Roever — Geometrical Properties of Lines of Force. 277 



a position OGj then the locus of the point of intersection P 

 is expressed by the equation 



X 



a V 



in which co = ^YOP, a = ^YOG and x = OD. Now 



a = 27r/i' =*arn, 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 (to — a) = irnx (7). 



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 OYt 

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

 the equation 



X — 3Jg _ <w 



V a 



Putting for a its value irn this equation becomes 



irn (x — x^) = vo) (8). 



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

 the general form 



VCD — Trnx = ^1 ( 9 ) , 



in which IT^ is a constant. 



If, as in Fig. 2, OP rotates about Oin a^ ^^^^ handed ) 



C right handed ) 



direction and PD moves to the < , > , and if PD has a 



( left 5 



position Ol^when OP has a position OG, then the locus of 



the point of intersection P is expressed by the equation 



V (a) — a) = — 'rrnx (10)« 



