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 magnetic field produced by electric currents is compared to the flow of an incompressible fluid, so that the magnetic vector is represented by the fluid velocity, then the electric currents correspond to the vortex-filaments in the fluid. This analogy correlates many theorems in hydrodynamics and electricity; for instance, the theorem that a re-entrant vortex-filament is equivalent to a uniform distribution of doublets over any surface bounded by it, corresponds to Ampère's theorem of the equivalence of electric currents and magnetic shells.

In his memoir of 1855, Maxwell had not attempted to construct a mechanical model of electrodynamic actions, but had expressed his inteution of doing so. "By a careful study," he wrote, "of the laws of elastic solids, and of the motions of viscous fluids, I hope to discover a method of forming a mechanical conception of this electrotonic state adapted to general reasoning", and in a foot-note he referred to the effort which Thomson had already made in this direction. Six years elapsed, however, before anything further on the subject was published. In the meantime, Maxwell became Professor of Natural Philosophy in King's College, London—a position in which he had opportunities of personal contact with Faraday, whom he had long reverenced. Faraday had now concluded the Experimental Researches, and was living in retirement at Hampton Court; but his thoughts frequently recurred to the great problem which he had brought so near to solution. It appears from his note-book that in 1857 he was speculating whether the velocity of propagation of magnetic action is of the same order as that of light, and whether it is affected by the susceptibility to induction of the bodies through which the action is transmitted.

The answer to this question was furnished in 1861-2, when Maxwell fulfilled his promise of devising a mechanical conception of the electromagnetic field.