Here () is the density of the total electromagnetic energy, are the components of the Poynting vector, are the components of the total electromagnetic force on unit charge, ) is the density of electrification at the given point, and represent the velocity through space of this electrification. Thus
,
where , and , are the electric and magnetic force intensities respectively, and
,
,
.
Equation (23) states merely that the rate of increase of energy in an elementary volume is equal to the activity of any foreign (i. e., non-electrical) forces which may act therein minus the outward flow of energy.
Now suppose we consider an electromagnetic system bounded by a rigid surface (), which moves uniformly through space with the velocity () along the axis of (); and further suppose that the volume inside this closed surface is divided into two parts by the plane partition () which is perpendicular to the x-axis and which, although fixed in the moving system, coincides at a given instant with the plane () fixed in space. If this system be considered as isolated, then no disturbance passes through the bounding surface ().
![](http://upload.wikimedia.org/wikisource/en/thumb/5/54/Comstock1908b.png/400px-Comstock1908b.png)
In equation (23) the time derivative of the energy-density