PYROMETER, an instrument for measuring high temperatures. As long ago as 1701, in a paper published anonymously in the Philosophical Transactions, Newton gave the results of attempts to estimate the temperature of red-hot iron by noting the time it took to cool to an observed temperature, assuming what has since been called Newton's Law of Cooling. The numerical results are given in terms of the degrees of a linseed-oil thermometer constructed by Newton. Its zero was the temperature of melting ice and its second fixed point the normal temper-ature of the human body, denoted by 12°. About the same time Guillaume Amonton in Paris made somewhat similar attempts to determine the temperature of the red-hot end of an iron bar, using for reference a rudimentary air-thermo-meter—the first of its kind in which the variation of atmospheric pressure was allowed for. Since the middle of the last century the different methods and instruments suggested for measuring high temperatures have been very numerous,—in fact the variation of almost every physical property of substances which alter with change of temper-ature has been utilized for this purpose. Measurements of the increase of pressure produced in a quantity of gas while its volume remains constant or of the increase of volume at constant pressure, of the heat given out by a mass of metal in cooling to an observed temperature, of the expansion of a metal or graphite bar or of a mass of clay are those which have been most frequently employed; but, besides these, the change in the electrical resistance of a wire, the saturation-pressure of the steam of various liquids, the pressure of gas dissociated from various solids, the electromotive force of a thermo-electric couple, the density of the vapour of a liquid, the change of shape of a compound spiral of different metals, have been used,— even the alteration in the wave-length of a note of given pitch has been suggested as capable of being made use of for pyrometric purposes. For reasons which will be given below, the numerical results obtained by one or other of the numerous forms of the gas-thermometer have a more definitely intelligible value. The gas-thermometer method and the calorimetric method were both employed by Pouillet for the accurate measurement of high temper-atures before 1836.

§ 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 assign-ment of numbers presupposes not only a definition of tem-perature 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, sees. 12, 24, 25, 30, 31, 32; and in sec. 35 of the same article the definition of the absolute thermodynamic scale of temper-atures 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
fO--°)dp
I JOK >
where p is the density of the vapour, per that of the liquid, _ 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 com-plete theory of what may soon become a practical method of expressing temperatures in the thermodynamic scale. Sir W. Thomson, in the article mentioned (sees. 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 tempera-tures 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 _ 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 instru-ment can be easily arranged, so that this observation is practically a very simple one. The pressure of mercury vapour has already been determined by Regnault for temperatures up to 550°. A thermoscopic method of pyrometry which is very similar to the above was sug-gested by Lamy.2 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 tempera-ture. The recombination of the dissociated gas with the solid is, however, a slow process, and the method has been pronounced by Weinhold 3 to be practically unsatis-factory.

§ 3. Gas Pyrometry. Measurement of High Tempera-tures by the Expansion of Air and other Gases and Vapours. —Temperatures may be expressed in the absolute thermo-dynamic scale by the method of the gas-thermometer, which is available for practical purposes even at very high temperatures. It has been shown4 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-thermo-meters, if similarly graduated, would give identical indica-tions 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 Regnault1 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 tempera-ture standard for scientific purposes throughout the whole range. The Kew standards are calibrated mercury-in-glass thermometers whose fixed points are repeatedly redeter-mined. 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 Eegnault2 and many others. The results obtained by different ob-servers 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 freezing-point and boiling-point, the method of measuring higher temperatures by continuing the scale of a mercury-thermo-meter beyond those limits is altogether untrustworthy in consequence of the very wide divergence between different mercury-thermometers at the same temperature, amount-ing sometimes to 10° or more 3 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 gas-thermometer is as follows. Let p0 be the pressure of a mass of gas at 0° C, pm the pressure of the same mass of gas at 100° C, the volume being the same, pt the observed pressure of the same mass of gas at some unknown temperature t, the volume still remaining the same, then
Pt-Po =J__ m
Pm-Po 100h
u be observed for the have—
(2).

