Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/112

or $ii\prime \int _{s}\left[\mathbf {ds\prime .} {\frac {[\mathbf {ds.r} ]}{r^{3}}}\right]$,

or $i\prime [\mathbf {ds\prime .B} ]$,

Where $\mathbf {B} =i\int _{s}{\frac {1}{r^{3}}}[\mathbf {ds.r} ]$.

Now this value of B is precisely the value found by Biot and Savart^[1] for the magnetic intensity at ds′ due to the current i in the circuit s. Thus we see that the ponderomotive force on a current-element ds′ in a magnetic field B is i′[ds′.B].

Ampère developed to a considerable extent the theory of the equivalence of magnets with circuits carrying currents; and showed that an electric current is equivalent, in its magnetic effects, to a distribution of magnetism on any surface terminated by the circuit, the axes of the magnetic molecules being everywhere normal to this surface:^[2] such a magnetized surface is called a magnetic shell. He preferred, however, to regard the current rather than the magnetic fluid as the fundamental entity, and considered magnetism to be really an electrical phenomenon: each magnetic molecule owes its properties, according to this view, to the presence within it of a small closed circuit in which an electric current is perpetually flowing.

The impression produced by Ampère's memoir was great and lasting. Writing half a century afterwards, Maxwell speaks of it as "one of the most brilliant achievements in science." "The whole," he says, "theory and experiment, seems as if it had leaped, full-grown and full-armed, from the brain of the 'Newton of electricity.' It is perfect in form and unassailable in accuracy; and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electrodynamics."

Not long after the discovery by Oersted of the connexion between galvanism and magnetism, a connexion was discovered between galvanism and heat. In 1822 Thomas Johann Seebeck

1. See ante, p. 86.
2. Loc. cit., p. 367.