Although the variation of the current with voltage depends
only on the velocity of the ions and their rate of recombination, the full mathematical analysis is intricate, and the equations, expressing the relation between current and voltage, are only integrable for the case of uniform ionization. The question is complicated by the inequality in the velocity of the ions and by the disturbance of the potential gradient between the plates by the movement of the ions. J. J. Thomson[1] has worked out the case for uniform production of ions between two parallel plates, and has found that the relation between the current i and the potential difference V applied is expressed by
Ai^2 + Bi = V
where A and B are constants for a definite intensity of radiation and a definite distance between the plates.
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Saturation Curve Radium, activity 1,000 plates 4·5 cms. apart
Fig. 3.
In certain cases of unsymmetrical ionization, which arise in the study of the radiations from active bodies, the relation between current and voltage is very different from that expressed by
- ↑ J. J. Thomson, Phil. Mag. 47, p. 253, 1899; Conduction of Electricity through Gases, p. 73, 1903.