In cases where the ionization is uniform between two parallel plates, the current will vary directly as the pressure; when however the ionization is not uniform, on account of the absorption of the radiation in the gas, the current does not decrease directly as the pressure until the pressure is reduced so far that the ionization is sensibly uniform. Consider the variation with pressure of the saturation current i between two large parallel plates, one of which is covered with a uniform layer of active matter.
Let λ1 = absorption constant of the radiation in the gas for unit pressure.
For a pressure p, the intensity I at any point x is given by
The saturation current i is thus proportional to
If r be the ratio of the saturation currents for the pressures p1 and p2,
The ratio is thus dependent on the distance d between the plates and the absorption of the radiation by the gas.
The difference in the shape of the pressure-current curves[[75]] is well illustrated in [Fig. 8], where curves are given for hydrogen, air, and carbonic acid for plates 3·5 cms. apart.