The visual discovery of the companions to Sirius and Procyon removes them from the list of dark stars, but others still remain unseen, although their existence is indicated by variable proper motions or by variable orbital motion, as in the case of ζ Cancri, where one of the components of a triple star moves around the other two in a series of loops whose presence indicates a disturbing body which has never yet been seen. 202. MULTIPLE STARS.--Combinations of three, four, or more stars close to each other, like ζ Cancri, are called multiple stars, and while they are far from being as common as are double stars, there is a considerable number of them in the sky, 100 or more as against the more than 10,000 double stars that are known. That their relative motions are subject to the law of gravitation admits of no serious doubt, but mathematical analysis breaks down in face of the difficulties here presented, and no astronomer has ever been able to determine what will be the general character of the motions in such a system. [Illustration: FIG. 129.--Illustrating the motion of a spectroscopic binary.] 203. SPECTROSCOPIC BINARIES.--In the year 1890 Professor Pickering, of the Harvard Observatory, announced the discovery of a new class of double stars, invisible as such in even the most powerful telescope, and producing no perturbations such as have been considered above, but showing in their spectrum that two or more bodies must be present in the source of light which to the eye is indistinguishable from a single star. In Fig. 129 we suppose _A_ and _B_ to be the two components of a double star, each moving in its own orbit about their common center of gravity, _C_, whose distance from the earth is several million times greater than the distance between the stars themselves. Under such circumstances no telescope could distinguish between the two stars, which would appear fused into one; but the smaller the orbit the more rapid would be their motion in it, and if this orbit were turned edgewise toward the earth, as is supposed in the figure, whenever the stars were in the relative position there shown, _A_ would be rapidly approaching the earth by reason of its orbital motion, while _B_ would move away from it, so that in accordance with the Doppler principle the lines composing their respective spectra would be shifted in opposite directions, thus producing a doubling of the lines, each single line breaking up into two, like the double-sodium line _D_, only not spaced so far apart. When the stars have moved a quarter way round their orbit to the points _A´_, _B´_, their velocities are turned at right angles to the line of sight and the spectrum returns to the normal type with single lines, only to break up again when after another quarter revolution their velocities are again parallel with the line of sight. The interval of time between consecutive doublings of the lines in the spectrum thus furnishes half the time of a revolution in the orbit.