THERMOMETER, from θεgμὸς , warm, and μετgέω, I measure; an instrument for indicating the temperature of bodies, or the intensity of their heat or cold, in terms of the expansion of one or more of them. But such an instrument is seldom adapted to afford any direct measure of absolute heat; for the expansion of every substance which has yet been properly tried, proceeds in some higher ratio than the corresponding increase of absolute heat. Of this, air affords a remarkable example, as will be seen in the sequel. Thermometers seem to have been invented about the end of the sixteenth or beginning of the seventeenth century, though, like many other useful inventions, it is not agreed to whom the honour of the first of them belongs. Boerhaave ascribes it to Cornelius Drebel, Fulgenzio to Paolo Sarpi, and Sanctorio claims this honour for himself, being supported by Borelli and Malpighi. But Μ. Libri, after bestowing a great deal of labour and research on the subject (Annales de chimie for December 1830), maintains, principally on the authority of Castelli and Viviani, that Galileo had invented the thermometer prior to 1597, and that Sagredo perfected it. There is nothing improbable however in thermometers having been really invented by several different persons, independently of each other, and much about the same time.

The first form of an instrument for indicating the temperature, seems to have been a very imperfect air-thermometer. It had been long known that air expands considerably with heat, and contracts again with cold, and that this expansion or contraction is greater or less according as the heat or cold applied is so. The principle, then, on which this air-thermometer was constructed is very simple. It consists of a glass tube, BE, fig. 1, Plate CCCCXCIV,, connected at one end with a large glass ball A, and having its other end immersed in an open vessel, or terminating in a ball DE, with a narrow orifice at D; which vessel or ball contains some coloured liquor that will not easily freeze. But the ball A must be first warmed, to expel a portion of the air through the orifice D; and then, while cooling again, the liquor, pressed by the atmosphere, will enter the hall DE. The quantity of included air is to be so adjusted that, at a mean temperature of the weather, the liquor may stand near the middle of the tube, as at C, when the weight of the liquor, and the elasticity of the included air, counterbalance the pressure of the atmosphere. As the temperature increases, the included air, expanding thereby, will drive the liquor into the lower ball, and consequently its surface will descend in the tube. On the contrary, as the temperature falls, the air in the ball contracts, and the liquor pressed by the atmosphere will ascend; and such ascent or descent will be more or less, according to the change of temperature. To the tube is affixed a graduated scale, by means of which the motions of the liquor in the tube, and consequently the variations in the temperature, may be observed.

This instrument having been found extremely defective, owing to the air in the tube being affected by every variation in the pressure of the atmosphere, the Florentine Academy, about the middle of the seventeenth century, instead of air, employed alcohol, which, being coloured, was enclosed in a fine glass tube, having a hollow ball at one end A, fig. 2, and closed at the other end D. The ball and tube were filled with alcohol, so as to stand at a convenient height, as at C, when the weather is of a mean temperature. This may be effected by immersing the open [7:21:237]end of the tube into a vessel of coloured alcohol, and then heating the ball to expel the greater part of the air, or by placing it under a receiver of the air-pump. When the thermometer is properly filled, the end D is closed by drawing it to a point, and slightly melting it at a lamp, and it is then said to be hermetically sealed. Formerly the included air was generally left of about one third its natural density, to prevent the alcohol in the tube from separating; but some now try to expel the air entirely, and assign the same reason for so doing. When the temperature increases, the alcohol expands, and rises in the tube; and when the heat decreases, it descends, as measured by means of an attached scale.

The alcohol thermometer, being unaffected by variations in the pressure of the atmosphere, soon came into general use, and was at an early period introduced into Britain by Mr Boyle. To this instrument, as then used, there are, however, many objections. The liquor employed not being always of the same strength, different tubes filled with it, and exposed to the same temperature, did not correspond. It was another defect, that the scale did not commence at any fixed point. The highest term was adjusted to the great sunshine heats of Florence, which are very variable and undetermined; and frequently the workman formed the scale after his own fancy. While the thermometer was so defective, it could not be of general use.

To discover some fixed point by which a determinate scale might be obtained, to which all thermometers might be accurately adjusted and rendered comparable among themselves, was the next desideratum. Mr Boyle, who had at an early period studied the subject, proposed the freezing point of oil of aniseeds; but this he soon abandoned. Dr Halley next proposed that thermometers should be graduated in a deep pit, where the temperature in all seasons is pretty uniform; and that the point at which the spirit of wine stood there, should be the commencement of the scale. But this was evidently so inconvenient that it also was speedily abandoned. The freezing point of water he regarded as a variable one.

