§ 2. The indications obtained by any of the numerous methods which have been suggested are, as a rule, expressed in terms of Centigrade or Fahrenheit degrees. This assignment of numbers presupposes not only a definition of temperature by which the size of the degree is determined but also a physical law which gives the relation between the measured interval of temperature and the standard degree. The various definitions of the standard degree that might be employed will be found in the article Heat, secs. 12, 24, 25, 30, 31, 32; and in sec. 35 of the same article the definition of the absolute thermodynamic scale of temperatures is given. In the same article (sec. 38) it is shown that the “absolute temperature” of a liquid in thermal equilibrium with its own vapour under a pressure p may be obtained from the formula

7 y (l-q∙)⅞ ∕ j p k ’ t = t 0 e p ° where p is the density of the vapour, pσ that of the liquid, κ the latent heat per unit-mass of the vapour corresponding to the saturation-pressure p. The dynamical equivalent of heat is represented by J. We have therefore the complete theory of what may soon become a practical method of expressing temperatures in the thermodynamic scale. Sir W. Thomson, in the article mentioned (secs. 39-45), has described arrangements for measuring the pressure of the saturated vapours of various liquids which will give that measurement in a thoroughly satisfactory manner up to, at any rate, some 600° C. For the higher temperatures mercury is the liquid employed. There are, however, some experimental data still wanting before the formula quoted above can be applied to the numerical calculation of the temperature. These are (1) the density p of the saturated vapour corresponding to the series of pressures, and (2) the corresponding latent heat κ of vaporization. These constants have not yet been actually observed. Instruments such as those figured in the article cited can, however, be employed with convenience and accuracy as continuous intrinsic thermoscopes, whose indications can supply a numerical measure of temperature after an empirical graduation. When used thus they possess the enormous advantage that the pressure of the saturated vapour at a definite temperature is perfectly definite, so that a single observation of the pressure is all that is necessary to determine the temperature, and the instrument can be easily arranged, so that this observation is practically a very simple one. The pressure of mercury vapour has already been determined by Régnault for temperatures up to 550°. A thermoscopic method of pyrometry which is very similar to the above was suggested by Lamy. He proposed to measure the pressure of carbonic-acid gas dissociated from calcium carbonate. There is experimental evidence to show that the pressure of the dissociated gas is definite at a definite temperature. The recombination of the dissociated gas with the solid is, however, a slow process, and the method has been pronounced by Weinhold to be practically unsatisfactory.

§ 3. Gas Pyrometry. Measurement of High Temperatures l>y the Expansion of Air and other Gases and Vapours. —Temperatures may be expressed in the absolute thermodynamic scale by the method of the gas-thermometer, which is available for practical purposes even at very high temperatures. It has been shown that the indications of a nitrogen or hydrogen gas-thermometer, whether it is arranged to show the increase of pressure at constant volume or the increase of volume at constant pressure, give for the temperature numerical results which are practically identical with the corresponding numbers on the absolute scale. It follows, therefore, that any two gas-thermometers, if similarly graduated, would give identical indications for the same temperature, no matter whether or not they are filled with the same kind of gas and whether or not the quantities of the gases are such that the pressure in the two thermometers is the same at any one temperature. This important property of gas-thermometers has been experimentally verified by Régnault by direct comparison up to 350° C. of instruments filled with different gases and at different pressures. For these reasons the readings of a properly arranged gas-thermometer have justly come to be regarded as furnishing the standard of temperature, at any rate outside the limits of the freezing and boiling points, and indeed may now be regarded as the temperature standard for scientific purposes throughout the whole range. The Kew standards are calibrated mercury-in-glass thermometers whose fixed points are repeatedly redetermined. Such instruments will not agree exactly with the gas-thermometer except at the freezing-point and boiling-point. Comparisons have been made between various mercury-thermometers and air-thermometers by Régnault and many others. The results obtained by different observers are not entirely concordant; but it is needless here to discuss them, for, whatever may be the divergence between the mercury and air thermometers in the freezingpoint and boiling-point, the method of measuring higher temperatures by continuing the scale of a mercury-thermometer beyond those limits is altogether untrustworthy in consequence of the very wide divergence between different mercury-thermometers at the same temperature, amounting sometimes to 10° or more at a temperature of 300°. The air-thermometer readings must therefore be regarded as the standard at any rate for temperatures beyond the boiling-point.

