ed 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