546 Electromagnetic Mass of a Moving Electron, 



Thus % = a'(x-vt), 



I£ this transformation be reversed we have 

 «=•«'/ +^y+Tj where a' = 



"-3 



and a' will be the same function of ( — v) that a' is of v. 



But the transformation shows that if x x x 2 be two points 

 fixed relative to A and f x f 2 their coordinates in B at any 

 time r, 



x 2 -x x — V(f 2 — fi) ; 

 i. £. a line of length / as seen by A appears to be of length 



— , as seen by B moving relatively to it. But this will be 



the same whichever be the direction of B's motion along the 

 axis of x, so that if a / -=f(o) 9 f(y)=f( — v), i.e. a / =u / . 



1 - 2 \= 1, i.e. a'—ll — ^ j . 



Thus the transformation is finally 



^(-5+.*) where ^l-J)"*. 



Now let points not on the axis of x be considered. Since 

 the axes of x and f coincide at all time, y and z always 

 vanish when t) and f vanish. 



Hence y—\rj and z — fi^ and X and //, will not change if 

 the velocity of motion of B be changed from v to — v ; thus 

 if \ = 4>(y); <l>(v)=<l>( r v). 



But since by reversing the transformation 



r) = y/\, <£( — #)= — , and therefore \ = 1. 



Similarly //,= 1. 



The general transformation between xyzt and ff/fr 

 is therefore 



7/ = 77, - = £ 



f#(-™+*)+w+^ 



