z = 



COFFIN. — EDGE CORRECTIONS IN CONDENSERS. 425 



Equation (c) now becomes: ' 



h . ( .- — 1 — « , V« — cr + a/< + 1 



il^^it-a){t^ l) + L_iMog 



Va TT \ ' 2 V« — a — V^ + 1 



,- Vt -a + i \/a {t+ 1)\ . 



+ t V« log . . ^ • i^) 



Vt — a — I Va {t + \)J 



From the values for h and g above we find, if we put 



« 2 V« 



a2-2« (1 +2 62) + 1 = 

 whose solution is 



a = 1 + 26-^ ± 2i Vl + ^'. 



We sliould expect a priori that a should be a function of i =r -, as it is 



their ratio alone which determines the shape and relative position of 

 the conductors. Since a must be greater than 1, we must take the 

 larger root. 



Suppose we take a point on one of the conductors so near to the value 

 < = that we may neglect t in comparison with 1 and a fortiori with a. 

 We obtain by suitable transformations of the logarithms using the 

 formula 



log ^1±1^ = 2 i tan-^ y +2n^i. 

 X — ly X 



Hence in formula (d), neglecting t and retaining 1 and a, we obtain 



h f /- . 1 — a ^ . , /- 



z = — ^ 1 — Va + I — - — (2 ? tan-i Va — i tt) 



+ Va (log ^^ + ^ TT + log tp)\ 



