# A proof of the constancy of the velocity of light

In the theory of *Ritz* light emitted by a source moving with velocity *u* is propagated through space in the direction of the motion of the source with the velocity *c+u*, *c* being the velocity of light emitted by a motionless source. In other theories (*Lorentz, Einstein* ) the velocity of light is always *c*, independent of the motion of the source. Now it is easily seen that the hypothesis of Ritz leads to results which are absolutely inadmissible.

Consider one of the components of a double star, and an observer situated at a great distance Δ. Let at the time *t*, the projection of the star's velocity in the direction towards the observer be *u*. Then from the law of motion of the star we can derive an equation:

(1) |

The light emitted by the star at the time *t* reaches the observer at the time . In Ritz's theory we have, neglecting the second and higher powers of . In other theories we have *a=0*. If now we put , we have

or | (2) |

The function *φ* will differ from *f*, unless *au* be immeasurably small. Therefore if one of the two equations (1) and (2) is in agreement with the laws of mechanics, the other is not. Now *a* is far from small. In the case of spectroscopic doubles *u* is not small, and consequently *au* can reach considerable amounts. Taking e.g. , and assuming a parallax of 0",1, from which years, we find approximately *au=4* days., i.e. entirely of the order of magnitude of the periodic time of the best known spectroscopic doubles.

Now the observed velocities of spectroscopic doubles, i. e. the equation (2), are as a matter of fact satisfactorily represented by a Keplerian motion. Moreover in many cases the orbit derived from the radial velocities is confirmed by visual observations (as for δ Equulei, ζ Herculis, etc.) or by eclipse-observations (as in Algol-variables). We can thus not avoid the conclusion that *a*=0, i.e. the velocity of light is independent of the motion of the source. *Ritz's* theory would force us to assume that the motion of the double stars is governed not by *Newton's* law, but by a much more complicated law, depending on the star's distance from the earth, which is evidently absurd.

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