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[[48]] 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
Ai2 + Bi = V
where A and B are constants for a definite intensity of radiation and a definite distance between the plates.
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 the above equation. Some of these cases will be considered in [section 47].
27. The general shape of the current-voltage curves for gases exposed to the radiations from active bodies is shown in [Fig. 3].
This curve was obtained for ·45 grams of impure radium chloride, of activity 1000 times that of uranium, spread over an area of 33 sq. cms. on the lower of two large parallel plates, 4·5 cms. apart. The maximum value of the current observed, which is taken as 100, was 1·2 × 10-8 amperes, the current for low voltages was nearly proportional to the voltage, and about 600 volts between the plates was required to ensure approximate saturation.
In dealing with slightly active bodies like uranium or thorium, approximate saturation is obtained for much lower voltages. Tables I. and II. show the results for the current between two parallel plates distant 0·5 cms. and 2·5 cms. apart respectively, when one plate was covered with a thin uniform layer of uranium oxide.
Table I.