MR. G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
697 
In order to understand the conditions of equilibrium which apply to such a surface, 
it is necessary to make a careful distinction between the mechanical force experienced 
by any portion of the charged surface, and the tendency to convection experienced 
by the charge upon that portion. 
Now, according to the statement of § 8, the mechanical force per unit volume, at 
any point where the magnetic density r is zero, is given by 
P = Ep + VCB - VGD, 
where C includes both the convection and the displacement currents so that 
C 
= pu -f 
K dE 
47r dt 
If we take unit area of the charged surface and suppose it enclosed by a very short 
cylinder whose ends are parallel and infinitely close to the tangent plane to the 
surface, and integrate P throughout the cylinder, we shall obtain the force experienced 
by unit area of the charged surface. An equivalent method is to find the difference 
in the Maxwell stress in the medium on the two sides of the surface. 
But when we consider the charge itself, we have to ask whether all the constituents 
of P are effective in tending to make the charge move relatively to the surface. 
When calculating, in § 10, the force experienced by a point-charge in motion, we were 
able to disregard the term — VGD because the “magnetic current” G was in circles 
about the axis of motion, and thus the force on a unit charge was reduced to 
E -f pYuH. But generally at a moving charged surface there will be a discontinuity 
in the magnetic induction and in consequence a surface “ magnetic current,” and it 
would seem at first sight as if this ought to be taken account of. But although the 
electric displacement D acts upon the magnetic current G, giving rise to the mechanical 
force — VGD, at right angles to both G and D, still there will be no change produced 
in the amount or distribution of the “ magnetic current.” And if there is no change 
in the “ magnetic current,” there can be none in the magnetic induction whose 
variations constitute that magnetic current. And still less will there be any change 
in what causes the magnetic induction, viz., the displacement and convection currents. 
We need not consider here the magnetic force which may arise from magnets or 
electric currents flowing in conductors, and which would be represented in terms of 
the differential coefficients of O, for there will be no discontinuities in this part of the 
magnetic force, since we have supposed that at all points on the surface r is zero 
and that there are no surface conduction currents. The action of the electric 
displacement upon this surface “ magnetic current ” will therefore avail nothing in 
producing convection of the charge from one part of the surface to another. The 
direct effect of the electric force upon the charge is taken account of in the first 
term of P, viz., the term E p. Now we have already seen in § 3 that the only 
MJDCCCXCVI,—A. 4 U 