It seems to have been reserved for the genius of Sir - Isaac Newton to determine this important point, on which the accuracy and value of the thermometer depends. He chose, as fixed, those points at which water freezes and boils; the very points which experiments have since determined to be the most fixed and convenient. Sensible of the disadvantages of spirit of wine, he tried linseed oil, which is capable of about fifteen times greater expansion. It has not been observed to freeze even in great colds, and it bears a considerable heat before it boils. With these advantages, it was, in 1701, used by Newton, who estimated by it the temperatures of boiling water, melting wax, boiling spirit of wine, and melting tin. His method of adjusting the scale was this. Supposing the bulb, when immersed in thawing snow, to contain 10,000 parts, he found the oil expand by the heat of the human body so as to take up 1/ 39 th more space, or 10,256 such parts; and by water boiling strongly 10,725, and by melting tin 11,516: so that, reckoning the freezing point as a common limit between heat and cold, he there began his scale, marking it 0°, and the heat of the human body he made 12°; and assuming the degrees of heat proportional to the expansion, or 256: 725;: 12: 34, this last will express the heat of boiling water, and, by the same rule, 72 that of melting tin.

To the application of linseed oil as a measure of heat and cold, there are insuperable objections. It is so viscid, and adheres so strongly to the sides of the tube, that it moves too slowly. In a sudden cold, so much remains adhering to the sides of the tube, that the top of the oil is seen lower than the temperature requires it

All the thermometers hitherto proposed having been liable to many inconveniences, this led Reaumur to attempt a new one, which was described in tire Mémoires de l’Académie for 1730. This thermometer was made with spirit of wine. He took a large ball and tube, graduating the latter such, that the space from one division to another might contain the 1000th part of the liquor as it stood at the freezing point, which he adjusted by an artificial congelation of water. Then putting the ball and part of the tube into boiling water, he observed whether it rose eighty divisions; if it exceeded these, he added water, or if it fell short of eighty divisions, he added rectified spirit. The liquor thus prepared served for making a thermometer of any size which would agree with his standard.

But as the bulbs were three or four inches in diameter, the surrounding ice would be melted before its temperature could be communicated to the whole bulb, and consequently the freezing point would be marked too high. Dr Martine accordingly found, that instead of 32° Fahrenheit, it corresponded with 34°, or a little above it. Doubts have often been started whether Reaumur had really ever put his thermometer in boiling water, considering that alcohol boils at a much lower temperature. But unless the upper end of the tube be open, or comparatively cold, the alcohol so enclosed will, owing to the increased pressure, scarcely boil at all, and more especially if a portion of air be included along with it. No doubt there will be some risk of bursting the bulb, though not much with such weak alcohol as Reaumur’s. It is however quite obvious that the boiling point of any liquid with which a thermometer may be filled is not necessarily the upper limit of its scale.

At length mercury was proposed as a fluid preferable to any yet employed in the construction of thermometers. The first idea of this is usually ascribed to Dr Halley; but he did not put it in practice, on account of the small expansibility of mercury. Boerhaave says the mercurial thermometer was first constructed by Olaus Roemer; but the honour of this is generally given to Fahrenheit of Amsterdam, who described it to the Royal Society of London in 1724.

Mercury is superior to alcohol and oil, except for very low temperatures, and is much more manageable than air. Of all liquids it is the most easily freed from air. It sustains a beat of 680° of Fahrenheit’s scale, and does not congeal till it fall 39 or 40 degrees below 0°. It is the most sensible of any fluid to heat and cold, even air not excepted. Count Rumford found that mercury was heated from the freezing to the boiling point of water in 58 seconds, while water took 133 and air 617 seconds. The expansion of mercury is only about 1 / 6 th of that of alcohol, but it is sufficient for most of the purposes of a thermometer. As to what is usually esteemed the chief thermometric property of mercury, that of its variations of volume being nearly proportional to the variations in its absolute heat; this at best only argues the mercurial thermometer to be a tolerably good measure of the variations of its own heat, or of that of any other mass of mercury, which certainly is a property of very limited importance, if, after all, it leave us in the dark regarding the relation which subsists between the degrees of the mercurial scale and the corresponding variations of the absolute heat in other bodies.

Perhaps the simplest mode of filling a mercurial thermometer is to put the mercury into a paper funnel tied round the top of the tube. But unless the bore be unusually large, no mercury will enter it till the air be more or less expelled by heating the bulb; and then, on allowing it to cool again, the atmospheric pressure will force in the mercury. This operation should be done cautiously, by alternately heating gently and then cooling the bulb, and at length making it boil so as completely to expel the air. It is almost needless to add, that the tube as well as the mercury should be perfectly clean. To close the extremity of the tube, it is first softened by heat and drawn to a capillary[7:21:238] orifice. Then, if it is wished to free the tube entirely of air, the bulb is heated fully to the highest temperature it is ever intended to measure, and whilst in that state, the mercury then filling the whole tube, the capillary point is to be melted in the flame of a lamp.

