Chapter XXXIX: Section XXXVI (1)

The Fixed Stars—Their Number—The Milky Way—Double Stars—Binary
Systems—Their Orbits and Periodic Times—Colours of the Stars—Stars
that have vanished—Variable Stars—Variation in Sun’s Light—Parallax
and Distances of the Fixed Stars—Masses of the Stars—Comparative Light
of the Stars—Proper Motions of the Stars—Apparent Motions of the
Stars—Motion and Velocity of the Sun and Solar System—The Nebulæ—Their
Number—Catalogue of them—Consist of Two Classes—Diffuse
Nebulæ—Definitely formed Nebulæ—Globular Clusters—Splendour of Milky
Way—Distribution of the Nebulæ—The Magellanic Clouds—Nebulæ round η
Argûs—Constitution of Nebulæ, and the Forces that maintain
them—Meteorites and Shooting Stars.

GREAT as the number of comets appears to be, it is absolutely nothing in comparison of the multitude of the fixed stars. About 2000 only are visible to the naked eye; but when the heavens are viewed through a telescope, their number seems to be limited only by the imperfection of the instrument. The number registered amounts to 200,000; their places are determined with great precision, and they are formed into a catalogue, not only for the purpose of ascertaining geographical positions by the occultations of the brightest among them, but also to serve as points of reference for marking the places of comets and other celestial phenomena. Sirius, α Centauri, and Arcturus are the brightest stars in the heavens; the others are classed according to their apparent lustre, from the first to the seventeenth magnitudes. Capella, α Lyræ, Procyon, and twenty or twenty-one more, are of the first magnitude; α Persei, γ Orionis, α Cygni, and in all fifty or sixty, are of the second; and of the third there are about 200, such as η Bootis and η Draconis, the numbers increasing as the magnitude diminishes. Those of the eighth magnitude are scarcely visible to the naked eye, and it requires a very good telescope to see stars of the seventeenth. This sequence is perfectly arbitrary; but Sir John Herschel has ascertained by actual measurement the comparative lustre of a great many—for example, he found that the light of a star of the sixth magnitude is 100 times less than that of one of the first magnitude, and that Sirius would make between three and four hundred of such little stars. Were the photometric scale completed, it would be of the greatest importance with regard to the variable stars.

The three or four brightest classes of stars are scattered pretty equably over the sky, with the exception of a zone or belt following the course of the great circle passing through ε Orionis and α Crucis, where they are very numerous, especially in the southern hemisphere. The stars of all magnitudes visible to the naked eye increase in numbers towards the borders of the Milky Way, which derives its lustre and name from the diffused light of myriads of stars; so numerous are they in some parts of it that more than 50,000 passed through the field of Sir William Herschel’s telescope in the course of an hour, in a zone only two degrees broad; in many places they are numerous beyond estimation, and most of them are extremely small on account of their enormous distances.

The Milky Way, which forms so conspicuous a part of the firmament, is a vast and somewhat flattened stratum or congeries of stars, encircling the heavens in a broad band, split through one part of its circumference into two streams of stars, bearing a strong resemblance to fig. 5, plate 5. It is contorted and broken in some places, and occasionally lengthened into branches stretching far into space. Its thickness is small compared with its length and breadth; yet in some places it is unfathomable even with the best telescopes; in others there is reason to believe that it is possible to see through it, and even beyond it, in its own plane. There is a gradual but rapid increase in the crowding of the stars on each side of the flat stratum towards the centre.

The solar system is deeply though excentrically plunged into this mass of stars, near that point where the circular stratum splits into two streams. Sir John Herschel’s description of the stars of the southern hemisphere shows that the Milky Way is a most magnificent object there. “The general aspect of the southern circumpolar regions (including in that expression 60° or 70° of south polar distance) is in a high degree rich and magnificent, owing to the superior brilliancy and large development of the Milky Way, which, from the constellation of Orion to that of Antinous, is a blaze of light, strangely interrupted, however, with vacant and entirely starless patches, especially in Scorpio, near α Centauri and the Cross, while to the north it fades away pale and dim, and is in comparison hardly traceable. I think it is impossible to view this splendid zone, with the astonishingly rich and evenly distributed fringe of stars of the 3rd and 4th magnitude, which forms a broad skirt to its southern border like a vast curtain, without an impression amounting almost to conviction, that the Milky Way is not a mere stratum, but annular, or at least that our system is placed within one of the poorer or almost vacant parts of its general mass, and that eccentrically, so as to be much nearer to the region about the Cross than to that diametrically opposite to it.”

