perfectly accurate, four values of the angle of position, and of the corresponding distances at given epochs, would be sufficient to assign the form and position of the curve described by the revolving star; this, however, scarcely ever happens. The accuracy of each result depends upon taking the mean of a great number of the best observations, and eliminating error by mutual comparison. The distances between the stars are so minute that they cannot be measured with the same accuracy as the angles of position; therefore, in order to determine the orbit of a star independently of the distance, it is necessary to assume, as the most probable hypothesis, that the stars are subject to the law of gravitation, and consequently that one of the two stars revolves in an ellipse about the other, supposed to be at rest, though not necessarily in the focus. A curve is thus constructed graphically by means of the angles of position and the corresponding times of observation. The angular velocities of the stars are obtained by drawing tangents to this curve at stated intervals, whence the apparent distances, or radii vectores of the revolving star, become known for each angle of position, because, by the laws of elliptical motion, they are equal to the square roots of the apparent angular velocities. Now that the angles of position estimated from a given line, and the corresponding distances of the two stars, are known, another curve may be drawn, which will represent on paper the actual orbit of the star projected on the visible surface of the heavens; so that the elliptical elements of the true orbit, and its position in space, may be determined by a combined system of measurements and computation. But, as this orbit has been obtained on the hypothesis that gravitation prevails in these distant regions, which could not be known à priori, it must be compared with as many observations as can be obtained, to ascertain how far the computed ellipse agrees with the curve actually described by the star.

y Virginis consists of two stars of nearly the same magnitude; they were so far apart in the beginning and middle of last century, that they were mentioned by Bradley, and marked in Mayer's catalogue, as two distinct stars. Since that time they have been continually approaching each other, till in January, 1836, one star was seen to eclipse the other, by Admiral Smyth at his Observatory at Bedford, and by Sir John Herschel at the Cape of Good Hope. A series of observations since the beginning of the

present century has enabled Sir John to determine the form and position of the elliptical orbit of the revolving star with extraordinary truth by the preceding method. According to his calculation, it came to its perihelion on the 18th of August of the year 1834. Its previous velocity was so great that the revolving star described an angle of 68° in one year. By the laws of elliptical motion its angular velocity must diminish till it arrives at its aphelion. The accuracy with which the motions of the binary systems are measured, and the skill employed in the deduction of the elliptical elements, are now so great, that the periodic time of y Virginis, determined by Sir John Herschel and Admiral Smyth from their respective observatories, combined with those of Sir William Herschel, only differ by two years, Sir John having obtained a period of 182 years, Admiral Smyth that of 180. By the aid of more numerous observations Mr. Fletcher has found that the true period is 184.53 years, and that the revolving star passed its perihelion in 1837. It is by such successive steps that astronomy is brought to perfection (N. 232).

Some of the double stars have very long periods, such as σ Coronæ, where the revolving star takes 737 years nearly to accomplish a circuit. Others again have very short periods, as n Coronæ,

η

Cancri, and έ Ursa Majoris, whose periodic times are 42.500, 58.91, and 58.26 years respectively: therefore each of these has performed more than one entire revolution since their motions were observed. Herculis, whose periodic time is only about 301 years, has accomplished two complete circuits, the lesser star having been eclipsed by the greater each time. The first of these two truly wonderful events, of one sun eclipsing another sun, was seen by Sir William Herschel in 1782.

The orbits and periodic times of so many of these binary systems having been determined proves beyond a doubt that sun revolves about sun in the starry firmament by the same law of gravitation that makes the earth and planets revolve about the sun (N. 232).

Since the parallax of 61 Cygni and that of a Centauri have been determined, Sir John Herschel has made the following approximation to the dimensions of their orbits and masses. The distance between the two stars of 61 Cygni, that is the radius vector of the revolving star, has hardly varied from 15′′5 ever since the earliest observations; while in that time the star has moved through 50°; it is evident therefore that the orbit must be

nearly circular. It is at right angles to the visual ray, and the periodic time is 514 years. The parallax or radius of the earth's orbit as seen from the star is 0'348, while the radius of the star's orbit as seen from the earth is 15"-5; hence the radius of the star's orbit is to that of the earth's orbit as 15′′-5 to 0′′-348, or nearly as 45 to 1. So the orbit described by the two stars of 61 Cygni about one another greatly exceeds that which Neptune describes about the sun. Since the mean distance of the stars and their periodic time are given, the sum of the masses of the two stars is computed to be 0.3529, that of the sun being 1. Thus our sun is not vastly greater nor vastly less than the stars composing 61 Cygni, which is a small inconspicuous star to the naked eye, not exceeding the 6th magnitude.

