﻿I 



deduced from the Electrical Theory of Matter. 71 



its effect at the point P in the system at rest at the time t ; 

 the time at which that instantaneous motion must have 



OP 



occurred is obviously t p-. The corresponding motion in 



the moving system will consequently be described at the time 

 and the time at which this motion will give rise 



<-¥) 



to its effect at the point P' in the moving system is 



'-*-") 



O'P" 

 ' 



where O'P" is the line joining 0' in the moving system to 

 the point P" in space which will be occupied by the point P' 

 when the effect due to the motion is felt at P'. Now it 

 would be possible to find the condition which we seek, 

 assuming any arbitrary value of k, but as we shall at a later 

 stage of the paper find it necessary, for other reasons, to take 

 k as e 1/2 , we shall, to save unnecessary labour in the calcur- 

 lation, at once restrict ourselves to this case, and of course in 

 doing this we are not making any assumption, we are simply 

 restricting the conditions of the problem. 



Now if P'M' (fig. 1) is the perpendicular on the zy plane 



Fi*. 1. 



Direction of motion. 



in the moving system, 0' being taken as the origin, we have 

 on writing 



MT' = f, P'P'' = S£ Or = r, 0'P" = /- 2 , 

 the result 



^=f (6) 



for P' travels a distance Sf while the disturbance originating 

 at 0' travels O'P". 