Those dark vacuities called “Coal Sacks” by the ancient navigators, which are so numerous between α Centauri and α Antaris, are among the most extraordinary phenomena in the southern hemisphere; they are of intense blackness, though by no means void of extremely small telescopic stars; the darkness arises from the contrast these nearly vacant spaces form with the excessive brilliancy of the surrounding part of the Milky Way, and the sudden sharp transition from light to darkness. The largest and most conspicuous of them is a pear-shaped vacuity close to the Southern Cross. That portion of the Milky Way that is split longitudinally through its centre lies between α Centauri and the constellation of Cygnus: the two bands are joined here and there by narrow bridges of condensed stars, stretching across the darker space between them. In Scorpio and Sagittarius Sir John Herschel describes the Milky Way as composed of definite clouds of light running into clusters of extremely minute stars like sand, not strewed evenly as with a sieve, but as if thrown down by handfuls, and by both hands at once, leaving dark intervals. In this astonishing profusion the stars are of all sizes, from the 14th to the 20th magnitude, and even down to nebulosity. After an interval the same profusion is renewed, the stars being inconceivably minute and numerous beyond description—they are in millions and millions. Thus there is great irregularity in their diffusion as well as magnitude—in some places intensely crowded, in others the deep blackness of the sky, over which they are thinly scattered, irresistibly led to believe that in these regions the power of our telescopes fairly penetrates through the starry stratum, and beyond it. Sometimes we look through a sheet of stars nearly of the same size, of no great thickness compared with their distance from us, and not unfrequently there is a double stratum, one of large stars spread over another of very small ones.

The most southerly of the two streams of stars which form the Milky Way in this part of the firmament maintains an unbroken course of extreme brilliancy, containing some of the finest clusters of stars in the heavens. One round γ Sagittarii is an intense aggregate of stars, in some parts of which they are so crowded as to exceed enumeration; at a very moderate estimate Sir John Herschel thinks this group cannot contain fewer than a hundred thousand stars. Other two groups between the constellations of the Shield and Ophiuchus stand out like promontories of intense brilliancy in the dark space that separates the starry streams of the Milky Way.

The distance of the fixed stars is too great to admit of their exhibiting a sensible disc, but they must be spherical if gravitation pervades all space, as there is every reason to believe it does. With a powerful telescope the stars are like points of light: their occultations by the moon are therefore instantaneous. Their twinkling arises from sudden changes in the refractive power of the air, which would not be sensible if they had discs like planets. Thus nothing can be known of their distance from us or from one another by their apparent diameters. Although from the appearance of the stars no inference can be drawn as to their distance, yet among the multitudes in the heavens a few are found near enough to exhibit distinct parallactic motions arising from the revolution of the earth in its orbit, from whence their distance from the sun has been computed: α Centauri, the brightest star in the southern hemisphere, is a very remarkable instance. Professor Henderson at the Cape of Good Hope determined its parallax to be 1ʺ by a series of observations on its position at opposite periods of the year, that is, from opposite points in the earth’s orbit. The result was afterwards confirmed by Mr. Maclear, who found the amount to be 0ʺ·913. The difference between the two is wonderfully small, considering the many unavoidable sources of error in the determination of such minute quantities (N. 230).

Since no star in the northern hemisphere has so great an amount of parallax, an arc of 1ʺ is assumed as the parallactic unit. Now radius is to the sine of 1ʺ as 206,265 is to 1; hence, α Centauri is 206,265 times more distant from the sun than the sun is from the earth. Light flying at the rate of 192,000 miles in a second must take 3 years and 83 days to come to us from that star.

