-----(u + v) = kdP/dx;
[eta]

therefore

k dP
u + v = [eta] - --.
n dx

Now [eta] is 1.036 X 10^-4, and the concentration of a solution is
usually expressed in terms of the number, m, of gram-equivalents per
litre instead of per cubic centimetre. Therefore

k dP
u + v = 1.036 X 10^-1 - -- --.
m dx

When the potential gradient is one volt (10^8 C.G.S. units) per
centimetre this becomes

u + v = 1.036 X 10^-7 X k/m.

Thus by measuring the value of k/m, which is known as the equivalent
conductivity of the solution, we can find u + v, the velocity of the
ions relative to each other. For instance, the equivalent conductivity
of a solution of potassium chloride containing one-tenth of a
gram-equivalent per litre is 1119 X 10^-13 C.G.S. units at 18 deg. C.
Therefore

u + v = 1.036 X 10^7 X 1119 X 10^-13
= 1.159 X 10^-3 = 0.001159 cm. per sec.

In order to obtain the absolute velocities u and v, we must find some
other relation between them. Let us resolve u into 1/2(u + v) in one
direction, say to the right, and 1/2(u - v) to the left. Similarly v
can be resolved into 1/2(v+u) to the left and 1/2(v-u) to the right.
On pairing these velocities we have a combined movement of the ions to
the right, with a speed of 1/2(u - v) and a drift right and left, past
each other, each ion travelling with a speed of 1/2(u + v),
constituting the electrolytic separation. If u is greater than v, the
combined movement involves a concentration of salt at the cathode, and
a corresponding dilution at the anode, and _vice versa_. The rate at
which salt is electrolysed, and thus removed from the solution at each
electrode, is 1/2(u + v). Thus the total loss of salt at the cathode
is 1/2(u + v) - 1/2(u - v) or v, and at the anode, 1/2(v + u) - 1/2(v
- u), or u. Therefore, as is explained in the article ELECTROLYSIS, by
measuring the dilution of the liquid round the electrodes when a
current passed, W. Hittorf (_Pogg. Ann._, 1853-1859, 89, p. 177; 98,
p. 1; 103, p. 1; 106, pp. 337 and 513) was able to deduce the ratio of
the two velocities, for simple salts when no complex ions are present,
and many further experiments have been made on the subject (see _Das
Leitvermogen der Elektrolyte_).

By combining the results thus obtained with the sum of the velo