•228 
MR. 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 
j 0 
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 tliat 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 lietween 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. 
I’his is perhaps sufflcieiit 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 Heaviside 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 
