MAGNETIC SHIELDING OF TRANSFORMERS 



421 



It has been shown (A. P. Wills, Phys. Rev., vol. 24, page 243, 

 February 1907) that for a shield of predetermined size, that is when 

 the smallest and the largest radii (ri and R^ in the case of three cylin- 

 ders. Fig. 2) are specified, the radii of the surfaces of the successive 



I 



Fig. 2. 



cylinders should be in a geometric progression to give the most efficient 

 shield. That is, we should have qi — qi — qz = qn = §23 = q- Equa- 

 tion (2) then becomes 



g = 1/4 m(1 - g' + 1/16 fx^n' -f M«' + 3/4 m«') + 1. (7) 



For two cylinders we get 



g = 1/4 m(1 -2^ + 1/4 M«^) + 1. (8) 



In these equations, the following relations hold between n and Rs 

 for (7) and ri and R2 for (8) 



Rs = rJ^[i^ R, = rif^\ (9) 



The effect upon the shielding efficiency of varying 5 (Fig. 3) from 



