The distance of 15 mms. was not sufficient to completely absorb all the radiation, so that the current had not reached its limiting value.
When more than one type of radiation is present, the saturation current between parallel plates is given by
i = A(1 - e^{λd}) + A_{1}(1 - e^{-λ_{1}d}) + &c.
where A, A_{1} are constants, and λ, λ_{1} the absorption constants of the radiations in the gas.
Since the radiations are unequally absorbed in different gases, the variation of current with distance depends on the nature of the gas between the plates.
44. Variation of the current with pressure. The rate
of production of ions by the radiations from active substances is
directly proportional to the pressure of the gas. The absorption of
the radiation in the gas also varies directly as the pressure. The
latter result necessarily follows if the energy required to produce
an ion is independent of the pressure.
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 λ_{1} = 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 I/I_{0} = e^{-pλ_{1}x}. The saturation current i is thus proportional to
[integral]_{0}^d pI dx = [integral]_{0}^d pI_{0}e^{-pλ_{1}x} . dx = (I_{0}/λ_{1}) (1 - e^{pλ_{1}d}).
If r be the ratio of the saturation currents for the pressures p_{1} and p_{2},
r = (1 - e^{-p_{1}λ_{1}d})/(1 - e^{-p_{2}λ_{1}d}).
