COFFIN. EDGE CORRECTIONS IN CONDENSERS. 425 



Equation (c) now becomes : 



- 1 — a , 

 1) - — — log 



h ■ ( m w, ■ in , 1 ~ a , Vt-a+Vt+l 



Vt - a + i Va (t + 1) \ 



+ i V« log • (d) 



V < — a — i V« {t + 1)/ 



From the values for A and <7 above we find, if we put 



l=b= a - 1 



2 V« 

 a 2 -2« (1 + 2 b 2 ) + 1 = 



whose solution is 



a 



= 1 + 2 b 2 ± 2 5 a/1 + & 2 . 



We should expect a priori that a should be a function of & = -, 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 

 t = 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 



x + i V ~ . , V 



log — — -A — 2 i tan -1 - + 2 n ir i. 

 x — xy x 



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



h ( r ■ 1 — a , . . , /- .x 



2 = — — ( — Va + i — - — (2 ?. tarn 1 Va — i tt) 



V"- 7T \ 



+ Va (log ^-^ + i *r + log « P )J. 



