696 MR, G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
R are derivable from potential functions and that two functions, 'F and Q can be 
found such that 
F = — V¥, R = — va 
Mr. Heaviside* has shown by a method, of which mine (in § 4) is only a translation 
into Cartesian symbols, that the two vectors E — gVHu and E + KVEu. are derivable 
from potential functions, and has deduced from them the values of E and H in terms 
of what I have denoted by 'P and O. And he has shown that if we take an 
eolotropic medium in which the specific inductive capacities and magnetic permea¬ 
bilities parallel to the three axes are 
K, 
Iv 
K 
O 3 o 
1 _ HL i - fib 
J - o x o 
V" V " 
and 
/L 
u 
id ’ 
17 2 
i-i’ 
and suppose that the same functions 'P and fl now represent the electric and 
magnetic potentials respectively, then the electric displacement at any point in the 
electrostatic problem is in the same direction as, and K/47T times as great as, the electric 
force E at the same point in the problem of a moving charged body. Similarly the 
magnetic induction in the statical problem is g times the magnetic force in the 
problem of a moving magnet. The analogy breaks down however when VNP and VO 
exist together. It is obvious that the electric and magnetic forces in the statical 
problems are identical with F and R in the problem of motion, for in both cases they 
are the negative “ slopes ” of "'P and fl. But I believe that I have not been antici¬ 
pated in giving the true explantion of the meaning of the vectors F and R. 
Equilibrium Conditions. 
15. I shall now consider the circumstances of a charged surface in motion, and 
shall begin by stating the nature of the surface upon which the charge is supposed to 
be deposited. The equations employed are those relating to the free ether, and 
would not necessarily apply to the interior of a mass of copper or other conducting 
substance. I do not know what happens at the surface, or at points in the interior, 
of a lump of copper when it is caused to move rapidly through the ether. The 
equations for a conductor at rest or in motion at a speed very small compared with 
that of light are well known, but very little is known for certain as to their form 
in rapidly moving masses of matter. The surface then is supposed to be formed of 
a thin film of some non-conducting substance whose electric and magnetic properties 
do not differ appreciably from those of free ether, and the charge is supposed to be 
deposited upon this surface. 
* ‘ Electromagnetic Theory,’ pp. 271, 276. ‘ Electrical Papers,’ vol. 2, p. 499, and foot-note to p. 514. 