We require, therefore, three observations of the pressure, two 4 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 p100 may be obtained from tables, since £>100 =p0(l + 100a), where 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 inde-pendent observations of the expansion of the material of the envelope. If the pressure of the gas be maintained constant, and the volumes vt, vlm, three temperatures f, 100°, 0°, we

%oo-'"o ~10Q
1 "De la Mesure des Températures," Mém. de VInst., xxi. p. 168.
2 Mém. de VInst., xxi. p. 191. 3 See HEAT, see. 26.

4 The two known temperatures at which the pressure is measured need not necessarily be 0° and 100°, though these are often the most convenient. The formula requires only slight modification to make it applicable when any two other known temperatures are adopted.
In like manner 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 temper-ature 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 blow-pipe 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 vt 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 v0 and vm can be calculated, using the known co-efficient of expansion of air, and thus all the requisite data for the deter-mination of t are obtained. This method was used by Regnault 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 Regnault. 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 alter-nately 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 sug-gested by which the density of the gas at the high temperature can be directly measured. Regnault 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 diy 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 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,, dm, d0 be the den-sities of the hydrogen at the temperatures t°, 100°, and 0° respect-ively, then for the same mass of gas m we have—
d
t
d^-dt da — d1{}{
.(3).
Vt dt = vm dm=vQ d\=m. The formula therefore becomes—
100 _
dt 100-

(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 St (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 dt=St/o-, and, since d0 and dlm can be taken from tables, all the necessary quantities in equation (3) are obtained. It will be noticed that the value of a, 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 <r as known, we may evidently deduce the value of dt, and thus by formula (3) the temperature, from an observation of St.
No. 1.
No. 2.
Fig. 2.

Mercury Vapour.—Regnault1 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 witli a ball stopper, shown in lig. 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 mass 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 0° and the boiling-point of cadmium (856°), 0-0000108 between 0° 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 Manometric Gas-thermometer.—In the constant-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 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 pt, plm, and p0 respectively of formula (1). Various forms have been given to the manometric apparatus in order that the mercury may be brougnt at each observation to the fiducial mark in the limb in connexion with the bulb. Balfour Stewart's5 has a screw adjustment. An instru-ment described by Codazza6 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.
77
t=
1 +

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 the manometer tube above the small beak of ^ which serves as the fiducial mark, are determined by the instru-ment-makers. The formula of reduction is—
1+at'J'
II- H„
all0 - 3/3A
where H is the pressure at the high temperature t, 770 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 temperatures7 used a platinum bulb and connecting tube. He employed the constant-pressure method and measured in the manometer tube the variation of volume. Regnault8 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. Becquerel9 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 Appliquée, 1863, p. 237, and Fortschritte der Physik, 1863, p. 84. Weinhold10 used a Jolly's thermometer fitted with a porcelain bulb and connecting tube, and Deville ana 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,12 intended for reading high temperatures rapidly to an accuracy of within two or three degrees. It consists of a small cylindrical bulb of glass or silver of 4 ce. capacity connected with a vertical stem of thermometer tubing of 0'2 mm. diameter. This stem terminates in an open vessel of mercury, and thus the pressure of the gas can be measured. Berthelot's instrument is graduated by reference to four fixed points, namely, the freezing-point and boiling-point of water, and the boiling-points of mercury and sulphur. In order that the mercury index may move easily in the tube, extreme care must be taken in drying the tube, and only perfectly pure mercury pan be used.

§ 4. The results obtained by any of the air-pyrometric methods just described may be employed to express directly the temperature of the pyrometer in numbers agreeing closely with the thermodynamic scale. The other instru-ments to which we now turn our attention can only be regarded as intrinsic thermoscopes, which, in order to give intelligible numerical results, must be graduated by direct comparison with an air-thermometer. Some of them may indeed be used by extrapolation to give a numerical measure of temperatures outside the practical range of the air-thermometer, employing for that purpose a formula verified for temperatures within the range. A case in point is the determination of the temperature of fusion of platinum by the calorimetric method described below. These intrinsic thermoscopes are frequently much more convenient in practice than any of the modifications of the air-pyrometer.

