickness of its bottom, would not affect the result. The effect of any change of temperature on the brass rules could easily be allowed for, were it at all worth appreciating.

It will now be sufficiently manifest, without farther explanation, that instead of using Mr Daniell’s scale-part, the amount of the expansion, as marked on the register by the index, might be equally well ascertained by the turns of a fine screw, as in Smeaton’s pyrometer; or, still more accurately, by means of the microscopes and micrometer, as used with Ramsden’s pyrometer, and others of that sort. The expansion might also be approximately measured by putting the register and index transversely between two graduated rules about 8 , 4 inches apart, and very slightly converging; which is similar to the mode in which Wedgwood measured his clay pieces.

But we suspect that the porcelain index itself must be a source of very considerable error or uncertainty, if its rate of expansion be different from, as it most probably exceeds, that of the blacklead. For, although it is likely that some points of the porcelain and blacklead which were in contact at the highest temperature to which they have been exposed, will continue in contact during and after the cooling, yet we are left quite in the dark as to the situation of these points; and consequently, we have no means of appreciating the length of that part of the index whose expansion is concerned. Nay,] a similar uncertainty must, in consequence, attach to the effective length of the blacklead register. By shortening the length of the index, these uncertainties might be expected to be lessened; but it is by no means clear how they could be entirely obviated, except, perhaps, by using an index and wedge which should expand at precisely the same rate as the register does. Could the platina ring be got slightly to hold upon the register without the aid of a wedge, but still in such a manner that all the parts of the ring would slide equally along the register by the pressure of the bar under trial, the ring itself might serve as the index. In that case, instead of cutting away any portion from the side of the register, it would be better merely to cut a longitudinal slit in it, running quite through the axis of the bore, for the purpose of receiving and making room for the motion of a rib to be fixed diametrically in the ring, and upon which the expanding bar under trial could act, so as to move all the parts of the ring equally along the register.

By keeping a rod of platina in the register, exposing it to heats of various intensities, and ascertaining in each case the excess of the expansion of the platina over that of the blacklead, Mr Daniell determined a variety of temperatures in terms of such excess, which, unfortunately, is always a very small quantity, that between 32° and 212° Fahrenheit being counted 180 degrees. These results, though incomparably nearer the truth than those obtained by Wedgwood’s pyrometer, must still be more or less tainted with some of the various errors to which we have either already alluded, or which are about to be noticed. But as our limits will by no means admit of fully discussing all the calculations, and attempting to correct them, we beg to refer the reader to the originals; and shall only attempt such an account of the principal sources of error as will sufficiently show the truth and importance of our allegations, which are, besides, applicable to most English books treating on this subject.

In deducing the numerical results from the experiments made with his pyrometer, particularly in computing the expansion of blacklead, Mr Daniell avails himself of the expansions which Dulonğ and Petit had obtained by the method already noticed, and these he finds to correspond surprisingly with his own. But independently of the doubts already hinted regarding their linear expansions, this agreement, as we shall presently see, argues nothing in favour of either determination; because the comparison has been made through the medium of a serious mistake, as we shall now endeavour to explain. The results of Dulong and Petit just referred to are those of the expansion of mercury and of several solids, given in the Annales de Chimie for 1818 (tome vii.), and regarding which they inform us, that the degrees inserted in the first columns of the tables are the upper limits of intervals of temperature, which are each of them reckoned from the freezing point, or 0° cent. Thus, regarding their Table IV., which bears more immediately on the present question, and has 100° and 300° occupying the first column, we are told that it “contains the mean dilatation of iron, copper, and platina, taken at first between 0° cent, and 100°, and then between 0° and 300°.” That is to say, the first line of these dilatations contains the 100th part of the whole expansion for the interval between 0° and 100° cent., and the second line the 300th part of the entire expansion for the interval between 0° and 300°. Indeed, it is either expressly mentioned or obviously implied in the course of the Memoir, that every one of their intervals which relate to the expansions in question, is reckoned from the freezing point, and none of them from any higher temperature.

