gravitation, connecting the stars thus demonstrated to be in a state of circulation about each other; and the extension of the Newtonian law of gravitation to these remote systems was a step so obvious, and so well warranted by our experience of its all-sufficient agency in our own, as to have been expressly or tacitly made by every one who has given the subject any share of his attention. We owe, however, the first distinct system of calculation, by which the elliptic elements of the orbit of a binary star could be deduced from observations of its angle of position and distance at different epochs, to M. Savary, who showed*, that the motions of one of the most remarkable among them ( Ursa) were explicable, within the limits allowable for error of observation, on the supposition of an elliptic orbit described in the short period of 58 years. A different process of computation conducted Professor Encket to an elliptic orbit for 70 Ophiuchi, described in a period of seventy-four years. M. Mädler has especially signalized himself in this line of inquiry (see note). Several orbits have also been calculated by Mr. Hind and Captain Smyth, and the author of these pages has himself attempted to contribute his mite to these interesting investigations. The following may be stated as the chief results which have been hitherto obtained in this branch of astronomy :

† Berlin Ephem. 1832.

* Connoiss, des Temps, 1830. The elements Nos. 1, 2, 3, 4 c, 5, 6 c, 7, 11 b, 12 a, are extracted from M. Mädler's synoptic view of the history of double stars in vol. ix. of the Dorpat Observations: 4 a, from the Connoiss. des Temps, 1830: 4 b, 6 b, and 11 a, from vol. v. Trans. Astron. Soc. Lond.: 6 a, from Berlin Ephemeris, 1832 : No. 8. from Trans. Astron. Soc. vol. vi.: No. 9, 11 c, 12 b, and 13 from Notices of the Astronomical Society, vol. vii. p. 22., and viii. p. 159., and No. 10 from the author's "Results of Astronomical Observations, &c. at the Cape of Good Hope," p. 297. The prefixed to No. 7. denotes the number of the star in M. Struve's Dorpat Catalogue (Catalogus Novus Stellarum Duplicium, &c. Dorpat. 1827), which contains the places for 1826 of 3112 of these objects.

The "position of the node in col. 4. expresses the angle of position (see Art. 204.) of the line of intersection of the plane of the orbit, with the plane of the heavens on which it is seen projected. The "inclination" in col. 6. is the inclination of these two planes to one another. Col. 5. shows the angle actually included in the plane of the orbit, between the line of nodes (defined as above) and the line of apsides. The elements assigned in this table to w Leonis, Bootis, and Castor must be considered as very doubtful, and the same may perhaps be said of those ascribed to μ 2 Bootis, which rest on too small an arc of the orbit, and that too imperfectly observed, to afford a secure basis of calculation.

(844.) Of the stars in the above list, that which has been most assiduously watched, and has offered phænomena of the greatest interest, is y Virginis. It is a star of the vulgar 3rd magnitude (308=Photom. 3.494), and its component individuals are very nearly equal, and as it would seem in some slight degree variable, since, according to the observations of M. Struve, the one is alternately a little greater, and a little less than the other, and occasionally exactly equal to it. It has been known to consist of two stars since the beginning of the eighteenth century; the distance being then between six and seven seconds, so that any tolerably good telescope would resolve it. When observed by Herschel in 1780, it was 5"66, and continued to decrease gradually and regularly till at length, in 1836, the two stars had approached so closely as to appear perfectly round and single under the highest magnifying power which could be applied to most excellent instruments—the great refractor at Pulkowa alone, with a magnifying power of 1000, continuing to indicate by the wedge-shaped form of the disc of the star its composite nature. By estimating the ratio of its length to its breadth and measuring the former, M. Struve concludes that, at this epoch (1836-41), the distance of the two stars, center from center, might be stated at 0"-22. From that time the star again opened, and at present (1849) the individuals are more than 2" asunder. This very remarkable diminution and subsequent increase of distance has been accompanied by a corresponding and equally remarkable increase and subsequent diminution of relative angular motion. Thus, in the year 1783 the apparent angular motion hardly amounted to half a degree per annum, while in 1830 it had increased to 5°, in 1834 to 20°, in 1835 to 40°, and about the middle of 1836 to upwards of 70° per annum, or at the rate of a degree in five days. This is in entire conformity with the principles of Dynamics, which establish a necessary connexion between the angular velocity and the distance, as well in the apparent as in the real orbit of one body revolving about another under the influence of mutual attraction; the former varying inversely as the square of the latter, what