§ 5. Discontinuous Intrinsic Thermoscopes.—The best ex-ample of the measurement of temperature by a discontinu-ous intrinsic thermoscope is that suggested by Prinsep. lie formed a series of definite percentage alloys of silver and gold and of gold and platinum. The melting-points of these alloys give a series of fixed temperatures lying be-tween the melting-points of silver and gold and of gold and platinum respectively. An observation is taken by exposing in the furnace, upon a small cupel, a set of small flattened specimens of the alloys, not necessarily larger than pin heads, and noticing which of them are fused.

The temperatures of fusion of these alloys have been determined by Erhard and Shertel ; their results are given in the following table, taken from Landolt and Bornstein's Physikalisch-chemische Tabelleln.

Table I.—The Fusing-Points of Prinsep's Alloys.

1. SILVER AND GOLD.
Per cent, of silver. Per cent, of gold. Fusing-point. Per cent, of silver. Per cent, of gold. Fusing-point.
100 80 60 20 40 954° 975° 995° 40
20 60 SO 100 1020° 1045° 1075°
2. GOLD AND PLATINUM.
Per cent, of gold. Per cent, of platinum. Fusing-point. Per cent, of gold. Per cent, of platinum. Fusing-point.
100
95 90 85 80 75 70 65 60 55 50 '5 10
15 20
25
so
35 40 45 50 1075° 1100° 1130° 1160° 1190° 1220° 1255° 1285° 1320° 1350° 1385° 45 40 35 30 25 20 15 10 5 55 60 65 70 75 80 85 90 95 100 1420° 1460° 1495° 1535° 1570° 1610° 1650° 1690° 1730° 1775°

It is said, however, that some difficulty is met with in the use of Prinsep's alloys in consequence of the property possessed by silver of taking up oxygen when melted and ejecting it on solidify-ing and of molecular changes in the alloys which make it unadvis-able to use the same specimen more than once. A similar method has recently been employed by Carnelley and Carleton Williams, in which metallic salts with high fusing-points were employed instead of alloys, the fusing-points being initially determined by a calorimetric method. These methods recall an old empirical method sometimes employed in porcelain manufacture for estimating the temperature of a furnace. Certain "pyrometrical beads" or "trials" —i.e., small hoops or gallipots of clay—indicated the temperature by their tint much in the same way as the proper temperature is indicated by the colour of steel in tempering.

§ 6. The Calorimetric Method.—This is a very conveni-ent method and is often practically employed for measur-ing the temperature of furnaces. The observation consists in determining the amount of heat given out by a mass of platinum, copper, or wrought-iron on cooling in water from the high temperature. The theory is simple. Let m be the capacity for heat of the calorimeter and of the water contained in it, M the mass of metal, T the tem-perature required, t the initial temperature of the water in the calorimeter, 0 the final temperature of the water after the introduction of the metal, and K the mean specific heat of the metal between the temperatures 9 and T. Then T_p_m(6 -t) M.K '

The value of K, the mean specific heat of the metal between the temperatures occurring in the experiment, must be determined by precisely similar calorimetric experiments, in which the high tem-perature T is determined by the application of one of the air-pyro-meter methods. The following table (II.) gives the best-known determinations of the mean specific heat of platinum for different ranges of temperature.

Table II.—Mean Specific Heat of Platinum.

