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.
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