COFFIN. — EDGE CORRECTIONS IN CONDENSERS. 433 



From which, given any value of K which determines the configuration of 

 the polygon, we can find m by the formula 



m = 1 + K ± a/A' (K +2), 

 and vice versa. 



The diagram in the wvplane consists of two parallel straight lines, the 

 angle being zero, and the value of t corresponding being t = + 1. 

 Hence 



dw dt 



w = <£ + i\j/ = 2?[log(* — 1) + const.]. 



Const. = 0, because \\j = as long as t > 1. When t passes through 



the value t = 1 and becomes less than 



v — v Z ^ unity, if/ increases by v = Bit. 



t = +l 



v = +oo v 



Hence B = -. 



IT 



Now the quantity of electricity on a strip of breadth x and depth unity 

 is by the general equation : 



q = !-(&- <£o) ; 



4 TV 



V 



and since w = - log (t — 1), 



[log(*--l)-log(-l)] 



TT" 



4 _2 



I 



.2 



iog(i-0, (0 



which gives the amount of electricity on a strip of breadth x, on the 

 under side of the upper plate from the corner 13, to a point P at a dis- 

 tance — x, from B. 



Let us now find a value of log (t — 1) so far from the edge and on 

 the lower surface of the upper plate that t may be considered nearly 

 equal to unity, say t = 1 — €. From (a) 

 voi. xx \ix — 28 



