THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
801 
This explanation if valid, would cany with it, by virtue of the principle of energy, 
the observed law of attraction of a permanent magnet on an ordinary electric current; 
and also, provided we could assume the law of action and reaction to be applicable, 
that of a magnetic field on the aggregate constituting a permanent magnet. And as 
in the case of currents maintained steady, when two permanent magnets move each 
other the energy in the medium surrounding them is increased by the mechanical 
work done, but the energy in their interiors is diminished by twice that amount. 
Whatever be the value of these remarks, it would seem that the difficulty with 
respect to permanent magnets can hardly be insuperable, as it must attach in some 
form to any theory which makes magnetic energy kinetic. For, on that hypothesis, 
this energy must be wholly cyclic when there are only permanent magnets on the 
field; and its sign would therefore have to be changed, just as above, in forming 
dynamical equations which take separate account of each magnetic molecule. If on 
the other hand the statistical view above adopted is allowed, the complication intro¬ 
duced by intermolecular actions will be avmided, and only the nveraged action between 
the two systems will remain. 
On the Ehcfrodynamic Equation.'^. 
109. The kinetic energy of the electric medium is 
cm 
dd df~ d!-) 
Let ns transform this expression to new variables (/’ g, h) which represent the 
components of the absolute rotation at each point ; and let us supj^ose that there is 
nowhere any discontinuity or defect of circuital character in these quantities. We 
must therefore assign to them very large but not infinite values in an indefinitely 
thin superficial layer of the conductors, which shall be continuous with their actual 
values outside and their null value inside that surface.* 'fhe object of doing this is 
to abolish all surface-integral terms which would otherwise enter, on integration ly 
parts, at each interface of discontinuity ; the surface-integral terms that belong to the 
infinitely distant boundary need not concern us, except in cases where radiation plays 
a sensible part. 
We may show as in ^ 52 that under these circumstances 
where 
T 
(It, 
(F, G, H) = 1'^ I (/. f/, h'), 
t' being the distance of the element dr from the element dr. 
* The procedure of thi.s section leave.s out dissip-ation, and so confines the cnrrents to the surfaces 
of the conductors. 
5 K 
MDCCCXCIV.-—A. 
