MAGNETIC SHIELDING IN HOLLOW IRON CYLINDERS. 635 



homogeneity in the iron when the shield is circularly magnetised. Let these fields be 

 denoted by the following symbols : — 



Transverse Field H ( . 



Circular Field H,. 



Longitudinal Field H,. 



Weakened Shielded Field (H),„. 



Negative Residual Field (H) r . 

 Leakage Field due to circular magnetisation (H),,. 

 Let the experimentally determined shielding ratio be 



H ' _ < 

 (H),„ -■' 



Brackets surrounding H denote, in all cases, magnetic fields within the shield. The 

 last-mentioned fields (H) r and (H) p will be discussed later. Meanwhile let 



H ' 

 (H) H -{-(H) r }-0 



'Theoretical Shielding Ratios for Shields A and B. 



§ 8. Neglecting the negative quantity bracketed with /* (m being large, any 

 inaccuracy thus introduced is within the limits of error in the experimental determina- 

 tions of the shielding ratio) in the formula (cylinder) given in § 1, we may write 



The shielding ratio, minus unity, is thus for all practical purposes proportional to the 

 geometrical factor and to the permeability. The usual definition of permeability is the 

 actual ratio, 



R 



it being assumed that the magnetic force H at any point produces the induction B at 

 that point. This may be called the ratio permeability. But it may also be defined as 

 the rate at which B is changing with respect to H, which is given by the tangent of 

 the B-H curve at any point. 



_dB 

 M ~rfH 



This is called the differential permeability. Two definitions of permeability are thus 

 available, and substituting these for m in the above formula we obtain two different 

 values of the theoretical shielding ratios. Let 



d B d dB 



£r-h +1= ^ and *B"aH +1= «*» 



