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.