Pouillet,5 by platinum reservoir air-thermo-meter. Weinhold,6 "by porcelain reservoir air - thermo-meter. Violle, by porcelain re-servoir air - thermo-meter.
Range of temp. Mean spec. heat. Range of temp. Mean spec. heat. Range of temp. Mean spec. heat.
o°-100°
„ 200°
„ 300° „ 400° „ 500° ,, 600° „ 700° ,, 800° „ 900° „ 1000° „ 1100° 0-03350 0-03392 0-03434 0-03476 0-03518 0-03560 0-03602 0-03644 0 036S6 0-03728 0-03770 10°-2 - 99°-l 16°-49-238°-5 16° '9 -246°-4 17°-2 -256°-8 23°-5 -476° 24°-6 -478° 25°-4 -507° 20°-7 -705° 23°-6 -766° 22°-3 -934° 17°-3 -952° 0-032S7 0-03270 0-03520 0-03411 0-03188 0-03230 0-03253 0-03333 0-03381 0-03396 0-03333 0°-100°
0°-7S4°
0°-1000° 0°-1177° 0-0323
0 0365
0 0377 0-0388

Tiolle's results give, if c0' be the mean specific heat between 0° and f, 0/=0-0317+ -000006<. Assuming this formula to hold beyond the verified limits, he obtains by calorimetric observations 1779° C. as the temperature of the melting-point of platinum. The true specific heat of wrought-iron at temperature t is accord-ing to Weinhold (I.e.) given by the formula c(=c0 + ai + /3i , where c„ = 0-105907, a = 0-00006538, /3 = 0-000000066477, and the total heat obtained from unit-mass of wrought-iron cooling from t% to t° is thereforeyj'^Co + at + /3P)dt. The specific heat of copper does not appear to have been accurately determined for high temperatures-The determinations by Bède, quoted by Landolt and Bornstein {op. cit., p. 178) are—
15°-100° mean specific heat 0-09331 ;
16°-172° „ „ 0-09483 ;
17°-247° „ „ 0-09680. There are two obvious sources of error of considerable amount in the use of the calorimeter for pyrometrical purposes, viz., (1) the liability of the metal to lose heat during its passage from the fur-nace to the calorimeter, and (2) the evaporation of water from the calorimeter. With the small mass of platinum generally used, the former source of error is likely to be very important, for the temperature of a mass of 50 grammes of mercury at 100° C. may fall a full degree in being carried to a calorimeter 3 feet away. It does not appear that any estimates of the amount of loss which may be so produced in calorimetric determinations have been published ; but in order to reduce the loss Salleron suggests the employment of a platinum or copper carrier in which to heat the mass of metal, and J. C. Hoadly uses a graphite crucible for that purpose. The second source of loss is more easily disposed of. Weinhold (I.e.) uses a calorimeter closed by a lid and quite filled with water. This is provided with a broad tube passing nearly to the bottom of the calorimeter, and the latter is tilted while the platinum mass is being introduced ; whereas Violle gets over the same difficulty by the use of a calorimeter provided with a platinum " éprouvette, " so that the heat is imparted more slowly to the water. In a calori-metric pyrometer for technical purposes, made by Messrs Siemens Brothers, the mass of metal employed is a copper cylinder. For a sketch and description of the. instrument, see IKON, vol. xiii. p. .304 (fig. 21).

§ 7. Continuous Intrinsic Thermoscopes.—The other pyro-inetric methods to which we have space to refer are those which depend on the continuous variation of some property •of a body with variation of temperature. Each instru-ment of this kind requires graduation by direct or indirect comparison with an air-thermometer. The methods may be grouped under three heads,—(1) the expansion of a rod of metal or earthenware; (2) the variation of electrical resistance of a wire; (3) the electromotive force of a thermo-electric junction.





(1) Expansion of Metals and Earthenware.—The necessity for the measurement of high temperatures has been most felt perhaps in pottery manufacture, and in consequence many attempts have been made by potters to establish a system of pyrometry based on the permanent contraction which clay undergoes when exposed to a high temperature. The action of Wedgwood's pyrometer described in the Phil. Trans., 1782, 1784, and 1786, depends on this property of clay. The linear contraction of a clay cylinder was measured by means of a metal groove with plane sides inclined to each other at a small angle, and the temperature was estimated numerically by comparing the contraction with that produced by a known difference of temperature. The results were.not very satisfactory, since the clay would contract the same amount by long-continued heating at a lower temperature as by a short exposure to a higher one. Wedgwood's estimate of the melting-point of cast iron was 20,577° Fahr.

