to diffusion would be analogous to friction, and would
contain terms which were independent of the relative velocity u2 - u1.
(2) For slow motions the resistance to diffusion is (approximately at
any rate) proportional to the relative velocity. (3) The coefficient of
resistance C is not necessarily always constant; it may, for example,
and, in general, does, depend on the temperature.

If we form the equations of hydrodynamics for the different fluids
occurring in any mixture, taking account of diffusion, but neglecting
viscosity, and using suffixes 1, 2 to denote the separate fluids,
these assume the form given by James Clerk Maxwell ("Diffusion," in
_Ency. Brit._, 9th ed.):--

Du1 dp1
[rho] --- + --- - X1[rho]1 + C12[rho]1[rho]2(u1 - u2) + &c. = 0,
Dt dx

where

Du1 du1 du1 du1 du1
--- = --- + u1 --- + v1 --- + w1 ---,
Dt dt dx dy dz

and these equations imply that when diffusion and other motions cease,
the fluids satisfy the separate conditions of equilibrium dp1/dx -
X1[rho]1 = 0. The assumption made in the following account is that
terms such as Du1/Dt may be neglected in the cases considered.

A further property based on experience is that the motions set up in a
mixture by diffusion are very slow compared with those set up by
mechanical actions, such as differences of pressure. Thus, if two gases
at equal temperature and pressure be allowed to mix by diffusion, the
heavier gas being below the lighter, the process will take a long time;
on the other hand, if two gases, or parts of the same gas, at different
pressures be connected, equalization of pressure will take place almost
immediately. It follows from this property that the forces required to
overcome the "inertia" of the fluids in the motions due to diffusion are
quite imperceptible. At any stage of the process, therefore, any one of
the diffusing fluids may be regarded as in equilibrium under the action
of its own partial pressure, the external forces to which it is
subjected and the resistance to diffusion of the other fluids.

5. _Slow Diffusion of two Gases. Relation between the Coefficients of
Resistance and of Diffusion._--We now suppose the diffusing substances
to be two gases which obey Boyle's law, and that diffusion takes place
in a closed cylinder or tube of unit sectional area at constant
temperature, the surfaces of equal density being p