not sufficiently often raised to require mention in
print.

II. _Kinetic Models of Diffusion._--Imagine in the first instance that a
very large number of red balls are distributed over one half of a
billiard table, and an equal number of white balls over the other half.
If the balls are set in motion with different velocities in various
directions, diffusion will take place, the red balls finding their way
among the white ones, and vice versa; and the process will be retarded
by collisions between the balls. The simplest model of a perfect gas
studied in the kinetic theory of gases (see MOLECULE) differs from the
above illustration in that the bodies representing the molecules move in
space instead of in a plane, and, unlike billiard balls, their motion is
unresisted, and they are perfectly elastic, so that no kinetic energy is
lost either during their free motions, or at a collision.

The mathematical analysis connected with the application of the
kinetic theory to diffusion is very long and cumbersome. We shall
therefore confine our attention to regarding a medium formed of
elastic spheres as a mechanical model, by which the most important
features of diffusion can be illustrated. We shall assume the results
of the kinetic theory, according to which:--(1) In a dynamical model
of a perfect gas the mean kinetic energy of translation of the
molecules represents the absolute temperature of the gas. (2) The
pressure at any point is proportional to the product of the number of
molecules in unit volume about that point into the mean square of the
velocity. (The mean square of the velocity is different from but
proportional to the square of the mean velocity, and in the subsequent
arguments either of these two quantities can generally be taken.) (3)
In a gas mixture represented by a mixture of molecules of unequal
masses, the mean kinetic energies of the different kinds are equal.

Consider now the problem of diffusion in a region containing two kinds
of molecules A and B of unequal mass. The molecules of A in the
neighbourhood of any point will, by their motion, spread out in every
direction until they come into collision with other molecules of
either kind, and this spreading out from every point of the medium
will give rise to diffusion. If we imagine the velocities of the A
molecules to be equally distributed in all directions, as they would
be in a homogeneous mixture, it i