The measurement of temperature by the expansion of a metal rod has been very frequently attempted. The first instrument to which the name of "pyrometer" was given wTas of this kind, and was devised by Muschenbroek, and others were devised in the early part of the century by Des Aguliers, Ellieot, Graham, Smeaton, Ferguson, Brogniart, Laplace, and Lavoisier, and later by Pouillet. We may say here that the only acccurate methods of measuring the extremely minute elongations of metal rods are those in which the expansion is referred by some optical arrangement to a scale kept quite uninfluenced by the source of heat which causes the expansion. In this respect Pouillet's method of employing the expansion of a rod is superior to those previously employed.

The relative expansion of a metal in an earthenware socket was employed by Daniell in his well-known pyrometer. The relative expansion was indicated by an index of porcelain which was pushed forward when the bar expanded and left behind when it contracted, so that after the apparatus had cooled the expansion could be measured at leisure by the scale provided ; due allowance was made for the expansion of the index itself. Quite recently the expansion of graphite has been employed for pyrometry by Steinle and Harting. As the result of his experience, however, Weinhold states that it is not possible to obtain trustworthy measurements of temperature from an instrument depending on the relative expan-sion of solid bodies.

An ingenious application of the relative expansion of gold, silver, and platinum was introduced by Breguet. Very narrow strips of the three metals are fastened together to form a compound ribbon-jpiral, and to the end of the spiral is attached a needle, which, as ihe temperature changes, moves over a graduated circle. The in-strument, of course, requires empirical graduation. A modification of it is sometimes used to measure the temperature of the hot blast of an iron furnace.

(2) Variation of Electrical Resistance.—A pyrometric method founded on the variation of the electrical resistance of a platinum wire has been practically carried out by Siemens, and was described by him in the Bakerian lecture (Proc. Roy. Soc, 1871). " Assuming a dynamical law, according to which the electrical resistance increases according to the velocity with which the atoms are moved by heat, a parabolic ratio of increase of resistance with increase of temperature follows, and in adding to this the coefficients (representing linear expansion and an ultimate minimum resistance) the resistance r for any temperature is expressed by the general formula r = aT- +fiT+y, which is found to agree very closely both with the experimental data at low temperatures supplied by Dr Matthiessen and with the experimental results varying up to 1000° C." The details of the experimental verification are not given in the abstract of the lecture, nor are the numerical values of the constants for platinum. But Weinhold gives the information, obtained by letter from the lecturer, that T is the absolute temperature, and the numerical values of the constants—
«=0'039369, (3 = 0-00216407, 7= -0-24127.

The experimental arrangement for practical purposes of the instrument as supplied by Messrs Siemens Brothers is exceedingly convenient. It is shown in fig. 4. P is the coil of platinum-wire wound on a cy- «^ Under of fireclay, and connected by stout platinum wires X, X, C with three bind-ing screws at the end of a stout iron tube 6 feet long, and thereby with an arrange-ment for compar-ing its resistance with that of a standard coil X, by means of dif-ferential volta-meters V, V. A current from six Leclanche cells is divided into two parts, one going through the standard coil X, the volta-meter V, and an additional pla-tinum wire, also marked X, join-ing the other branch again at the end of the platinum coil, while the other branch includes the voltameter V, the connect-ing wire X, and / the coil P. The ' wire O is com-mon to both circuits. The amount of gas generated in the voltameters is inversely proportional to the resistances of the respective branch circuits. Thus, if V and V be the volumes of gas in the two voltameters respectively,
V _ Resistance of P and its connexions
V Resistance of X and its connexions

The leading wires from the screws of the iron tube to the com-mutator BBC are bound together in one cable, so that they have the same resistance ; thus the observed variation in the ratio of the resistances may be regarded as entirely due to the variation in the resistance of P. The height of the liquids in the two voltameters can be adjusted by the short glass tubes S, S' sliding vertically on the wooden support to which the voltameters are attached. They are connected by means of india-rubber tubing with the voltameters. The commutator BBC is used to reverse the direction of the current every ten seconds during the observation, which lasts long enough to give a sufficient supply of gas in the voltameter tubes. By this artifice the error due to variation in the polarization of the electrodes is avoided.

