Roever — Geometrical Properties of Lines of Force. 275 

 in which K is a constant. If in equation (1) x = 



HE = \co = Xa, 



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

 stituting this value of K, equation (1) becomes 



X ( co — a ) = 7Tffa3 



(2), 



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

 makes an angle a with OY. If in equation (1) co = 



K = TTOX = Tr<7X . 



Substituting this value of K, equation (1) becomes 



nr<j (x — x Q ) = \a> (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 OY aud 

 at a distance x from O. If, 

 as in Fig. 2, the line and 

 plane have charges of like 



~0' |r7 *" D VB signs the equation of a line of 



Fig. 2. force is 



\oj + ircrx = K' (4), 



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



K' = \co = Xa. 

 Substituting this value of K ', equation (4) becomes 



X ( co — a ) = — it ax ( 5 ) . 



