674 Mr. G. H. Livens on the Mathematical 



It appears, then, that the vector H is in reality the mechani- 

 cally effective part of the total magnetic force from which 

 the local part in the polarization has been rejected, and it 

 will therefore be derived from a potential under the usual 

 appropriate conditions. 



If the magnetization I is partly rigid (I ) and partly 

 induced (L) by the total force B, and if the induction 

 follows a linear isotropic law, we should write 





It = fcB ; 



and then 



H =^B-4ttI 



wherein 



fJb = 1 — iiir/c. 



. The new " permeability " coefficient \x here introduced, 

 which expresses the permeability of the medium to mechani- 

 cally effective magnetic force, is practically equivalent to 

 the reciprocal of the ordinary permeability, and it is actually 

 equal to this reciprocal when there is no permanent magnetism 

 in the medium concerned *. This inversion will naturally 

 lead to a revision of our physical ideas on magnetic induction; 

 for it is now the induction of mechanical and not electro- 

 motive force that is under review. 



In paramagnetic media k is positive and less than \tt, 

 so that fjb<l, and it is very small for the strongly ferro- 

 magnetic media near their saturation point. Free space is 

 thus the most permeable paramagnetic substance, and the 

 ferromagnetic media are almost impermeable. In diamag- 

 netic media k is negative, so that /n>l; so that here the 

 permeability is still larger than it is in free space. 



Let us pursue these relations further. The energy required 

 to establish the permanent polarity of intensity 1 at each 

 point of space is 



-hP 



(Bdl ), 



the volume integral being extended throughout all space. 

 The usual argument proves that in the statical case 



- ( dv\ °(B<n )= -^ (wdv+ (dv f {Bdl ). 



* The fact that the relation between the permeability as usually 

 defined and that here employed is a function of the permanent mag- 

 netism must not be regarded as detrimental to the present suggestion. 

 It may be due entirely to the older definition. 