The voltametric arrangement for comparing the resistances simplifies very greatly the apparatus required. In a laboratory the resistances may be, of course, more accurately compared by means of resistance - coils and a galvanometer. For technical purposes the temperatures up to 1400° are reduced from the observations by means of a very convenient slide rule. For temperatures beyond 1400° the calculation has to be gone through. The experimental data upon which the verification of the formula and the determination of the constants rest are not very numerous. Besides the measurements of Siemens referred to above, there is an experimental comparison by Weinhold of the results obtained from the instrument and those of an air-thermometer. For these observations the iron cover of the coil was removed. The results up to 500°, which in each case are the mean of from five to ten observations, show an agreement within 9°; those between 500° and 1000°, comprising one observa-tion at each of six temperatures, three of these between 531° and 553° and three between 933° and 992°, show differences of about + 26° at the lower limit and - 53° at the upper. The arrangement for comparing the resistances was found to be satisfactory and sufficiently sensitive. Specimens of this instrument were also sub-mitted to experiment by a committee of the British Association (Report, 1874), but their attention was confined to the resolution of the question whether the platinum coil gave the same resist-ance after being repeatedly heated and cooled. It was found that this was not the case unless the coil was carefully protected by a platinum sheath.

(3) Thermo-electric Methods.—The measurement of high temper-atures by means of a thermo-electric junction has been attempted many times. A platinum-iron element was employed by ltosetti to measure the temperature of flames. E. Becquerel- used a platinum-palladium element. The best-known results on the variation of the electro-motive force with temperature are those of Tait, in the Edin. Phil. Trans., xxvii. ; but full details of the measurement of temperature in his experiments are not given. It would appear, however, from Begnault's observations,4 and from the well-known effect of slight differences in the physical state or composition of the metals used, that it is in every case necessary for the observer with a thermo-junction to conduct his own comparison with an air-thermometer or other standard method.

§ 8. The application of the variation in the wave-length of sound to the measurement of the density of air and con-sequent determination of the temperature has been sug-gested by Cagnard de Latour, Damon-Ferrand, Mayer, and Chautard. The method is liable to difficulties which need not be detailed here, but which are obviously sufficient to cause the experiments to be regarded rather as scientific curiosities than as pyrometric measurements.

§ 9. Hitherto we have confined our attention to the ques-tion whether any instrument described is capable of giving trustworthy indications of the temperature of the instru-ment itself; in order to be satisfied as to whether they fulfil their object, we have still to consider whether they can be easily made to take up the temperature of the body or enclosure under investigation. This is a very difficult question, and it seems doubtful whether with such an instrument as Siemens's electrical pyrometer, of which the coil is contained in a massive sheath of iron connected to about 6 feet of stout iron tube, thermal equilibrium between the coil and the enclosure is possible. We have not space to discuss the matter, but it seems not unlikely that the differences which still exist between the results of different observers may be due to the method of exposure of the pyrometer. In connexion with this the researches of Regnault5 with reference to the determination of the boiling-point of mercury and sulphur are very important. He observed that his thermometers, when exposed directly to the steam, indicated too high a temperature, and that it was therefore necessary for the socket enclosing the ther-mometer to dip into the liquid to such an extent that the surface of the liquid was above the level of the top of the thermometer bulb. Whether or not this may account for some of the differences between the results obtained for the boiling-point of zinc by Deville and Troost and by E. Becquerel and Violle it is difficult to say.

The following table (III.) will show the divergence among the best of the high-temperature measurements.