One or two tenths of a second becomes a very great error when the maximum amount of parallax is only 1ʺ, and on that account, with the exception of α Centauri, it has been found impracticable to determine the annual changes in the apparent motions of single stars affected by precession, nutation, aberration, and the variations of temperature of the instruments used in observing. However, as two stars in juxtaposition are equally affected by all of these; the difference in their motions is independent of them. Of two stars apparently in close approximation, one may be far behind the other in space. They may seem near to one another when viewed from the earth in one part of its orbit, but may separate widely when seen from the earth in another position, just as two terrestrial objects appear to be one when viewed in the same straight line, but separate as the observer changes his position. In this case the stars would not have real, but only apparent motion. One of them would seem to oscillate annually to and fro in a straight line on each side of the other, a motion that could not be mistaken for that of a binary system where one star describes an ellipse about the other; or if the edge of the orbit be turned towards the earth, where the oscillations require years for their accomplishment. The only circumstances that can affect the stars unequally, and which must be eliminated, are the proper motion of the stars in space, and specific aberration, a very minute quantity arising from peculiarities in the star’s light. This method of finding the distances of the fixed stars was proposed by Galileo and attempted by Dr. Long without success. Sir William Herschel afterwards applied it to some of the binary groups; and although he did not find the thing he sought for, it led to the discovery of the orbital motions of the double stars.

M. Struve was the first to apply this method, and that in a very difficult case. He perceived that a very small star is close to α Lyræ, and by a series of most accurate differential measurements from 1835 to 1838 he found that α Lyræ has a parallax of 0ʺ·261, which was afterwards corroborated by the observations of M. Peters; hence α Lyræ is 789,600 times more distant from the sun than the earth is.

It was natural to suppose that in general the large stars are nearer to the earth than the small ones; but there is now reason to believe that some stars, though by no means brilliant, are nearer to us than others which shine with greater splendour. This is inferred from the comparative velocity of their proper motions; all the stars have a general motion of translation, which tends ultimately to mix those of the different constellations; but none that we know of moves so rapidly as 61 Cygni, and on that account it was reckoned to be nearer to us than any other, for an object seems to move more quickly the nearer it is. Now M. Bessel saw that two minute and probably very remote stars are very near 61 Cygni, their directions from that star being at right angles to one another; so that, during the revolution of the earth, one of these distances was a maximum and the other a minimum alternately every three months. This alternation, although it indicated a parallax or difference of parallaxes of only 0ʺ·348, was maintained with such perfect regularity every three months, that it leaves not a doubt of its accuracy, which was afterwards confirmed by the observations of M. Peters at Polkova. It follows from that small parallax that 61 Cygni must be 592,700 times farther from the earth than the sun is—a distance that light would not pass over in less than nine years and three months.

Mr. Henderson found the parallax of Sirius, the brightest of all the stars, to be only 0ʺ·230; it is consequently more distant than 61 Cygni, though the latter is but of the 6th magnitude.

M. Argelander has calculated that the apparent magnitude of the stars depends upon their distance. Supposing them all to be of the same size, the smallest visible in Sir William Herschel’s 20 feet reflecting telescope, namely those of the 17th magnitude, would be 228 times farther off than those of the first magnitude; and M. Peters of Polkova from the annual parallax of thirty-five, seven of which are now very accurately determined, has ascertained the distance of the nearest of them to be such, that light flying at the rate of 95 millions of miles in a second would take 15 years and a half to come from them to the earth, and that a star of the 17th magnitude might be extinguished for 3541 years before we should be aware of it. (N. 231.)

The great gulfs that separate the stars from the sun, and probably from one another, no doubt maintain the stability of the stellar system, in the same manner that in the solar system the distances of the planets from the sun and the satellites from their primaries are so arranged as to preserve their mutual disturbances within due limits. The stars supposed to be nearest the sun are probably in a great zone which crosses the Milky Way between η Argûs and α Crucis. It comprises the bright stars of the constellations Orion, Canis Major, the Southern Cross, Centaur, Lupus, and Scorpio. The axis of the zone is inclined at an angle of 20° to the medial line, or circle, passing through the centre of the Milky Way.

