>: 
the problem of the propagation of light in transparent substances, 
moving with a constant velocity. I shall now treat a more general 
case. I shall transform the original equations into a set of formulae, 
whieh, instead of quantities belonging to the individual electrons, 
contain only such as relate to the state of visible parts of the body 
and are therefore accessible to our observations. These formulae will 
hold for bodies of very different kinds, moving in any way we like. 
The greater part of the results have already been established by 
Poincaré in the second edition of his Hlectricité et Optique. The mode 
of treatment is however rather different. 
$ 2. With some exceptions, I shall use in the fundamental equa- 
tions the same notation and the same units as on former occasions. 
The aether will again be supposed to remain at rest and to penetrate 
the charged particles; the equations of the electromagnetic field are 
therefore to be applied to the interior of the electrons, as well as to 
the spaces between them, We shall consider a distribution of the 
charges with a finite volume-density, whose value is a continuous 
function of the coordinates. If we speak of “electrons”, we think 
of the charges as confined to certain small spaces, wholly separated 
from one another; however, in writing down our first equations, we 
may as well imagine a charge distributed over space in any arbitrary way. 
We shall conceive the charges as being carried by “matter”, though 
we might, if we chose, leave the latter out of consideration. We 
should then speak of the forces acting, not on charged matter, but 
on the charges themselves. 
Let us call 
g the density of the charge, 
» the velocity of the charged matter, 
d the dielectric displacement, *) 
8 the current, 
bh the magnetic force, 
V the velocity of light. 
Then we shall have 
TORO ET Ue hast AED a cg bns ade nj 
d 
ss +. Div (o v) zb 5 5 ; ° ° - ‘ ° ° . (11) 
1) The dielectric displacement, the current and the magnetic force are here 
represented in small type, because we wish to keep in reserve large type for 
corresponding quantities which we shall have to introduce later on. 
