•.".Ml 'I'nuis. Anid. Sri. of St. Louis. 



(," )", then the locus of the poinl of Interned ion is expressed 



by 1 In- equal ion 



2u (.••' ..■;-') /••' (2 — vereiu «>) (M). 



Equations (84) and (85) may be simultaneously expressed in 

 the general form 



r '•' versin CO | 2u» 8 A"', ( 86 ), 



in which /i ', li i constant . 



Equations (88) and (86) represent identical ourves. 

 Equations (2€), (87), (29), (80) have the same forms as 

 equations (81), (82), (84), (.">. r >) reepeetively, and tins 



shows : — 



I. That the ourve representing s line of foroe prooeeding 

 from a system consisting of an eleotrified plane and an eleo- 

 t rifled point, is the locus of the intersection of two straight 

 lines haying motions in :i plane which passes through the 

 eleotrified point and is perpendioular to the eleotrified plane ; 



one Line haying 8 motion of rotation about the electrified 

 point and the other a motion of translation perpendicular to 

 Itself ami parallel to the eleotrified plane. The rotation is 



such that the versine of the angle which the rotating line 

 makes with 07 (a line which passes through the eleotrified 

 point and is perpendioular to the electrified plane) ohanges at 



B uniform rate, and the translation is such that if the moving 

 line were the meridian line ol' a cylinder of revolution whose 

 axis is () )', the area of cross section of t he cylinder would 

 ohange at B uniform rale. 



II. Thai the constants *, m, v and u are related by tho 

 equation 



"' _ ™L = J (37). 



III. Thai if the eleotrified point be considered us being 



above the eleotrified plane 



