Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/344

objection.^[1] Before proceeding to consider models which are not constituted by a continuous medium, mention must be made of a suggestion offered by Riemann in his lectures^[2] of 1861. Riemann remarked that the scalar-potential φ and vector-potential a, corresponding to his own law of force between electrons, satisfy the equation

${\dot {\phi }}+{\text{div }}\mathbf {a} =0$;

an equation which, as we have seen, is satisfied also by the potentials of L. Lorenz^[3] This appeared to Riemann to indicate that φ might represent the density of an aether, of which a represents the velocity. It will be observed that on this hypothesis the electric and magnetic forces correspond to second derivates of the displacement—a circumstance which makes it somewhat difficult to assimilate the energy possessed by the electromagnetic field to the energy of the model.

We must now proceed to consider those models in which the aether is represented as composed of more than one kind of constituent: of these Maxwell's model of 1861-2, formed of vortices and rolling particles, may be taken as the type. Another device of the same class was described in 1885 by FitzGerald^[4]; this was constituted of a number of wheels, free to rotate on axes fixed perpendicularly in a plane board; the axes were fixed at the intersections of two systems of perpendicular lines; and each wheel was geared to each of its four neighbours by an indiarubber band. Thus all the wheels could rotate without any straining of the system, provided they all had the same angular velocity; but if some of the wheels were revolving faster than others, the indiarubber bands would become strained, It is evident that the wheels in this model play the same part as the vortices in Maxwell's model of 1861-2: their rotation is

1. Cf. H. Witte, Ueber den gegenwärtigen Stand der Frage nach einer mechanischen Erklärung der elektrischen Erscheinungen; Berlin, 1906.
2. Edited after his death by K. Hattendorff, under the title Schwere, Elektricitüt, und Magnetismus, 1875, p. 330.
3. Cf. p. 299.
4. Scient. Proc. Roy. Dublin Soc., 1885; Phil. Mag, June, 1885; FitzGerald's Scient. Writings, pp. 142, 157.