A very great number of stars undergo periodical changes of lustre, varying in some cases from complete extinction to their original brilliancy, strongly suggesting the idea that they are temporarily obscured, and sometimes completely hid, by opaque bodies revolving round them in regular periodic times, as the planets do about the sun.

The star Mira, or ω Ceti, which was first noticed to be periodical by Fabricius, in 1596, appears about twelve times in eleven years, or in periods of 331^d 8^h 4^m 16^s; it remains at its greatest brightness about a fortnight, being then on some occasions equal to a large star of the second magnitude; then it decreases during about three months, till it becomes completely invisible to the naked eye, in which state it remains about five months; after that it continues increasing during the remainder of its period. Such is the general course of its changes; but it does not always return to the same degree of brightness, nor increase and diminish by the same gradations, neither are the successive intervals of its maxima equal. From the observations and investigations of M. Argelander, the mean period given is subject to fluctuation, embracing 88 such periods, and having the effect of gradually lengthening and shortening alternately those intervals to the extent of 25 days one way and the other. The irregularities in the degree of brightness attained at the maximum are probably also periodical. For four years previous to 1676 it did not appear at all; and on October 5, 1839, it exceeded α Ceti, and equalled β Aurigæ, in lustre. These irregularities may be occasioned by periodical perturbations among opaque bodies revolving about the star. Algol, or β Persei, is another very remarkable instance of a variable star. It has the size of a star of the second magnitude for two days and thirteen and a half hours, and then suddenly begins to diminish in splendour, till, in about three hours and a half, it is reduced to the size of a star of the fourth magnitude; it then begins again to increase, and in three hours and a half more regains its brightness, going through all these vicissitudes in 2^d 20^h 48^m 54^s·7. Sir John Herschel and Mr. Goodricke, by whom the variable nature of this star was discovered in 1782, considered this to be a case strongly indicative of the revolution of an opaque body, which, coming between us and Algol, cuts off a large portion of the light. This star has been constantly observed, and the more recent observations, compared with the ancient ones, indicated a diminution in the periodic time. It is even proved that this decrease is not uniformly progressive, but is actually proceeding with accelerated rapidity, which, however, will probably not continue, but will by degrees relax, and then be changed into increase, according to the laws of periodicity, which, as well as their causes, remain to be discovered. The first minimum of this star, in 1844, happened on January 3rd, at 4^h 14^m Greenwich time. γ Hydræ also vanishes and reappears every 494 days. β Lyræ was discovered to be variable, in 1784, by Mr. Goodricke, and its period was ascertained by Argelander to be 12^d 21^h 53^m 10^s, in which time a double maximum and minimum takes place, the two maxima being nearly equal, but the two minima unequal; besides these semi-periods, there is a slow aberration of period, which appears to be periodical itself: from its discovery to 1840 the time was continually lengthening, but more and more slowly, till, in 1840, it ceased to increase, and has since been slowly on the decrease.

The stars δ Cephei and η Aquilæ, or Antinoi, were discovered to be variable in 1784; their respective periods, being 5^d 8^h 47^m 39^s and 7^d 4^h 13^m 53^s, have since been accurately determined. Besides these, the variations of between 30 and 40 have been approximately ascertained, and a great many more among the smaller stars have been discovered to be variable by Mr. Hind, who has remarked that many of those stars which continue visible at their minimum appear hazy and indistinct, as though some cloudy or nebulous medium intervened. Some of the variable stars are red, and others present successive changes through blue, yellow, and red. When the brightness is increasing the star has a blueish tinge, when it is past its maximum lustre it assumes a yellow tint, and while on its decrease it becomes ruddy with flashes of bright red light. These changes are very marked in a small star near the star 77, at the extremity of the south wing of Virgo.

