THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
763 
tractions of the conductors on the dielectric system are derived from a potential 
energy function T — W, only in the latter case the value of tins function is 
more difficult to determine ; hence the tractions of the dielectric on the conductors 
are derived from a potential energy function — (T — W). Of this potential function 
the first part gives the electrodynamic forces acting on the conductors, the second 
part the electrostatic forces. This mode of treatment is clearly perfectly general, and 
applies, for instance, with the appropriate modification of statement, to the deter¬ 
mination of the electrodynamic forces of an element of a continuous non-linear current 
flowing through a conducting medium ; it will be shown presently that the electric 
dissipation-function can contribute nothing to the ponderomotive forcive. 
That the part of the forcive which is due to the variation of this potential 
energy W is correctly expressible by means of the electrostatic traction KF^/Stt on 
the surfaces of the conductors, may be verified as follows. Suppose an element of 
surface dS of the conductor to encroach on the dielectric by a normal distance dn ; 
the energy that was in the element of volume dS dn of the dielectric has been 
absorbed ; and in addition the energy of the mass of the remaining dielectric has 
been altered by the slight change of form of the surface of the conductor in the 
neighbourhood of the element dS. Now the dielectric is in internal equilibrium, 
therefore its internal energy in any given volume is a minimum ; therefore the change 
produced in that energy by any small alteration of constraint, such as the one just 
described, is of the second order of small quantities. Hence the encroachment of the 
element dS of the conductor diminishes the total energy W simply by the amount 
contained in the volume dS dn ; and therefore that encroachment is assisted somehow 
by a mechanical traction equal to the energy per unit volume of the dielectric at the 
place, that is, of intensity KF^Stt. 
Electrodipiamic effect of motion of n clmrged^ Body. 
59. When a charged body moves relatively to the surrounding sether, with a 
velocity small compared with the velocity of electric propagation, it practically 
carries its electric displacement-system [f g, h) along with it in an equilibrium 
configuration. Thus the displacement at any point fixed in the cether will change, 
and we shall virtually have the field filled with electric currents which are completed 
in the lines of motion of the charged elements of the body, so long as that motion 
continues. On this view. Maxwell’s convection-current is not differentiated from 
conduction-current in any manner whatever, if we except the fact that viscous decay 
usually accompanies the latter. 
A metallically coated glass disc, rotating in its own plane without altering its 
position in space, would on this theory produce no convection-current at all; but if 
the coating of the disc is divided into isolated parts by scratches, as in Eowland and 
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