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166 hypotheses, and these values differ by a term of the first order in β. If then the Doppler effect is measured, by observation of the wave-length, different results should lie obtained according as the one or the other hypothesis is adopted. Now observations of the Doppler effect have already been made by measuring the displacement of the spectral lines, employing either prisms or diffraction-gratings. In the cage of prisms it may be observed that all the theories of dispersion hitherto admitted lead to the supposition that this phenomenon can only depend on the frequency of the incident luminous vibrations. Consequently the displacement of the spectral lines may be caused by the simple variation in frequency due to the Doppler effect, and this whether, for the light, the hypothesis of a stationary æther is adopted, or a ballistic or emissive theory. From this point of view, therefore, the question whether the velocity of propagation of the light emitted by a source does or does not change with the velocity of the latter remains unanswered.

But the Doppler effect has been established with diffraction-gratings as well as with prisms, and for astronomical as well as terrestrial sources. Now the function of a grating, from the geometrical point of view, may be regarded as depending exclusively on the values of the incident wave-lengths; the positions of the successive spectral lines remain exactly determined by those values. But since, according to the ballistic or emissive hypothesis, the value of λ does not vary with the velocity of the source, we see that the grating should not give an appreciable result in the study of the Doppler effect, and this, as is known, is not in agreement with experience. We may then conclude from observations of the Doppler phenomenon in the stars and the limb of the sun with moving mirrors (Galitzin & Wilip), or again in the canal rays (Stark, Paschen), that the velocity of light is absolutely constant and independent of the movement of the source; this is equivalent to the rejection of the ballistic or emissive theory. This is Tolman's opinion, in contradiction to that of Stewart. Indeed, it should be borne in mind that the ordinary grating theory may not apply exactly in the case of a mechanical (ballistic or emissive) theory of