energy is proportional to the absolute temperature; so that it is represented by this temperature multiplied by a constant quantity which is a universal

constant.

This result is not an hypothesis but a very great probability. This probability increases when it is noted that the same value for the constant is met with in the study of very varied phenomena; for example, in certain theories on radiation. Knowing the mass and energy of a molecule, it is easy to calculate its speed; and we find that the average speed is about 400 metres per second for carbonic anhydride, 500 for nitrogen, and 1850 for hydrogen at 0° C. and at ordinary pressure. I shall have occasion, later on, to speak of much more considerable speeds than these as animating other particles.

The kinetic theory has permitted the diffusion of gases to be explained, and the divers circumstances of the phenomenon to be calculated. It has allowed us to show, as M. Brillouin has done, that the coefficient of diffusion of two gases does not depend on the proportion of the gases in the mixture; it gives a very striking image of the phenomena of viscosity and conductivity; and it leads us to think that the coefficients of friction and of conductivity are independent of the density; while all these previsions have been verified by experiment. It has also invaded optics; and by relying on the

principle of Doppler, Professor Michelson has succeeded in obtaining from it an explanation of the length presented by the spectral rays of even the most rarefied gases.

But however interesting are these results, they would not have sufficed to overcome the repugnance of certain physicists for speculations which, an imposing mathematical baggage notwithstanding, seemed to them too hypothetical. The theory, moreover, stopped at the molecule, and appeared to suggest no idea which could lead to the discovery of the key to the phenomena where molecules exercise a mutual influence on each other. The kinetic hypothesis, therefore, remained in some disfavour with a great number of persons, particularly in France, until the last few years, when all the recent discoveries of the conductivity of gases and of the new radiations came to procure for it a new and luxuriant efflorescence. It may be said that the atomistic synthesis, but yesterday so decried, is today triumphant.

The elements which enter into the earlier kinetic theory, and which, to avoid confusion, should be always designated by the name of molecules, were not, truth to say, in the eyes of the chemists, the final term of the divisibility of matter. It is well known that, to them, except in certain particular bodies like the vapour of mercury and argon, the molecule comprises several atoms, and that, in com

pound bodies, the number of these atoms may even be fairly considerable. But physicists rarely needed to have recourse to the consideration of these atoms. They spoke of them to explain certain particularities of the propagation of sound, and to enunciate laws relating to specific heats; but, in general, they stopped at the consideration of the molecule.

The present theories carry the division much further. I shall not dwell now on these theories, since, in order to thoroughly understand them, many other facts must be examined. But to avoid all confusion, it remains understood that, contrary, no doubt, to etymology, but in conformity with present custom, I shall continue in what follows to call atoms those particles of matter which have till now been spoken of; these atoms being themselves, according to modern views, singularly complex edifices formed of elements, of which we shall have occasion to indicate the nature later.

CHAPTER IV

THE VARIOUS STATES OF MATTER

§ 1. THE STATICS OF FLUIDS

THE division of bodies into gaseous, liquid, and solid, and the distinction established for the same substance between the three states, retain a great importance for the applications and usages of daily life, but have long since lost their absolute value from the scientific point of view.

So far as concerns the liquid and gaseous states particularly, the already antiquated researches of Andrews confirmed the ideas of Cagniard de la Tour and established the continuity of the two states. A group of physical studies has thus been constituted on what may be called the statics of fluids, in which we examine the relations existing between the pressure, the volume, and the temperature of bodies, and in which are comprised, under the term fluid, gases as well as liquids.

These researches deserve attention by their interest and the generality of the results to which they

have led. They also give a remarkable example of the happy effects which may be obtained by the combined employment of the various methods of investigation used in exploring the domain of nature. Thermodynamics has, in fact, allowed us to obtain numerical relations between the various coefficients, and atomic hypotheses have led to the establishment of one capital relation, the characteristic equation of fluids; while, on the other hand, experiment in which the progress made in the art of measurement has been utilized, has furnished the most valuable information on all the laws of compressibility and dilatation.

The classical work of Andrews was not very wide. Andrews did not go much beyond pressures close to the normal and ordinary temperatures. Of late years several very interesting and peculiar cases have been examined by MM. Cailletet, Mathias, Batelli, Leduc, P. Chappuis, and other physicists. Sir W. Ramsay and Mr S. Young have made known the isothermal diagrams1 of a certain number of liquid bodies at the ordinary temperature. They have thus been able, while keeping to somewhat restricted limits of temperature and pressure, to touch upon the most im

1 By isothermal diagram is meant the pattern or complex formed when the isothermal lines are arranged in curves of which the pressure is the ordinate and the volume the abscissa.-ED.