Sir John Herschel, after having described the glory of the starry heavens, asks, “For what purpose are we to suppose such magnificent bodies scattered through the abyss of space? Surely not to illuminate _our_ nights, which an additional moon of the thousandth part the size of our own would do much better, nor to sparkle as a pageant void of meaning and reality, and bewilder us with vain conjectures. Useful, it is true, they are to man as points of exact and permanent reference; but he must have studied astronomy to little purpose who can suppose man to be the only object of his Creator’s care, or who does not see in the vast and wonderful apparatus around us provision for other races of animated beings. The planets, we have seen, derive their light from the sun, but that cannot be the case with the stars. These doubtless then are themselves suns, and may perhaps, each in its sphere, be the presiding centre round which other planets or bodies, of which we can form no conception from any analogy offered by our own system, may be circulating.”

Another circumstance shows how probable it is that dark bodies are revolving among the stars. The proper motion of Sirius is very irregular—sometimes it is rapid, and at other times slow; the cause is ascribed by MM. Bessel and Peters to a dark companion which revolves with Sirius about their common centre of gravity, and by its attraction disturbs the equable motion of the star.

Sometimes stars have all at once appeared, shone with a bright light, and vanished. Several instances of these temporary stars are on record. A remarkable one occurred in the year 125, which is said to have induced Hipparchus to form the first catalogue of stars. Another star appeared suddenly near α Aquilæ in the year 389, which vanished after remaining for three weeks as bright as Venus. On the 10th of October, 1604, a brilliant star burst forth in the constellation of Serpentarius, which continued visible for a year; and on the 11th of November, 1572, a star all at once shone forth in Cassiopeia, which rapidly increased in brightness till it surpassed that of Jupiter so much as to be visible at midday. It began to decrease in December of the same year, and, in March, 1574, it had entirely disappeared, having exhibited a variety of tints. It is suspected, however, that this star is periodically variable and identical with stars which appeared in the years 945 and 1264. A more recent case occurred in the year 1670, when a new star was discovered in the head of the Swan, which, after becoming invisible, reappeared, and, having undergone many variations in light, vanished after two years, and has never since been seen. On the 28th of April, 1848, Mr. Hind discovered a star of the 5th magnitude in the constellation Ophiuchus, which was very conspicuous to the naked eye, and where he was certain no star even so bright as the 9th magnitude had ever existed, nor was there any record of such a star. From the time of its discovery it continued to diminish till it became extinct. Its colour was ruddy, and was thought to undergo remarkable changes, probably an effect of its low position, as its polar distance was 102° 39ʹ 14ʺ.

Sir John Herschel discovered very singular variations in the star η of the constellation Argo. It is surrounded by a wonderful nebula, and between the years 1677 and 1826 it varied twice from the 4th to the 2nd magnitude; but in the beginning of 1838 it suddenly increased in lustre, so as to be nearly as bright as α Centauri. Thence it diminished, but not below the first magnitude till April 1843, when it had again increased, so as to surpass Canopus, and nearly equal Sirius in splendour. With regard to this singular phenomenon, Sir John Herschel observes, that “Temporary stars heretofore recorded have all become totally extinct. Variable stars, as far as they have been carefully attended to, have exhibited periodical and regular alternations (in some degree at least) of splendour and comparative obscurity; but here we have a star fitfully variable to an astonishing extent, and whose fluctuations are spread over centuries, apparently in no settled period, and in no regular progression. What origin can we ascribe to these sudden flashes and relapses? What conclusions are we to draw as to the comfort or habitability of a system depending for its supply of light and heat on so variable a source? Its future career will be a subject of high physical interest. To this account I will only add, that in the beginning of 1838 the brightness of this star was so great as materially to interfere with the observations of that part of the nebula surrounding it.” Sir John has also discovered that α Orionis is variable, a circumstance the more remarkable as it is one of the conspicuous stars of our hemisphere, and yet its changes had never been remarked. The inferences Sir John draws from the phenomena of variable stars are too interesting not to be given in his own words. “A periodic change existing to so great an extent in so large and brilliant a star as α Orionis cannot fail to awaken attention to the subject, and to revive the consideration of those speculations respecting the possibility of a change in the lustre of our sun itself, which were first put forth by my father. If there be really a community of nature between the sun and the fixed stars, every proof that we obtain of the extensive prevalence of such periodical changes in those remote bodies adds to the probability of finding something of the kind nearer home. If our sun were ever intrinsically much brighter than at present, the mean temperature of the surface of our globe would of course be proportionally greater. I speak now not of periodical, but secular changes. But the argument is complicated with the consideration of the possible imperfect transparency of space, which may be due to material non-luminous particles, diffused irregularly in patches analogous to nebulæ, but of great extent—to cosmical clouds, in short, of whose existence we have, I think, some indication in the singular and apparently capricious phenomena of temporary stars, and perhaps in the recent extraordinary increase, and hardly less sudden diminution, of η Argûs.” Mr. Hind has come to the same conclusion with Goodricke and Sir John Herschel, that the changes in the variable stars are owing to opaque bodies revolving round them; indeed there are strong reasons to believe that there are solar systems analogous to our own in the remote regions of space. Our sun requires nine times the period of Algol to perform a revolution on its axis, while, on the other hand, the periodic time of an opaque revolving body, sufficiently large to produce a similar temporary obscuration of the sun seen from a fixed star, would be less than fourteen hours.

