Boever — Geometrical Properties of Lines of Force. 277 



a position OG, then the locus of the point of intersection P 

 is expressed by the equation 



x 

 — » 



v 



in which co = ^.YOP, a = ^.YOG and x = O'D. Now 

 a = 2irn' = nrn, in which n is the number of half rotations 

 made by OP in a unit of time. For this value of a the above 

 equation becomes 



v (co — a) = irnx (1). 



If, however, PD has a position Y'G' (which is parallel to YO 

 and at a distance x trom it) when OP has a position OY, 

 then the locus of the point of intersection P' is expressed by 

 the equation 



x — x __ co 

 v a 



Putting for a its value tth this equation becomes 



TTIl ( X X Q ) = VCD ( 8 ) . 



Equations (7) and (8) may be simultaneously expressed in 

 the general form 



vco — irnx — K 1 ( 9 ) , 



in which K x is a constant. 



If, as in Fig. 2, OP rotates about in a \ left handed I 



t right handed > 



direction and PD moves to the < ^ v , and if PD has a 



( left 5 



position Or"when OP has a position OG, then the locus of 



the point of intersection P is expressed by the equation 



V (CO a) = TT71X (10)' 



