THE ELECTRIC AND LUMINTEEROUS MEDIUM. 
747 
long as the potential energy is derived from a forcive emanating and transmitted 
nearly instantaneously from all parts of the medium and not merely from the 
contiguous elements, its location is expressed, quite sufficiently for dynamical purposes 
which are concerned with a finite volume of the medium and finite velocity of 
propagation, by attaching it to the element on which the forcive acts. The medium 
of MacCullagh therefore, on a saving hypothesis of this kind, appears to escape the 
kind of objection above mentioned. 
Part II,— Electrical Theory, 
39, The next stage in the development of the present theory is the application of 
the properties of non-vibrational types of motion of the primordial medium to the 
explanation of the phenomena of electricity. In accordance with the interpretation 
of MacCullagh’s equations, on the ideas of the electro-magnetic theory of light, 
the electric displacement in the medium is its absolute rotation {f, g, h) at the place, 
and the magnetic force is the velocity of its movement d/dt {$, yj, {). At tlie 
beginning, our view will be confined to rotational movements- unaccompanied )y 
translation, such namely as call into play only the elastic forces which are taken to 
be the cause of optical and electro-motive phenomena ; but later on we shall attempt 
to include the electrical and optical phenomena of moving bodies. 
In the ordinary electro-magnetic system of electric units we should have 
47r( /’, g, h) = curl (f, g, {); but in purely theoretical discussions it is a great simpli¬ 
fication to adopt a new unit of electric quantity such as will suppress the factor 47r, 
as Mr, Heaviside has advocated. Except in this respect, the quantities are all 
supposed to be specified in electro-magnetic units. 
It may be mentioned that a scheme for expressing the equations of electro¬ 
dynamics by a minimal theorem analogous to the principle of Least Action, has 
recently been constructed by von Helmholtz,^ 
Conditions of Dielectric Equilibrium. 
40. The conditions of electro-motive equilibrium in a general ceolotropic dielectric 
medium are to be derived from the variation of the potential-energy function 
On conducting this variation, we have 
* H. VON Helmholtz, “ Das Princip der kleinsten Wivknng in dei’ Electro-dynamik,” ‘ Wied, Ann.,' 
vol. 47, 1892. 
5 C 2 
