COFFIN. — EDGE CORRECTIONS IN CONDENSERS. 435 



We must fiod the true value of the iudefinite term 



w^ + 1 , m+ 1 



— -r lOfiJ -. 



2 m * ??i — 1 

 Writing it iu the form - we have 



d 7)1+1 



dm ® w — 1 _ (/»" +1)- __ , -, 

 ~d 2m ~ (m2 _ 1)2 T 



Limit m= vooC?m m^ + 1 



Hence 



y / 2 /^ , , , , 



5 = - — — X + — (1 - log 2; 



i TT h \ IT 



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 



TT TT 



h X .318 and k X .195. 



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



9 = -L (^^ _ ,^„) = ^^ [log (a - 1) - log (- 1)] 



4 TT •* TT 



= T-2 log (1 - «) = 7^ log "*' ' 



4 71 4 TT 



9 = 2V^ log ^' 



Now the equation m = 1 + /T^- \''K{K-\- 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- 



