many years, attention was directed chiefly to magnetic fields of a steady, or at any rate non-oscillatory, character; in such fields, the motion of the particles of the medium is continuously progressive; and it was consequently natural to suppose the medium to be fluid.
Maxwell himself, as we have seen,[1] afterwards abandoned this conception in favour of that which represents magnetic phenomena as rotatory. "According to Ampère and all his followers," he wrote in 1870,[2] "electric currents are regarded as a species of translation, and magnetic force as depending on rotation. I am constrained to agree with this view, because the electric current is associated with electrolysis, and other undoubted instances of translation, while magnetism is associated with the rotation of the plane of polarization of light."
But the other analogy was felt to be too valuable to be altogether discarded, especially when in 1858 Helmholtz extended it[3] by showing that if magnetic induction is compared to fluid velocity, then electric currents correspond to vortex-filaments in the fluid. Two years afterwards Kirchhoff[4] developed it further. If the analogy has any dynamical (as distinguished from a merely kinematical) value, it is evident that the ponderomotive forces between metallic rings carrying electric currents should be similar to the ponderomotive forces between the same rings when they are immersed in an infinite incompressible fluid; the motion of the fluid being such that its circulation through the aperture of each ring is proportional to the strength of the electric current in the corresponding ring. In order to decide the question, Kirchhoff' attempted, and solved, the hydrodynamical problem of the motion of two thin, rigid rings in an incompressible frictionless fluid, the fluid motion being irrotational; and found that the forces between the rings are numerically equal to those which the rings would exert on