To render a very slender thread of mercury more distinctly visible, Dr Wilson of Glasgow introduced tubes with flattened bores. This form, which is now in very general use, has often been objected to, as tending to render the bore unequal; but from attentively witnessing the process of drawing tubes, we are rallier at a loss to see any ground for the objection. The uniformity of a bore may be easily tested by trying whether the same minute quantity of mercury occupies the same length in every part of the tube when shifted through it. There is however one fortunate circumstance regarding tubes, which seems to be entirely overlooked, namely, that the bore, whether cylindrical or flattened, is seen considerably magnified by the refraction of the glass.

The bulbs of thermometers are generally spherical. Sometimes, however, to suit particular purposes, or to acquire more speedily the temperature of contiguous bodies, other figures are given them, such as that of a pear, an egg, a lens, or a cylinder. When a bulb is exposed to any pressure materially different from the mean of the atmosphere, its size, especially if large and thin in the glass, is so much affected as sensibly to alter the height of the mercury in the stem; but this is so different in different thermometers, that the requisite correction can only be ascertained for any one by actual trial.

The fixed points which are now universally adopted for thermometers are the boiling and freezing points of water. The boiling water point, it is well known, varies some degrees according to the pressure of the atmosphere. In an exhausted receiver water boils at 98° or 100° Fahrenheit, whereas in Papin’s digester it may require 400°. Nay, unless the bottom of the digester be hotter than the top, the pressure of the steam will completely prevent any boiling till the vessel burst. Hence it appears that water boils at a lower point, according to its height in the atmosphere, or to the smaller pressure of the air upon it.

The history, as well as the mode of applying the variations in the boiling point of water to the mensuration of heights, has been given by Sir John Leslie under the article Barometrical Measurements, vol. iv. p. 401, which probably was written for the Supplement to the former edition of this work, before Dr Wollaston hail described his thermometrical barometer in the Philosophical Transactions for 1817. But at the Dublin meeting of the British Association, Colonel Sykes, after objecting to this refined apparatus, as expensive, and so fragile as to be extremely liable to accidents in travelling on mountains, described a variety of very satisfactory measurements which he had made with common thermometers.

As artists may be obliged to adjust thermometers under very different pressures of the atmosphere, M. Deluc, in his Recherches sur les Mod. de l’Atmosphere, from a series of experiments, has given an equation for this difference, in Paris measure, which has been verified by Sir George Shuckburgh; who, as well as Dr Horsley and Dr Maskelyne, has adapted the equation and rules to English measures, and reduced the allowances into tables. Dr Horsley’s rule deduced from Deluc’s is this:

99000 / 899 log. z -92·804= h , where h denotes the height of a thermometer plunged in boiling water above the point of melting ice, in degrees of Fahrenheit, and z the height of the barometer in 10ths of an inch. From this rule he has computed the correction in the second column of the following table:
[table]

In the first column is the height of the barometer, in inches. The second shows the correction to be applied, according to the sign, to 212° of Fahrenheit, to find the true boiling point, which for all intermediate states of the barometer may be had with sufficient accuracy by taking proportional parts. The fourth column contains a correction for the same purpose, according to the experiments of Sir George Shuckburgh. See Philosophical Transactions, vol. lxiv. art. 20 and 30.

The temperature of steam in a nearly closed vessel is more steady, and slightly lower than that of boiling water; and the latter is from 2° to 4° higher in a glass vessel than in one of metal. It is of material importance that the water be pure, because foreign substances are apt to affect both the freezing and boiling points.

The Royal Society, fully apprised of the importance of adjusting the fixed points of thermometers, appointed a committee to consider the best method for this purpose. See Philosophical Transactions, vol. lxvii. part ii. art. 37.

Although the boiling point be placed rather higher on some thermometers than on others, this produces very little error in observations on the weather, at least in this climate; for an error of 1½° in the boiling point will make an error only of half a degree in the position of 92°, and of not more than a quarter in that of 62°. It is only in nice experiments, or with hot liquors, that this can be of importance. In adjusting the freezing as well as the boiling point, the tube ought to be kept of the same temperature as the ball. Many a thermometer, whilst undergoing this operation, has little more than the bulb immersed in the bath which is to give the requisite temperature, the stem being just allowed to take its chance of holding some unknown temperature intermediate between those of the bath and of the air. The indications of such an instrument, though pretty well adapted for ordinary chemical purposes, must be somewhat uncertain. But it is evidently impossible to apply a correction for this, either to an instrument so vaguely graduated, or indeed to the very best of thermometers when used with the stem at an unknown temperature; so that tables formed upon the idea that the stem has always the same temperature as the air of the apartment, cannot be expected to afford the proper correction, especially considering how rapidly hot air and vapour may rise around the stem, from a hot liquor. A mode of lessening this error will afterwards be noticed.

