6 98 
MR. G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
way in which alterations in the electrical distribution can be produced, when there 
is no conduction, is by convection, and hence since the term — YGD can produce no 
changes in the electrical distribution, it must be omitted in estimating the tendency 
to convection. This is only what we might expect if we notice that the “magnetic 
current” is not a necessary accompaniment of a moving charged surface. For in 
the case of an infinite cylinder uniformly charged and in motion along its length 
there are no “ magnetic currents ” at all, since there is no change in the magnetic 
induction along any line parallel to the length of the cylinder. 
An example of a somewhat similar kind occurs when an electric current flows 
through a conductor in a magnetic field. The magnetic field gives rise to a 
mechanical force which is experienced by the conductor, but there is no change 
produced in either the strength of the current or in its distribution, provided, at 
least, that the conductor is not of bismuth (when its resistance would be altered by 
the magnetic field) and that the “ Hall effect ” is disregarded. 
The convection current pu is a true part of the electric current. The substance 
upon which the charge is deposited experiences, therefore, the force pYuB per unit 
volume, or /xYuH per unit of charge. But the charge must move when the sub¬ 
stance conveying it moves, and thus we may regard the charge as experiencing the 
force. Hence the term must be included in estimating the tendency to convection. 
In contrast to the “ magnetic current,” the convection current pu depends only upon p 
and u, and is not dependent upon the manner in which p is distributed. 
If we use F to denote the “ tendencv to convection,” we have finallv 
F = E + p-YuH. 
But E — pYHu — — VT, so that F = — VT. 
Since d' is the potential whose “slope” is the “tendency to convection,” it will 
be convenient to call 'F the “electric convection potential.” In the same way ft may 
be called the “ magnetic convection potential.” 
Equilibrium Surfaces. 
16. Since the “ tendency to convection ” experienced by a unit moving charge is 
given by F — — V'F, it follows at once that F is everywhere perpendicular to the 
surface ' V F = constant. The surface \F — constant may therefore be termed an 
equilibrium surface, for a small concentrated charge which is constrained to remain 
upon the surface will not tend to move about upon it. And the result of § 15 shows 
us that this statement remains true for each part of the charge, even when a charge 
is distributed over the whole of the surface. 
Now consider what happens in the case of a charged surface in motion when the 
