Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/339

we obtain the equation

$\epsilon {\ddot {\mathbf {e} }}+c^{2}{\text{ curl curl }}\mathbf {e} =0$,

which is no other than the equation of motion of MacCullagh's aether,^[1] the specific inductive capacity e corresponding to the reciprocal of MacCullagh's constant of elasticity. In the analogy thus constituted, electric displacement corresponds to the twist of the elements of volume of the aether; and electric charge must evidently be represented as an intrinsic rotational strain. Mechanical models of the electromagnetic field, based on FitzGerald's analogy, were afterwards studied by A. Sommerfeld,^[2] by R. Reiff,^[3] and by Sir J. Larmor.^[4] The last-named author^[5] supposed the electric charge to exist in the form of discrete electrons, for the creation of which he suggested the following ideal process^[6]:—A filament of aether, terminating at two nuclei, is supposed to be removed, and circulatory motion is imparted to the walls of the channel so formed, at each point of its length, so as to produce throughout the medium a rotational strain. When this has been accomplished, the channel is to be filled up again with aether, which is to be made continuous with its walls. When the constraint is removed from the walls of the channel, the circulation imposed on them proceeds to undo itself, until this tendency is balanced by the elastic resistance of the aether with which the channel has been filled up; thus finally the system assumes a state of equilibrium in which the nuclei, which correspond to a positive and a negative electron, are surrounded by intrinsic rotational strain.

Models in which magnetic force is represented by the velocity of an aether are not, however, secure from objection, It is necessary to suppose that the aether is capable of lowing like a perfect fluid in irrotational motion (which would corre-

1. Cf. p. 155.
2. Ann. d. Phys, xlvi (1892), p. 139.
3. Reiff, Elasticität und Elektricität, Freiburg, 1893.
4. Phil. Trans. clxxxv (1893), p. 719.
5. In a supplement, of date August, 1894, to his above-cited memoir of 1893.
6. Phil. Trans. clxxxv (1894), p. 810; cxc (1897), p. 210; Larmor, Aether and Matter (1900), p. 326.