In the ordinary manufacture of thermometers, it is reckoned sufficient to place the new instrument horizontally in a bath along with a standard thermometer, and to mark on it the corresponding degree, or part of a degree; next, either to change the temperature of the same bath, or to put the instruments together into a bath of a different temperature, marking the degree as before. The space between the two points so marked is then divided equally into the corresponding number of degrees (regard of course being had to any fraction), and the like division, if necessary, [7:21:239] is extended both ways beyond the two points. This method, however, does not provide against any inequality in the bore of the tube. But it is obvious that any error from such inequality might be obviated by marking a sufficient number of points at different temperatures; and also that by the same means an alcohol thermometer may be graduated to agree with a mercurial one, notwithstanding their very different rates of expansion. This we should think greatly preferable to the perpetual application of corrections for their difference. However, when an alcohol thermometer does require a correction, this ought to be effected by means of a table formed from actual comparison with a good mercurial one; because alcohol thermometers differ so much among themselves that no general table can be applicable to all. See Dr Richardson’s remarks, with examples of this, in Journal of the Royal Geographical Society, vol. ix. p. 332.

As the division of the scale is an arbitrary matter, thermometers differ much in this circumstance. Fahrenheit made 180 degrees between the freezing and boiling water points, Celsius made 100, Reaumur 80, Amontons 73, and Newton only 34. For a general comparison of various scales, see fig. 4. A very accurate method of verifying the scales of thermometers, and an example of the discordance of two standard thermometers, are given by Professor Forbes in the Philosophical Transactions for 1836, p. 577. The history of several thermometers is briefly given in the article Βαrομετεr, and a description of the Differential Thermometer, and of metallic thermometers, will be found under the article Meteorology. For a differential thermometer Dr Marshall Hall employs a mercurial thermometer, with a very minute bore and large degrees; and to avoid an inconveniently long tube, he has a ball at the top, into which he can at pleasure throw up a portion of the mercury. But, owing to the quantity of mercury actually used being thus rendered variable and uncertain, the indications of such an instrument are not comparable with those of a common thermometer. About twenty years ago, the journals announced a great improvement which Dr Howard had made on Leslie’s differential thermometer, by substituting alcohol for sulphuric acid. But had the learned doctor been sufficiently acquainted with the subject, he would have known that Leslie had purposely avoided using any liquid which sensibly emits vapours; because a variable quantity of elastic vapours mixed with the included air, must necessarily occasion similar but incomparably greater uncertainties than those in Dr Hall’s instrument.

As to the point at which the scale ought to commence, various opinions have been entertained. If we knew the beginning or lowest degree of heat, all would agree that this ought to be the lowest point of the thermometer; but we know neither the lowest nor the highest degrees of heat; we observe only the intermediate parts. All we can do, then, is to begin it at some invariable point, to which thermometers made in different places may easily be adjusted. Fahrenheit began his scale at the point where snow and salt congeal. Kirwan and Blagden proposed the freezing point of mercury. Sir Isaac Newton, Hales, Reaumur, and Celsius, adopted the freezing point of water. Fahrenheit’s zero is placed at an artificial cold which few can ever experience. There would be several advantages in adopting the freezing point of mercury. It is the lowest degree to which liquid mercury can be applied; and it would supersede the use of the signs plus and minus on a mercurial thermometer. But it is not a point well known, for few can have an opportunity of seeing mercury congealed. As to the abolition of negative numbers, it would not counterbalance the advantage of using a well-known point. Of heat and cold we can only judge by our feelings. The po'∣Dt, then, at which the scale should commence, ought to be one which can form to us a standard of heat and cold.

Such is the freezing point of water chosen by Newton; for of all the general effects of cold it is the most remarkable. It therefore suits thermometers to be used all over the globe; for even in the hottest countries there are mountains perpetually covered with snow.

The thermometers at present in most general use, are Fahrenheit’s in Britain, Holland, and North America; De l’Isle’s in Russia; Reaumur’s and the centigrade in France; and Celsius’s, the same as the last named, in Sweden. They are generally filled with mercury. But here it may be proper to observe, that the mercurial thermometer which goes by the name of Reaumur’s, was not in use till long after his time, and was first introduced by Deluc.

The relative values of the degrees of Fahrenheit F, of Celsius C, and Reaumur R, are expressed by the following formulae.

F = 32 + 9 / 5 C = 32 + 9 / 4 R.

C = 5(F-32) / 9 = 5 / 4 R.

R = 4(F-32) / 9 = 4 /

These expressions are perfectly general, proper regard being always had to the signs when any of the symbols become negative. The formulae usually given in books of chemistry expressly for negative degrees are not simply useless, but so wild that they cannot fail to mislead and perplex those whom they are intended to guide. In Fahrenheit’s scale it is seldom necessary to use either fractions or negative degrees, which is by no means the case with the other two. Instead of a single thermometer whose scale would extend from the freezing to the boiling point of mercury, or through nearly 720° F., and which must either be inconveniently long, or have exceedingly minute degrees, it is better to have several thermometers, each of which will in succession apply to a different part of the whole range, so as to embrace or share the whole among them. In this way, while the degrees may be large, the stem of each thermometer, containing but a small proportion of the whole mercury, will occasion so much the less error when its temperature differs from that of the bulb. Fig. 3 shows a thermometer adapted to the ordinary atmospheric temperatures. In thermometers intended for corrosive liquors, the divisions or degrees are sometimes marked on the bare glass. In some, either the scale does not extend quite down to the bulb, or a portion of it is made to fold up with a joint.

