Moever — Geometrical Properties of Lines of Force. 275 

 in which E is a constant. If in equation (1) cc = 



-ff' = \(o = \a, 



in which a is the special value of co for which x = 0. Sub- 

 stituting this value of K, equation (1) becomes 



\ (to — a) = ircrx 



(2), 



which is the equation of a line of force whose direction at O 

 makes an angle a with OY. If in equation {1) o) = 



IT = TTfTX = 



7r<TX„ 



Substituting this value of K, equation (1) becomes 



TTa (x — xA = \(o 



(3). 



This is the equation of a 

 line of force which never 

 reaches but approaches an 

 asymptote Y'G' (Fig. 1.) 

 which is parallel to OT' and 

 at a distance x^ from O. If, 

 as in Fig. 2, the line and 

 plane have charges of like 



0' p^Y '^ i> -D'-S signs the equation of a line of 



Fig. 2. force is 



XctI + TTGX = A"' (4), 



in which ^' is a constant. If in equation (4) x = 



E.' ■=. Xco = \a. 



Substituting this value of K\ equation (4) becomes 



X (co «)= 77 (7X 



;(5). 



