AND OF A DISK OF SENSIBLE THICKNESS. 677 



Determining A t so as to make I (X + Xj (^ + ^ 2 ) dg a minimum, and re- 

 membering that E = ZlA <l , we find 



A -A 5 

 *' 



101' 



30. 



and we obtain as a second approximation 



I 



36 g _101 



Unless the length of the cylinder considerably exceeds 7 '245 times its 

 diameter, this approximation is of little use, for this ratio makes A t infinite. 

 It shews, however, that when the ratio of the length to the diameter increases 

 without limit, the electric density becomes more nearly uniform, and the 

 expression for K a approximates to the true capacity. 



We may go on to a third approximation by determining _4 2 and A, so that 

 (X,, + A, + X 4 ) (\fj + \ji, + </ 4 ) dg shall be a minimum ; whence 



g _ 3373 



5 " f'' 



A 1 = A <> - 



-- 



30 /\ 1260/ 196 



, 

 A -A 9 21 



^,-^o 



/ 101W 6989X 45' 

 \ " 30/V 126 0/ 196 



and 



01 A_J ? V 210/ 



36_101 400 / 101\r/o IglWo 6989 \ 45 1 



^- /x I * f\f\ I I * AA I t ' io/r\/ in/?l 



_ 

 30 \ 30 /\ 30 A 1260/ 196J 