The general principle employed in the use of the gasthermometer is as follows. Let p 0 be the pressure of a mass of gas at 0° C., 7> 100 the pressure of the same mass of gas at 100° C., the volume being the same, p t the observed pressure of the same mass of gas at some unknown temperature t, the volume still remaining the same, then Pt~Po. _ < ∩∖

2 ’ ιoo - Po lθθ

We require, therefore, three observations of the pressure, two to graduate the instrument and the third to measure the temperature. If the thermometer has been filled with gas of a perfectly definite kind— e.g., properly dried and purified air, nitrogen, or hydrogen—and the containing vessel has been previously thoroughly dried, the value of ∕> 100 may be obtained from tables, since jo 100 =∕> 0 (l + 100α), λvhere a is the tabulated coefficient of expansion of the gas at constant volume. It is practically impossible to keep the volume of the gas constant in consequence of the expansion of the envelope. A correction must be applied on this account, the value of which is derived from independent observations of the expansion of the material of the envelope. If the pressure of the gas be maintained constant, and the volumes υ t , v 100 , t∣ 0 be observed for the three temperatures i o , 100°, 0°, we have—

Vt-V n ... t , 2 x r 100 -ι⅛ 1∞

In like manner ι ’ 100 - v 0 may be taken from a table of the coefficients of expansion of gases. The different methods which have been suggested for the employment of this property of gases to measure high temperatures are very numerous. We give details of a few of them.

(1) The Constant-Pressure Method.— The following is a very simple and practical plan of employing the method for obtaining a reading of the temperature. A glass or porcelain bulb, provided with a fine neck, is very carefully dried and filled with perfectly dry air; it is then exposed to the source of the heat whose temperature is to be investigated in such a manner that the point of the neck just projects from the furnace. "When the equilibrium of temperature is reached, the neck is hermetically sealed by a blowpipe or oxy-hydrogen flame, and the bulb is withdrawn and allowed to cool, and weighed. The neck is then immersed in water or mercury and the point broken off. In consequence of the previous expansion of the air the pressure in the interior is much less than the atmospheric pressure, and the liquid consequently enters the bulb. When so much has entered that the pressure is the same inside and out (the difficulty of the comparative opacity of the porcelain is not insurmountable), the end is closed by a small piece of wax, and the bulb removed and weighed, with the liquid it contains. The bulb is then completely filled with the liquid, and weighed a third time. The difference between the third and first weighings gives a value υ t of formula (2), which only requires correction for the expansion of the envelope, while the difference between the second and first weighings gives a value of the volume from which v 0 and ι> 100 can be calculated, using the known co efficient of expansion of air, and thus all the requisite data for the determination of t are obtained. This method was used by Régnault to determine the coefficient of expansion of air, and has since been described as “a new pyrometer.”

In the process just described the volume of the residual gas is measured; its pressure, after cooling, may be measured instead, by an arrangement which was suggested by Régnault. The bulb is provided with a long fine neck, to the end of which a tap is fitted and so arranged that it can be easily connected with a manometer. The bulb is exposed to the high temperature, the tap being left open, and when the final temperature is reached the tap is closed and the bulb allowed to cool; it is then connected with the manometer, and, if the tap be a three-way tap, drilled as shown in fig. 1, it is easy to expel all the air from the bulb side of the manometer, between the mercury surface and the tap. The residual pressure is then measured by the manometer. A correction is required for the expansion of the bulb and for the part of the connecting tube not exposed to the high temperature. Instead of measuring the volume of the residual gas in the manner thus described, Deville and Troost have pumped the hot air out of the porcelain bulb by means of a Sprengel pump, and measured the volume of air delivered by the pump. On this plan a series of observations can be made at the same temperature, a three-way tube with suitable taps serving to put the bulb alternately in connexion with a vessel to supply dry air and with the pump. Crafts and Meier have obtained results by sweeping out the air with a current of hydrochloric-acid gas, which was separated from the air it carried by being passed through water.

An instrument for observing the continuous variation of volume of a gas at constant pressure is figured and described by Sir W. Thomson in Heat (sec. 65). Arrangements have also been suggested by which the density of the gas at the high temperature can be directly measured. Regnault, Ixiii. p. 39. ] has described a hydrogen pyrometer based on this principle suitable for measuring the temperature of a porcelain furnace. A wrought-iron tube of known capacity is permanently fixed in the furnace; it is filled with pure dry hydrogen by passing a current of the gas through it for some time. The current of gas is then stopped, and after the gas has attained the temperature of the furnace it is swept out by a current of dry air and passed over red-hot copper oxide. The water thus

formed is collected in sulphuric acid tubes and its amount determined by their increase in weight, and from this observation the density of the hydrogen in the wrought-iron tube is calculated. An arrangement of taps makes the observation a very easy one when the apparatus is once set up. The formula (2) requires in this case to be slightly modified. Thus let d t , <7 100 , d 0 be the densities of the hydrogen at the temperatures t a , 100°, and 0° respectively, then for the same mass of gas m we have—

t⅛ d t =υ 100 d 100 =v 0 d 0 =m.

