Page:Elektrische und Optische Erscheinungen (Lorentz) 109.jpg

(§ 17), and that these forces do some work, as soon as the body is displaced by the velocity ${\mathfrak {p}}$.

Now, we imagine (limited by plane surfaces and surrounded by aether) a transparent body K, upon which a system of plane waves is falling, and from which reflected and refracted light-bundles are emanating again. Let us put a fixed, closed surface $\sigma$ around it, and calculate for a time interval which is equal to the relative period T,

1°. the amount of energy A, which is flows rather in- than outwards through $\sigma$,

2°. the growth B of the electric energy within the surface, and

3°. the work C of the forces mentioned above.

For simplification we assume, that the amplitudes be constant, and that the body will be continuously hit by rays in the same way, which is the case, when the light source, or the diaphragm that serves to limit a bundle of sunlight, shares the translation of K. After expiration of time T, the energy itself has again the original value within the body, and even the energy located in $\sigma$ wouldn't be changed, when also the surface would be displaced by the velocity ${\mathfrak {p}}$. As regards the calculation of B, consequently only the energy in certain parts of space that lie in the direct vicinity of $\sigma$, come into consideration.

Eventually, we will find

$A=B+C$,

(104)

by which its is proven, that we were always (as regards our developments) in agreement with the energy theorem.

However, I don't want to hinder myself with the verification of equation (104), since it might be preferable to treat the question more generally.