228 ME. G. H. LIVENS ON THE 



the present stage to say which of the two expressions does represent the true energy 

 distribution, but any examination of the mechanical inter-relations of the different 

 magnetic masses in the field postulates a previous decision as to the proper expression 

 to be taken as representing the available energy of these masses in its normal form, 

 respecting both its total amount and proper distribution. Once this decision has been 

 made it is unsafe to employ the method of integration by parts unless due regard is 

 paid to the surface integrals thereby introduced. 



The distribution of energy interpreted in terms of ideal magnetic matter which is 

 properly equivalent to the expression 



is such that the energy in any volume of the field consists of a distribution throughout 

 it of density at each point equal to 



together with a surface distribution of density 



over its surface. This corresponds properly to POISSON'S distribution of magnetic 

 matter and emphasises the necessity for the inclusion of surface distributions of 



magnetic matter. 



This explains why it is that the above theory determines properly the forces on 

 the permanent magnets as a whole, but fails to give a consistent account of the 

 internal forces between different parts of the same magnet. At the surface of "an 

 ordinary magnet it may quite legitimately be assumed that owing to the existence of 

 a transition layer, the normal component of the magnetisation vanishes there, and 

 consequently the surface integrals applied to the outer surfaces of any such body 

 would also vanish ; the two different expressions for the contained energy thus become 

 equivalent. 



This is perhaps sufficient to justify a summary rejection of this new interpretation 

 of the energy relations of the magnetic field, as being at most no better than the 

 older one which it presumed to displace. The real trouble in both cases seems to have 

 arisen mainly in an effort to discover an analogy in the relations of the electric and 

 magnetic fields. HERTZ and HEAVISIDK were the first to insist on the existence of 

 this analogy, and practically all the modern writers follow them in this matter, even 

 so far as to regard it as providing sufficient justification for certain fundamental 

 formulae of the theory. A close scrutiny of the subject will, however, reveal the fact 

 that although the mathematical relations connecting the magnetic force induction and 