The formula therefore becomes—

d 0 - d t d 1M _ t . d o -d wo '^'d t 100 k 1 "

(2) The formula shows how the temperature of air in any experiment may be determined when its density at that temperature is observed. It is sometimes more convenient to determine instead the density of some vapour which at ordinary temperatures would be a solid or a liquid, and to deduce from that observation the density of air at the corresponding temperature. Thus, suppose that the density δ< (expressed in grammes per cc.) of the vapour of any given liquid or solid is observed, and that independent observations show that the specific gravity of the vapour, referred to air at the same temperature and pressure, is <r, then we have d t =δ t ∣ σ, and, since d 0 and tZ 100 can be taken from tables, all the necessary quantities in equation (3) are obtained. It will be noticed that the value of σ, the specific gravity of the vapour, is to be derived from independent observations. Apart from direct experimental evidence in any particular case, there is the generally accepted theory, based on the law of Avogadro, that the specific gravity of a gas or vapour referred to hydrogen at the same temperature and pressure is represented by half the number expressing the molecular weight of the substance of which the vapour is composed. For elements, with few exceptions (of which mercury is one), the ratio of the atomic weights gives the specific gravity referred to hydrogen at the same temperature and pressure. At any rate, if there are sufficient data for us to regard σ as known, we may evidently deduce the value of d t , and thus by formula (3) the temperature, from an observation of δ t , Mercury Vapour.— Reguault, lxiii. p. 39. ] suggested the direct observation of the density of mercury vapour for the purpose of determining the temperature. The process is as follows. A quantity of mercury is placed in a wrought-iron flask provided with a perforated lid as shown in fig. 2, No. 1. The flask is then exposed to the temperature to be measured, and when thermal equilibrium is attained the small lid is slid along so that the neck is closed. The flask is then taken out and allowed to cool. The mercury is collected and weighed; the volume of the flask is determined and corrected for the expansion of the iron; and these two observations determine the density of mercury (in grammes per cc.) at the temperature in question. The specific gravity of mercury vapour referred to air at the same temperature and pressure is known to be 6'92. A porcelain flask with a ball stopper, shown in fig. 2, No. 2, may be used instead of the iron flask.

Iodine Vapour. Deville and Troost's Pyrometer.— Some of the best-known determinations of very high boiling-points have been made by Deville and Troost,, lviii. p. 257. ] who employed iodine in a manner similar to that in which Régnault employed mercury. Some iodine was contained in a porcelain flask of about 300 cc. capacity, with a fine neck, which just protruded from the source of heat and was loosely closed by means of a stopper; when the temperature was reached and the iodine completely volatilized, the stopper was fused on to the nozzle by means of an oxy-hydrogen blowpipe. The mass of the iodine remaining in the flask was determined by weighing, after it had cooled; the volume of the flask had been previously determined; thus the density of the iodine vapour could be found. A correction of the volume of the flask was necessary in consequence of the expansion of the Bayeux porcelain of which it was composed. This was obtained from independent observations of the linear elongation of a rod of porcelain for temperatures up to 1500°; their results gave a coefficient of cubical expansion of 0'0000108 between 0° and the boiling-point of cadmium (856°), 0'0000108 between 0° and thθ melting-point of silver (1000°), from 0Ό00016 to 0Ό00017 between 1000° and 1400°, reaching Ό00020 towards 1500°. The specific gravity of iodine vapour was taken to be 8716, referred to air at the same temperature and pressure; this assumption was justified by additional observations with air and by using the number in a determination of the density of steam at the boiling-point of mercury.

(3) The Manometric Gas-thermometer.— In the con stant-pressure methods of measuring temperature which have just been described one experiment gives only a single observation of the temperature.

The continuous variation of temperature can be better observed by the constant-volume method. This method as used for temperatures up to that at which glass softens (about 550° C.) was thoroughly investigated by Régnault, whose normal instrument is discussed under Heat, sec. 24. The difference of pressure between the gas contained in the bulb and the atmosphere is measured by an open mercury-manometer. The barometric pressure must also be observed in order to obtain the values p t , p- i00 , and p tj respectively of formula (1). Various forms have been given to the manometric apparatus in order that the mercury may be brought at each observation to the fiducial mark in the limb in connexion with the bulb. Balfour Stewart’s has a screw adjustment. An instrument described by Codazza β is provided with an air-compression manometer, and thus the necessity of a separate observation of the barometric height is dispensed with. Various other suggestions have been made for securing the same object.

The most convenient form of the instrument for general use is Jolly’s (described in PoggendorfFs Jubelband, p. 82,1874), and represented in fig. 3. The two vertical tubes of the manometer are connected by an india-rubber tube properly strengthened by a cotton covering, and they can be made to slide vertically up and down a wooden pillar which supports them; they are provided with clamps for fixing them in any position and a tangent screw for fine adjustment. The connexion between the bulb and the manometer is made by means of the convenient three-way tap described above. The scale of the instrument is engraved on the back of a strip of plane mirror before silvering, and the divisions are carried sufficiently far across the scale for the reflexions of the two surfaces of the mercury to be visible behind the scale. Parallax can thus be avoided and an accurate reading obtained without the necessity of using a kathetometer. In order to allow for the expansion of the glass of the reservoir a weight-thermometer bulb is supplied with the instrument, made from another specimen of the same kind of...