226 
MR. G. H. LTVENS ON THE 
another and more involved form. The fundamental basis of this theory is the 
assumption of a distribution of true magnetic matter of density at any place equal to 
= -div b, = ~ div B 
d-TT 
wherein I,j is the density of the permanent magnetic polarity. This magnetic matter 
is supposed to be distributed continuously throughout the space but so that the 
amount in any portion of the matter is zero, a condition which is perhaps rather 
difficult of realisation, as it would make the distribution in any particular portion of 
the matter dependent on the distribution in all the surrounding portions. 
In this theory the magnetic energy is first calculated on analogy with the'electro¬ 
static energy ; the magnetic induction vector B is regarded as a sort of composite 
displacement produced by the acting force H, so that the energy per unit volume is 
An J 
(HcZB). 
This expression is then verified to be equivalent in the purely statical case to the 
volume integral 
r rp." 
dv (j) dp„ 
taken over the entire field, the surface integral over the infinite boundary 
contributing nothing in all regular cases; 0 is the magnetic potential of the field. 
In generalising the theory to the case where the field is due to linear currents the 
same physical basis is adopted as regards the expression 
jdv j^HdB), 
which still therefore remains valid, and when there are no permanent magnets about 
this is easily verified by the usual argument to be equivalent to the summation 
-X 1 J(^N 
c J 
over the different current elements, J denoting the typical current strength and N 
the induction through its circuit. When there are permanent magnets present this 
expression becomes 
jc^rj ipdp„^+^X ^ J (^N. 
It is then shown that the mechanical forcive on the magnetic matter in any one of 
its co-ordinates is derivable as the appropriate negative gradient of this energy 