П

Of all the double stars a Centauri is the most beautiful: it is the brightest star in the southern hemisphere, equal, if not superior, to Arcturus in lustre. The distance between the two stars has been decreasing at the rate of half a second annually since the year 1822, while the angular motion has undergone very little change, which shows that the plane of the orbit passes through the earth like the orbits of 44 Boötes, and π Serpentarii ; that is to say, the edge of the orbit in these three stellar systems is presented to the earth, so that the revolving star seems to move in a straight line, and to oscillate on each side of its primary. Were this libration owing to parallax, it would be annual from the revolution of the earth about the sun; but as years elapse before it amounts to a sensible quantity, it can only arise from a real orbital motion seen obliquely. In this case five observations are sufficient for the determination of the orbit, provided they be exact; but the quantities to be measured are so minute, that it is only by a very long series of observations that accuracy can be attained. In 1834 Captain Jacob determined the periodic time of the revolving star of a Centauri to be 77 years, and the distance between the two to be 17"-5; and since the decrease is half a second annually, the distance or radius vector of the revolving star was 12"-5 in the year 1822; and as Mr. Henderson had determined the parallax or radius of the earth's orbit as seen from the star to be '913, it follows that the real semi-axis of the revolving star's orbit is 13 times greater than the semi-axis of the earth's orbit as a minimum. The real dimensions of the ellipse therefore cannot be so small as the orbit of Saturn, and may possibly

exceed that of Uranus. It is very probable that an occultation of one of the suns by the other will take place in 1867, or a very close appulse of the two stars.

Singular anomalies have appeared in the motions of 70 Ophiuchi, which was discovered to be a binary system by Sir William Herschel in 1779, and which has since nearly accomplished a revolution. Various orbits have been computed: those which best represent the angles of position fail with regard to the distances of the stars from one another, and vice versa. But it is a very remarkable fact that the errors are periodical, being for considerable periods of time alternately in excess and defect. Captain W. S.

Jacob, who determined the periodic time of the revolving star to be 93 years, attributes this anomaly to the disturbing action of an opaque body revolving round the lesser star. Assuming that to be the case, and computing, he found that the errors were considerably diminished both in the angle of position and distance. It is a subject of the highest interest, and well worthy of the attention of such astronomers as have the means of making the necessary observations. Among the triple systems, as Cancri, two of the stars revolve about one another in 58.9 years; but the motion of the third and most distant is so slow, that it has only accomplished a tenth part of its revolution about the other two since the system was discovered.

The

It appears from the calculations of Mr. Dunlop that σ Eridani accomplishes a revolution in little more than 30 years. motion of Mercury is more rapid than that of any of the planets, being at the rate of 107,000 miles an hour. The perihelion velocity of the comet of 1680 was 880,000 miles an hour; but, if the two stars of ☛ Eridani, or of έ Ursa Majoris, be as remote from one another as the nearest fixed star is from the sun, the velocity of the revolving star must exceed the power of imagination to conceive. The elliptical motion of the double stars shows that gravitation is not confined to the planetary motions, but that systems of suns in the far distant regions of the universe are also obedient to its laws. The stellar systems present a kind of sidereal chronometer, by which the chronology of the heavens will be marked out to future ages by epochs of their own, liable to no fluctuations from such disturbances as take place in our system. Some stars are apparently double, though altogether unconnected, one being far behind the other in space, as a Lyræ,

which apparently consists of two stars, one of the first, the other of the eleventh magnitude. Aldebaran, a Aquila, and Pollux are remarkable instances of these optically double stars. It has been shown how favourable that circumstance is for ascertaining the parallax of the nearest of the two. (N. 232.)

The double stars are of various hues: sometimes both stars are of the same colour, as in « Centauri and 61 Cygni, where the larger stars are of a bright orange and the smaller ones a deeper tint of the same, but they most frequently exhibit the contrasted colours. The large star is generally yellow, orange, or red; and the small star blue, purple, or green. Sometimes a white star is combined with a blue or a purple, and more rarely a red and white are united. In many cases these appearances are due to the influence of contrast on our judgment of colours. For example, in observing a double star, where the large one is a full ruby red, or almost blood colour, and the small one a fine green, the latter loses its colour when the former is hid by the cross wires of the telescope. That is the case with y Andromedæ, which is a triple star, the small one, which appears green, being closely double. Cancri is an instance of a large yellow star and a small one which appears blue by contrast. Still there are a vast number where the colours are decidedly different, and suggest the curious idea of two suns, a red and a green, or a yellow and a blue, so that a planet circulating round one of them may have the variety of a red day and a green day, a yellow day and a blue day. Sir John Herschel observes, in one of his papers in the Philosophical Transactions, as a very remarkable fact, that, although red stars are common enough, no example of a solitary blue, green, or purple star has yet been produced.

Sirius is the only star on record whose colour has changed. In the time of Ptolemy it was red; now it is one of the whitest stars in the heavens.

M. Struve has found that, out of 596 bright double stars, 375 pairs have the same intensity of light and colour; 101 pairs have different intensity, but the same colour; and 120 pairs have the colours of the two stars decidedly different.

Certain rays, which exist in the sun's light, are wanting in the spectra of every coloured star, and probably never existed in the light of these stars, as there is no reason to believe that they are absorbed by the stars' atmosphere, though they may be by