THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
755 
in estimating the energy of the medium in terms of the flow of displacement these 
surface sheets must be included, after the manner of vortex sheets in hydrodynamics. 
In the same way, when the electric charge on a conductor is executing oscillations, 
a vortex sheet of changing electric displacement, such as will make the displace¬ 
ment in the field everywhere circuital, must be supposed to exist on the surface of 
the conductor. 
49. There is this difierence between actual electric current-systems and the 
permanently circulating currents, or vortex rings, in this sethereal medium, that the 
latter move in the medium so that their strengths remain constant throughout all 
time, while alteration of the strength of an electric current is produced by electro¬ 
dynamic induction. In our condenser circuit, however, the strength of the current 
depends on the rate of movement of the plates of a condenser, that is, it is affected 
by changes in the rotational strain-energy of the portions of the medium which are 
situated in the gaps across the conducting curcuit. Motion of the condenser-plates 
produces a flow of displacement across any closed surface which passes between them, 
and therefore is to be taken as producing an equal and opposite flow where this 
surface intersects the connecting circuit. That ideal flow, or current, the repre¬ 
sentation of the action of the channel of discontinuity on the elastic transmission 
in the medium, implies on the other hand a hydrodynamical circulation of the medium 
round the conducting circuit, which provides the kinetic energy of the electric current. 
A current in a conductor has practically no elastic potential energy, because for 
movements of ordinary velocity the medium is always sensibly in an equilibrium 
condition, any beginning of an electromotive disturbance of the steady motion being 
instantly equalized before it has time to grow. A complete current, consisting of a 
flexible vortex-ring, or even circulating in a rigid core in the free aether, will thus 
maintain its strength unaltered, that is, the surrounding aether will move so that the 
electrodynamic induction in the circuit is always null ; but if the current-curcuits are 
completed across the dielectric or through an electrolytic medium, this constraint to 
nullity of induction will be thereby removed, and constancy of circulation will no 
longer be a characteristic of such a broken vortex-ring, so to speak, in the medium. 
50. The above mode of representing the surface-terms in the kinetic energy of 
course supposes that the intensities of the vortex sheets have been somehow already 
determined, or else that they are to be included in the scheme of variables of the 
problem. When the conductors are of narrow section, then as regards their action at 
a distance all that is wanted is the aggregate amount of flow across the section, that 
is, the electric current in the wire in the ordinary sense ; and the introduction into 
the energy of terms calculated with reference only to these aggregates of flow is 
sufficient as regards the effect at distances from the conductors that are great com¬ 
pared with the dimensions of their cross sections. But if the details of the distribu¬ 
tion round the section are required, the term in the energy must be more minutely 
specified as a surface-integral due to the interaction of the different elementary fila- 
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