# Page:DeSitterConstancy2.djvu/1

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In my communication to the meeting of February of this year (see these Proceedings, Vol 15, page 1297) I pointed out that the existence of spectroscopic doubles whose motion obeys the laws of Kepler, is incompatible with the theory of Ritz, while in agreement with that of Lorentz.

Since then Messr. P. Guthnick[1] and E. Freundlich[2] have brought forward the hypothesis that the velocity of light might depend on the velocity of the source in a manner differing from the simple addition postulated by the theory of Ritz. The most simple hypothesis would be

${\displaystyle v=c+\varkappa u,\ }$

where v is the velocity of light emitted by a source having the velocity u. The problem then is no longer to decide whether ${\displaystyle \varkappa =0}$ or ${\displaystyle \varkappa =1}$, intermediate values being excluded, but to assign an upper limit to ${\displaystyle \varkappa }$.

We have then, using the notations of my former paper

${\displaystyle a=\varkappa {\frac {\Delta }{c^{2}}}.}$

If the true orbit is a circle, then the equation (1) becomes:

 ${\displaystyle u=u_{0}\cos {\frac {2\pi }{T}}\left(t-t_{0}\right)}$ (1)

If ${\displaystyle \varkappa }$ is very small we find for the equation (2) the following approximate expression
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1. Astronomische Kriterien für die Unabhängigkeit der Fortplanzungsgeschwindigkeit des Lichtes von der Bewegung der Lichtquelle, Astr. Nachr. 4670 (195, 265).
2. Zur Frage der Konstanz der Lichtgeschwindigkeit, Physik. Zeitschr. 14, 835).