102 Prof. A. W. Rlicker on the Magnetic 



Then the above ratio becomes 



9%^! 9a 1 3 />t 1 



(2 / . 1 +l)(2 + /. 1 )a 1 3 -2(^ 1 -l)V ~ 9a 1 > 1 + 2(^ 1 -l) 2 (a 1 3 -a 3 ) 



If fjbi is so great that a small integer may be neglected with 

 regard to it, this reduces to 



_ 3 



2/^i «i — a 



but this approximate form is only valid if a,\ and a are not 

 nearly equal. 



It will be observed that the shielding depends only on the 

 ratio of a x : a , and not on the absolute dimensions. 



If the shell is thin, let « =a 1 — t. Then, if squares and 

 higher powers of t are neglected, 





^0 



3^ + 2(^-1) 





If/*! 



is not large this 



may be written 







■\j/ 



_j 2(Mi-l) 2 



t 





^0 



3fa 



CLi 



Tfto 



is large it becomes 









^ 1 





In this approximation we have neglected terms of the 

 order fjqf/ai. The expression 



^ , 2 £ 



is only valid if terms of the order //<x 2 £ 2 / a i 2 are negligible ; and 

 as fii is by supposition large, they may be very much greater 

 than those which have already been rejected. 



As an example, if t/a 1 = 0'01, the ratio of the shielded to 

 the unshielded field is 3/13 if /a x = 500, and 3/23 if ^=1000. 



The following Table of Values is calculated for cases in 

 which aj— a is not small, on the assumption that ^=1000. 

 The corresponding numbers can be obtained in any other case 

 when //-! is large by remembering that the ratio under inves- 

 tigation varies inversely as ^. 



