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THE previous lecture described the appearance and behaviour of red-shifts in the spectra of nebulae, and called attention to the alternative possible interpretations. If red-shifts are produced in the nebulae, where the light originates, they are probably the familiar velocity-shifts, and they measure an expansion of the universe. If the nebulae are not rapidly receding, red-shifts are probably introduced between the nebulae and the observer; they represent some unknown reaction between the light and the medium through which it travels.

In principle, at least, it is possible to distinguish between the alternatives, because a rapidly receding nebula should appear fainter than a stationary nebula at the same distance. The test cannot be applied directly, for apparent faintness, which we wish to compare with distance, is itself our only measure of great distance. However, the problem may be approached indirectly. The parallel assumptions of motion and no motion lead to different distances for nebulae of the same measured apparent luminosity. Thus there are alternative scales of distance, and they furnish quite different conceptions of our sample of the universe. It is possible that the wrong scale may introduce anomalies which can be detected or at least suspected.

With this end in view, the effects of recession on apparent luminosity, and, consequently, on estimated distances, were calculated, and the laws of red-shifts were formulated precisely both with and without the recession factors. The assumption of no motion led to a strictly linear law which indicates that the region of space explored with spectrographs is thoroughly homogeneous. This result implies that the explored region is too small a sample to furnish positive information concerning the universe at large. We merely infer that the universe is vastly greater than the sample, and the conclusion seems quite plausible.

The assumption of motion, on the other hand, led to a non-linear law of red-shifts, according to which the velocities of recession accelerate with distance or with time counted backward into the past. A universe that has been expanding in this manner would be so extraordinarily young, the time-interval since the expansion began would be so brief, that suspicions are at once aroused concerning either the interpretation of red-shifts as velocity-shifts or the cosmological theory in its present form.

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