COFFIN. — EDGE CORRECTIONS IN CONDENSERS. 435 



We must find the true value of the indefinite term 



rri 2 + 1 , m + 1 



—z log -. 



2 m & m — 1 



Writing it in the form - we have 



d »!+l 



d^n g ^^l (m 2 + l) 2 _ j 



d 2m (m 2 - I) 2 . 



Limit m= ^&>dm rn? + 1 



Hence 



? = -I77,^ + v( 1 - lo = 2) ) 



which is the correct result required. 



Since for a plate of no thickness the parenthesis of the correction is 

 unity and for infinite thickness is 2 (1 — log 2) = .614. 



The correction then always lies between the values: - and - .614 or 



7T 7T 



h X .318 and h X .195. 



The amount of electricity on the end A B is given by : 



q = ,- (<#>„ ~ *b) = A Dog (« ~ 1) - lo S (- 1)] 



4 7T "± 7T 



= rb log(1 - a ) = iT 2lo§m2; 



? = 2^i l0 § m - 



Now the equation m = 1 + A" + V^(A'+ 2) gives the value of m for any 



value of K= -, the ratio of the thickness of the upper plate to its dis- 

 h 



tance from the lower. We must take the positive value of the radical as 

 m > 1. 