Shortly after Dulong and Petit had published this account of their valuable researches on heat, a translation of it appeared in the Annals of Philosophy (first series, vol. xiii.); and prefixed to the same volume is a Historical Sketch of the Sciences for 1818, which, amongst other things, professes to give an abstract of the principal points treated by Dulong and Petit in the Memoir referred to. But most unfortunately, in this Sketch, which seems to have been hastily got up, the results of these learned foreigners have been sadly misconstrued as far as regards expansion. For the numbers they have given as the upper limits of those intervals of temperature, which are each of them reckoned from the freezing point, are in the Sketch (page xii.) taken as so many points of temperature, at each of which respectively the expansions of the several bodies for one degree, as recorded in the other columns of the tables, take place; a mistake so egregious, that it quite unhinges the thing altogether, because the expansion, instead of being, as in the original, the mean for the whole interval, is thus made to belong to its highest degree alone. Now it would seem to have been somehow or other from this Sketch that Mr Daniell had taken up his leading ideas of the question; at least he has adopted a very similar misconstruction; for, in his Table II., which he gives as equivalent to Dulong and Petit’s Table IV. above mentioned, he has, in place of 300° cent, or 540° Fahrenheit, made the second interval to be only equal to the first, which is 100° cent, or 18θ° Fahrenheit, a sense in which similar temperatures are also erroneously used in the Sketch (p. xii.). The effect of this unfortunate oversight is to make the expansions of iron, copper, and platina, especially that of iron, much smaller in the higher temperatures than Dulong and Petit found them to bc; although, for want of data, we can only compute the effect of the error with certainty on the whole interval of 540°, without separating that of the higher temperature from the lower. Thus, Mr Daniell, by means of his very laborious but erroneous mode of computing from the numbers of Dulong and Petit, makes the linear expansion of 6*5 inches of iron, from 32° to 572° Fahrenheit, to be only ∙025841887 inch. But the expansion of iron in the unit of volume, as given by Dulong and Petit for that interval, or from 0° to 300° cent., is

Now, one third of this taken as the linear expansion, and [7:18:753]multiplied by 6∙5, becomes ∙028634361 inch. The error or deficiency of the former value is therefore ∙002792474, and this would require to be added to ∙00878 (Mr Daniell’s expansion of 6∙5 inches of blacklead), which will increase it to ∙01157. But even this last number, if otherwise correct, is still too small, because the expansion above 572° up to the boiling point of mercury, to which he carried that of the blacklead, ought to have been computed at some higher rate, but for which we have no data. Such are specimens of the very erroneous conclusions which the above unfortunate oversight has led Professor Daniell to draw from the experiments of Dulong and Petit.

It seems to be from the same source, the Historical Sketch, that at least nine tenths of all the excerpts or abstracts that have been written in English, of the experiments of Dulong and Petit, are scarcely one whit more correct than the preceding, as far as regards expansion; although we have met with no such misconstruction of them in any foreign work. That such errors were very prevalent in this country, had been briefly noticed by Mr Mciklc in the Philosophical Magazine for September 1830; which, if not quite in time to have saved the paper which Mr Daniell inserted in the Philosophical Transactions of that year from the errors in question, must have been sufficiently so for the one of next year, and for his revised version of both afterwards given, with those errors entire, in the Philosophical Magazine. It is no doubt also from the Sketch (page xvii.), that in English books, the specific heat of platina, professedly from Dulong and Petit, is usually made ∙0355 at all temperatures, and therefore often regarded as a remarkable exception to the general law; whereas, between 0° and 100°, the mean value should only be O335; the larger number ∙0355 being the mean for the whole interval between 0° and 300°. But the Sketch contains various other inaccuracies; and some, like the one last noticed, occur also in the English translation of the Memoir.

