Electricity in a uniform plane conducting Surface. 399 

 We may write (4) thus (§ 8), 



whence, regarding the source and sink for the present as mere 

 points, the value n = cc will correspond to the former, and 

 n =—oo to the latter, while n = denotes the straight line at 

 equal distances from both. 



20. Let the distances from (the middle point of A B) of 

 the points D and D' (fig. 2), in which the circle of potential U 

 cuts A B, be called / and /'; then, a being as usual half the dis- 

 tance between the poles, 



where yp is the ratio of the radii vectores of the given circle. 

 Hence 



and 



For the radius of the circle, we have evidently 



and for the distance of its centre from O, 



d=l + p = l'—p = a — 



also 



P *=Ck.CB = {d+a)h=d*-a\ 



where h{ — d—a) is the distance of the centre of the equipoten- 

 tial circle from the nearest pole. 



21. In order to draw a system of equipotential circles with 

 compasses, it is most convenient to have given the distances of 

 the centres from the nearest pole, and also the distances from 

 the same point of one of the intersections with A B, the line 

 joining the poles — that is, in fig. 2 the distance B C and either 

 B D or B D'. Now 



2E2 



fj? n - 



