Roever — Geometrical Properties of Lines of Force. 289 



PD moves to the< ^'^ f , and if PD has a position OT 

 ( left > 



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



intersection P is expressed by the equation 



-(versino) — versin a) , 



2 TTX' 



8U J 



or 



v' (versin (o — versin a) = 2«a^ (31), 



in which a> = ^YOP, a = ^YOG and x = OD. If, 

 however, OP has a position OY when Pi? has a position 

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

 pressed by the equation 



s 



• • o versin o) 



inr — TTX^ 2 



^ 8U 



or 



2u (x^ — x^^) = v^ 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 



v* versin <o — 2ux^ — ^i (33), 



in which 5^ is a constant. If, as in Fig. 2, OP rotates 



about O in a < > direction and PD moves to 



C right handed > 



the ^ ,^^ > > and if PD has a position Ol^when OP has a 



position 0(t, then the locus of the point of intersection is 

 expressed by the equation 



v^ (versin &> — versin a) = — 2wa;^ (34). 



If, however, OP has a position OO when PD has a position 



