Roever — Geometrical Properties of Lines of Force, 275 

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



K = Xa> = Xa, 



in which a is the special value of o) for which a; = 0. Sub- 

 stituting this value of K^ equation (1) becomes 



X ( <w — a ) = TTox 



(2), 



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

 makes au angle a with OY. If in equation (1) a> = 



K •= — trax = — TTox^. 



Substituting this value of K, equation (1) becomes 



ira {x — a;^,) = \(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 OT' and 

 at a distance x^ from O. If, 

 as in Fig. 2, the line and 

 plane have charges of like 

 WW signs the equation of a line of 

 force is 



\(o + irax = K' (4), 



in which .ff' is a constant. If in equation (4) £c = 



E' = \a) = \a. 



Substituting this value of K\ equation (4) becomes 



\ {(1) — a) = — "Jrax K^)* 



