132 Prof. A. Anderson on Scala?* and Vector 



point of Q, we may call it. The position of Q' is the same- 



as that of Q at a time t , where r is the distance of Q* 



G 



from a point P in the field whose coordinates are „r, y, z.. 

 I proved in the paper referred to that, if 



F 

 A= 



H) 



where Fit \ is any function of t and u r is the- 



resolved part along Q'P of the velocity of Q when at Q', 

 V 2 A-- 2 ^ = at P. 



The velocity of Q' is, of course, not the same as the 



velocity of Q when at Q', the latter is a function r of [t—~ 

 the former is not. c 



Suppose now that there is a distribution of electricity fin 

 motion. The whole distribution may be conceived as divided 

 np into elemental charges. Let dq be the element charge 

 at Q. It is clear that, if 



A 





('.-?>' 



where r is the distance of Q' the companion point of Q from 

 any point P, and u r the resolved part of the velocity of do 

 when at Q' along Q'P, 



V 2 A-^|- 2 -=0 atP, 



if the density of the moving electric distribution be zero 

 at P. If the distribution is a volume and surface distri- 

 bution on moving bodies unaltered by the motion of the 

 bodies, we may write 



where dT and dB are elements of volume and surface, p and c 



