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-4'. (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 wedsje whose 

 edge is the line A and whose semi- 

 angle is co is 



The number of lines of force convero;iug to — tii' through the 

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



iV' ' = 2m' 



CO 



The number of lines of force proceeding to the right 

 between the two parallel lines of intersection of the wedges is 



N'—]!^' = 2mco — 2m'w'. 



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 w' = 0, 



JST— N' - 2mco = 2ma, 



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

 bining these equations gives 



7nco 



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 



vio) + rn'o)' = ma (2). 



