COFFIN. — EDGE CORRECTIONS IN CONDENSERS. 431 



t J X '^ J y/X J xVX 



(147) (120) (142) 



where the numbers refer to the formulae used. In the use of (142) the 

 product de or (c — a) (c — b) must be positive ; this is true, as a and b 

 both lie on the same side of a and the differences are either both positive 

 or both negative. Hence we have 





/-Ti ( ^/X-^\/de d-\-e 1 \ „ 



2c—{a-\-b)\ 



2 



^^ ^ *\ t-c 2V(c-a)(c-b)J 



As a check on this formula, put a = i ; we obtain 



z 



-p, = (< — «) + (c — o) log (< — c ) + const., 



which is the same as special case (b). 



To apply this to our problem, put a ^= a, 5 = 0, c=l; then we 

 have 



C 



/-7 2 — a, / ,— , 2-«\ 



= ^t{t-a) + ~^- log (V< (<-«) + <- 1 + ^— j 



,- , / \^t (t — a) + \/\ — a 2 — a 1 . 



- Vi — « log -^—^ -^ + — :: ) + r. 



Using when convenient m = V 1 — a, this equation may be transformed 

 into 



1^= Vt{t - a) + —^—\og 



m^ + 1 (a/^ + a/< — a)' 



— w log — - — — - + r. (c) 



