190 Lines of Force due to given Static Charges. 



which has two branches, going to infinity, one issuing from A, 

 the other from B. 



(b) The other group consists of lines, each of which has a 

 closed branch joining A and B, and a branch going off to 

 infinity (both ways). This latter does not pass through 

 •either A or B, and is convex to AB. 



The last line of this group consists of the limited line AB 

 and an open branch at a finite distance from the axis. 



28. Moreover, as the line infinity parallel to the axis is 

 obviously a line of force, there must be a third group of lines, 

 each consisting of a single branch going to infinity and lying 

 beyond the last branch of the second group, which goes to 

 Infinity. 



We have, accordingly, three groups of lines in this case. 



29. Again, the line which passes through the point of 

 equilibrium obviously separates the lines belonging to the 

 first two groups. 



If AB = 2c, p = distance from A, B of the point of 

 equilibrium, the line through the point of equilibrium should 

 satisfy the condition 



c c 3 __ r + s + 1 



P P 9 



Also p 3 = qapc. 



In the case of fig. VI., 



q = 14, p = 8a, c = 3a. 



p = 6*9 nearly, 

 and r + s + 1 = 45*08 nearly. 



30. In the diagram, therefore, the final index number of 

 the last line which has a finite branch should be 45. This is 

 found to be the case. Moreover, each of the lines 28 to 44 

 consists of branches going from A and B to infinity while 

 each of the lines 45 to 56 of a closed branch and another 

 going to infinity. 



Beyond the last branch of these latter, which goes to 

 infinity, are lines, consisting of a single branch, likewise 

 going off to infinity. 