ever be the curve described and whatever the law of the attractive force. It fortunately happens that Bradley, in 1718, had noticed and recorded in the margin of one of his observation books, the apparent direction of the line of junction of the two stars, as seen on the meridian in his transit telescope, viz., parallel to the line joining two conspicuous stars a and 8 of the same constellation, as seen by the naked eye. This note, rescued from oblivion by the late Professor Rigaud, has proved of singular service in the verification of the elements above assigned to the orbit, which represent the whole series of recorded observations that date up to the end of 1846 (comprising an angular movement of nearly nine-tenths of a complete circuit), both in angle and distance, with a degree of exactness fully equal to that of observation itself. No doubt can, therefore, remain as to the prevalence in this remote system of the Newtonian law of gravitation.

(845.) The observations of § Ursa Majoris are equally well represented by M. Mädler's elements (4 c of our table), thus fully justifying the assumption of the Newtonian law as that which regulates the motions of their binary systems. And even should it be the case, as M. Mädler appears to consider, that in one instance at least (that of p Ophiuchi), deviations from elliptic motion, too considerable to arise from mere error of observation, exist (a position we are by no means prepared to grant*), we should rather be disposed to look for the cause of such deviations in perturbations arising (as Bessel has suggested) from the large or central star itself being actually a close and hitherto unrecognized double star than in any defect of generality in the Newtonian law.

(846.) If the great length of the periods of some of these bodies be remarkable, the shortness of those of others is hardly less so. Herculis has already completed two revo

p Ophiuchi belongs to the class of very unequal double stars, the magnitudes of the individuals being 4 and 7. Such stars present difficulties in the exact measurement of their angles of position which even yet continue to embarrass the observer, though, owing to later improvements in the art of executing such measurements, their influence is confined within much narrower limits than in the earlier history of the subject. In simply placing a fine single wire parallel to the line of junction of two such stars it is easily possible to commit an error of 3° or 4°. By placing them between two parallel thick wires such errors are in great measure obviated.

lutions since the epoch of its first discovery, exhibiting in its course the extraordinary spectacle of a sidereal occultation, the small star having twice been completely hidden behind the large one. n Coronæ, Cancri, and Ursæ have each performed more than one entire circuit, and 70 Ophiuchi and y Virginis have accomplished by far the larger portion of one in angular motion. If any doubt, therefore, could remain as to the reality of their orbitual motions, or any idea of explaining them by mere parallactic changes, or by any other hypothesis than the agency of centripetal force, these facts must suffice for their complete dissipation. We have the same evidence, indeed, of their rotations about each other, that we have of those of Uranus and Neptune about the sun; and the correspondence between their calculated and observed places in such very elongated ellipses, must be admitted to carry with it proof of the prevalence of the Newtonian law of gravity in their systems, of the very same nature and cogency as that of the calculated and observed places of comets round the central body of our own.

(847.) But it is not with the revolutions of bodies of a planetary or cometary nature round a solar center that we are now concerned; it is with that of sun round sun—each, perhaps, at least in some binary systems where the individuals are very remote and their period of revolution very long, accompanied with its train of planets and their satellites, closely shrouded from our view by the splendour of their respective suns, and crowded into a space bearing hardly a greater proportion to the enormous interval which separates them, than the distances of the satellites of our planets from their primaries bear to their distances from the sun itself. A less distinctly characterized subordination would be incompatible with the stability of their systems, and with the planetary nature of their orbits. Unless closely nestled under the protecting wing of their immediate superior, the sweep of their other sun in its perihelion passage round their own might carry them off, or whirl them into orbits utterly incompatible with the conditions necessary for the existence of their inhabitants. It must be confessed, that we have