L. Page — Fundamental Relations of Electrodynamics. 61 



4/1-4 sin 2 e 

 c 



r — r 



J »* 



^"7 



sin 6' - " 8in 6 



I/I-:! si 



sin 8 6 



cos 6' = cos 6 



Y I --£ sin 2 



The direction of the lines of force, as viewed from K (0), 

 and hence the direction of the intensity, will be OP, and not 

 O'P'. Now d& as viewed from K (0) will not be perpen- 

 dicular to OP. Let d S be the component of d S', as viewed 

 from ~K (0), which is perpendicular to OP. Then a short 

 calculation gives 



1 



a to =^ / Q — a to 



- / v 

 VI r sin 2 



Now the density of the lines of force at P in K (0) is to 

 the density of the lines of force at P' in K (v), at the instant 

 when P and P' coincide, as dS' is to dS ; that is to say in the 



ratio 1:4/1—— sin 2 0. Hence we have 



f c 2 



E 1 



E ' 4/1-4" sm 2 6 

 r c 2 



But E' = -A-, = A 

 ?• 2 ?* 2 



. 1 

 Therefore E = 4r 





-3 



sin 2 61 



r 2 / y 2 . , A f 



