420 The Theory of Aether and Electrons in the 



Kiemann, and Clausing, and from Lorentz' own earlier work, 

 lies in the conception which is entertained of the propagation 

 of influence from one electron to another. In the older writ- 

 ings, the electrons were assumed to be capable of acting on 

 each other at a distance, with forces depending on their 

 charges, mutual distances, and velocities ; in the present 

 memoir, on the other hand, the electrons were supposed to 

 interact not directly with each other, but with the medium in 

 which they were embedded. To this medium were ascribed the 

 properties characteristic of the aether in Maxwell's theory. 



The only respect in which Lorentz' medium differed from 

 Maxwell's was in regard to the effects of the motion of bodies. 

 Impressed by the success of Fresnel's beautiful theory of 

 the propagation of light in moving transparent substances,* 

 Lorentz designed his equations so as to accord with that 

 theory, and showed that this might be done by drawing a 

 distinction between matter and aether, and assuming that a 

 moving ponderable body cannot communicate its motion to 

 the aether which surrounds it, or even to the aether which 

 is entangled in its own particles ; so that no part of the aether 

 can be in motion relative to any other part. Such an aether 

 simply space endowed with certain dynamical properties. 



The general plan of Lorentz' investigation was to reduce all 

 the complicated cases of electromagnetic action to one simple 

 and fundamental case, in which the field contains only free 

 aether with solitary electrons dispersed in it ; the theory which 

 he adopted in this fundamental case was a combination of 

 Clausius' theory of electricity with Maxwell's theory of the 

 aether. 



Suppose that e (x, y, z) and e(x, y', z) are two electrons. 

 In the theory of Clausius,f the kinetic potential of their mutual 

 action is 



ee' 



(xx + yy + ss' - c 2 ) ; 



so when any number of electrons are present, the part of the 



*Cf. pp. 116 etxqq. t Cf. p. 262. 





