104 Prof. A. W. Rticker on the Magnetic 



Calling these shielding factors Si, S 2 , &c, the unshielded 

 and shielded forces in the direction of the radius are given by 



, /2Pi , 2.3P 2 S , 3.4.P 3 ^ , ^ ) 



and by 



. J2PiSi, 2.3.P 2 5S 2 | 3.4.P 3 fr% \ 



respectively. 



If we consider any point on the diameter on which the 

 axis of the magnet lies and on the side towards which it is 

 moved, all the P's are equal to unity. 



The larger b becomes, the more important are the terms 

 in which the shielding factors S 2 , S 3 are small, and the more 

 efficient is the shielding. The total force is, however, in- 

 creased, as all these terms are added to the first. In other 

 words, the force is increased owing to the approach of the 

 magnet to the point considered, and it is only the addition 

 to its original value which is better shielded. The average 

 shielding is improved, but the force is increased. 



The converse statement holds good for the side from which 

 the magnet is moved. In that case the P's are alternately 

 — 1 and +1, the shielding is less efficient, but the force is 

 diminished. 



It may be worth while to illustrate this by a numerical 

 example. Let the magnet be placed on a diameter at a 

 distance from the centre = half the external radius ; and let 

 the forces be calculated at points on the same diameter, the 

 distances of which from the exterior of the shell are also half 

 the external radius. 



Then b = a 1 /2, r = 3a 1 /2. 



Let the thickness of the shield be 0*01 of the radius, so 

 that £/<&! = O'Ol, and let the permeability be 500. 

 The unshielded force is : — 



_4j> {0-593 Pi + 0-593 P 8 + 0-395 P 3 + 0-219 P 4 + 0-100 P 8 

 + 0-051 P 6 + 0-023 P 7 + 0-010 P 8 + &c.}. 



Multiplying each term by the corresponding shielding 

 factor, the shielded force is : — 



-p 3 {0-137 Pi + 0-085 P 2 + 0-041 P 3 + 0-018 P 4 + 0-008 P 5 

 + 0-003 P 6 + 0-0011 P 7 + 0-0004 P 8 }. 



