hemical equilibrium, be all active in turn. The
charge on each, as we have seen, can be expressed in absolute units, and
therefore the velocity with which they move past each other can be
calculated. This was first done by Kohlrausch (_Gottingen Nachrichten_,
1876, p. 213, and _Das Leitvermogen der Elektrolyte_, Leipzig, 1898)
about 1879.

In order to develop Kohlrausch's theory, let us take, as an example,
the case of an aqueous solution of potassium chloride, of
concentration n gram-equivalents per cubic centimetre. There will then
be n gram-equivalents of potassium ions and the same number of
chlorine ions in this volume. Let us suppose that on each
gram-equivalent of potassium there reside +e units of electricity, and
on each gram-equivalent of chlorine ions -e units. If u denotes the
average velocity of the potassium ion, the positive charge carried per
second across unit area normal to the flow is n e u. Similarly, if v
be the average velocity of the chlorine ions, the negative charge
carried in the opposite direction is n e v. But positive electricity
moving in one direction is equivalent to negative electricity moving
in the other, so that, before changes in concentration sensibly
supervene, the total current, C, is ne(u + v). Now let us consider the
amounts of potassium and chlorine liberated at the electrodes by this
current. At the cathode, if the chlorine ions were at rest, the excess
of potassium ions would be simply those arriving in one second,
namely, nu. But since the chlorine ions move also, a further
separation occurs, and nv potassium ions are left without partners.
The total number of gram-equivalents liberated is therefore n(u + v).
By Faraday's law, the number of grams liberated is equal to the
product of the current and the electro-chemical equivalent of the ion;
the number of gram-equivalents therefore must be equal to [eta]C,
where [eta] denotes the electro-chemical equivalent of hydrogen in
C.G.S. units. Thus we get

n(u + v) = [eta]C = [eta]ne(u + v),

and it follows that the charge, e, on 1 gram-equivalent of each kind
of ion is equal to 1/[eta]. We know that Ohm's Law holds good for
electrolytes, so that the current C is also given by k.dP/dx, where k
denotes the conductivity of the solution, and dP/dx the potential
gradient, i.e. the change in potential per unit length along the lines
of current flow. Thus

n