442 The Theory of Aether and Electrons in the 



that is to say, at the place 



(f ! + Af cosh a, 77, + AT?, + A?) 



at the instant (^ - sinh a . Af/c). Thus at the instant ^, this 

 charge will occupy the position 



(f i + Af cosh a + sinh a . Af . 0^/e, 771 + AT; + sinh a . Af . v yi /c, 



1 + Af + sinh a . A f . v ai /c). 



The charges corresponding to those in the original system which 

 were at the instant t contained in a volume A| AT? A will 

 therefore in the derived system at the instant t l occupy a volume 



cosh a + sinh a . v x jc . 



AS, 



sinh a .Vyjc 1 



sinh a . v z jc 1 

 or, 



(cosh a + sinh a . v x jc) A? Aj A. 



Thus if jOi denote the volume-density of electric charge in the 

 transformed system, we shall have 



pi (cosh a + sinh a . v x jc) = p ; 



this equation expresses the connexion between pi and p. We 

 have moreover 



dx fix fix dx 



~ ($_ dt dt dt 



v x , sech a 



= c tann a + - , 



cosh a + v Xl c^sinha 



and similarly 



v yi 



cosh a + v Xl c~ l sinh a 

 and 



cosh a + v Xl c l sinh a 



