k1k2 d[rho]1 k1k2 d[rho]2
[rho]1u1 = - ---- -------, and [rho]2u2 = - ---- -------.
CP dx CP dx

We may now define the "coefficient of diffusion" of either gas as the
ratio of the rate of flow of that gas to its density-gradient. With
this definition, the coefficients of diffusion of both the gases in a
mixture are equal, each being equal to k1k2/CP. The ratios of the
fluxes of partial pressure to the corresponding pressure-gradients are
also equal to the same coefficient. Calling this coefficient K, we
also observe that the equations of continuity for the two gases are

d[rho]1 d([rho]1u1) d[rho]2 d([rho]2u2)
------- + ----------- = 0, and ------- + ----------- = 0,
dt dx dt dx

leading to the equations of diffusion

d[rho]1 d / d[rho]1\ d[rho]2 d / d[rho]2\
------- = -- ( K ------- ) , and ------- = -- ( K ------- ),
dt dx \ dx / dt dx \ dx /

exactly as in the case of diffusion through a solid.

If we attempt to treat diffusion in liquids by a similar method, it is,
in the first place, necessary to define the "partial pressure" of the
components occurring in a liquid mixture. This leads to the conception
of "osmotic pressure," which is dealt with in the article SOLUTION. For
dilute solutions at constant temperature, the assumption that the
osmotic pressure is proportional to the density, leads to results
agreeing fairly closely with experience, and this fact may be
represented by the statement that a substance occurring in a dilute
solution behaves like a perfect gas.

6. _Relation of the Coefficient of Diffusion to the Units of Length and
Time._--We may write the equation defining K in the form

I d[rho]
u = -K X ----- ------.
[rho] dx

Here -d[rho]/[rho]dx represents the "percentage rate" at which the
density decreases with the distance x; and we thus see that the
coefficient of diffusion represents the ratio of the velocity of flow to
the percentage rate at which the density decreases with the distance
measured in the direction of flow. This percentage rate being of the
nature of a number divided by a length, and the velocity being of the
nature of a length divided by a time, we may state that K is of two
dimensions in length and - 1 in time, i.e. dimensions L^2/T