In noticing the labours of Dulong and Petit, Professor Daniell regrets that those able experimenters had not corrected their final results as to what he considers an important error of calculation, supposed to have been pointed out by Mr Crichton, regarding the expansion of mercury, particularly as employed by Dulong and Petit in determining the expansions of glass and of several metals, in the manner which we have briefly described above. It is, perhaps, rather unusual for writers of eminence to adopt any correction of errors, however important or clearly pointed out; because the public are generally expected to imbibe whatever may emanate from such authorities, and to listen to no insinuations of their being incorrect. But the following considerations will, in a great measure, account for Mr Crichton’s corrections not having been adopted :—Isí, Though it does not seem to be generally known in this country, Μ. Petit, who had taken the most active part in these valuable researches, particularly in the mathematical investigations and calculations, had died nearly four years before Mr Crichton’s paper appeared in the Annals of Philosophy for April 1824; so that Μ. Petit, who was a young man of great promise, has long been outlived by his senior and distinguished colleague, Μ. Dulong, whose recent decease science has now to deplore. 2d, We have nothing like satisfactory evidence that Dulong and Petit have, after all, employed the erroneous modes of calculation imputed to them; and we shall soon see that, in at least one of these, it is Mr Crichton himself who is in the error. To determine the expansion of mercury in glass, Dulong and Petit filled with that fluid a glass tube which had its open end drawn into a capillary tube; and on heating this from zero up to different temperatures, they weighed the corresponding portions of mercury which were expelled. But they have nowhere said, nor is it so much as even implied in their Memoir, that they held the increase of volume to be in the exact ratio of the weight of mercury expelled, which would be to neglect the expansion of the expelled portion itself. This, however, Mr Crichton assumes that they did; and he thence concludes that they have made the expansion of mercury in glass, when heated up from zero to 100° cent., to be too small in the ratio of 63∙8 to 64*8. We have no data for determining how far this supposed error would affect the expansions of the solid bodies operated on by Dulong and Petit; though it would no doubt be to a much smaller extent than that resulting from the above errors, into which Mr Daniell has himself fallen, in the temperatures. However, we find that it would but very slightly derange the indications of a mercurial thermome-tèr up to 300° cent., or 572° Fahrenheit. For example, if Dulong and Petit have been right, the series of centigrade temperatures on the common mercurial thermometer would stand thus: 0°, 100°, 203° ∙20, 307° ∙69; and if they have been wrong, 0°, 100°, 203° ∙25, 307° ∙82; we mean in respect of those on their air-thermometer taken as uniform.

The preceding is by no means the only error with which Mr Crichton charges Dulong and Petit. Besides other things of which we have no means of judging, he blames them for holding the volume of mercury expelled by heat from the glass tube, to be equal to the absolute expansion of mercury diminished by the expansion of the glass; which, however, is a thing so palpably true, that scarcely any reasoning can make it clearer than it is. But the extreme palpability of this does not prevent Mr Crichton from going on with a process of reasoning sui generis, from which he concludes, that the expansion of the glass is much smaller than the difference between the absolute expansion of mercury and its expansion in glass. Since in this Mr Crichton has, without doubt, deceived not only himself, but many of his readers, it may be useful briefly to show how it has been done. In the first place, he has sadly obscured his formulae, by representing by unity each of two things of very different values, more especially since both enter into the same expression. The one of these is the, expansion of mercury in glass, and the other the expansion of the glass alone. The like may be said of his using the term co-efficient to mean what other people would call a denominator, or, in some cases, a reciprocal. But his principal error is, that in order to correct the capacity or contents of the vessel for the expansion of the glass, he makes a deduction, not from its contents as expanded at 100° cent., but from its contents at the freezing point, or at least from 63∙8 times what he now uses as the expansion of mercury in glass; and in the preceding part of his paper he had made the contents of the vessel at zero to be just equal to 63∙8 times the expansion which mercury seems to undergo in a glass vessel, by being heated from zero to 100° cent. In this case, therefore, the error lies with Mr Crichton himself.

