﻿78 Dr. W. F, G. Swarm on the Effects of Uniform Motion 



to which the point P' has moved by the time that the effect 

 due to the electronic motion at 0' is felt there. Thus writing 



OP=S and 0'P /, = S2 



we have, for the values of yjr and y]r f at corresponding points 

 and times 



cv cy. 



* ffw K'-¥)]' 



where Ws and W s / are the values of the velocities of the 

 corresponding electrons in the two systems, resolved along 

 OP and O'P" respectively. Since, as we have seen on 



page 72, 



v c r + c ~ t€ + c 2 * 



and since - a .v is u s , *. £• the velocity of the system 

 resolved along OP, we have 



Now if I, m, n and l f , m\ n are the direction cosines of the 



lines OP and O'P" respectively, we have, using the notation 



?;S 9 

 of page 71, and remembering that 8[j = — ? 



i. e .,r=j.-{i+g)" 1 + ^ = (u 90+g)" 1; 



also we see at once that 



Observing that 

 we have 



