286 Trans. Acad. Sci. of St. Louis. 



cylinder of revolution whose axis is OY, the area of cross- 

 section of the cylinder would change at a uniform rate. 



The force at a distance r from an electrified point whose 



m 

 charge is m \b f = -^. The flow of force through a circular 



cone whose vertex is m and whose serai-angle is w is 



iV= "2 X 27r (1 — cos ft)) r^ = 27rm versin w. 



The flow of force from a circular area of an electrified 

 plane whose charge is a per unit area is 



M = 27rfT X TTX^ 



in which x is the radius of the circle. 



In Fig. 1. let O represent the electrified point and AB the 

 trace of the electrified plane which is perpendicular to the 

 plane of the paper. Through O draw two lines, one YO per- 

 pendicular to the plane AB and the other OP making an angle 

 (o = ^YOP with YO. Also at a distance x = O'D from O 

 draw a line PD parallel to YO. The flow of force from the 

 mass m through the circular cone whose axis is OY and whose 

 meridian line is OP is 



iV= 27rm versin w. 



The flow of force through the circular cylinder whose axis is 

 0!Fand whose meridian line is PD is 



M= ^TT^ax^. 



Then if the point and plane have charges of unlike signs the 

 flow of force through the circle of intersection of the cone and 

 the cylinder is N — M = 27rwi versin w — iir^aT?. UN — M 

 is constant the circle of intersection is confined to a definite 

 path. This path is the bounding surface to a tube of force, 

 and the meridian curve of this tube must be a line of force. 

 Hence the equation of a line of force is 



