Page:Zur Theorie der Strahlung bewegter Koerper.djvu/7

that this energy is completely absorbed and not transformed into work. Namely this can also be directly shown, when one introduces the values for $p_{1}$ and $p_{2}$, which we will give in the following section. In order of not interrupting the progression of the investigation, I transfer the proof of this theorem into § 4 of this treatise. Thus in expression (1), the first summand is the energy provided by the radiating bodies, the second one is the energy stemming from work. We denote the latter by $L$, thus we set

$L=2\pi cD\int _{0}^{\pi /2}\sin \phi \ d\phi \left({\frac {p_{1}}{{\mathfrak {B}}_{-}}}-{\frac {p_{2}}{{\mathfrak {B}}_{+}}}\right).$

(2)

2.

We now want to introduce the values for magnitudes $p_{1}$ and $p_{2}$, which we preliminarily left undetermined. It was surely introduced at first by Abraham in his treatises already cited. Namely, these values have been derived from Lorentz's theory of electromagnetism. Since one can arrive at the same expressions in another way (see § 3 of the present work), their correctness seem to be even more plausible. According to Abraham, the radiation pressure upon a surface is numerically equal to the incident or emanated radiation divided by the speed of light, namely this pressure acts in the absolute direction of radiation. Let $\varphi$ be the angle, which is enclosed by the absolute direction of the radiation (emanated under the relative angle $\phi$) with the direction of $c$. Then the magnitude denoted earlier as $p_{1}$, is

$p_{1}={\frac {1}{\mathfrak {B}}}i\ \cos \varphi ,$

since we understood under $p_{1}$ the – solely effective – normal pressure component. A relation between $\varphi$ and $\phi$ can be easily obtained by the following figure 2, which is essentially identical with Fig. 1 of my cited treatise, and which surely needs nor further explanation.