where _A_, _A₁_ are constants, and λ, λ₁ 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 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 $$ \frac {I} {I₀} = e^{- p λ_1 x} $$ The saturation current _i_ is thus proportional to $$ \int₀^d pI dx = \int₀^d pI₀e^{-pλ_1 x} dx = \frac{I₀}{λ_1} (I − e^{pA_1d}) $$ If _r_ be the ratio of the saturation currents for the pressures _p₁_ and _p₂_, $$ r = \frac {1 − e^{-p_1λ_1 d}} {1 − e^{-p_2λ_1 d}} $$ 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. [Illustration: Fig. 8.] For the purpose of comparison, the current at atmospheric pressure and temperature in each case is taken as unity. The actual value of the current was greatest in carbonic acid and least in hydrogen. In hydrogen, where the absorption is small, the current over the whole range is nearly proportional to the pressure. In carbonic acid, where the absorption is large, the current diminishes at first slowly with the pressure, but is nearly proportional to it below the pressure of 235 mms. of mercury. The curve for air occupies an intermediate position. In cases where the distance between the plates is large, the saturation current will remain constant with diminution of pressure until the absorption is so reduced that the radiation reaches the other plate.