The principle of the method employed by Mr Prinsep^[4. Philosophical Transactions for 1828, p. 82. ] for ascertaining high temperatures, particularly those of furnaces, by means of the least fusible substance each can melt, has already been briefly alluded to, and differs very materially from that of Mr Daniell. The former, which we shall now describe more in detail, was, after trying various plans, fixed upon by Mr Prinsep, as possessing considerable claims to accuracy, and having the great advantage of being identifiable, as he styles it, at any time and in any part of the world. In other words, it can show [7:18:754] when the temperatures or intensities in different eases are equal, though it cannot determine in what ratio ι⅛nequal intensities differ among themselves. The fusing points of pure metals are determinate and constant; they also comprehend a very extensive range of temperature; and the unoxidable or noble metals, gold, silver, and platina, alone embrace a range from the comparatively low melting point of silver up to the high ignition of platina. There are, it is true, only three fixed points in this scale; but between these as many more as are requisite may be interpolated, by alloying those three metals, or rather any two of them together ata time, in different proportions, though the like by no means holds with every kind of alloys. When such a series as that now proposed has been once prepared, the heat of any furnace may be expressed by the alloy of least fiisibility which it is just capable of melting. Besides the unity of determinations which such a pyrometer affords, several other advantages might be mentioned: 1st, The smallness of the apparatus, nothing more being neeéssary than a little cupel, containing, in separate cells, eight or ten pyrometric alloys, each of the size of a pin’s head; "2d, the durability of these alloys, since the specimens melted in one experiment would need only to be flattened by the hammer to be again ready for action, because without some such change of figure it would be uncertain whether they had again been melted or not; and, 2>d, the facility of notation, since two letters with the decimal of the alloy would express the maximum heat. Thus, S∙3G might be used for an alloy of seven tenths of silver with three tenths of gold; and G∙23P would express gold containing twenty-three per cent. of platina. As gold melts at a heat not very much above that required by silver, Mr Prinsep as* Sumed only ten degrees between them, distinguishing each degree by a successive addition in the alloy of ten per cent, of gold to the pure silver; the tenth degree being of course denoted by pure gold. These alloys are easily made, and require no comment; but to suit more accurate researches they may be farther subdivided, preserving still, for convenience, the decimal notation. From the fusing point of pure gold up to that of pure platina, Mr Prinsep assumed 100 degrees, adding one per cent. of the latter metal to the alloy for each successive degree. Now, although the melting points of the alloys used by Mr Prinsep apparently bear some relation to the proportions of the pure metals employed; yet, since the melting point of every alloy does not so much as lie between those of its component pure metals, but in many cases is lower than either of them, it must be merely an accidental coincidence, should any of Mr Prinsep’s degrees correspond to equal increments of heat. They will, however, as was before observed, always indicate the same intensity; and their absolute values, or even those in terms of the thermometer, being a matter rather of speculation than of practical interest, are to be sought for by other expedients, such as comparing the expansions of a bar of platina with the fusing points of the alloys.

The following are a few trials which Mr Prinsep made with his pyrometrie alloys in different furnaces and in different parts of the same furnace. The disparity of heat is greater than might have been supposed; and where, as in assaying the precious metals, so much depends upon the exact temperature at which that operation is performed, it would be useful to know every difference in this respect obtaining in various countries, and its effect upon the quality or standard of bullion. The temperatures are denoted by the least fusible alloys melted in the several cases. Muffle of an assay furnace, front S∙0G

Muffle of an assay furnace, middle, average S∙3G

Muffle of an assay furnace, behind, average S ’ 5G

Calcutta charcoal, being better than that of Be nares, heats the muffle to G∙04P

Calcutta silver-melting furnaces, of English con struction, the specimens being in an iron pot....G ’ 075P Calcutta open native furnace G∙06P

Calcutta blast-furnace, for melting musters G ’ 2P

Blacklead table-furnace without chimney G ’ 08P

Apex of condensed air blowpipe flame G ’ 2P

Melting point of copper by two trials under a muffle...G∙03P Melting point of east iron, about G - 3P

Highest heat of a forge with the charcoal of Be nares G∙55P

Mr Prinsep says he lays little stress on the melting points of copper or iron, owing to their being tried on such a small scale. The alloys of gold and silver lose in weight by exposure to heat; but they are easily replaced, as the gold may always be again purified. The platina alloys are very durable, but they sometimes gain in weight. Mr Prinsep enters at considerable length into an examination of the changes which the composition of the alloys underwent by repeated fusion; but whether, or to what extent, their melting points may be altered thereby, is a question never once mentioned, though of incomparably more importance to the present subject.

