Shielding of Concentric Spherical Shells. 97 



most effective shields; and we are thus led to enquire which 

 is the best arrangement that can be made under specified 

 conditions as to the magnitude of the space at our disposal or 

 as to the weight of the shielding material used. The answer 

 to this question is supplied by the following discussion. 



As the formulae are somewhat heavy, I shall for the most 

 part confine myself to shells formed of the same material and 

 separated by air-gaps. 



The second problem, to the result of which I think it is 

 desirable to draw attention, is that which defines the relations 

 between the shielding exerted by a number of concentric 

 shells, (1) on external space when the magnetic forces are 

 produced within the shells ; and (2) on the enclosed space 

 when the magnetic forces are produced outside. A full dis- 

 cussion of this is given below. 



The whole of the investigation is subject to three limita- 

 tions. I have confined myself: — 



(1) to cod centric shells ; 



(2) to cases in which the equipotential surfaces are sur* 

 faces of revolution about a line through the common 

 centre of the shells ; 



(3) to the case in which the permeability of each shell is 

 constant. 



As regards the first two limitations, I think it will be 

 seen that the conclusions arrived at are capable of generaliza* 

 tion in such a way as to enable a better approach to be made 

 to good shielding arrangements than would be the case if the 

 results of the discussion in the simple case of spherical shells 

 were unknown. The third limitation no doubt affects the 

 applicability of the formulae to practice. In spite of this, 

 however, I venture to think that they afford some useful 

 guidance, and that at all events they help to put the practical 

 problem in definite terms. 



The Relation between the Shielded and Unshielded Fields when 

 the Shielded Space is (1) within, (2) without the Shielding 

 Shells. 



Take the common centre of the shells as origin. Let the 

 potential within any shell be expanded in terms of zonal 

 spherical harmonics, then the terms corresponding to F n will 

 be of the form 



( A ^+^i)p»- 



Each such term can be discussed independently, and it is 

 Phil. Mag. S. 5. Vol. 37. No. 224. Jan. 1894. H 



