700 
MR. G. I 1 . C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
surface. There is no disturbance within it. The same is true when there are other 
electrical disturbances outside the surface, and the surface is still an equilibrium 
surface for the whole system. 
But if there are sources of magnetic disturbance in the neighbourhood of the 
surface, and T' is still constant over the surface, it will also be constant throughout 
the interior of the surface. Yet the electric and magnetic forces do not now vanish 
at internal points, for parts of these forces are derived from the “ magnetic convection 
potential” Cl. Since T is constant inside the surface, it follows from equations 
(26) to (31) that the field there is given by 
Ei 
E 2 = 
E, = 
= 0. 
fin cm 
u dz 
fiu dCl 
diy 
h 3 
h 3 
da 
dx 
] da 
* dy 
i_ da 
« dz 
But though there is now both electric and magnetic force inside the surface there 
is no mechanical force on a small moving charge since F is zero because F is 
constant. Outside the surface the field is the resultant of the fields due, the one 
to a and the other to TL 
We have already seen that when 12 = 0 there is neither electric nor magnetic 
force inside an equilibrium surface. The lines of magnetic force just outside the 
surface must be tangential to it since there is no magnetic force inside the surface 
and no distribution of magnetism upon it. The lines of magnetic force are also in 
planes perpendicular to the axis of x since H x = 0 when 12 = 0. Hence the lines of 
magnetic force on the surface itself are the lines in which the surface is cut by planes 
perpendicular to the axis of x. 
It is easy to show by analysis that throughout the field, as long as 12 = 0, the 
lines of magnetic force are given by the sections of the surfaces F = constant by the 
planes x = constant. 
For by (29), (30), and (31), when 12 = 0, 
7 r T r Kw fpp T K u d x l r 
Hi —■ 0 JuU —- 7 Ho — — ~z 
1 " « dz 3 a. dy 
Hence, if dyjdz refer to one of the lines of force, 
dy_ 
dz 
H, 
dV/dW 
dz / dy 
But at all points of the section of the surface T' = c made by the plane x — c, we 
have y and 2 connected by the relation 'P = c, while, of course, x is constant. 
