s obvious that the process of
diffusion will be greater, _ceteris paribus_, the greater the velocity
of the molecules, and the greater the length of the free path before a
collision takes place. If we assume consistently with this, that the
coefficient of diffusion of the gas A is proportional to the mean
value of Wala, where wa is the velocity and la is the length of the
path of a molecule of A, this expression for the coefficient of
diffusion is of the right dimensions in length and time. If, moreover,
we observe that when diffusion takes place in a fixed direction, say
that of the axis of x, it depends only on the resolved part of the
velocity and length of path in that direction: this hypothesis readily
leads to our taking the mean value of 1/3w_a l_a as the coefficient of
diffusion for the gas A. This value was obtained by O. E. Meyer and
others.

Unfortunately, however, it makes the coefficients of diffusion unequal
for the two gases, a result inconsistent with that obtained above from
considerations of the coefficient of resistance, and leading to the
consequence that differences of pressure would be set up in different
parts of the gas. To equalize these differences of pressure, Meyer
assumed that a counter current is set up, this current being, of
course, very slow in practice; and J. Stefan assumed that the
diffusion of one gas was not affected by collisions between molecules
of the _same gas_. When the molecules are mixed in equal proportions
both hypotheses lead to the value 1/6([w_a l_a] + [w_b l_b]), (square
brackets denoting mean values). When one gas preponderates largely
over the other, the phenomena of diffusion are too difficult of
observation to allow of accurate experimental tests being made.
Moreover, in this case no difference exists unless the molecules are
different in size or mass.

Instead of supposing a velocity of translation added after the
mathematical calculations have been performed, a better plan is to
assume from the outset that the molecules of the two gases have small
velocities of translation in opposite directions, superposed on the
distribution of velocity, which would occur in a medium representing a
gas at rest. When a collision occurs between molecules of different
gases a transference of momentum takes place between them, and the
quantity of momentum so transferred in one second in a unit of volume
giv