Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/373

or, by virtue of the fundamental equations for dielectrics,

$[-\mathbf {{\dot {B}}.D} ]+[\mathbf {{\dot {D}}.B} ]$,   or   $(\partial /\partial t)[\mathbf {D.B} ]$.

This result compels us to adopt one of three alternatives: either to modify the theory so as to reduce to zero the resultant force on an element of free aether; this expedient has not met with general favour;^[1] or to assume that the force in question sets the aether in motion: this alternative was chosen by Helmholtz,^[2] but is inconsistent with the theory of the aether which was generally received in the closing years of the century; or lastly, with Thomson,^[3] to accept the principle that the aether is itself the vehicle of mechanical momentum, of amount [D.B] per unit volume.

Maxwell's theory was now being developed in ways which could scarcely have been anticipated by its author. But although every year added something to the superstructure, the foundations remained much as Maxwell had laid them, the doubtful argument by which he had sought to justify the introduction of displacement-currents was still all that was offered in their defence. In 1884, however, the theory was established^[4] on a different basis by a pupil of Helmholtz', Heinrich Hertz (b. 1857, d. 1894).

The train of Hertz' ideas resembles that by which Ampère, on hearing of Oersted's discovery of the magnetic field produced by electric currents, inferred that electric currents should exert ponderomotive forces on each other. Ampère argued that a current, being competent to originate a magnetic field, must be equivalent to a magnet in other respects; and therefore that currents, like magnets, should exhibit forces of mutual attraction and repulsion.

1. It was, however, adopted by G. T. Walker, Aberration and the Electromagnetic Field, Camb., 1900.
2. Berlin Sitzungsberichte, 1893, p. 649; Am. d. Phys. lii (1894), p. 135. Helmholtz supposed the aether to behave as a frictionless incompressible fluid.
3. Loc. cit.
4. Ant. d. Phys. xxiii (1884), p. 84: English version in Hertz's Miscellaneous Pipers, translated by D. E. Jones and G. A. Schott, p. 273.

2 A