admirably studied by M. Ch. Ed. Guillaume-exhibits in the matter of dilatation are now utilized so as to almost completely annihilate the influence of variations of temperature.

§ 5. THE MEASURE OF TEMPERATURE

From the three mechanical units we derive secondary units; as, for instance, the unit of work or mechanical energy. The kinetic theory takes temperature, as well as heat itself, to be a quantity of energy, and thus seems to connect this notion with the magnitudes of mechanics. But the legitimacy of this theory cannot be admitted, and the calorific movement should also be a phenomenon so strictly confined in space that our most delicate means of investigation would not enable us to perceive it. It is better, then, to continue to regard the unit of difference of temperature as a distinct unit, to be added to the fundamental units.

To define the measure of a certain temperature, we take, in practice, some arbitrary property of a body. The only necessary condition of this property is, that it should constantly vary in the same direction when the temperature rises, and that it should possess, at any temperature, a well-marked value. We measure this value by melting ice and by the vapour of boiling water under normal pressure, and the successive hundredths of its variation, beginning with the melting ice, defines the percentage.

Thermodynamics, however, has made it plain that we can set up a thermometric scale without relying upon any determined property of a real body. Such a scale has an absolute value independently of the properties of matter. Now it happens that if we make use for the estimation of temperatures, of the phenomena of dilatation under a constant pressure, or of the increase of pressure in a constant volume of a gaseous body, we obtain a scale very near the absolute, which almost coincides with it when the gas possesses certain qualities which make it nearly what is called a perfect gas. This most lucky coincidence has decided the choice of the convention adopted by physicists. They define normal temperature by means of the variations of pressure in a mass of hydrogen beginning with the initial pressure of a metre of mercury at 0° C.

M. P. Chappuis, in some very precise experiments conducted with much method, has proved that at ordinary temperatures the indications of such a thermometer are so close to the degrees of the theoretical scale that it is almost impossible to ascertain the value of the divergences, or even the direction that they take. The divergence becomes, however, manifest when we work with extreme temperatures. It results from the useful researches. of M. Daniel Berthelot that we must subtract +0.18° from the indications of the hydrogen thermometer towards the temperature -240° C., and add

+0.05° to 1000° to equate them with the thermodynamic scale. Of course, the difference would also become still more noticeable on getting nearer to the absolute zero; for as hydrogen gets more and more cooled, it gradually exhibits in a lesser degree the characteristics of a perfect gas.

To study the lower regions which border on that kind of pole of cold towards which are straining the efforts of the many physicists who have of late years succeeded in getting a few degrees further forward, we may turn to a gas still more difficult to liquefy than hydrogen. Thus, thermometers have been made of helium; and from the temperature of 260° C. downward the divergence of such a thermometer from one of hydrogen is very marked.

The measurement of very high temperatures is not open to the same theoretical objections as that of very low temperatures; but, from a practical point of view, it is as difficult to effect with an ordinary gas thermometer. It becomes impossible to guarantee the reservoir remaining sufficiently impermeable, and all security disappears, notwithstanding the use of recipients very superior to those of former times, such as those lately devised by the physicists of the Reichansalt. This difficulty is obviated by using other methods, such as the employment of thermoelectric couples, such as the very convenient couple of M. le Chatelier; but the graduation of these in

struments can only be effected at the cost of a rather bold extrapolation.

M. D. Berthelot has pointed out and experimented with a very interesting process, founded on the measurement by the phenomena of interference of the refractive index of a column of air subjected to the temperature it is desired to measure. It appears admissible that even at the highest temperatures the variation of the power of refraction is strictly proportional to that of the density, for this proportion is exactly verified so long as it is possible to check it precisely. We can thus, by a method which offers the great advantage of being independent of the power and dimension of the envelopes employed -since the length of the column of air considered alone enters into the calculation—obtain results equivalent to those given by the ordinary air thermometer.

Another method, very old in principle, has also lately acquired great importance. For a long time we sought to estimate the temperature of a body by studying its radiation, but we did not know any positive relation between this radiation and the temperature, and we had no good experimental method of estimation, but had recourse to purely empirical formulas and the use of apparatus of little precision. Now, however, many physicists, continuing the classic researches of Kirchhoff, Boltzmann, Professors Wien and Planck, and taking their starting-point from the laws of thermodynamics, have given formulas which

establish the radiating power of a dark body as a function of the temperature and the wave-length, or, better still, of the total power as a function of the temperature and wave-length corresponding to the maximum value of the power of radiation. We see, therefore, the possibility of appealing for the measurement of temperature to a phenomenon which is no longer the variation of the elastic force of a gas, and yet is also connected with the principles of thermodynamics.

This is what Professors Lummer and Pringsheim have shown in a series of studies which may certainly be reckoned among the greatest experimental researches of the last few years. They have constructed a radiator closely resembling the theoretically integral radiator which a closed isothermal vessel would be, and with only a very small opening, which allows us to collect from outside the radiations which are in equilibrium with the interior. vessel is formed of a hollow carbon cylinder, heated by a current of high intensity; the radiations are studied by means of a bolometer, the disposition of which varies with the nature of the experiments.

This

It is hardly possible to enter into the details of the method, but the result sufficiently indicates its importance. It is now possible, thanks to their researches, to estimate a temperature of 2000° C. to within about 5°. Ten years ago a similar approximation could hardly have been arrived at for a temperature of 1000° C.