﻿Organic Substances and the Electron Theory. 205 



by Prof. H. M. Macdonald ('Electric Waves/ p. 176) in the 

 form 



X=-^S^-^',&c. (A) 



dr r x ov K '■ 



a = ^ r ^- 2, — 5— — s-^T * 5 &C. (B) 



Oj/O £ r ± ozat n 



where r x is the distance of the field point xyz from x x yiz u 

 fi^ifb the position of electron 1 at time t, 



£l Vl bl j J) >) ~" ~9 



C 



c being the velocity of light, 



and i/r =— 2— 4- sr- • • • + s~---- 



the summation being taken for all the electrons. 

 The electrokinetic energy is 



»*- 



where 



u = |? - - ^ , &c. (C), and 4ttc 2 /= X (D) ; 



and since from (B) and (0) 



the energy is, using (A) and (D), 



the integral being taken through all space. 



If the velocities are small enough compared with c, the 

 expression for the energy reduces to the following (the dashes 

 being now omitted) : 



