334 
PHYSICS: H. A. LORENTZ 
Proc. N. a. S. 
the current of conduction, by B the magnetic induction. We shall suppose 
the matter to be isotropic, so that at each point we have to introduce only 
one e (dielectric constant), one permeability ju, and one conductivity 
These quantities may change from place to place; they, as well as E, H, 
etc., are considered as continuous functions. If there are different bodies, 
transition layers in which the properties gradually change from one body 
to the other, are supposed to exist at the common boundary. (This is 
only for the purpose of mathematical convenience; the thickness of the 
transition layer can be supposed to diminish indefinitely, and so we can 
pass to the limiting case of a sharp demarcation.) Let there be two 
kinds of impressed forces ("electromotive" forces), the one Fi'producing 
dielectric displaTcment, the other F2 producing conduction currents.^ 
The meaning of this is that the dielectric displacement is determined by 
D = 6(E + Fi) (1) 
and the conduction current by 
C = (7(E + F2) (2) 
The forces Fi and F2 are again continuous functions of the coordinates. 
Each of them may be confined to a limited space and these two spaces 
may lie one outside the other or they may overlap more or less. At a 
definite point there is but one E, the same in (1) and (2). 
In addition to (1) and (2) we have 
B = mH (3) 
curl H = ^ (D + C) (4) 
curl E - ^ B (5) 
div (D + C) = 0 (6) 
div B = 0 (7) 
Electric energy per unit of volume D2/2e. 
Magnetic energy per unit of volume* V2(B.H). 
Joule-heat per unit of volume and unit of time C^/o-. 
Work of Fi per unit of volume and unit of time (Fi-D). 
Work of F2 per unit of volume and unit of time (F2 C). 
We shall suppose that the forces Fi and F2 are started during an infinitely 
short interval of time A/, ending at the instant ^ = 0; from this latter 
onward they remain constant. Finally there will be a steady state. In 
what follows the integrations with respect to the time are extended up to 
