Electromagnetic Mass of a Moving Electron, 545 

 transformation must be of the form 



a'x + b't + c' 



? = 



T = 



ax + bt-tc ' 

 ax + bt + c 



Now f will not in general be infinite unless x is infinite, 

 and also when x and t are zero f and r are also zero. Hence 

 the transformation must be of the simpler form 



tj = ax-r bt x = 



A 

 or A = (a'b"-l'a"). 



r=a"x+b"t t = -*"tj + *'T 



the coefficients a f , b r , a", b" being functions of the relative 

 velocity v. 



Now if a point starts from A at time £ = and travels 

 with B, its coordinate f is always zero by virtue of the 

 relation x=vt. 



Hence b f =-—a r v, 



i.e. %—a(x — vt). 



Now consider what is involved in saying that if a point 

 moves along the axis of x relative to A with the velocity c 

 of light, it also moves with velocity c relative to B. If 

 a point moves from the position x at time t to the position 

 x + 8x at time t-\ ■ Bt let the corresponding changes in f and t 

 be Sf, St. 



Then 8jjj = a'8x + b'8t 9 



8T = a r/ 8x + b"8L 



Hence -. /CN 7 ._ 



3g_ a f hx + b'ht 



hT~a"hx-rb"ht* 



Hence if the point has velocity n in A's system of co- 

 ordinates and v in that of B 



a'n + V 



~a"n + b"' 

 In particular if n = + c, v = + c, 



so that b" = a f and a" = —„ = y 



c 2 c 2 



