JRoever — Geometrical Properties of Lines of Force. 287 

 wi versin &) — Trax^ = K (25), 



in which K is a constant. If in equation (25) a: == 

 K = m versiu w = m versin a, 



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

 stituting this value of A', equation (25) becomes 



wi (versin eo — versin a) = Tro-a;- {^^)- 



For CO = equation (25) becomes 



I^ = — Trax"^ = — TTax^. 



Substituting this value of A% equation (25) becomes 



ira {x^ — Xq2) = w versin « (27). 



If the point and plane have charges of like signs the 

 equation of a line of force is 



m versin co -\- irax^ ^= K' (28), 



in which iT' is a constant. For x = this equation becomes 



K' = m versin a. 



Substituting this value of IT', equation (28) becomes 



771 (versin co — versin a) = — irtrx^ (2&). 



For CO = TT equation (28) becomes 



K ' = 2m + irax^ 



Substituting this value of K', equation (28) becomes 



TTo- (x^ — Xq2) = m (2 — versin <d) (30). 



