Electromagnetic Mass of a Moving Electron. 541 



The assumption on which the theory is built is that the 

 fr»rce=; from sources exterior to the electron balance those 

 due to the electron itself : this is the assumption that there 

 is no inertia other than electromagnetic, and we deduce the 

 equation ^ _ ^^ 



dt ~ dt ' 



where W is the electromagnetic energy, and A is the work 

 done by the forces due to the electron itself. 



If v is the velocity of the centre of the electron, i>= (v + 1\) 

 the velocity of the charge at any point of it, F the mechanical 

 force per unit charge, we have 



(vF) being the vector product of v and F. 



If £ V K are the coordinates relative to the centre of the 

 electron of the element of charge whose velocity is v, and 

 xy z of the same element when the electron is at rest, £=/3#, 

 V—y, ?=s ; so that the velocity « x of the charge relative to 

 the centre is 



d% d/3 xv dv 



= .v 



it ' dt c 2 /3 dt 



in the direction of the axis of x. 



Thus, if Fa; is the component of F in that direction, 



-fo = v j pF x dr + J px -£ FJt, 



= -v K-^LxF x dT, 

 K being the total mechanical force on the electron ; 



= -v K-^p x(F x ) dr ; 



where the suffix in the last integral refers to the corre- 

 sponding quantities when the electron is at rest, so that the 

 region of integration is spherical. 



For quasistationary motion W is a function of v only, 

 and therefore 



cW _ dW dv _dW 



dt dv dt ~~ dv ' 

 Phil Mag. S. 6. Vol. 14. No. 82. Oct. 1907. 2 



