Shielding of Concentric Spherical Shells. 129 



In the paper the cube of this quantity is indicated by the 

 symbol Ij = a /a n =a n z /a B , where n refers to the outermost 

 surface. 



The other quantity e is a function of the permeability. In 

 the cases which I am now considering, 



6= (2g + l)*(/* + 2) = 27 a PP roximate ^ 



when fi is large. 



If we suppose the innermost radius of the shells (a ) to be 

 fixed, and the thickness of the space utilized for shielding to 

 increase gradually from zero to a . thickness t, the material 

 employed is most efficient if fashioned in the form of a single 

 shell until 



t 3 



- =(1 + e)*-l = j- approximately, 



if //, is large. 



After that the material will be better employed if we divide 

 it into separated shells ; but the result obtained by the best use 

 of the given quantity of material can be still further improved 

 by filling up the space between the shells with more of the 

 material, provided the thickness of the whole shell occupied 

 by the shielding machinery is less than the value given by 



A= ( i+^-i=a/5> 



if fi is large. 



After this limit is passed it becomes positively injurious to 

 fill the whole of the shielding space with the permeable 

 material. 



Better results can always be obtained by two shells with 

 the same internal and external radii. 



If the ratio of these radii (a 3 /a = v'L) is given, the best 

 arrangement of two shells is defined by the equations 



where X is given by the equation 



\ 3 (X-l)-L(\-l + e) = 0. 



The best arrangement for three shells, if the ratio of the 

 Phil Mag. S. 5. Vol. 37. No. 224. Jan. 1894. K 



