Is the Speed of Light Independent of the Velocity of the Source?

Recent observations of regularly pulsating x-ray sources in binary star systems are analyzed in the framework of the "emission" theory of light. Assuming that light emitted by a source moving at velocity $v$ with respect to an observer has a speed $c^{\prime }=c+kv$ in the observer's rest frame, we find that the arrival time of pulses from the binary x-ray sources implies $k<\mathrm{}2\mathrm{}\times {10}^{-9\mathrm{}}$. This appears to be the most direct and sensitive demonstration that the speed of light is independent of the velocity of the source.