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= 2'7rax. 



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- 

 I) D' 'B ular to AB and OP makes an 

 angle co = ^YOP with OY. 

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

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

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

 is 



A 



O' 

 Fig. 1. 



iV^=2X 



Ui. 



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

 whose trace is O. The flow of force throuo;h the rectansrular 

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

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



M= 27raXf 



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

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

 oi^ unlike signs, the flow of force between the plane OP" and 

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

 N — 31 = 2\co — 27rax. If in this equation we make N' — 3f 

 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 



\co — 7r(TX = Ii (1)» 



