The current observed is consequently small. With increase of the voltage there is an increase of speed of the ions and a smaller number recombine. The current consequently increases, and will reach a maximum value when the electric field is sufficiently strong to remove all the ions before appreciable recombination has occurred. The value of the current will then remain constant even though the voltage is largely increased. This maximum current will be called the “saturation” current, and the value of the potential difference required to give this maximum current, the “saturation P.D.”[47] The general shape of the current-voltage curve is shown in Fig. 2, where the ordinates represent current and the abscissae volts. [Illustration: Fig. 2.] 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. [Illustration: 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. 0·5 cms. apart