Herschel did, indeed, discover changes of distance, but not of the character to indicate parallax. Following this by further observation, he found that the motions were not uniform nor rectilinear, and by a clear analysis of the movements he established the remarkable and wholly unexpected fact that in all these cases the motion is due to a revolution about their common centre of gravity.[[11]] He gave the approximate period of revolution of some of these: Castor, 342 years; δ Serpentis, 375 years; γ Leonis, 1,200 years; ε Bootis, 1,681 years.
Twenty years later Sir John Herschel and Sir James South, after re-examination of these stars, confirmed[[12]] and extended the results, one pair of Coronæ having in the interval completed more than a whole revolution.
It is, then, to Sir William Herschel that we owe the extension of the law of gravitation, beyond the limits of the solar system, to the whole universe. His observations were confirmed by F.G.W. Struve (born 1793, died 1864), who carried on the work at Dorpat. But it was first to Savary,[[13]] and later to Encke and Sir John Herschel, that we owe the computation of the elliptic elements of these stars; also the resulting identification of their law of force with Newton’s force of gravitation applied to the solar system, and the force that makes an apple fall to the ground. As Grant well says in his History: “This may be justly asserted to be one of the most sublime truths which astronomical science has hitherto disclosed to the researches of the human mind.”
Latterly the best work on double stars has been done by S. W. Burnham,[[14]] at the Lick Observatory. The shortest period he found was eleven years (κ Pegasi). In the case of some of these binaries the parallax has been measured, from which it appears that in four of the surest cases the orbits are about the size of the orbit of Uranus, these being probably among the smallest stellar orbits.
The law of gravitation having been proved to extend to the stars, a discovery (like that of Neptune in its origin, though unlike it in the labour and originality involved in the calculation) that entrances the imagination became possible, and was realised by Bessel—the discovery of an unknown body by its gravitational disturbance on one that was visible. In 1834 and 1840 he began to suspect a want of uniformity in the proper motion of Sirius and Procyon respectively. In 1844, in a letter to Sir John Herschel,[[15]] he attributed these irregularities in each case to the attraction of an invisible companion, the period of revolution of Sirius being about half a century. Later he said: “I adhere to the conviction that Procyon and Sirius form real binary systems, consisting of a visible and an invisible star. There is no reason to suppose luminosity an essential quality of cosmical bodies. The visibility of countless stars is no argument against the invisibility of countless others.” This grand conception led Peters to compute more accurately the orbit, and to assign the place of the invisible companion of Sirius. In 1862 Alvan G. Clark was testing a new 18-inch object-glass (now at Chicago) upon Sirius, and, knowing nothing of these predictions, actually found the companion in the very place assigned to it. In 1896 the companion of Procyon was discovered by Professor Schaeberle at the Lick Observatory.
Now, by the refined parallax determinations of Gill at the Cape, we know that of Sirius to be 0".38. From this it has been calculated that the mass of Sirius equals two of our suns, and its intrinsic brightness equals twenty suns; but the companion, having a mass equal to our sun, has only a five-hundredth part of the sun’s brightness.
Spectroscopic Binaries.—On measuring the velocity of a star in the line of sight at frequent intervals, periodic variations have been found, leading to a belief in motion round an invisible companion. Vogel, in 1889, discovered this in the case of Spica (α Virginis), whose period is 4d. 0h. 19m., and the diameter of whose orbit is six million miles. Great numbers of binaries of this type have since then been discovered, all of short period.
Also, in 1889, Pickering found that at regular intervals of fifty-two days the lines in the spectrum of ζ of the Great Bear are duplicated, indicating a relative velocity, equal to one hundred miles a second, of two components revolving round each other, of which that apparently single star must be composed.
It would be interesting, no doubt, to follow in detail the accumulating knowledge about the distances, proper motions, and orbits of the stars; but this must be done elsewhere. Enough has been said to show how results are accumulating which must in time unfold to us the various stellar systems and their mutual relationships.
Variable Stars.—It has often happened in the history of different branches of physical science that observation and experiment were so far ahead of theory that hopeless confusion appeared to reign; and then one chance result has given a clue, and from that time all differences and difficulties in the previous researches have stood forth as natural consequences, explaining one another in a rational sequence. So we find parallax, proper motion, double stars, binary systems, variable stars, and new stars all bound together.