﻿0.>J 



♦s- 



,B* 



, BQ 



+ By 



♦s- 



,B* 





, BR 



+ B-- " 



,B<t> 



Electron Theory of Matter. 25 



uniformly and without relative motion of its parts with the 

 velocity it actually possesses. The remaining terms in the 

 electromotive force, due to acceleration and to relative motion, 



are only of order- relative to the principal term, and may 

 be neglected. ^ 



Let (P, Q, R, S, T, U) be the stress which balances the 

 internal electromotive force. It is given by the equations : 



BU 

 ■da, 



BT 



(3.6' 



where p' is the electric density. 



When p is a function of <3> alone the stress reduces to a 

 hydrostatic pressure 



P=-$P , d<!>. 



This occurs when p' is constant. 



When the electricity is distributed over the surface of the 

 electron there is a discontinuity of pressure at the surface. 



When the electron is an oblate spheroid of eccentricity /?, 

 with its minor axis in the line of motion, the pressure in either 

 case is constant at the surface. This is the case with the 

 forms of electron proposed by Lorentz and by Bucherer. 



§ 6. The stress just considered may be accounted for in 

 two ways : — 



(1) We may suppose it due to attractions between the ele- 

 mentary parts of the electron. In that case the attractions 

 cannot follow the Newtonian law ; otherwise two negative 

 electrons would have no electrostatic action on each other, 

 since the new hypothetical force would balance the electro- 

 static repulsion between the electrons when at rest. Hence 

 the new force cannot be used to account for gravitation, and 

 we require to postulate two types of actions at a distance in 

 addition to the electromagnetic actions. This explanation is 

 equivalent to Jeans' s assumption of additional forces between 

 electric charges. These forces not only require explanation 

 themselves, but are hardly consonant with an electron 

 theory. 



(2) We may suppose the stress due to interaction between 

 the electron and the pettier. 



The simplest assumption is that the electron is an oblate 



