The atomistic hypothesis shows itself remarkably fecund in the study of phenomena produced in gases, and here the mutual independence of the particles renders the question relatively more simple and, perhaps, allows the principles of mechanics to be more certainly extended to the movements of molecules.

The kinetic theory of gases can point to unquestioned successes; and the idea of Daniel Bernouilli, who, as early as 1738, considered a gaseous mass to be formed of a considerable number of molecules animated by rapid movements of translation, has been put into a form precise enough for mathematical analysis, and we have thus found ourselves in a position to construct a really solid foundation.  It will be at once conceived, on this hypothesis, that pressure is the resultant of the shocks of the molecules against the walls of the containing vessel, and we at once come to the demonstration that the law of Mariotte is a natural consequence of this origin of pressure; since, if the volume occupied by a certain number of molecules is doubled, the number of shocks per second on each square centimetre of the walls becomes half as much.  But if we attempt to carry this further, we find ourselves in presence of a serious difficulty.  It is impossible to mentally follow every one of the many individual molecules which compose even a very limited mass of gas.  The path followed by this molecule may be every instant modified by the chance of running against another, or by a shock which may make it rebound in another direction.

The difficulty would be insoluble if chance had not laws of its own.  It was Maxwell who first thought of introducing into the kinetic theory the calculation of probabilities.  Willard Gibbs and Boltzmann later on developed this idea, and have founded a statistical method which does not, perhaps, give absolute certainty, but which is certainly most interesting and curious.  Molecules are grouped in such a way that those belonging to the same group may be considered as having the same state of movement; then an examination is made of the number of molecules in each group, and what are the changes in this number from one moment to another.  It is thus often possible to determine the part which the different groups have in the total properties of the system and in the phenomena which may occur.

Such a method, analogous to the one employed by statisticians for following the social phenomena in a population, is all the more legitimate the greater the number of individuals counted in the averages; now, the number of molecules contained in a limited space—­ for example, in a centimetre cube taken in normal conditions—­is such that no population could ever attain so high a figure.  All considerations, those we have indicated as well as others which might be invoked (for example, the recent researches of M. Spring on the limit of visibility of fluorescence), give this result:—­that there are, in this space, some twenty thousand millions