That was written a quarter of a century ago, when spectroscopic analysis, as we now know it, had no existence. Accordingly, while the fatal objection to Doppler’s original theory is overlooked on the one hand, the means of applying the principle underlying the theory, in a much more exact manner than Doppler could have hoped for, is overlooked on the other. Both points are noted in the article above referred to, in the same paragraph. “We may dismiss,” I there stated, “the theory started some years ago by the French astronomer, M. Doppler.” But, I presently added, “It is quite clear that the effects of a motion rapid enough to produce such a change” (_i.e._ a change of tint in a pure colour) “would shift the position of the whole spectrum—and this change would be readily detected by a reference to the spectral lines.” This is true, even to the word “readily.” Velocities which would produce an appreciable change of tint would produce “readily” detectible changes in the position of the spectral lines; the velocities actually existing among the star-motions would produce changes in the position of these lines detectible only with extreme difficulty, or perhaps in the majority of instances not detectible at all. It has been in this way that the spectroscopic method has actually been applied. It is easy to perceive the essential difference between this way of applying the method and that depending on the attempted recognition of changes of colour. A dark line in the spectrum marks in reality the place of a missing tint. The tints next to it on either side are present, but the tint between them is wanting. They are changed in colour—very slightly, in fact quite inappreciably—by motions of recession or approach, or, in other words, they are shifted in position along the spectrum, towards the red end for recession, towards the violet end for approach; and of course the dark space between is shifted along with them. One may say that the missing tint is changed. For in reality that is precisely what would happen. If the light of a star at rest gave every tint of the spectrum, for instance, except mid-green alone, and that star approached or receded so swiftly that its motion would change pure green light to pure yellow in one case, or pure blue in the other, then the effect on the spectrum of such a star would be to throw the dark line from the middle of the green part of the spectrum to the middle of the yellow part in one case, or to the middle of the blue part in the other. The dark line would be quite notably shifted in either case. With the actual stellar motions, though all the lines are more or less shifted, the displacement is always exceedingly minute, and it becomes a task of extreme difficulty to recognize, and still more to measure, such displacement.