Roever — Geometrical Properties of Lines of Force. 277 



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

 is expressed by the equation 



CO — ax 

 a V 



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

 a = 27711 = irn, 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 {(o — 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 OY", 

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

 the equation 



X — ^0 _ ^ 

 V ~ a 



Putting for a its value tt/i this equation becomes 



irn (x — Xq) = vco (8). 



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

 the general form 



vo) — Tvnx =^ J^i ( 9 ) > 



in which JT, is a constant. 



-1 



T# -TT o/-»7-> L ^ u i. /~i - ^ left handed > 



If, as in Fig. 2, OP rotates about O in a < . , , , , ?• 



c right handed > 



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



C left > 



position O^Twhen OP has a position 06r, then the locus of 



the point of intersection P is expressed by the equation 



V {io — a) = — "i^nx (10). 



