RELATIONS TO OTHER SCIENCES 135 



(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 represent- 

 ation of the propagation of periodic disturbances in the ether, but 

 makes impossible the existence of a permanent deformation, neces- 

 sary, 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 gyro- 

 static 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 perpendicu- 

 lar 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 electro- 

 dynamics, if we consider the current in ordinary conductors as due to 

 the displacement of electrified particles. 



