electrode A in the time t taken for the air to pass along the electrode.
Then
If ρ2 be the ratio of the number of the negative ions that reach the electrode A to the total number passing by, then
Therefore
Similarly the ratio ρ1 of the number of positive ions that give up their charge to the external cylinder to the total number of positive ions is given by
In the above equations it is assumed that the current of air is uniform over the cross-section of the tube, and that the ions are uniformly distributed over the cross-section; also, that the movement of the ions does not appreciably disturb the electric field. Since the value of t can be calculated from the velocity of the current of air and the length of the electrode, the values of the velocities of the ions under unit potential gradient can at once be determined.
The equation (1) shows that ρ 2 is proportional to V ,— i.e. that the rate of discharge of the electrode A varies directly as the potential of A , provided that the value of V is not large enough to