“Mr. Faraday’s researches ... were undertaken with a view to test an idea which he had long possessed that the forces of attraction and repulsion exercised by free electricity are not the resultants of actions exercised at a distance, but are propagated by means of molecular action among the contiguous particles of the insulating medium surrounding the electrified bodies, which he therefore calls the dielectric. By this idea he has been led to some very remarkable views upon induction, or, in fact, upon electrical action in general. As it is impossible that the phenomena observed by Faraday can be incompatible with the results of experiment which constitute Coulomb’s theory, it is to be expected that the difference of his ideas from those of Coulomb must arise solely from a different method of stating and interpreting physically the same laws; and further, it may, I think, be shown that either method of viewing this subject, when carried sufficiently far, may be made the foundation of a mathematical theory which would lead to the elementary principles of the other as consequences. This theory would, accordingly, be the expression of the ultimate law of the phenomena, independently of any physical hypothesis we might from other circumstances be led to adopt. That there are necessarily two distinct elementary ways of viewing the theory of electricity may be seen from the following considerations....” In the pages which follow, Lord Kelvin develops the consequences of an analogy between the conduction of heat and electrostatic action, which he had pointed out three years earlier (1842), in his paper on “The Uniform Motion of Heat in Homogeneous Solid Bodies,” and discusses its connection with the mathematical theory of electricity. The problem of distributing sources of heat in a given homogeneous conductor of heat, so as to produce a definite steady temperature at each point on the conductor is shewn to be _mathematically_ identical with that of distributing electricity in equilibrium, so as to produce at each point an electrical potential having the same value as the temperature. Thus the fundamental laws of the conduction of heat may be made the basis of the mathematical theory of electricity, but the physical idea which they suggest is that of the propagation of some effect by means of the mutual action of contiguous particles, rather than that of material particles attracting or repelling at a distance, which naturally follows from the statement of Coulomb’s law. Lord Kelvin continues:--