Table III.—Determinations of the Boiling-Point of Zinc.

Pressure. Temp. Method. Observer. Reference.
759-54 mm. 701-2 „
718-9 „ 760 1039"
1040° 932'
891°
1035°
929°-954°
910°-925°
930° Iodine vapour pyro-meter
Platinum reservoir air-thermometer
Porcelain reservoir air-thermometer
Porcelain reservoir air-thermometer
Air-thermometer ..
Hydrogen - thermo-meter
Porcelain reservoir air-thermometer Deville and Troost, 1859
B. Becquerel, 1863
Weinhold, 1873 ....
Deville and Troost, 1880
Violle, 1882 § S, (2)
§ (3)
§ 3, (3) § 3, (1)
§ 3, (3)
2 Ann. de Chim., lxviii. p. 49. 3 See ELECTRICITY.

§ 10. Perhaps the most important modern attempts at the development of pyrometry are those connected with the identification of the law connecting the temperature of a body with the amount and nature of the energy which it radiates. On such attempts depends the possibility of measuring the temperature of a hot body by means of the light it emits. This is evidently a most desirable object, since, if that were possible, one of the great difficulties of pyrometry—the bringing of the measuring instrument to the temperature of the body under investigation—would immediately disappear. At present, however, there is no general agreement among scientific men as to the form the relation takes. We cannot here do more than refer to the "Report on Spectrum Analysis," in the British Asso-ciation's Reports for 1881 and 1884, for references to the-literature of the subject. See RADIATION. (W. N. S.)


Footnotes

"Scala Graduum Caloris,"in Phil. Trans., xxii. p. 824.

2 Comptes Rendus, lxix. p. 347.
3 " Pyrometrische Versuche," Pogg. Ann., cxlix. p. 186.
4 See HEAT, sees. 46-67.

Mem. de VInst., xxi. 6 Comptes Pendus, xc. 727, 773.
7 C. JR., xc. 606.
8 Throughout this article the term " density " is used whenever the
mass of a unit of volume of a substance is referred to.
Ann. de Chim., [3], lxiii. p. 39.


1 Ann de Chimie, [3], lxiii. p. 39.
2 Mean of results of Von Meyer, Dumas, Mitscherlich, and Bineau.
3 Ann de CJnmie, [3], lviii. p. 257.


5 Pliil. Trans., cliii. p. 425.
? Comptes Rendus, iii. (1836), p. 782.
9 Ann. de Chimie, lxviii. p. 49.
4 Mém de VInst., xxi.
6 Dingler's Journal, ccx. p. 255.
8 Mém de I'Inst., xxi. p. 263. 10 Pogg. Ann., cxlix. u See Deville and Troost on glass and other envelopes for high-temperature instruments, Ann. de Chimie, [3], lviii. p. 265. 12 Ann. de Chimie, [4], xiii. p. 144.

Phil. Trans., 1828, p. 79.
Jahrb. fur das Berg- mid Huiten-Wesen in Sachsen, 1879.
Determinations of temperature by a porcelain air-thermometer. Errors in general less than 20°.
Determinations of temperature by a porcelain air-thermometer. Errors in general less than 20°.
See Chem. Soc. Jour., 1876, i. 489 ; 1877, i. 365 ; 1878.
5 C. P., iii. p. 786 (1836). 6 Pogg. Ann., cxlix.
Jahrb. fur das Berg- mid Huiten-Wesen in Sachsen, 1879.
7 Phil. Mag., [5], iv. p. 318. 8 Chem. News, xxvii. 77.
Jour, of Franklin Inst., xciv. p. 252.
! 10 Phil. Mag., [5], iv. p. 318.

See Beckert, Zeitschr. f. anal. Chem., xxi. p. 248, 1882.
Pogg. Ann., cxlix. p. 206.

Ann. de Chim., 1878.
4 Mêm. de I'Inst., xxi. p. 241. 5 M'em. de l'Inst., xxvi. p. 513.