Having explained the means which Mr Prinsep had provided for ascertaining the relative heat of a furnace, we turn to the more interesting portion of his experiments on pyrometrie subjects, namely, the determination of the melting points of pure silver, and of its alloys with gold, in degrees of an air-thermometer. But we shall begin with the description of the apparatus employed, which at last satisfied his expectations, and furnished the results presently to be enumerated. In fig. 4, Plate CCCCXIX,, it is shown in full operation. A represents a retort or bulb of pure gold, weighing about 6500 grains, and containing nearly ten cubic inches of air. B is a tube also of pure gold, which at its outer end is firmly joined by a small gold collar to a similar tube C, of pure silver; the bore of the latter tube is larger than that of the gold; but to prevent any undue influence from the unequal heating of the air contained in them both, and to confine the operation as much as possible to the gold bulb, the two tubes are nearly filled up by putting in wires of the same metals, so as to leave only a very minute crevice for the air to pass. The outer part of the tube C is kept cool with a wet towel, to protect the stopeocks and flexible tube D. This tube D completes the communication of the air bulb with the glass reservoir E, which is intended as a substitute for an inconvenient length of graduated tube. This reservoir is at first nearly filled with olive oil, and is furnished with a safety tube and bulb F, into which the oil rises when the air of the retort A begins to flow, and has a stopeock below, for the purpose of restoring the equilibrium of pressure, by drawing out a portion of the oil. In the collar of the reservoir E, however, there i⅛ another stopcock aperture leading into a graduated glass tube G, in which a small bubble of *oil is made to traverse. As this tube was very accurately divided into 200ths of a cubie inch, and may be read off to a tenth of that quantity, the equilibrium of the pressure is capable of very delicate adjustment. The furnance, as the figure exhibits, was situated behind a wall in an adjoining apartment, so as to screen the exterior apparatus entirely from the heat. A small thermometer in the bulb F, however, serves to note any minute change of temperature in the reservoir E. The furnace and muffle need no description, being of the ordinary assay construction. The little pyrometric cupels p, p, p, contain alloys of silver and gold, as already described. Fig. 5 represents one of these cupels on a larger scale, with the lid raised, showing three of the alloys melted, and the rest retaining their previous form.

Out of the numerous experiments which Mr Prinsep made with this apparatus, we have selected the few following[7:18:755] results; but for the full details of these and many more, we beg to refer to the original description, where they are given at great length.
[table]

The second column is the volume, in cubic inches, of the air expelled from the gold bulb, after all corrections. The third gives the contents of the heated gold bulb. The fourth contains the expansion converted into degrees, at the rate of three eighths-for 180 degrees. The fifth column shows the temperature of the air. The sixth is the heat of the furnace, being the sum of the fourth and fifth. The seventh shows the heat of the furnace by the pyrometric cupels. The heat, in No. 1, exhibited an orange colour; in No. 2, bright orange; No. 3, bright red; No. 4, bright orange; No. 5, silver wire melted; No. 9, full red heat; No. 10, fresh air was put into the gold bulb; and in No. 11, the cupel at the back of the bulb was S. 3G.

From the construction of the apparatus, it must be evident that the temperature is to be deduced from the measured volume of air expelled from the heated gold bulb; which volume, again, is to be found by the weight of the oil drawn from the reservoir, together with the adjustment of the bubble of oil in the graduated glass tube. The necessary calculation, however, embraces several corrections, some of them of minor effect, and of known and certain influence, as the formulae for barometrical and thermometrical change, specific gravity of the oil, &c.; others which may affect materially the results, and are by no means so certain in their power, such as the expansion of gold at high temperatures, and the absolute law of gaseous expansion. This last has been treated at considerable length under the article Hygrometry (vol. xii. page 114). At high temperatures a very small difference in the quantity of air ejected produces a considerable change in the corresponding temperature; in other words, this air-thermometer has the disadvantage of becoming less sensible, in respect of the scale of the common thermometer, with every increase of heat; for the portion of air which is expelled from the hot bulb must necessarily be cooled to a known point before it can he measured.^[5. “That the air-thermometer,” says Mr Prinsep, “cannot be expected to give indications perfectly accordant, those who have kept registers of the sympiesometer will be ready to grant.” But the case of the sympicsometer furnishes no authority on the subject; because one very good reason for its own incongruities is to be found in the faulty mode of correcting it for temperature, which is such that its indications can .never keep pace with those of a good barometer, even were it liable to no other objection. ] But this objection, which was started by Mr Prinsep himself, does not apply to bis apparatus in respect of a scale of temperature graduated on the idea that air expands in geometrical progression for equal increments of heat, as it has been shown to do in the article just cited. The substitution of a reservoir of oil or mercury in place of a mere graduated tube, is essential where the instrument is to be suddenly thrust into the fire, as the rapid motion of a bubble of liquid in a tube would either, if of oil, leave it as a film lining the tube, or, if of mercury, allow a passage for the air past the side of it. The capacity of the reservoir employed by Mr Prinsep was equal to that of a tube 50 feet long, and of the same bore as the adjusting tube G. But it is evident that a bulb of gold can only be used at temperatures lower than its own melting point, so that the temperatures for the less fusible alloys are left undetermined.

