stars are so enormous that no conceivable rate of approach or recession could affect their brilliancy discernibly. Only the most rapid thwart-motions yet recognized would carry a star over a space equal to the moon's seeming diameter in 500 years, so that a corresponding motion of recess or approach would only change a star's distance to about the same relative extent, and it is obvious that such a change could not make a star, even in that long period, change appreciably in brightness.
It will seem, then, utterly incredible that astronomers have learned not merely whether certain stars are receding or approaching, but have actually been enabled to determine respecting this kind of motion what they cannot determine respecting the more obvious thwart-motion, viz., the rate at which the motion takes place.
This is rendered possible by what is known of the nature of light. Light travels through space in waves, not as a direct emanation. Now, let us compare a star's action in emitting such waves with some known kind of wave-action, and we shall at once recognize the effects of very rapid motion on the star's part. Conceive a fixed paddle-wheel turning at a uniform rate in water, and that every blade as it reaches the water raises one wave, that wave being transmitted in a given direction. Then there would be a succession of waves separated from each other by a constant distance. But, suppose the paddle-wheel itself to be carried in the given direction. It is clear that, after one blade has raised its wave, the next blade, descending in the same time as before, will reach the water closer to the preceding wave than if the paddle-wheel had been at rest; for the moving wheel will have carried the blade closer, so that now a succession of waves will result as before, but they will have their crests closer together. And obviously, if the wheel were carried in the contrary direction, the wave-crests would be farther apart than if the wheel had been at rest.
Thus, reverting to the stars, we infer that if a star is approaching, the light which comes to us from it will have its waves closer together than if the star were at rest, and vice versa. Now, the distance between the wave-crests of light signifies a difference of color, the longer waves producing red and orange light; waves of medium length, yellow and green light; and the shorter waves producing blue, indigo, and violet light. So that, if a star were shining with pure red light, it might by approaching very rapidly be caused to appear yellow, or even blue or indigo, according to the rate of approach; while, if a star were shining with pure indigo light, it might by receding very rapidly be caused to appear green or yellow, or even orange or red.
But stars do not shine with pure-colored light, but with a mixture of all the colors of the rainbow; so that the attempt to estimate a star's rate of approach or recession by its color would fail, even though we knew the star's real color, and even though stars moved fast enough to produce color-changes. The spectroscopist has, however, a much