It is not improbable that the freezing points of many old thermometers may have originally been marked too low, either from using water cooled artificially, or the ice of brackish or of other impure water. At any rate, it is now found, that when placed in melting ice, they generally stand above their freezing points. But supposing this to be a real deterioration which has taken place during the lapse of time, the following would seem to be the most probable of the causes which have been assigned for it, particularly in mercurial thermometers. 1. A permanent contraction of the bulb, gradually induced by the excess of the atmospheric pressure over that within, owing to the air having been more or less expelled. 2. If, after the air has been entirely expelled from the bulb, either some of it still remain in the tube, although sealed, or the tube have been left quite open, the air will gradually insinuate itself again between the mercury and glass of the tube, till it at length enter the bulb and form a complete lining to the inside of the glass. By this means, the air, slightly displacing the mercury, will raise it higher in the stem. 3. A rather questionable change, independently of the preceding, is supposed gradually to take place for some time in the molecular structure of the glass. But why this process should contract[7:21:240] rather than enlarge the bulb has never been explained; only we presume it could be prevented by previously annealing it properly. However, such of the original alcoholic thermometers of the Academia del Cimento as have been preserved and examined, are said to have undergone no change in their freezing points during a period of more than two hundred years, which rather argues against any change in the dimensions of the glass.

As in meteorological observations it is necessary to attend to the greatest rise and fall of the thermometer, attempts have been made to construct instruments which might register the greatest degree of heat or of cold which took place during the absence of the observer. In 1757 Lord Charles Cavendish presented to the Royal Society a thermometer to mark the greatest heat, and another the greatest cold. The first consists of a glass tube AB, fig. 5, with a cylindrical bulb B at the lower end, and capillary at the top, over which is fixed a glass ball C. The bulb and part of the tube are filled with mercury, the top of which shows the degrees of heat as usual. The upper part of the tube above the mercury is filled with alcohol, and so is the ball C almost to the top of the capillary tube. When the mercury rises, the spirit of wine is also raised, and runs into the ball C, which is so made that the liquor cannot return when the mercury sinks; consequently the height of the spirit of wine in the ball, added to that in the tube, will give the greatest degree of heat to which the thermometer has pointed since last observation. To prepare for a new observation, the instrument must be inclined till the liquor in the ball cover the end of the capillary tube.

The thermometer for showing the greatest cold is represented in fig. 6 by the crooked tube ABCD. It contains alcohol, together with as much mercury as fills both legs of the syphon, and part of the hollow ball C. The temperature is shown by the rise or fall of the mercury in the leg AB. When the mercury in the longer leg sinks by cold, that in the shorter will rise and run over into the ball C, from which it cannot return when the mercury subsides in the shorter and rises in the longer leg. The upper part of the shorter leg will therefore be filled with a column of spirits, of a length proportional to the increase of heat; the lower end of which, by means of a proper scale, will show how much the mercury has been lower than it is; which being subtracted from the present height, will give the lowest point to which the mercury has fallen. To prepare for a new observation, the mercury is made to run back from the ball into the shorter leg, by inclining the tube and heating the ball.

Another self-registering thermometer was proposed by Mr Six in 1782. It is principally filled with alcohol, though mercury is also employed for supporting an index. ab, fig. 7, is a thin tube of glass, sixteen inches long and five sixteenths of an inch caliber: cde and fgh are smaller tubes, about one twentieth of an inch caliber. These three tubes are occupied with alcohol, except the space between d and g, which is filled with mercury. As the alcohol contracts or expands in the middle tube, the mercury falls or rises in the outside tubes. An index, represented in fig. 8, is placed on the surface, within each of these tubes, so light as to float upon it. k is a small glass tube three fourths of an inch long, hermetically sealed at each end, and enclosing a piece of steel wire. At each end l , m, of this small tube, a short tube of black glass is fixed, of such a diameter as to pass freely up and down within each of the outside tubes ce or fh of the thermometer. From the upper end of the index is drawn a spring of glass to the fineness of a hair, which presses lightly against the inner surface of the tube, and prevents the index from descending when the mercury descends. When the alcohol in the middle tube expands, it presses down the mercury in the tube hf and consequently raises it in the tube ec; so that the index on the left-hand tube is left behind and marks the greatest cold, and the index in the right-hand tube rises and marks the greatest heat.

