180 L. Page — Relativity and the Ether. 



(c) Transformation Equations. 



The strain in the ether at a point P in K, in so far as it is 

 due to a single charged particle, is defined by E and c at that 

 point. It is desired to find E' in K' at the same point and 

 instant. As usual axes will be so oriented that K ' has the 

 velocity v relative to iTin the positive Z direction. Let x, y, z 

 be the coordinates of P, and x-{-dx, y + dy, z + dz the 

 coordinates of a point \evy close to P on the same tube of 

 strain. Then from (1) and (2) it follows that 



p \lz 

 dx' = dx + 



dy' = dy + 



1 — /3 COS a 

 I — fi COS a 



1 — pcosa 



where a is the angle between c and v. Hence 



E x + \ fvx(cxE)l 



%y+ !TvX(CXE)l 

 jr ' _ ° b =L>- 



e ? : = e 2 



give the strain E' in K' in terms of E and c in K at the same 

 point and instant, and the relative velocity v of the two 

 systems. Consider now the resultant ether strain due to all 

 particles whose fields extend to the point in question. If we 

 make the same substitutions as before, 



7? ' 



E, 



+ iL< 



' XH 1 



■Ux 





Vi- 



P 



V ' 



E > 



♦K- 



xh] 



-J y 



-^Y 





Vi- 



-/»' 



K 



= K 







(16) 



