Remark on Dr Peddie's Proof of the Potential Theorems regarding Uniform Spherical Shells

Extract

On reading Dr Peddie's paper, the following modification of the proof, which avoids summation, occurred to me:—

If in Figure 7 we take a point S on the circle BQD such that PQ + PS = 2a, where a is the radius, and a corresponding point S′ such that PQ′ + PS′ = 2a, then it is clear by Dr Peddie's construction that the potential at P due to the zone of the spherical surface lying between planes through Q and Q′ perpendicular to BD is given by 2πσ(PQ′−PQ) · a/CP, and is therefore equal to that due to the corresponding zone between S and S′, since