Dr Rutherford’s register thermometers, which are more generally used than any other, are described in the article Meteorology, and in the Transactions of the Royal Society of Edinburgh, vol. iii.

The following ingenious contrivance by Mr Keith of Ravelstone, besides being well adapted for marking the maximum and minimum, may also be employed to register the temperature in a continuous form for almost any length of time. AB, fig. 9, is a thin glass tube about fourteen inches long and three fourths of an inch caliber, close or hermetically sealed at top. To the lower end, which is open, is joined the crooked glass tube BE, seven inches long and four tenths of an inch caliber, and open at top. The tube AB is filled with alcohol, and the tube BE with mercury. This is properly an alcohol thermometer, and the mercury is used merely to support a float E of ivory or glass, with a wire EH for raising one index or depressing another, according as the mercury rises or falls. The float-wire, by means of an eye at a, moves easily along the small harpsichord wire GK. L, L' are the two indexes, made of thin black oiled silk, which slide up or down with a very slight force. The one above the knee points out the greatest rise, and the one below shows the greatest fall, of the thermometer.

To prepare for an observation, both indexes are brought close to the knee H. It is evident, that when the mercury rises, the knee of the float-wire will carry with it the upper index L. When the mercury again subsides, it leaves the index, which will not descend by its own weight. As the mercury falls, the float-wire brings along with it the lower index L', which it leaves behind as it had formerly left the upper. The scale to which the indexes point is placed parallel to GK. A cylindrical glass cover is placed over the part GF.

The continuity of the register is to be effected by attaching to the float-wire a soft pencil, which is to bear lightly upon a cylinder covered with paper, and revolving on a vertical axis by means of clock-work, once in a month. At each month’s end the paper is to be removed and a clean one put in its place. The paper is to be ruled horizontally with a set of lines to mark the degrees, as on the scale of a thermometer; and also vertically with lines to note the days of the month, and other smaller divisions of time. See Transactions of Royal Society of Edinburgh, vol. iv.

Owing to the moving force in metallic thermometers becoming so exceedingly feeble at the outstretch, that the least resistance will make them stop too soon, and then perhaps let them go too far by a start, they are not well suited for register thermometers, though often recommended for this purpose. But Dr Ure’s “thermostat,” for regulating temperature (Dictionary of Manufactures), depends on the same principle.

Various schemes have at different times been proposed for poising a thermometer so nicely across an axis, that a very slight change of temperature should disturb the equilibrium sufficiently to produce a very sensible change in the position of the instrument. Register thermometers in this form are liable to the same objection as the metallic sort. But the principle of the balance has been employed in various forms, and on a large scale, for opening and shutting doors to regulate the temperature of apartments, by admitting just the requisite quantity of cold air. For this purpose, Dr Cumming suspended and counterpoised a large ball and tube containing air, and having its open end immersed in a cistern of mercury. The arrangement was such, that as the ball rose or fell with the expansion or contraction of the included air, it closed or opened the door or window of the apartment. To obviate the effect of changes [7:21:241]of atmospheric pressure, the counterpoise carried a large barometer tube, which also was immersed in mercury, and had its upper part empty like any common barometer.

A species of thermometer contrived for observing the force of solar radiation, and named an actinometer, consists of a large hollow cylinder of glass, having its upper end contracted and joined to a thermometer tube, terminated at the top in a hall drawn out to a point, and broken off, so as to leave a small orifice. The lower end of the cylinder is closed by a silver or silver-plated cap cemented on it, and furnished with a screw, also of silver, passing through a collar of waxed leather, which is pressed into forcible contact with its thread, by a tightening screw of large diameter enclosing it, and working into the silver cap by the aid of a strong key or wrench. The cylinder is filled with a deep-blue liquid, ammonio-sulphate of copper, and the ball at the top being left purposely full of air, and the point closed with melted wax, it becomes, in any given position of the screw, a thermometer of great delicacy, the tube being furnished with a graduated scale. The cylinder is enclosed in a chamber blackened on three sides, and on the fourth or face defended from currents of air by a thick glass, removeable at pleasure. The design of the screw is to vary at pleasure the capacity of the cylinder, and thus to drive, if necessary, a portion of the liquid up into the ball, which acts as a reservoir, or, if necessary, to draw back from that reservoir such a quantity as shall just fill it, leaving no bubble of air in the cylinder.

