If i_{2} is the value of the current when the electric field is reversed, and K_{2} the velocity of the negative ion,
i_{2} = (9V^2/(32πd^3))K_{2},
and i_{1}/i_{2} = K_{1}/K_{2}.
The current in the two directions is thus directly proportional to the velocities of the positive and negative ions. The current should vary directly as the square of the potential difference applied, and inversely as the cube of the distance between the plates.
The theoretical condition of surface ionization cannot be fulfilled by the ionization due to active substances, as the ionization extends some centimetres from the active plate. If, however, the distance between the plates is large compared with the distance over which the ionization extends, the results will be in rough agreement with the theory. Using an active preparation of radium, the writer has made some experiments on the variation of current with voltage between parallel plates distant about 10 cms. from each other[1].
The results showed
(1) That the current through the gas for small voltages increased more rapidly than the potential difference applied, but not as rapidly as the square of that potential difference.
(2) The current through the gas depended on the direction of the electric field; the current was always smaller when the active plate was charged positively on account of the smaller mobility of the positive ion. The difference between i_{1} and i_{2} was greatest when the gas was dry, which is the condition for the greatest difference between the velocities of the ions.
An interesting result follows from the above theory. For given values of V and d, the current cannot exceed a certain definite value, however much the ionization may be increased. In a similar way, when an active preparation of radium is used as a source of surface ionization, it is found that, for a given voltage
- ↑ Rutherford, Phil. Mag. Aug. 1901.
