XIII. On electrical motions in a spherical conductor

Abstract

This paper treats of the motions of electricity produced in a spherical conductor by any electric or magnetic operations outside it. The investigation was undertaken some time ago in illustration of Maxwell’s theory of Electricity. This theory is so remarkable, more especially in the part which it assigns to dielectric media in the propagation of electromagnetic effects, that it seemed worth while to attack some problem in which all the details of the electrical processes could be submitted to calculation, although it was evident beforehand, from the researches of Helmholtz and others, that the results (so far as they are peculiar to the theory) would be of far too subtle a character to admit of comparison with experiment. In studying the mathematical character of the problem above stated I was led to a certain system of formulæ which I have since utilised in two communications to the London Mathematical Society, and which seem likely to be of use in a great variety of physical questions. 1 consists mainly of a recital of the fundamental equations and of the conditions to be satisfied at the surface of a conductor. It is assumed, in the first instance, that the magnetic susceptibility of the conductor is zero.