130 Magnetic Shielding of Concentric Spherical Shells. 



innermost and outermost radii is given (a 5 /a = v^L),is de- 

 fined by the equations: 



— /V , 



«4 °0 



6U3 6^2 a ^ 



where X is defined by the equation 



X l (\-l)-L^(\-lH-e)=0. 



In both cases, when the permeability is great the best 

 arrangement is that in which the radii of the successive 

 bounding surfaces of the shells are in Geometrical Pro- 

 gression. 



The ratio of the shielded to the unshielded field when the 

 best arrangement is adopted is 



L 2 e 2 , IA 3 



and 



(\-l) 2 -i\ 4 -L(l-e)} (x _i)4 {x f_ L i (1 _ 6)} 



for two and three shells respectively, X being in each case 

 determined from the equation given above as appropriate to 

 that case. 



When the permeability is great and the shells are not very 

 thin, these expressions become 



(i/L-iy and u7E~i? respectively * 



The conditions for the best arrangement in the form of 

 two shells, when (1) the innermost radius and the total volume 

 of the permeable material, and (2) the innermost and outer- 

 most radii and the total volume of permeable material are 

 given, are less symmetrical but are set forth above. 



In any case of an arrangement in the form of two shells of 

 materials of different permeability, in order to obtain the best 

 result, the thickness of the shell formed of the more permeable 

 material should be greater, and that of the shell of less per- 

 meable material should be less than is given by the above 

 rules. 



The equations are obtained by which the best arrangement 

 can be calculated, if the permeabilities and external and 

 internal radii are given. 



