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 _E₀_ − _E₁_ ---------- _K_ _d_ and, in the course of the next half alternation, _E₀_ + _E₁_ ---------- _K_ _d_ towards the plate _A_. If _x₁_ is less than _d_, the greatest distances _x₁_, _x₂_ passed over by the positive carrier during two succeeding half alternations is thus given by _E₀_ − _E₁_ _x₁_ = ---------- _KT_ _d_ and _E₀_ + _E₁_ _x₂_ = ---------- _KT_ _d_ 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 _x₁_ of the plate _B_. This number is equal to 1 --- _x₁_ _qT_ 2 (2) All the carriers which are left within the distance _x₁_ from _B_ at the end of the previous half alternation. The number of these can readily be shown to be 1 _x₁_ --- _x₁_ ---- _qT_ 2 _x₂_ 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 recombination takes place. This must obviously be the case, since the positive carriers travel further in a half alternation towards _A_ than they return towards _B_ during the next half alternation. The carriers thus move backwards and forwards in the changing electric field, but on the whole move towards the plate _A_. The total number of positive carriers produced between the plates during a complete alternation is 2_dqT_. The ratio ρ of the number which reach _B_ to the total number produced is thus given by $$ \rho = \frac {\frac {1}{2} x_1qT + \frac {1}{2} x_1 \frac {x_1}{x_2} qT} {2dqT} = \frac {1}{4} \frac {x_1}{d} \frac {x_1 + x_2} {x_2} $$ . Substituting the values of _x₁_ and _x₂_, we find that $$ K = \frac {2 (E₀ + E_1) d^2} {E₀ (E₀ − E_1) T} \rho $$ . In the experiments, the values of _E₀_, _E₁_, _d_, and _T_ were varied, and the results obtained were in general agreement with the above equation. The following were the results for thorium: _Plates 1·30 cms. apart._ _E₀_ + _E₀_ − Alternations ρ _K_ _E₁_ _E₁_ per second 152 101 57 ·27 1·25