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.