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 (n and Rs in the case of three cylin- 

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



-*He 



Fig. 2. 



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

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

 tion (2) then becomes 



g = 1/4 m(1 - q' + 1/16 m'w' + Mw' + 3/4 fxn') + 1. (7) 



For two cylinders we get 



g = 1/4 m(1 - 5^ + 1/4 MW^) + 1. (8) 



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

 for (7) and ri and i?2 for (8) 



i?3 = n/V?, R2 - ri/^\ (9) 



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



