Suppose that the ions are produced at a constant rate _q_ per cubic centimetre per second in the gas between parallel plates distant _l_ cms. from each other. When no electric field is applied, the number _N_ present per c.c., when there is equilibrium between the rates of production and recombination, is given by _q_ = α_N_², where α is a constant. If a small potential difference _V_ is applied, which gives only a small fraction of the maximum current, and consequently has not much effect on the value of _N_, the current _i_ per sq. cm. of the plate, is given by _NeuV_ _i_ = ----- _l_ where _u_ is the sum of the velocity of the ions for unit potential gradient, and _e_ is the charge carried by an ion. _uV_ ---- _l_ is the velocity of the ions in the electric field of strength _V_ --- _l_ The number of ions produced per second in a prism of length _l_ and unit area of cross-section is _ql_. The maximum or saturation current _I_ per sq. cm. of the plate is obtained when all of these ions are removed to the electrodes before any recombination has occurred. Thus _I_ = _q . l . e_, and $$ \frac{i}{I} = \frac{NuV}{ql^2} = \frac{uV}{l^2\sqrt{q\alpha}} $$ This equation expresses the fact previously noted that, for small voltages, the current _i_ is proportional to _V_. Let _i/I_ = ρ, then $$ V = \frac {\rho l^2 \sqrt {q\alpha}} {u} $$ 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.