Boever — Geometrical Properties of Lines of Force. 289 



PD moves to the \ r,ght I , and if PD 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 



s . 



-( versin <w — versin a) 



2 ttx 1 



SU A 



or 



v 2 (versin &> — versin a) = 2wx 2 (31), 



in which o> = ^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 



5 



, 9 -x versin oj 



lTX i TTXq I 



A SU 



or 



2u (x 2 — x 2 ) = v 2 versin a> (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 2 versin co — 2wx 2 = K 1 (33), 



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



about in a < l > direction and PD moves to 



C right handed 3 



the \ nght I , and if PD has a position OF when OP has a 

 £ left 5 



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



expressed by the equation 



v 2 (versin &> — versin a) = — 2wx 2 (34). 



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



