122 Prof. A. W. Riicker on the Magnetic 



outer surface was given, if very thin shells are used, lamination 

 is injurious. The higher the permeability the smaller is the 

 lower limit of thickness above which lamination is useful. If 



3 



the permeability is great, the limit is r— x radius. If we put 



1 1 1 



« 3 R «Q 



in equation (29), we get a 2 =a 3 , i.e. the thickness of the 

 external shell vanishes in the limiting case. 



I now proceed to give some numerical examples of the 

 application of these formula?. Equation (30) is troublesome, 

 but when /jl is large so that | and rj are nearly equal it may 

 be simplified. 



It then reduces to 



ao V"lO + ^V 3 "s)"'i("R)"R = °' * ' (81) 



We have already seen that when the radius of the outer 

 shell is twice the smallest radius, the best result is obtained 

 when the volume of the shells is five times the volume of the 

 space enclosed by the smaller shell. 



The above equation may be used to determine whether a 

 still better arrangement is possible with the same volume of 

 material, if we suppose the radius of the external surface 

 variable. 



If «o=l, 1/R=5, and equation (31) is found to have a 

 root such that 



l/a 3 =9*5 nearly. 



This gives 



a 3 = VW5 = 2*118 ; 



and, as in the previous calculation we assumed a 3 =2, it is 

 evident that the two critical points nearly coincide. 

 In this case we get 



« 1 = % (l-« 3 /R) = 9/19, 

 from a 2 = 18/101. 



The magnitude of the shielded field is practically the same 

 as before. 



It must be remembered that neither the equation in a 3 nor 

 the ratio ^/^ are valid when f is put =77 if the shells are 

 thin or (which amounts to the same thing) if R is large. 



The best method of dealing with the problem is, then, as 

 follows : — 



