Roever — Geometrical Constructions of Lines of Force. 221 



m = 4 and — m' = — 1, respectively; and Fig. 9 shows a few 

 of the lines of force proceeding from a system consisting of 



two electrified points A and A having charges m = 4 and 

 m' = 1 respectively. 



If m — m', numerically, equation (24) becomes 

 ( 1 — cos (w ) — (1 — oos &)' ) = 1 — cos a 



cos (y' — cos &) = 1 — cos a (28). 



or 



This is the equation of a closed curve passing through A 

 and A . A line of force is only an arc of this curve. 



If a, = a' = 0, then, from equation (24), 



m 



versin 6 = 1 — cos 6 = 



m — m 



-, (1 —cosa).. (29). 



This determines the direction of the asymptote to a line of 

 force. 



