constructed by Sir Wm. Herschel, with the express object of facilitating these researches, and the reader will find them, and a full account of his method of comparison, in the Phil. Trans. 1796, and subsequent years.

(598.) We come now to a class of phænomena of quite a different character, and which give us a real and positive insight into the nature of at least some among the stars, and enable us unhesitatingly to declare them subject to the same dynamical laws, and obedient to the same power of gravitation, which governs our own system. Many of the stars, when examined with telescopes, are found to be double, i. e. to consist of two (in some cases three) individuals placed near together. This might be attributed to accidental proximity, did it occur only in a few instances; but the frequency of this companionship, the extreme closeness, and, in many cases, the near equality of the stars so conjoined, would alone lead to a strong suspicion of a more near and intimate relation than mere casual juxtaposition. The bright star Castor, for example, when much magnified, is found to consist of two stars of between the third and fourth magnitude, within 5′′ of each other. Stars of this magnitude, however, are not so common in the heavens as to render it at all likely that, if scattered at random, any two would fall so near. But this is only one out of numerous such instances. Sir Wm. Herschel has enumerated upwards of 500 double stars, in which the individuals are within half a minute of each other; and to this list Professor Struve of Dorpat, prosecuting the enquiry by the aid of instruments more conveniently mounted for the purpose, has recently added nearly five times that number. Other observers have still further extended the catalogue, already so large, without exhausting the fertility of the heavens. Among these are great numbers in which the interval between the centers of the individuals is less than a single second, of which & Arietis, Atlas Pleiadum, y Coronæ, ronæ, and Herculis, and and a Ophiuchi, may

Co

CC

be cited as instances. They are divided into classes according to their distances the closest forming the first class.

(599.) When these combinations were first noticed, it was considered that advantage might be taken of them, to ascertain whether or not the annual motion of the earth in its orbit might not produce a relative apparent displacement of the individuals constituting a double star. Supposing them to lie at a great distance one behind the other, and to appear only by casual juxtaposition nearly in the same line, it is evident that any motion of the earth must subtend different angles at the two stars so juxtaposed, and must therefore produce different parallactic displacements of them on the surface of the heavens, regarded as infinitely distant. Every star, in consequence of the earth's annual motion, should appear to describe in the heavens a small ellipse, (distinct from that which it would appear to describe in consequence of the aberration of light, and not to be confounded with it,) being a section, by the concave surface of the heavens, of an oblique elliptic cone, having its vertex in the star, and the earth's orbit for its

D

B

base; and this section will be of less dimensions, the more distant is the star. If, then, we regard two stars, apparently situated close beside each other, but in

reality at very different distances, their parallactic ellipses will be similar, but of different dimensions. Suppose, for instance, S and s to be the positions of two stars of such an apparently or optically double star as seen from the sun, and let A B CD, abcd, be their parallactic ellipses; then, since they will be at all times similarly situated in these ellipses, when the one star is seen at A, the other will be seen at a. When the earth has made a quarter of a revolution in its orbit, their apparent places will be Bb; when another quarter, Cc; and when another, D d. If, then, we measure carefully, with micrometers adapted for the purpose, their арраrent situation with respect to each other, at different times of the year, we should perceive a periodical change, both in the direction of the line joining them, and in the distance between their centers. For the lines A a and C c cannot be parallel, nor the lines Bb and Dd equal, unless the ellipses be of equal dimensions, i. e. unless the two stars have the same parallax, or are equidistant from the carth.

(600.) Now, micrometers, properly mounted, enable us to measure very exactly both the distance between two objects which can be seen together in the same field of a telescope, and the position of the line joining them with respect to the horizon, or the meridian, or any other determinate direction in the heavens. The meridian is chosen as the most convenient; and the situation of the line of junction between the two stars of a double star is referred to its direction, by placing in the focus of the eye-piece of a telescope, equatorially mounted, two cross wires making a right angle, and adjusting their position so that one of the two stars shall just run along it by its diurnal motion, I while the telescope remains at rest; noting their situation; and then turning the whole system of wires round in its own plane by a proper mechanical movement, till the other wire becomes exactly parallel to their line of junction, and reading off on a divided circle the angle the wires have moved through. Such an appa

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.

He

(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. 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

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