Page:Radio-activity.djvu/343

 Let d = distance between the plates, T = time of a half alternation, ρ   = ratio of the excited radio-activity on the plate B to the sum of the radio-activities on the plates A and B, K = velocity of the positive carriers for a potential-gradient of 1 volt per centimetre.

On the assumption that the electric field between the plates is uniform, and that the velocity of the carrier is proportional to the electric field, the velocity of the positive carrier towards B is

((E_{0} - E_{1})/d)K,

and, in the course of the next half alternation,

((E_{0} + E_{1})/d)K

towards the plate A.

If x_{1} is less than d, the greatest distances x_{1}, x_{2} passed over by the positive carrier during two succeeding half alternations is thus given by

x_{1} = ((E_{0} - E_{1})/d)KT, and x_{2} = ((E_{0} + E_{1})/d)KT.

Suppose that the positive carriers are produced at a uniform rate of q per second for unit distance between the plates. The number of positive carriers which reach B during a half alternation consists of two parts:

(1) One half of those carriers which are produced within the distance x_{1} of the plate B. This number is equal to

(1/2)x_{1}qT.

(2) All the carriers which are left within the distance x_{1} from B at the end of the previous half alternation. The number of these can readily be shown to be

(1/2)x_{1}(x_{1}/x_{2})qT.

The remainder of the carriers, produced between A and B during a complete alternation, will reach the other plate A in the course of succeeding alternations, provided no appreciable recombi