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 of molecules. Each of these must receive in the space of a millimetre about ten thousand shocks, and be ten thousand times thrust out of its course. The free path of a molecule is then very small, but it can be singularly augmented by diminishing the number of them. Tait and Dewar have calculated that, in a good modern vacuum, the length of the free path of the remaining molecules not taken away by the air-pump easily reaches a few centimetres. By developing this theory, we come to consider that, for a given temperature, every molecule (and even every individual particle, atom, or ion) which takes part in the movement has, on the average, the same kinetic energy in every body, and that this 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.