It is possible that the decrease of light in some of the variable stars may arise from large spots on their surface, like those occasionally seen in the radiant fluid masses on the surface of the sun. One of these spots which was measured by Sir John Herschel on the 20th of March, 1836, with its penumbra, occupied an area of 3780 millions of square miles; and the black central part of a spot that appeared on the 25th of May following would have allowed the globe of the earth to drop through it, leaving a thousand miles clear of contact all around this tremendous abyss.

All the variable stars on record of which the places are distinctly indicated have occurred without exception in, or close upon, the borders of the Milky Way, and that only within the following semicircle, the preceding having offered no example of the kind.

Many stars have actually disappeared from the heavens. 42 Virginis seems to be of the number, having been missed by Sir John Herschel on the 9th of May, 1828, and not again found, though he frequently had occasion to observe that part of the sky. Mr. Cooper, of the Markree Observatory, has given a list of fifty stars that are missing since the publication of his list of stars in 1847. Comparing the present state of the heavens with more ancient catalogues, a much greater number have disappeared.

Thousands of stars that seem to be only brilliant points of light, when carefully examined are found to be in reality systems of two or more suns, many of which are known to revolve about one another. These binary and multiple systems are very remote, requiring powerful telescopes to show the stars separately. They are divided into eight classes, according to the proximity of the two stars. The first class comprises only such as are less than 1ʺ of space apart; those of the second class are more apart than 1ʺ and less than 2ʺ, &c. &c. Sometimes the two stars are of equal magnitude, but more frequently a conspicuous star is accompanied by a smaller companion. In some cases the conspicuous star itself is double, as in ζ Cancri, ξ Scorpio, 11 Monocerotis, and 12 Lyncis, which are triple stars. Each of the two stars of ε Lyræ is a beautiful and close double star; so that which in a common telescope appears merely to be a double star, is found to be quadruple with a very excellent instrument. The multiple system of θ Orionis is one of the most remarkable objects in our hemisphere. To the naked eye and with an ordinary telescope it seems to be a single star, but it really consists of four brilliant stars forming a trapezium, and accompanied by two excessively minute and very close companions, to perceive _both_ of which is the severest test of a telescope.

The first catalogue of double stars in which their places and relative positions are given was accomplished by the talent and industry of Sir William Herschel, who made so many great discoveries, and with whom the idea of their combination in binary and multiple systems originated; and that important fact he established by the discovery of a revolving motion in 50 or 60, and by the determination of the revolution of one star about the other of Castor or α Geminorum, the largest and finest double star in the northern hemisphere. He even assigned the approximate periodic times of this and of several other binary systems. More than 100 stars are now known to be stellar systems. The positions of many hundreds were measured by Sir John Herschel and Sir James South; and the catalogue of the double stars in the northern hemisphere, which have been micrometrically measured, has been increased to more than 6000 by MM. Bessel, Struve, and British astronomers.

