between the plates is directly proportional to the strength of the electric field, in a weak field the ions take so long to travel between the electrodes that most of them recombine on the way.
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.”4
The general shape of the current-voltage curve is shown in Fig. 2, where the ordinates represent current and the abscissae volts.
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