PYROMETER 131 formed is collected in sulphuric acid tubes and its amount deter- mined 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 , d m , d be the den- sities of the hydrogen at the temperatures t, 100, and respect- ively, then for the same mass of gas in we have v t d t = v m d m =v d Q = m. The formula therefore becomes AT. 4 ? d - d d 100 _ ^ d t 100' .(3). (2) The formula shows how the temperature of air in any experi- ment 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 d t (expressed in grammes per cc.) of the vapour of any given liquid or solid is observed, and that independent observa- tions show that the specific gravity of the vapour, referred to air at the same temperature and pressure, is ff, then we have d t =8 t /<r, and, since d ti and d loo can be taken from tables, all the necessary quantities in equation (3) are obtained. It will be noticed that the value of IT, the specific gravity of the vapour, is to be derived from independent observations. Apart from direct experimental evi- dence 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 suffi- cient data for us to regard cr as known, we may evidently deduce the value of d t , and thus by formula (3) the temperature, from an observation of S t . Mercury Vapour. Regnault 1 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 temper- ature 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 den- sity of mercury (in grammes per cc.) at the temperature in question. The specific gravity 2 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, 3 who employed iodine in a manner similar to that in which Regnault 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 niass of the iodine remaining in the flask was determined by weigh- ing, after it had cooled ; the volume of the flask had been pre- viously 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 observa- tions 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 and the boiling-point of cadmium (856), 0-0000108 between and the melting-point of silver (1000), from 0-000016 to 0-000017 between 1000 and 1400, reaching -000020 towards 1500. The specific gravity of iodine vapour was taken to be 8'716, 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 Manomclric Gas-thcrmomctcr. In the constant-pressure methods of measuring temperature which have just been described one experiment gives only a single observation of the temperature. 1 Ann de Chimie, [3], Ixiii. p. 39. 2 Mean of results of Von Meyer, Dumas, Mitscherlich, and Bineau. 3 Ann. de Chimie, [3], Iviii. p. 207. No. 1. No. 2. Fig. 2. The continuous variation of temperature can be better observed by the constant-volume method. This method as used for tem- peratures up to that at which glass softens (about 550 C.) was thoroughly investigated by Regnault, 4 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 m , and p respectively of formula (1). Various forms have been given to the mauometric 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 5 has a screw adjustment. An instru- ment described by Codazza 6 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 Poggendorff s Jubelband, p. 82, 1874), and repre- sented in fig. 3. The two vertical tubes of the manometer are connected by an india-rubber tube properly strengthened by a cotton cover- ing, 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 ne- cessity of using a kathetometer. In order to allow for the expansion of the glass of the reservoir a weight -thermometer bulb is sup- plied with the instrument, made from another specimen of the same kind of glass, and the relative expansion of the mercury and the glass can thus be determined by the observer him- self. The volume of the air-bulb and that of the capillary tube and the small portion of Fl g- 3. the manometer tube above the small beak of glass, the point of which serves as the fiducial mark, arc determined by the instru- ment-makers. The formula of reduction is t = aH -3pJl 1 + v ' IT T+^t')' where H is the pressure at the high temperature t, H the pressure at the temperature of the air t', v'/v the ratio of the volume of the connecting tube, &c., to the volume of the bulb, a the coefficient of expansion of the air, and 3/3 the coefficient of cubical expansion of the glass. A similar instrument with a bulb which will resist higher temperatures may be used beyond the softening -point of glass. Pouillet in his classical research on high temperatures 7 used a platinum bulb and connecting tube. He employed the constant- pressure method and measured in the manometer tube the variation of volume. Regnault 8 mentions a platinum air -pyrometer and gives instructions for drawing the platinum connecting tube ; but no results of measurements obtained with it are given. E. Becquerel a published an account of results obtained with a platinum reservoir air-thermometer, which were objected to by Deville and Troost on the ground that platinum becomes porous at high temperatures, and their objection is supported by an experiment described by them in the Repertoire de Chimie Appliquee, 1863, p. 237, and Fortschritte der Physik, 1863, p. 84. Weinhold 10 used a Jolly's thermometer fitted with a porcelain bulb and connecting tube, and Deville and Troost are of opinion that porcelain forms the only suitable material for gas - thermometer bulbs for very high tempera- tures. 11 For use at high temperatures the gas-thermometer should be filled with gas at a low pressure, so that when heated there may be no great difference of pressure between the interior and the external air. It is perhaps unnecessary here to insist upon the necessity for the complete desiccation of the interior of the bulb and of the gas employed. (4) The last modification of the gas -thermometer to which it is necessary to call attention is that designed and used by Berthelot, 1 ' intended for reading high temperatures rapidly to an accuracy of within two or three degrees. It consists of a small cylindrical bulb ' Mem de I'Inst., xxi. 5 pui Trans., cliii. p. 425. 1 Dingler's Journal, ccx. p. 255. 7 Comptes Rendus, iii. (1836), p. 782. I Mem de I'Inst., xxi. p. 263. 9 Ann. de Chimie, Ixviii. p. 49. lu Fogg. Ann., cxlix. 11 See Deville and Troost on glass and other envelopes for high-temperature instruments, Ann. de Chimie, [3], Iviii. p. 265. !2 Ann. de Chimie, [4], xiii. p. 144.
