based upon Electromagnetic Theory. 57 L 



when viewed from the positive end. The/' and;' axes are 

 so chosen as to be parallel with the line of: intersection of the 

 "planes of the two orbits, and the positive direction along 

 the^'-axis is defined by the vector Jcxk'. This defines both 

 the i and i' axes. The circular motion of the first point 

 charge may now be defined by the equation 



Y 1 = a 1 {$ 1 i + C 1 j) (4) 



That of the second point by 



r 2 = a 2 (S 2 ;' + 2t /), (5) 



and the position of the centre, 2 , by the constant vector 



x = xi + yj-\-zk . (6) 



The symbols Si, C 1? S 2 , and U 2 are abbreviations for the 

 sines and cosines of the angles respectively 



/ "R\ 

 co l t + e i and a)/ + ^ = fl) 2 N--j f 3 . . . (7) 



The i ! and k' axes may be transformed into the i and k 

 axes by the relations 



i' = (cos a) i+ (sin u)k (8) 



k' = - (sin ot)i + (cos ol) k (9; 



Whence, in terms of the ?', j, and k axes, r 2 becomes 



r 2 = a 2 (S 2 cos ai + C 2t /-f-S 2 sin uk). . . (10) 



Let R denote the variable vector from the position of the 

 second point at the time t — Hjc = t ! to the position of the first 

 point at the time t. Then, we have 



R^^ — r— r 2 . . . .^ . . . (il) 



By the use of (4), (6), and (10), we find 



R = ( — x +-aiSi — rt^S^cosa)/ 



+ (-y + aA-a s Cj )j 



+ ( — ~ — <u$., sin u)k. . . . (12) 



2 Q 2 



