278 Trans. Acad. Sci. of St. Louis. 



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

 G'Y', then the locus of the point of intersection P' is 

 expressed by the equation 



7rn {x — Xf^) = V { TT — io) (11)- 



Equations (10) and (11) may be simultaneously expressed 

 in the general form 



voj + 7r7ix = K^' (12), 



in which ^/ is a constant. 



Equations (9) and (12) represent identical curves in the 

 same manner as do equations (1) and (4). 



Equations (2), (3), (5), (6) have the same forms as equa- 

 tions (7), (8), (10), (11) respectively and this shows: — 



I. That the curve representing a line of force proceeding 

 from a system consisting of an electrified plane and an electri- 

 fied line parallel to the plane, is the locus of the intersection 

 of two straight lines having motions in a plane which is per- 

 pendicular to the electrified line ; one line having a motion of 

 uniform rotation about the electrified line as an axis, and the 

 other a motion of uniform translation perpendicular to itself 

 and parallel to the electrified plane. 



II. That the constants a, X, v and a = ttu are related by 

 the equation 



X Try _ V / 1 ^ / 



a a n 



III. That if the electrified line be considered as being above 

 the electrified plane 



1. The system having electric charges of unlike signs 



( right handed ) 

 corresponds to the case in which OP has < , \. hinded S 



r riijht ) r?- a 

 rotation and PD has a motion to the < I'^j,, r • ^^^- ^' 



o' 



