COFFIN. — EDGE CORRECTIONS IN CONDENSERS. 419 



When t is positive, i^^ = ; 



when t is negative, \j/ = v. 



.' . D { TT ^ V i, or D — - , 



and the final expression is 



V 



w — -log t. (a) 



Now to find the amount of electricity on the under side of the upper 

 phite, from the edge {t = ft) to a point so far in (z = — x + hi) that 

 the charge is uniform, we have, since 



1 , . 



'k IT 



or using eq. (a) 



V 



q = j^^(}ogtp -log 6). 



When t is very small and positive 



Z = - X -^ hi = - C \~ - h\0gtp ^ \ - ^ ^ ' -hTTl\, 



-x = - cH-^ -b\ogt/\ 



-X I --lb 

 from which 



V I — X 



1 -25 

 -h 



and since (7 = 



-log ft), 



h-K 



= 4;;i[^+K^""°«0] 



When ft is unity, which brings the two edges symmetrically above one 

 another, the correction becomes 



^ = 4 



^hy"^ 2-J)' 



When t is very small and negative, z = — a: + o^, and the quantity of 

 electricity on the upper side of the lower plate is 



