The Kelvin transformation for a torus

A perturbation method was given recently for solving electrostatic problems involving a conducting torus which is freely charged or influenced by a uniform field parallel to its axis. It was forseen that one limitation of the method, the fact that no external influence other than the one just mentioned is allowable, could be removed in the case of a circular torus (anchor ring) by means of the Kelvin transformation and superposition, and the present paper develops this aspect. A number of presumably new results are given for a torus influenced by a given charge located on its axis, and it is shown how the procedure can be extended for a very general axisymmetric situation involving a given charge distribution.