To use the instrument, examine, first, whether there be any air in the cylinder, which is easily seen by holding it level and tilting it, when the air, if any, will be seen to run along it. If there be any, hold it upright in the left hand, and the air will ascend to the root of the thermometer tube. Then, by alternately tightening and slackening the screw with the right hand, as the case may require, it will always be practicable to drive the air out of the cylinder into the ball, and suck down liquid, if any, from the ball to supply its place, till the air is entirely evacuated from the cylinder, and the latter, as well as the whole stem of the thermometer tube, is full of the liquid in an unbroken column. Then, holding it horizontally, face upwards, slowly and cautiously turn back the screw, till the liquid retreats to the zero of the scale. The observer must station himself in the sunshine, or in some sharply terminated shadow, so that without inconvenience, or materially altering his situation, or the exposure of the instrument in other respects, he can hold it at pleasure alternately in full sun and total shadow, and by that means find the difference in the effects, or the force of solar radiation. If placed in the sun, he must be provided with a screen of pasteboard or tin plate, large enough to shade the whole of the lower part or chamber of the instrument, from which it should not be less than two feet distant, and should be removeable in an instant. But farther details and examples in the use of this and various other meteorological instruments will be found in the Report of the Royal Society (August 1839), on the Instructions for the Scientific Expedition to the Antarctic Region.

Ever since Dulong and Petit published their valuable researches on heat (some of which have been particularly discussed under the article Pyrometer), and in which they have made the air-thermometer the standard of temperature, their example in the latter respect has been so very generally followed, as to render it of importance to ascertain whether the adoption of such a standard can consist with other admitted principles; more especially since the theory of the air-thermometer, as usually laid down in first-rate books on the subject, is full of contradiction. We shall therefore now endeavour to set the matter in a proper light, employing for this purpose the same data, and nearly the same notation, as those with which Baron Poisson commences his memoir in the Annales de chimie, tome xxiii. p. 337.

Let g be the density of the air, p the pressure, and θ the temperature in degrees of any common scale of an air-thermometer; then a being ∙00208 if Fahrenheit’s scale be employed, and b another constant, we have p — bg (1 + aθ ). This is commonly called the law of Mariotte, but was first discovered by Hooke when assistant to Boyle. With the centigrade scale, a would be ·00375; but both values of it would need to be slightly lessened if they were wished to agree with Rudberg’s experiments on the expansion of air (Poggendorff’s Annalen, xli. and xliv.), which perhaps require confirmation. Fortunately the present investigation has no dependence on the precision in the values of any constants. Let q be the difference between the total quantity of heat which a given mass of air may contain under the pressure p and temperature θ, and that which it contains under a pressure and temperature chosen arbitrarily. Then the specific heat of the air, or that which would raise its temperature one degree, being directly as dq, and inversely do as di, may be expressed by dq / dθ . When such rise takes place under a constant pressure, we have from the above equation, with p constant, dθ = — dg × 1+g θ / ag : and when under a constant volume, or with g constant, dθ = dp × 1+a θ / ap . The specific heat, when the pressure is constant, will therefore be — dq / dg × ag / 1+a θ ; and with the volume constant, dq / dg × ap / 1+a θ . Now , from the experiments of

Gay Lussac and Welter, which were carried through a great range both of temperature and pressure (Mécanique céleste, V. 97 and 127), it appears that the former of these two specific heats always exceeds the latter in a constant ratio, which, if it be called that of k to l , we shall have g dq / dg + kp dq / dp = 0..................(A).

Thus far the process does not materially differ from that pursued by Poisson and several other foreign mathematicians; but on integrating this equation, their next step is to modify the integral to suit the common theory of the air-thermometer, which assumes the variations of absolute heat to be proportional to those of the volume under a constant pressure. In this they do not seem to have been aware that equation (A) is utterly incompatible with any such assumption, as we shall now endeavour to explain. For it is evident that the value of dq in the first term of the equation, is always to dq in the second, as — dg / g to dp / kp ; whereas, if not only the differential of absolute heat in air under a constant pressure had been proportional to — dg / g the differential of the volume, but if, in like manner,

(as the common theory, when coupled with the constancy of the ratio of k to 1, assumes), the differential of heat under a constant volume had varied as dp the differential of the pressure, then the value of dq in the first term would dp necessarily have been to that in the second as — dg / g**************** to Ndp, where N is a constant. Now each of the former ratios is obviously the same with that of f to p~. which cannot e i hop dp 1

coincide with the ratio of — to N⅛>, unless N = τ-; that f i kgp [7:21:242] is, unless the product of the density into the pressure always form a constant quantity, which is extremely absurd. But it is equally clear, that if any other ratio which differs from the first one were assumed to subsist among the differentials, it must lead to the like absurdity of requiring some of the quantities to be both variable and constant at the same time. Whoever therefore admits the law of Mariotte, and the constancy in the ratio of the specific heats, has no alternative but to reject the common graduation, and indeed every other which would not make the differentials of heat follow the same proportion as do those of the logarithms of the volume and of the pressure, compounded of course with the ratio of k to 1. Hence the only function of the integral of equation (A) which can consist with the data is q = A + B (1 / k log. p — log.g ) (B), where A and B are constants. This shows plainly that, under a constant pressure, air expands in geometrical progression for equal increments of heat, as has been deduced from the same data by a very different process under the article HYGROMETRY, and where it is shown that the value of k is most probably 1·3333.

