Shielding of Concentric Spherical Shells. 

 Also from (8), 



L 2 e 2 (l-e) 



113 



1 dV 



2Le 2 



+ 



ylr dL ~ (X-l) 2 X 4 -L(l- e) ' (\-l) £ {A< 4 -L(l-e)} 2 



LV dX 



*\X-1 \ 4 -L(l-e)J (x--; 



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



and if we substitute in this the values of X, L, and dX/dh 

 proper to the limiting point, we get 



j_^_ 1- \/~e 



ylr dL~ 4(1+ ^e)' 



which is the same as the value obtained in the case of the 

 single shell. 



The shielding factor in the limiting case is obtained by 

 putting \ <2 = L = (1+ \/e) 2 in (8), or in the corresponding 

 expression for a single shell. In either case 



Since 





Ve(l+ \/e) 



6 = ^ = 



ft(N + l) a 



(Jfy + l)(N + ^)> 



which increases with N ; g. e. with (w + l)/n, and therefore 

 diminishes as n increases, the thickness of the shell at the 

 limit is less for the higher harmonic terms, but the shielding 

 at the limit is better. 



If (j, is so large, however, that we may write 



_(N+1) 2 __ (2n+l) 2 



the limiting thicknesses and the shielding factors for the 

 principal harmonic terms vary very slowly. If ^=400 we 

 get :— 



n. 



e. 



L= 



(1+ Ve) 2 . 



aja - 

 (1+ Ve)i 



*APo- 



1. 



2. 

 3. 



•0112 

 •0104 

 •0102 



1-223 

 1-214 

 1-212 



1-069 

 1-067 

 1066 



•058 

 056 

 •055 



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



