Page:Zur Theorie der Strahlung bewegter Koerper.djvu/10

 or that to the mechanical mass of our system, also an apparent mass

$\mu=\frac{8}{3}\frac{E_{0}}{\mathfrak{B}^{2}}$|undefined

has been added. Namely, the introduction of that mass is quite similar to that of the electromagnetic mass. If we (for the moment) denote the energy of a resting electron with $$\epsilon_{0}$$, then the electromagnetic mass of it is equal to $$\tfrac{4}{3}\tfrac{\epsilon_{0}}{\mathfrak{B}^{2}}$$ or $$\tfrac{8}{5}\tfrac{\epsilon_{0}}{\mathfrak{B}^{2}}$$, depending on whether one deals with surface or volume charge. The relation is thus the same in terms of order of magnitude. Also the exact expressions have a certain similarity, since the quantity $$\log\tfrac{1+\sigma}{1-\sigma}$$ plays a role in both of them.

3.

In this section, I still want to make same remarks concerning the value of the radiation pressure.

The total pressure upon one of the surfaces $$A$$ or $$B$$ – it is irrelevant as to whether it is imagined as black of reflecting – has the value

$\begin{array}{ll} P & =2\pi(p_{1}+p_{2})\cos\phi\ \sin\phi\ d\phi\\ \\ & =4\pi i_{0}\frac{\cos^{2}\phi\ \sin\phi\ d\phi}{\mathfrak{B}(1-\sigma^{2})\sqrt{1-\sigma^{2}\sin^{2}\phi}}.\end{array}$|undefined

Herein, we want to introduce the radiation density $$\rho$$, which for example falls upon $$B$$. It is

$\rho=\frac{2\pi i\ \sin\phi\ d\phi}{\mathfrak{B}_{-}}=\frac{2\pi i_{0}\ \sin\phi\ d\phi\cdot\mathfrak{B}}{\mathfrak{B}_{-}^{2}\sqrt{1-\sigma^{2}\sin^{2}\phi}}$|undefined

(this is given from (5)).