118 Prof. A. W. Riicker on the Magnetic 



In the limiting case when \ 2 =L=(1+ Ve) 2 ? 



wu, r _ y<i+_vi) 



^/Yo — ~2 ' 



which is, as it should he, the same as the value obtained by 

 inserting the same values of X and L in the corresponding 

 expression for two shells. When e is negligible as compared 

 with \ and L we get from (22) \ 5 = L, and from (23) 



jL e 3 L 6 s x 5 (N+i) 6 l 



to" KL-1) 5 ~^-1) 5 ~ NV X (^L-1) 5 

 If we take the numbers before employed, viz. : — 

 yu,=501, a =8a 3 , N = 2, 

 we have \ = v^8 = 1*516 ; 



\0-516J 



0*00016. 



The results so far obtained in the special case 'to which 

 numerical calculation has been applied may be summed up as 

 follows, the arrangement being the best in each case : — 





Volume of 

 Material used. 



External 

 Field. 





1-0 

 5-0 

 4-8 

 7-0 



0-018 

 0-0006 

 0-00016 

 0-0102 



Two shells 



Three shells 



Single shell 





The great advantage of the lamination of the shielding 

 material is here well exhibited. 



As the external field varies slowly in the neighbourhood of 

 the minimum, a considerable economy of material may be 

 effected without much sacrifice of efficiency. Thus, in the 

 case of two shells, we have seen that whereas to secure the 

 minimum external field (0*0006 of the unshielded field) the 

 volume of the material used must (in the case considered) be 

 five times the internal volume, a practically identical result 

 (0*0007) can be obtained by the use of a volume 3*66, while an 

 efficiency four times greater can be obtained by a volume 4*8. 



