680 MR. Gf. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
where K is the specific inductive capacity, and /x the magnetic permeability of the 
medium. The components of the electric force E parallel to the axes of x, y, and 2 
will be denoted by E l5 E 3 , E 3 respectively. The same notation will also be applied 
to the other quantities. 
If E, D, H, B are all measured in the same system of units, then the principles to 
be employed in the formation of the fundamental equations may be expressed as 
follows:—(1). The line-integral of the magnetic force taken once round any closed 
circuit fixed in space is equal to 47 t times the total amount of electric current flowing 
through the circuit, the positive directions of the current and of the integration 
being related to each other in the same way as the translation and rotation of a 
right-handed screw working in a fixed nut. 
If H and € are the magnetic force and the electric current respectively, the set of 
differential equations which expresses this result may be written 
curl E = 4 ttC.(3). 
Now it was an essential part of the theory, as Maxwell left it, that the variation 
of the electric displacement constitutes a true current whose amount and direction is 
expressed by or — . But Professor G. F. Fitzgerald* has shown that there 
ought also to be included the convection current pu, where p is the volume density of 
electrification and u is its velocity. Since we are not concerned with conduction 
currents we may leave them out of account. We have, then, 
curl H — 47r^? 4- 47rpu = K-^ 4- 47jym.(4). 
(2.) The line-integral of the electric force taken once round any closed circuit fixed 
in space is equal to minus the total amount of magnetic current through the circuit, 
the positive directions of the magnetic current and of the integration being related 
as in (1). 
There is no evidence for the existence of a magnetic conduction current, involving 
a waste of energy. The only constituent of the magnetic current is that which arises 
dB d H . . , , 
, — or ix --- when ix is constant. 
’ dt r dt r 
We might include a fictitious magnetic convection current ru when r is the volume 
density of magnetism, but for the present we omit it. The relation may thus be 
expressed by 
from the increase in the magnetic induction, viz. 
curl E = 
dB _ dH 
dt P dt 
Equations (4) and (5) must be satisfied at all points of the field. They at once 
* ‘ B. A. Report,’ 1883, p. 404. 