Extravagant as are the inconsistencies which necessarily result from coupling any of the common scales of temperature with the two principles above specified, yet this singular oversight, from its having originated in a work of no less authority than the Mécanique céleste ( v . p. 128), has been implicitly copied into almost every subsequent production on the same subject. For example, we find it pervading the very valuable and extensive writings of Baron Poisson, whose recent decease science has now to deplore; as also those of Navier, and of other eminent French writers, whenever they have occasion to treat on heat or sound. But a most notable instance of the sort is to be found in Mr Lubbock’s recent treatise On the Heat of Vapours, as will presently be noticed.

Since dg will vanish and change its sign in the first term of equation (A) just when dq in that term does so, it is evident that, although the first term may occasionally take the form of a vanishing fraction, it will never vanish nor change its sign. For a similar reason, the second term of equation (A) will never vanish nor change its sign. But since the sum of the two values of dq, regard being had to their signs, will be a measure of the rate at which the air may be gaining or losing heat; so it is only when those two values of dq are equal, and with contrary signs destroy each other, making, as it were, the decrement of heat annihilate the increment, that the absolute heat can be constant. In that case, which may imply the sudden compression or dilatation of air, equation (A) admits of being greatly simplified; because both terms being then divisible by the same value of dq, we have — dg / g = dp / kp . Hence k log.g = log.p + C; so that if the initial values of g and p be called g ' and p', we shall have C = k log. pt — log. p'; and k log. g / g' = log. p / p' , or (g / g' ) k = p / p' , as might likewise have been readily deduced from equation (B). But we have taken this other method that it might be clearly seen what a mistake some are in who suppose equation (A) to be restricted to the case in which the absolute heat is constant. For it is now evident that under such a restriction there could have been no use whatever in that equation containing dq, or indeed in its having the partial differential form at all. However, through some inadvertency, Mr Lubbock has so seriously misconstrued the investigations of the foreign mathematicians as to allege that their “theorems rest upon the condition that the absolute is constant while the sensible heat varies. This,” says he, “is the most restricted hypothesis which can be made upon the nature of heat.” Now we presume that if such an able mathematician as Mr Lubbock had only paid a little more attention to the writings of these authors, he would have found that they have restricted themselves to no such hypothesis. For although they have not overlooked the particular case just alluded to, in which air may be so suddenly compressed or dilated as to have its temperature altered without the absolute heat having had time either to gain or lose, they have treated the subject in a sufficiently general manner to include every other case. Thus it was by means of the variable part of the integral of equation (A) that they intended to express the change of absolute heat which may at any time accompany a change in g, in p, or in both together; and this they might have done quite consistently, had they not unfortunately modified the

1

integral into the form A + B —*****, with the view of making it embrace the common theory of temperature. But the most curious thing in the whole is, that Mr Lubbock has, after all, borrowed from them this very formula to be a principal link in his investigation, and then coupled it of new with an additional expression to embrace the theory just mentioned, as if the latter had not already had a sufficient share in it. See Phil. Magazine for May 1840, p. 439.

Since the constancy in the ratio of the specific heats enables us to distinguish between the heat which is absorbed in the enlargement of the volume, under a constant pressure, and that which alone raises the temperature; showing the latter to exceed the former in the constant ratio of 1 to k — 1; it is evident, that if at any stage of a very extensive increase of temperature, the expansion were to cease, the increment of heat which could add the next degree to the temperature would be the same, no matter what volume the air had by this time acquired; and that such increment would be equal to the decrement of heat for each successive degree of a uniform scale, were the enlarged volume of air now cooled down to the first temperature without suffering any contraction; so that the specific heat is in all cases independent of the magnitude of a constant volume. However, Professor Kelland, without adducing any proof, asserts in his Theory of Heat, that the specific heat is greater with a greater volume, which we now see to be utterly incompatible with the constancy in the ratio of the specific heats, a principle which he also admits and employs. The like may be said of his coupling this principle with the common scale of temperature, and also of his asserting that, in the sudden compression of air, the increase of temperature measured by that scale is proportional to the diminution of the volume; whereas it is the changes in their logarithms that are proportional, as is shown under our articles Hygrometry and Sound . At first sight, and indeed until some adequate means be used to test the soundness of such cases as the preceding, every thing in them may seem to be quite correct. Perhaps opposite errors may have destroyed each other, as sometimes happens from discarding or adopting, at certain stages of the process, quantities which may then seem quite inconsiderable, but which ultimately have sufficient influence to change the character of the final result. It is in this way that in the Theory of Heat (p. 98-95) results have been obtained which it is utterly impossible to deduce from the same data by any legitimate reasoning; as will be found to have been long since shown in the discussion of a similar case in the Edinb. Phil. Journal for July 1827, p. 154. (e. e. e.) Thermometer, Differential. See the preceding article, and Barometer, Climate, Cold, and Meteorology.