Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/5

We denote the aberration angle (the angle between the absolute and relative beam direction) by $\alpha$; it is

(8)	$\sin \alpha =\beta \sin \psi ,\ \cos \alpha ={\sqrt {1-\beta ^{2}\sin ^{2}\psi }}.$

Finally, it is given by differentiation of equation (6):

(9)	$\sin \varphi \ d\varphi =\sin \psi \ d\psi {\frac {c'^{2}}{c^{2}\cos \alpha }},$

an equation that povides the relation of the opening angle of a light pencil in terms of absolute and relative beam path.

If the mirror is moving with arbitrary velocity in the direction of its normal (or also perpendicular to it), then the law of reflection for the relative beam direction is strictly satisfied.^[1]

Under "relative" we will always understand "relative to a system moving moving with velocity ${\mathfrak {w}}$. When we are dealing with different velocities of the reference system, we will say in short: relative "with respect to ${\mathfrak {w}}$".

§ 2.

As the positive sense of the normal, or simply as the normal of the surface element of a material body, we want – once and for all – define the direction, which is directed from the body to the outside (into the surrounding aether). By that, also the positive sense of the normal at a radiating or reflecting surface element is given. Now, if the surface element is moving in the sense of the positive or negative normal, then in the following we want to speak in short about its positive or negative motion.

1. This is given from both the electromagnetic theory (see M. Abraham, Boltzmann-Festschrift p. 81. 1904) as well as from Huyghens' principle, (see F. Hasenöhrl, Sitzungsber. d. k. Akad. d. Wissensch. zu Wien IIa 113. p. 469. 1904). If the mirror is moving into another direction, then this law is only true up to magnitudes of order $\beta$. Yet the law of reciprocity is always exactly valid for relative rays, i.e., a relative ray can always traverse the same way in both directions; this is a consequence of thermodynamics (see F. Hasenöhrl, Sitzungsber. d. k. Akad. d. Wissensch. zu Wien IIa. 113. p. 493. 1904)