In the course of his pyrometric researches, Mr Prinsep repeatedly found that, on heating a cast-iron retort from 80° up to 1800° Fahrenheit, it had, even after having again become cold, acquired each time a permanent enlargement, which, by three successive heatings, amounted to fully a ninth part of its original capacity. Each successive increase, however, was so much less than the preceding, that the first heating did nearly as much in that way as both the other two. It does not appear to have occurred to Mr Prinscp that there is any connection between such an augmentation of volume and the expansion which occurs in the solidification of iron at the casting of it; but we shall now endeavour to show, that they are just parts of one and the same process. It is curious, that in almost every book in which the expansion of iron in congealing is mentioned, it is, without giving so much as the shadow of reason or evidence, said to be momentary or instantaneous. But in many of the innumerable forms of the castings of iron, we have often observed cases occurring which cannot be reconciled with its momentarily expanding in the act of solidification, unless it also continue to expand considerably as long as it is kept very hot; and more especially unless the parts which were first congealed continue to expand whilst they remain in contact with any of the liquid metal. This impossibility of reconciling the phenomena with a momentary expansion is particularly remarkable, when in the structure of the article cast there occurs a massy nucleus of metal with arms or leaves of more slender dimensions proceeding from it. In that case, the interior of the nucleus is generally the last in congealing, and if so, it is almost never quite sound, there being always a deficiency of metal to complete such part of the casting as is last in congealing, which occasions it to be of a spongy texture, and, perhaps, to have cavities in it of a very different sort from those which are really owing to mere airbubbles. Sometimes a cavity is open through the surface, which may be owing to its occurring so near the outside that the thin crust is depressed or broken quite through by the atmospheric pressure. When a hole is cast through the middle of a massy part of the iron, by means of a previously dried core, the metal next the hole is generally amongst the last in congealing, because such a core has almost no tendency to cool it; and, therefore, owing to the foresaid deficiency of metal, the hole where it passes through the interior is usually wider than the core, and, perhaps, has one or more cavities branching off from it.

Such cases as have now been instanced are of very common occurrence; but to some people they have appeared so very paradoxical as to lead them to deny that any expansion whatever can occur during the casting. At first sight, the sponginess and cavities might, no doubt, be easily accounted for, as some have pretended to do, by supposing iron to contract, instead of expanding, at the time of congealing. But that an expansion really occurs on that occasion, is so well attested^[6. Particularly by Mr Mushet, in the Philosophical Magazine, vol. xviii. p. 1, first series. ] as to be placed beyond any doubt; and, therefore, such expansion, taken in connection with the preceding facts, and the important one noticed by Mr Prinsep, leaves us no alternative but to conclude, that the final deficiency of metal is owing to the exterior crust having, after its own formation, continued to expand, and thereby [7:18:756]to acquire a greater capacity within than the mere expansion of the interior parts at the time of their congelation enables them to fill up.^[7. Mr Prinsep not only never hints at there being any connection between the expansion which occurs in casting, and that which he observed; but the following quotation from the Philosophical Transactions for 1828, page 87, besides being curious, and the only remark he has made on the subject, sufficiently shows that he had no idea of the nature of the latter increase. “The augmentation,” says he, “which is more remarkable, exceeds the dilatation due to the temperature to which it was exposed; for as iron expands O105 in 180 degrees, the increase of bulk upon 10 cuþic inches should be ∙105 X 3 = ’ 315 at 1800 β Fahrenheit, or near the melting point of silver; whence it may be concluded that the dilatation of iron is not equable, as has been also proved by Messrs Dulong and Petit.” We shall only add, that the experiments of these distinguished foreigners having been made on wrought iron, it is very doubtful if they bear on the question of permanent expansion. ] The sponginess and cavities which so often occur in the texture of the iron in the interior parts of an unbored cannon, and in those of shot, seem readily referrible to the same source.

