Our list of distances ([§ 189]) contains four double stars whose periodic times and major axes have been fairly well determined, and we find in the accompanying table the information which they give about the masses of double stars and the size of the orbits in which they move:
| Star. | Major axis. | Minor axis. | Periodic time. | Mass. |
|---|---|---|---|---|
| α Centauri | 47 | 40 | 81 y. | 2 |
| 70 Ophiuchi | 56 | 48 | 88 | 3 |
| Procyon | 34 | 31 | 40 | 3 |
| Sirius | 43 | 34 | 52 | 4 |
The orbit of Uranus, diameter = 38, and Neptune, diameter = 60, are of much the same size as these double-star orbits; but the planetary orbits are nearly circular, while in every case the double stars show a substantial difference between the long and short diameters of their orbits. This is a characteristic feature of most double-star orbits, and seems to stand in some relation to their periodic times, for, on the average, the longer the time required by a star to make its orbital revolution the more eccentric is its orbit likely to prove.
Another element of the orbits of double stars, which stands in even closer relation to the periodic time, is the major axis; the smaller the long diameter of the orbit the more rapid is the motion and the shorter the periodic time, so that astronomers in search of interesting double-star orbits devote themselves by preference to those stars whose distance apart is so small that they can barely be distinguished one from the other in the telescope.
Although the half-dozen stars contained in the table all have orbits of much the same size and with much the same periodic time as those in which Uranus and Neptune move, this is by no means true of all the double stars, many of which have periods running up into the hundreds if not thousands of years, while a few complete their orbital revolutions in periods comparable with, or even shorter than, that of Jupiter.
201. Dark stars.—Procyon, the next to the last star of the preceding table, calls for some special mention, as the determination of its mass and orbit stands upon a rather different basis from that of the other stars. More than half a century ago it was discovered that its proper motion was not straight and uniform after the fashion of ordinary stars, but presented a series of loops like those marked out by a bright point on the rim of a swiftly running bicycle wheel. The hub may move straight forward with uniform velocity, but the point near the tire goes up and down, and, while sharing in the forward motion of the hub, runs sometimes ahead of it, sometimes behind, and such seemed to be the motion of Procyon and of Sirius as well. Bessel, who discovered it, did not hesitate to apply the laws of motion, and to affirm that this visible change of the star's motion pointed to the presence of an unseen companion, which produced upon the motions of Sirius and Procyon just such effects as the visible companions produce in the motions of double stars. A new kind of star, dark instead of bright, was added to the astronomer's domain, and its discoverer boldly suggested the possible existence of many more. "That countless stars are visible is clearly no argument against the existence of as many more invisible ones." "There is no reason to think radiance a necessary property of celestial bodies." But most astronomers were incredulous, and it was not until 1862 that, in the testing of a new and powerful telescope just built, a dark star was brought to light and the companion of Sirius actually seen. The visual discovery of the dark companion of Procyon is of still more recent date (November, 1896), when it was detected with the great telescope of the Lick Observatory. This discovery is so recent that the orbit is still very uncertain, being based almost wholly upon the variations in the proper motion of the star, and while the periodic time must be very nearly correct, the mass of the stars and dimensions of the orbit may require considerable correction.
The companion of Sirius is about ten magnitudes and that of Procyon about twelve magnitudes fainter than the star itself. How much more light does the bright star give than its faint companion? Despite the tremendous difference of brightness represented by the answer to this question, the mass of Sirius is only about twice as great as that of its companion, and for Procyon the ratio does not exceed five or six.
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.