202 



Trans. Acad. Sci. of St. Louis. 



Fig. 1. 



Now consider the case of two par- 

 allel straight lines electrified oppo- 

 sitely and situated at two points A 

 and^'. (Fig. 1.) Let the charge on 

 line A be -\-m and that on A' be — m' 

 such that m^ m' numerically. The 

 number of lines of force leaving the 

 mass m through the wedge whose 

 edge is the line A and whose semi- 

 angle is (o is 



The number of lines of force converging to — m' through the 

 wedge whose edge is the line A and whose semi-angle is to' is 



N' = 2m'co'. 



The number of lines of force proceeding to the right 

 between the two parallel lines of intersection of the wedges is 



iV^ — iV' = 2ma) — 2m'Q)'. 



The locus of all such lines of intersection constitutes a tube 

 of force, the right section of which is a line of force. If in 

 the above equation a»' = 0, 



iV^— N' = 2mco = 2ma, 



in which a is the special value of co for which w' = 0. Com- 

 bining these equations gives 



mo) — m CO = ma. 



.(1), 



which is the equation of a line of force whose direction at A 

 makes an angle a with AX. When the lines A and A have 

 charges of like sign the equation of a line of force is 



mm + nico' = ma (2). 



