Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/289

returned to the question of the process by which electric action is propagated through space. In this memoir he proposed to replace Poisson's equation for the electrostatic potential, namely,

$\nabla ^{2}V+4\pi \rho =0$,

by the equation

$\nabla ^{2}V-{\frac {1}{c^{2}}}{\frac {\partial ^{2}V}{\partial t^{2}}}+4\pi \rho =0$,

according to which the changes of potential due to changing electrification would be propagated outwards from the charges with a velocity c. This, so far as it goes, is in agreement with the view which is now accepted as correct; but Riemann's hypothesis was too slight to serve as the basis of a complete theory. Success came only when the properties of the intervening medium were taken into account.

In that power to which Gauss attached so much importance, of devising dynamical models and analogies for obscure physical phenomena, perhaps no one has ever excelled W. Thomson^[1]; and to him, jointly with Faraday, is due the credit of having initiated the theory of the electric medium. In one of his earliest papers, written at the age of seventeen,^[2] Thomson compared the distribution of electrostatic force, in a region containing electrified conductors, with the distribution of the flow of heat in an infinite solid: the equipotential surfaces in the one case correspond to the isothermal surfaces in the other, and an electric charge corresponds to a source of heat.^[3]

1. As will appear from the present chapter, Maxwell had the same power in a very marked degree. It has always been cultivated by the "Cambridge school" of natural philosophers.
2. Camb. Math. Journal, iii (Feb. 1842). p. 71; reprinted in Thomson's Papers on Electrostatics and Magnetism, p. 1. Also Camb. and Dub. Math. Journal, Nov., 1845; reprinted in Papers, p. 15.
3. As regards this comparison, Thomson had been anticipated by Chasles, Journal de I'Éc. Polyt. xv (1837), p. 266, who had shown that attraction accord. ing to Newton's law gives rise to the same fields as the steady conduction of heat, both depending on Laplace's equation ∇²V = 0.
   It will be remembered that Ohm had used an analogy between thermal conduction and galvanic phenomena.