Moever — Geometrical Properties of Lines of Force. 287 

 m versin g> — ttox^ = K ( 25 ) , 



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

 K = m versin o> = m versin a, 



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

 stituting this value of iT, equation (25) becomes 



m (versin o) — versin a) = tt^cc* i^^)- 



For <w = equation (25) becomes 



K = — irax^ = — TTox^. 

 Substituting this value of iT, equation ( 25 ) becomes 



tra {7? — x^) = m versin to (27). 



If the point and plane have charges of like signs the 

 equation of a line of force is 



m versin a> + nrax^ = E' (28), 



in which JT' is a constant. For a; = this equation becomes 



K' = m versin a. 



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



m (versin &> — versin a) = — ttctx^ (2&). 



For o) =V equation (28) becomes 



K' = 2771 + ITOX^ 



Substituting this value of K\ equation (28) becomes 



ira {y? — x^) ■= m {2 — versin &>) (30). 



