making
The frequency of the light is evidently
a result which except for second order terms is identical with that obtained for Case I.
To sum the matter up, when the source is set in motion, whichever of the two hypotheses as to the velocity of light is true, the frequency of the light will be changed by practically the same amount, but the wave-length will be changed if one of the hypotheses is true and entirely unaffected if the other is true. Light emitted from moving sources, whether they are astronomical bodies or the moving mirrors arranged by Belopolsky, unquestionably does show the Doppler effect. We must investigate whether both the frequency and the wave-length are changed by the motion of the source.
The determination of the Doppler effect is made by a measurement of the displacement of some particular line from its normal position in the spectrum. When the spectrum is produced by a prism it is difficult to say whether the position of a given line would depend upon its frequency or its wave-length. Spectroscopic measurements made with the help of a grating are, however, actual determinations of wave-length. Since such measurements do show a change in wave-length of the light from many of the stars, and especially in light coming from the approaching and receding limbs of the sun, where the velocity of rotation is known from observations on the sun spots, we have, at first sight, strong evidence in favor of our first hypothesis that the velocity of light is independent of the source.
We must notice in these experiments, however, that the measurements of wave-length are made only after the light has been reflected from the surface of the grating and consider the possibility that this reflecting surface would act as a new source, giving to
