(18) Ether in Matter. We extend thus, by a bold deduction, these principles to a region for which they have not been designed, and thus admit implicitly the possibility of a material representation of the ether. However, as I have already pointed out, an attempt at such a representation raises many difficulties, and the efforts so far made to extend these principles in a more precise manner have not been successful. The most profound attempt, that of Lord Kelvin, the gyrostatic ether, lends itself rigorously only to the representation of the propagation of periodic disturbances in the ether, but makes impossible the existence of a permanent deformation, necessary, however, for the representation of a constant electrostatic field. The gyrostats would turn back again at the end of a finite time, and the system would cease to react against a deformation which has been imposed. Moreover, it would appear impossible to include in this conception the permanent existence of electrons, centres of deformation in the medium.
To get around this difficulty, Larmor had occasion, in the material image which he proposed for the ether, to superimpose on the gyrostatic system of Lord Kelvin the properties of a perfect fluid, of which the displacements representing the magnetic field should be at each instant irrotational in order not to produce an electric field by the rotation of the gyrostats present in the medium. But a great difficulty is added to the preceding: if the motion of a fluid satisfies at every moment the condition of being irrotational for infinitely small displacements, it is not so for finite displacements, and a magnetic field could not continue to exist without giving rise to an electric field.
I believe it impossible to overcome these difficulties and to give a material image of the ether, whose properties are entirely distinct, and probably much more simple than those of matter.
(19) Action and Reaction. Let us, however, retain this view in order that we may meet new difficulties. By means of Lagrange's equations Lorentz obtains two external forces acting on each electron in motion, two terms representing the action of the electromagnetic field. One force is parallel to the electrostatic field; it is the ordinary electric force, due to the superposition of the electric field produced by the electron on the external electric field: the other is perpendicular to the direction of the velocity of the electron and of the external magnetic field; it is the electromagnetic force analogous to the force of Laplace exerted by a magnetic field on an element of current, and due to the superposition on the external magnetic field of the magnetic field produced by the electron during its motion. This double result includes all the elementary laws of electromagnetism and of electrodynamics, if we consider the current in ordinary conductors as due to the displacement of electrified particles.
