ratus is called a position micrometer; and by its aid we determine the angle of position of a double star, or the angle which their line of junction makes with the meridian; which angle is usually reckoned round the whole circle, from 0 to 360, beginning at the north, and proceeding in the direction north, following (or east) south, preceding (or west).

(601). The advantages which this mode of operation offers for the estimation of parallax are many and great. In the first place, the result to be obtained, being dependent only on the relative apparent displacement of the two stars, is unaffected by almost every cause which would induce error in the separate determination of the place of either by right ascension and declination. Refraction, that greatest of all obstacles to accuracy in astronomical determinations, acts equally on both stars; and is therefore eliminated from the result. We have no longer any thing to fear from errors of graduation in circles from levels or plumb-lines-from uncertainty attending the uranographical reductions of aberration, precession, &c.—all which bear alike on both objects. In a word, if we suppose the stars to have no proper motions of their own by which a real change of relative situation may arise, no other cause but their difference of parallax can possibly affect the observation.

(602.) Such were the considerations which first induced Sir William Herschel to collect a list of double stars, and to subject them all to careful measurements of their angles of position and mutual distances. He had hardly entered, however, on these measurements, before he was diverted from the original object of the enquiry (which, in fact, promising as it is, still remains open and untouched, though the only method which seems to offer a chance of success in the research of parallax,) by phænomena of a very unexpected character, which at once engrossed his whole attention. Instead of finding, as he expected, that annual fluctuation to and fro of one star of a double star with respect to the other, that alternate annual increase and decrease of their

CHAP. XII.

BINARY STARS.

389

distance and angle of position, which the parallax of the earth's annual motion would produce,―he observed, in many instances, a regular progressive change; in some cases bearing chiefly on their distance,—in others on their position, and advancing steadily in one direction, so as clearly to indicate either a real motion of the stars themselves, or a general rectilinear motion of the sun and whole solar system, producing a parallax of a higher order than would arise from the earth's orbitual motion, and which might be called systematic parallax.

(603.) Supposing the two stars in motion independ ently of each other, and also the sun, it is clear that for the interval of a few years, these motions must be regarded as rectilinear and uniform. Hence, a very slight acquaintance with geometry will suffice to show that the apparent motion of one star of a double star, referred to the other as a center, and mapped down, as it were, on a plane in which that other shall be taken for a fixed or zero point, can be no other than a right line. This, at least, must be the case if the stars be independent of each other; but it will be otherwise if they have a physical connection, such as, for instance, real proximity and mutual gravitation would establish. In that case, they would describe orbits round each other, and round their common center of gravity; and therefore the apparent path of either, referred to the other as fixed, instead of being a portion of a straight line, would be bent into a curve concave towards that other. The observed motions, however, were so slow, that many years' observation was required to ascertain this point; and it was not, therefore, until the year 1803, twentyfive years from the commencement of the enquiry, that any thing like a positive conclusion could be come to respecting the rectilinear or orbitual character of the observed changes of position.

(604.) In that, and the subsequent year, it was distinctly announced by Sir William Herschel, in two papers, which will be found in the Transactions of the Royal Society for those years, that there exist sidereal

systems, composed of two stars revolving about each other in regular orbits, and constituting what may be termed binary stars, to distinguish them from double stars generally so called, in which these physically connected stars are confounded, perhaps, with others only optically double, or casually juxtaposed in the heavens at different distances from the eye; whereas the indi viduals of a binary star are, of course, equidistant from the eye, or, at least, cannot differ more in distance than the semidiameter of the orbit they describe about each other, which is quite insignificant compared with the immense distance between them and the earth. Between fifty and sixty instances of changes, to a greater or less amount, in the angles of position of double stars, are adduced in the memoirs above mentioned; many of which are too decided, and too regularly progressive, to allow of their nature being misconceived. In particular, among the more conspicuous stars,-Castor, y Virginis, § Ursæ, 70 Ophiuchi, σ and Coronæ, & Bootis, n Cassiopeia, y Leonis, Herculis, ♪ Cygni, μ Bootis, ε 4 and 5 Lyræ, λ Ophiuchi, μ Draconis, and Aquarii, are enumerated as among the most remarkable instances of the observed motion; and to some of them even periodic times of revolution are assigned, approximative only, of course, and rather to be regarded as rough guesses than as results of any exact calculation, for which the data were at the time quite inadequate. For instance, the revolution of Castor is set down at 334 years, that of y Virginis at 708, and that of y Leonis at 1200 years.

(605.) Subsequent observation has fully confirmed these results, not only in their general tenor, but for the most part in individual detail. Of all the stars above named, there is not one which is not found to be fully entitled to be regarded as binary; and, in fact, this list comprises nearly all the most considerable objects of that description which have yet been detected, though (as attention has been closely drawn to the subject, and observations have multiplied) it has, of late,

CHAP. XII.

ELLIPTIC ORBITS OF BINARY STARS.

391

begun to extend itself rapidly. The number of double stars which are certainly known to possess this peculiar character is between thirty and forty at the time we write, and more are emerging into notice with every fresh mass of observations which come before the public. They require excellent telescopes for their observation, being for the most part so close as to necessitate the use of very high magnifiers, (such as would be considered extremely powerful microscopes if employed to examine objects within our reach,) to perceive an interval between the individuals which compose them.

(606.) It may easily be supposed, that phænomena of this kind would not pass without attempts to connect them with dynamical theories. From their first discovery, they were naturally referred to the agency of some power, like that of 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 581 years. A different process of computation has conducted Professor Encket to an elliptic orbit for 70 Ophiuchi, described in a period of seventy-four years; 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.

(607.) Of these, perhaps, the most remarkable is y Virginis, not only on account of the length of its period, but by reason also of the great diminution of apparent distance, and rapid increase of angular motion about each other, of the individuals composing it. It is a bright star of the fourth magnitude, and its component stars are almost exactly equal. It has been known to consist of two stars since the beginning of the eighteenth century, their distance being then between six and seven seconds; so that any tolerably good telescope would resolve it. Since that time they have been constantly approaching, and are at present hardly more than a single second asunder; so that no telescope, that is not of very superior quality, is competent to show them otherwise than as a single star somewhat lengthened in one direction. It fortunately happens, that Bradley, in 1718, noticed, and recorded in the margin of one of his observation books, the apparent direction of their line of junction, as being parallel to that of two remarkable stars, a and 8 of the same constellation, as seen by the naked eye; and this note, which has been recently rescued from oblivion by the diligence of Professor Rigaud, has proved of signal service in the investigation of their orbit. They are entered also as distinct stars in Mayer's catalogue; and this affords also another means of recovering their relative