we have q = [alpha]n0^2 + i/ed. If X0 be the value of X when x = 0,
kX0n0e = i, and,

kX0^2 i^2 [alpha] i^2
C = ----- = ------------ = --------- . -------- (2).
8[pi] n0^2ke.8[pi] 8[pi]ke^2 q + i/ed

Since [alpha]/8[pi]ke is, as we have seen, less than unity, C will be
small compared with il, if i/(eq + i/d) is small compared with l. If
I0 is the saturation current, q = I0/ed, so that the former expression
= id/(I0 + i), if i is small compared with I0, this expression is
small compared with d, and therefore _a fortiori_ compared with l, so
that we are justified in this case in using equation (1).

From equation (2) we see that the current increases as the square of
the potential difference. Here an increase in the potential difference
produces a much greater percentage increase than in conduction through
metals, where the current is proportional to the potential difference.
When the ionization is distributed through the gas, we have seen that
the current is approximately proportional to the square root of the
potential, and so increases more slowly with the potential difference
than currents through metals. From equation (1) the current is
inversely proportional to the cube of the distance between the
electrodes, so that it falls off with great rapidity as this distance
is increased. We may note that for a given potential difference the
expression for the current does not involve q, the rate of production
of the ions at the electrode, in other words, if we vary the
ionization the current will not begin to be affected by the strength
of the ionization until this falls so low that the current is a
considerable fraction of the saturation current. For the same
potential difference the current is proportional to k, the velocity
under unit electric force of the ion which carries the current. As the
velocity of the negative ion is greater than that of the positive, the
current when the ionization is confined to the neighbourhood of one of
the electrodes will be greater when that electrode is made cathode
than when it is anode. Thus the current will appear to pass more
easily in one direction than in the opposite.

Since the ions which carry the current have to travel all the way from
one electrode to the other, any obstacle which is impervious to these
ions will, if placed between the electrodes, stop the curre