This equation expresses the fact previously noted that, for small voltages, the current i is proportional to V.
Let
i/I = ρ,
then
Now the greater the value of V required to obtain a given value of ρ (supposed small compared with unity), the greater the potential required to produce saturation.
It thus follows from the equation that:
(1) For a given intensity of radiation, the saturation P.D. increases with the distance between the plates. In the equation, for small values of ρ, V varies as l2. This is found to be the case for uniform ionization, but it only holds approximately for non-uniform ionization.
(2) For a given distance between the plates, the saturation P.D. is greater, the greater the intensity of ionization between the plates. This is found to be the case for the ionization produced by radio-active substances. With a very active substance like radium, the ionization produced is so intense that very large voltages are required to produce approximate saturation. On the other hand, only a fraction of a volt per cm. is necessary to produce saturation in a gas where the ionization is very slight, for example, in the case of the natural ionization observed in a closed vessel, where no radio-active substances are present.