Water and iron are usually supposed to follow similar laws of congelation, but their phenomena are certainly very different; for water, in place of continuing to expand, as iron may do, for an indefinite time, seems to cease to expand as soon as it assumes the solid form. We have often observed, that on exposing water in a thin vessel during intense frost, the exterior parts congeal first all around, next the vessel as well as on the top, so as to incase completely the remaining liquid with a crust of ice, which at length bursts, perhaps the vessel too, and part of the water escapes through the fissures. This no doubt is owing partly to the atmospheric pressure having prevented such crust from ever being larger than just to contain the water, and partly’to the interior parts expanding subsequently to the crust having ceased to expand; so that, in place of a deficiency, there is here an excess of material within. On the contrary, nothing like bursting ever occurs in the case of iron; though frequently it happens that its more slender parts, in cooling, crack or break spontaneously, from their not having been able to preserve a temperature sufficiently high to continue the permanent part of the expansion so long after congelation as the rest has done, and also from their contracting sooner than the rest by the more sudden cooling. That the temporary part of the whole expansion which obtains in cast iron at a high temperature, is so great as to exceed the permanent part, appears from the subsequent contraction which occurs in cooling, as displayed by the well-known fact, that any lengthy casting is always sensibly shorter than its pattern; notwithstanding that the walls or inner surfaces of the mould, especially when formed of soft materials, have, by yielding to the weight of the liquid iron, and to the just-mentioned permanent part of the expansion, made room for some addition to all the dimensions of the pattern; so that the breadth, thickness, or such other of these dimensions as are small, generally exceed the corresponding ones of the pattern. From Mr Prinsep’s experiments, however, we may learn the very important caution, that after trying to what extent any substance has been expanded whilst hot, it should also be ascertained whether any of its dimensions have thereby undergone any permanent change. Some of the stories so often repeated regarding remarkable exceptions to the general laws of expansion, are very likely referrible to this kind of source. Thus, glass vessels have sometimes been observed to acquire a permanent enlargement by lotìg exposure to heat; and, in many researches, such a change in the vessel is apt to be mistaken for one of the opposite sort in any fluid it may contain. The case noticed by Mr Prinsep being that of a little iron retort, the mass would be small and the metal thin; and, therefore, at the time it had been cast, it must have cooled so soon that it could then have had almost no opportunity of continuing to expand permanently after its solidification. Hence, on being afterwards heated by Mr Prinsep, it would likely be in a state to expand so much the more. For, supposing the volume to undergo no change from oxidation or other chemical action, it is probable that long-continued annealing at a high temperature would give to cast iron a volume which it would not afterwards exceed, unless exposed to a still greater heat. On this principle, it might be supposed that a sufficient annealing might expand all the parts in the same ratio, and thereby ultimately fill up all the vacancies of the interior; but the rigidity of the iron puts this out of the question; and at any rate, granting that the annealing did bring the parts quite close together, they would not likely be united by cohesion at a heat so far below that required for welding.

Thç preceding view of the subject, we presume, will be found to tracé to a common source, and thereby to reconcile in a satisfactory manner, the various phenomena above mentioned, which depend upon the permanent expansion of cast iron, and have so often been regarded as paradoxical. The continued enlargement of the crust is most probably owing to some change of texture or arrangement, such as crystallization occurring not only, as is usually supposed, at the instant of congelation, and perhaps, too, before it, but continuing to go on in the solid part of the iron for a long while after, if it be kept sufficiently hot; and the nature of the mould very likely modifies this result, as it certainly does several others. Thus, a piece of iron cast in a metallic mould, being more suddenly cooled than if cast in sand, is much harder, and has, besides, a very different texture. But whilst it is not improbable that the contact of the metallic mould may be equally or more favourable to a particular arrangement of the particles, such process will be so much the sooner stifled by the more sudden cooling. As to wrought iron, its fracture sometimes exhibits a crystalline texture, which is a particularly bad symptom of its strength, but one, perhaps, which may have some connection with a permanent expansion. Bismuth and antimony are known to expand at the time of congealing; but how closely in this respect they may resemble cast iron, has not, as far as we know, been ascertained. (e. e. e.)