112 Prof. A. W. Riicker on the Magnetic 



Above this limit, if for a given a and a s we choose a x and 

 a 2 so that 



e-ocH-' 



the two shells will shield better than one, i. e. better than if 

 the whole of the space between the innermost and outermost 

 surfaces were filled with the permeable material. 



It of course follows a fortiori that the best arrangement of 

 the two shells will, under these circumstances, give better 

 results than the single shell, a conclusion which can be verified 

 directly. 



For we must by (8) and (2) have 



LV Lg 



(\-l) 2 {\ 4 -L(l-e)} K L-(l-e)' 

 where 



\ B (\-i)-L(\-l + e) = 0. 



Eliminating L, the inequality becomes 



(l-e){6-(\-l) 2 } 2 >0. 



which, since e is always positive and < 1, must always be true. 



At the limiting point the curves which give the relations 

 between L and the ^'s for one and two shells respectively 

 touch each other. 



For, as in the case of a single shell, 



V 



yjr L-(l-e)' 

 1 d& _ <l-<0 



f dL ~ {L-(i- e )r 



At the limiting point L = (1 + x/e) 2 ; 



_l_d¥_ 1- s/1 



yjr dL " 4(1+ y/e)' 



In the case of two shells we have from (7) , 

 {\2(4\-3)-L}J- = X-l + e, 



and since at the limiting point \ 2 =L = (1+ ^e) 2 , 



d\ _ 1 



dL"~4(l + Ve)' 



