fusion." By what has been said this
ratio remains finite, however small the actual gradient and flow may
be., and it is natural to assume, at any rate as a first
approximation, that it is constant as far as the quantities in
question are concerned. Thus if the coefficient of diffusion be
denoted by K we have q= -K(d[rho]/dx).

Further, the rate at which the quantity of substance is increasing in
an element between the distances x and x+dx is equal to the difference
of the rates of flow in and out of the two faces, whence as in
hydrodynamics, we have d[rho]/dt =-dq/dx.

It follows that the equation of diffusion in this case assumes the
form

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

which is identical with the equations representing conduction of heat,
flow of electricity and other physical phenomena. For motion in three
dimensions we have in like manner

d[rho] d / d[rho]\ d / d[rho]\ d / d[rho]\
------ = -- ( K ------ ) + -- ( K ------ ) + -- ( K ------ );
dt dx \ dx / dy \ dy / dz \ dz /

and the corresponding equations in electricity and heat for
anisotropic substances would be available to account for any parallel
phenomena, which may arise, or might be conceived, to exist in
connexion with diffusion through a crystalline solid.

In the case of a very dilute solution, the coefficient of diffusion of
the dissolved substance can be defined in the same way as when the
diffusion takes place in a solid, because the effects of diffusion will
not have any perceptible influence on the solvent, and the latter may
therefore be regarded as remaining practically at rest. But in most
cases of diffusion between two fluids, both of the fluids are in motion,
and hence there is far greater difficulty in determining the motion, and
even in defining the coefficient of diffusion. It is important to notice
in the first instance, that it is only the relative motion of the two
substances which constitutes diffusion. Thus when a current of air is
blowing, under ordinary circumstances the changes which take place are
purely mechanical, and do not depend on the separate diffusions of the
oxygen and nitrogen of which the air is mainly composed. It is only when
two gases are flowing with unequal velocity, that is, when they have a
relative motion, that these changes of relative distribution, which