qAd = iA/e + αn2·Ad,
q = i/ed + αn2.
If u1 and u2 are the velocities with which the positive and negative ions move, nu1e and nu2e are respectively the quantities of positive electricity passing in one direction through unit area of the gas per second, and of negative in the opposite direction, hence
i = nu1e + nu2e.
If X is the electric force acting on the gas, k1 and k2 the velocities of the positive and negative ions under unit force, u1 = k1X, u2 = k2X; hence
n = i/(k1 + k2)Xe,
and we have
| q = | i | + | αi2 | . |
| ed | (k1 + k2)2 e2X2 |
But qed is the saturation current per unit area of the plate; calling this I, we have
| I − i = | dαi2 |
| e(k1 + k2)2X2 |
or