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

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

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

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 ${\tfrac {8}{5}}{\tfrac {\epsilon _{0}}{{\mathfrak {B}}^{2}}}$,^[1] 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

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

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

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

(this is given from (5)).

1. See M. Abraham, Drude's Ann., X, p. 151, 1903.