general, optical methods are the most capable of giving exact
results, and the following may be distinguished, (a) _By refraction in a
horizontal plane._ If the containing vessel is in the form of a prism,
the deviation of a horizontal ray of light in passing through the prism
determines the index of refraction, and consequently the density of the
stratum through which the ray passes, (b) _By refraction in a vertical
plane._ Owing to the density varying with the depth, a horizontal ray
entering the liquid also undergoes a small vertical deviation, being
bent downwards towards the layers of greater density. The observation of
this vertical deviation determines not the actual density, but its rate
of variation with the depth, i.e. the "density gradient" at any point,
(c) _By the saccharimeter._ In the cases of solutions of sugar, which
cause rotation of the plane of polarized light, the density of the sugar
at any depth may be determined by observing the corresponding angle of
rotation, this was done originally by W. Voigt.

3. _Elementary Definitions of Coefficient of Diffusion._--The simplest
case of diffusion is that of a substance, say a gas, diffusing in the
interior of a homogeneous solid medium, which remains at rest, when no
external forces act on the system. We may regard it as the result of
experience that: (1) if the density of the diffusing substance is
everywhere the same no diffusion takes place, and (2) if the density of
the diffusing substance is different at different points, diffusion will
take place from places of greater to those of lesser density, and will
not cease until the density is everywhere the same. It follows that the
rate of flow of the diffusing substance at any point in any direction
must depend on the density gradient at that point in that direction,
i.e. on the rate at which the density of the diffusing substance
decreases as we move in that direction. We may define the _coefficient
of diffusion_ as the ratio of the total mass per unit area which flows
across any small section, to the rate of decrease of the density per
unit distance in a direction perpendicular to that section.

In the case of steady diffusion parallel to the axis of x, if [rho] be
the density of the diffusing substance, and q the mass which flows
across a unit of area in a plane perpendicular to the axis of x, then
the density gradient is -d[rho]/dx and the ratio of q to this is
called the "coefficient of dif