274 



Trans. Acad. Sci. of St. Louis. 



of force from a rectangular portion of this plane whose length 

 is x and whose width is unity is 



M = 2w<jx. 



In Fig. 1. let O be the trace 

 of an electrified straight line and 

 AB the trace of an electrified 

 plane, both of which are per- 

 pendicular to the plane of the 

 paper. Through the line whose 

 trace is O pass two planes, 

 whose traces are OY and OP 

 respectively; OY is perpendic- 

 * ular to AB and OP makes an 

 angle w = Z70P with OY. 

 Also at a distance x = O' D from Opass a plane whose trace 

 is DP, which is perpendicular to AB. The flow of force 

 through the angle ©from a unit length of the electrified line 

 is 



jsr= 2\co, 



in which X is the charge per unit length of the electrified line 

 whose trace is O. The flow of force through the rectangular 

 prism determined by the planes OY and DP, and two planes 

 perpendicular to the line Oaud at a unit's distance apart, is 



M — 2-irax, 



A 



O' 

 Fig. 1. 



in which a is the charge per unit area of the electrified plane 

 whose trace is AB. Then it the line and plane have charges 

 of unlike signs, the flow of force between the plane Ol^and 

 the line of intersection P of the planes OP and DP is 

 N — M = 2\co — 27rox. If in this equation we make JV' — M 

 constant we confine P to a certain path. This path is the 

 right section of a cylindrical surface which bounds a tube of 

 force. Hence the locus of P is a line of force whose equa- 

 tion is 



Xa) — ir ax = K ( 1 ) , 



