420 BELL SYSTEM TECHNICAL JOURNAL 



magnetic field. The permeability used in this case will, of course, 

 be the effective permeability for the particular conditions and fre- 

 quency under consideration. These relations refer only to that 

 portion of the shielding effect which is independent of the eddy 

 currents ie\ (Fig. 1), and the total shielding effect will, in general, 

 be somewhat greater. 



In an article in the Physical Review of October, 1899, A. P. Wills 

 considers the cases of three concentric cylinders and spheres. Due 

 to the fact that spherical shields are less suited for our purpose I 

 will give the equations for cylindrical shields only. Wills' formula for 

 three cylinders for large values of permeability is given by the following 

 equation : 



g = 1/4 /i { (1 — qiq^qz) + 1/16 ix^fiifinninnna 



+ 1/4 ju[(WlW3 + W1W2 — «l«2W3)Wl2 



+ («1«3 + «2W3 — WiW2«3)W23 — W1W3W12W23] } +1. (2) 



In this equation 



. = |, (3) 



where He is the density of the magnetic field at a point P with the 

 shield removed and Hi is the density of the magnetic field at that 

 point when enclosed by the shield, fj, is the permeability of the 

 material at the frequency in question. We have 



qi = nV-Rl^ wi = 1 - gi, 



52 = ^2V^2^ «2 = 1 - §2, ** 



53 = rs''IR,\ n,= I - §3, (4) 



212 = -RlV^2^ W12 = 1 — §12, 



§23 = Ri^lri, fiiz = \ — q23, 



where n, Ri, r^, etc., are the various radii of the cylinders as shown 

 by Fig. 2. 



By making qz = \ (or Uz = 0), in (2), we get the relation for two 

 concentric cylinders. 



g = 1/4 /i(l - qiq2 + l/Annifiifin) + 1. (5) 



By making 52 = 1 (or W2 = 0), (5) changes into an equation for one 

 shell only 



g = 1/4 Ml -g) + 1. (6) 



