Eoever — Geovietrical Properties of Lines of Force. 289 



FD moves to the ^ ^'^'^^ I, and ii PI) has a position OY 



( left > 



when OP has a position OG, then the locus of the point of 



intersection P is expressed by the equation 



-(versinw — versina) , 



2 ^ TTX^ 



SU d 



or 



v^ (versin a> — versin a) = 2uy? (31), 



in which w = ^YOP, a = ^YOG and x = O'D. If, 

 however, OP has a position OY when PZ) has a position 

 Y'G\ then the locus of the point of intersection P' is ex- 

 pressed by the equation 



s 



o ■> a versin co 



TTx' — irx^^ 2 



d SU 



or 



2u {x^ — a;^^^ = ^2 versin (o (32), 



in which x^ is the distance between the parallel lines YO and 

 Y'G'. Equations (31) and (32) may be simultaneously ex- 

 pressed in the general form 



■y^ versin &> — 2ux^ — ^i (33), 



in which K\ is a constant. If, as in Fig. 2, OP rotates 



about in a < ' i direction and PD moves to 



C right handed 3 



the \ ^ > , and if PD has a position OiFwhen OP has a 

 (> left 5 ^ 



position OG, then the locus of the point of intersection is 



expressed by the equation 



v^ (versin w — versin «) = — ^ux^ (34). 



If, however, OP has a position 00' when PD has a position 



