COFFIN. — EDGE CORRECTIONS IN CONDENSERS. 419 



When t is positive, \p = ; 



when t is negative, \/s = v. 



n ■ • r, v 



.'. Dnr = vi, or £>■=-, 



and the final expression is 



V , / s 



w = - log £. (a) 



7T 



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

 plate, from the edge (t = b) to a point so far in (z = — x + /* *) that 

 the charge is uniform, we have, since 



or using eq. (a) 



1 

 <1 = -J— (9t=p — 9*=^) 



4: 7T 



9 = 4^2 (log*, -log J). 



When t is very small and positive 



z = - x + hi = - O (~ - b\ogt P + 1 - ( * ^ - JttH, 



_ x = _ fff^-^- -Mog* P J 

 - x 1—26 

 from which 



„ /_ x 1 -2b . ,\ 

 * == 4n\cb + -2ir- ]0gb )> 



and since C= -= — , 



&7T 



=4^[^ + K^ i+losS )]' 



When 6 is unity, which brings the two edges symmetrically above one 

 another, the correction becomes 



* = 4 



Vk {* + £)• 



When £ is very small and negative, z = — x + oi, and the quantity of 

 electricity on the upper side of the lower plate is 



