L. Page — fundamental Relations of Electrodynamics. 63 



At a given instant in K (<?), two charged bodies (fig. 2), one 

 at A and the other at B, have velocities relative to K (o) of v 

 and u cm./sec. respectively. AB = r. Choose axes XZ so 

 that z is parallel to u. Let the origin be at B. We wish to 

 find the force on the charged body at B, dne to the other 

 charged body. To find this force we must observe from the 



Fig. 2. 



system K (u). Bnt according to the time synchronism of 

 it (u), when the one charged body is at B, the other will not 

 be at A. It will be at C, a point whose coordinates are found 

 to be 



z = 



r cos <£ 



uv . 

 r sin <& — r — — sin 

 c 2 



uv cos (0—cf>) 



X = — 



no cos (0—4>) 



These distances, as measured in K (u), are (the primes refer 

 to K (u) ), 





COS <f> A/ 



uv cos ($ — <$>) 



X = 



r sin <i — r — v sin 

 e 



uv cos (6 — <f>) 



and the distance between the charges is 



r — 



1 — 



u 2 ) A 



, 1 — 2— -sin4>sin0 + - -sin 2 r cos-<j>' 



uvcos(0—j>) & c 1 c 2 