Extensive catalogues of double stars in the southern hemisphere have been published by the astronomers in our colonial establishments. To these Sir John Herschel added 1081 during his residence at the Cape of Good Hope: the angles of position and distances of the stars from one another he measured, and found that many of them have very rapid orbital motions. The elliptical elements of the orbits and periodic times of fifteen have been determined by the most eminent astronomers with wonderful accuracy, considering the enormous distances and the extreme delicacy and difficulty of the subject. M. Savary has the merit of having first determined the elements of the orbit of a double star from observation. The difficulty of doing so is great, because the nearest fixed star is 211,000 times farther from the sun than the earth is, and the orbit itself is only visible with the best telescopes; consequently a very small error in observation occasions an enormous error in the determination of quantities at that distance.

In observing the relative position of the stars of a binary system, the distance between them, and also the angle of position, that is, the angle which the meridian, or a parallel to the equator, makes with the line joining the two stars, are measured. The different values of the angle of position show whether the revolving star moves from east to west, or the contrary; whether the motion be uniform or variable, and at what points it is greatest or least. The measures of the distances show whether the two stars approach or recede from one another. From these the form and nature of the orbit are determined. Were observations 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.

γ 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 γ 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 η Coronæ, ζ Cancri, and ξ Ursæ 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. ζ Herculis, whose periodic time is only about 30-1/4 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 α 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 15ʺ·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 0ʺ·348, while the radius of the star’s orbit as seen from the earth is 15ʺ·5; hence the radius of the star’s orbit is to that of the earth’s orbit as 15ʺ·5 to 0ʺ·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.

Of all the double stars α 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 α Centauri to be 77 years, and the distance between the two to be 17ʺ·5; and since the decrease is half a second annually, the distance or radius vector of the revolving star was 12ʺ·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 13-1/2 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 versâ_. 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 ζ 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.

It appears from the calculations of Mr. Dunlop that ς Eridani accomplishes a revolution in little more than 30 years. The 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 ς Eridani, or of ξ Ursæ 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 α Lyræ, which apparently consists of two stars, one of the first, the other of the eleventh magnitude. Aldebaran, α Aquilæ, 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 α 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 γ Andromedæ, which is a triple star, the small one, which appears green, being closely double. ι 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 the earth’s. There are no defective rays in the white light of Sirius, Procyon, and others; but Sir David Brewster found in the spectrum of the orange-coloured light of ζ Herculis a defective band in the red space, and two or more in the blue; consequently, the orange colour of the star is owing to a want of blue rays; for flames in which certain rays are wanting take the colour of the predominating rays. If the black rays in the solar spectrum were owing to the absorption of the sun’s atmosphere, the light from the margin of his disc, having to pass through a greater thickness of it, would exhibit deeper lines than that which comes from his centre; but, as no difference is perceptible, it may be inferred that the analogous bands in the light of the coloured stars are not due to the absorption of their atmospheres, but that they arise from the different kinds of combustion by which these bodies are lighted up.

All the ordinary methods fail for finding the parallax when the distances of the stars are very great. An angle even of one or two seconds, viewed in the focus of our largest telescopes, does not equal the thickness of a spider’s thread, which makes it impossible to measure such minute quantities with any degree of accuracy. In some cases, however, the binary systems of stars furnish a method of estimating an angle of even the tenth of a second, which is thirty times more accurate than by any other means. From them the actual distances of some of the more remote stars will ultimately be known.

Suppose that one star revolves round another in an orbit which is so obliquely seen from the earth as to look like an ellipse in a horizontal position, then it is clear that one-half of the orbit will be nearer to us than the other half. Now, in consequence of the time which light takes to travel, we always see the satellite star in a place which it has already left. Hence, when that star sets out from the point of its orbit which is nearest to us, its light will take more and more time to come to us in proportion as the star moves round to the most distant point in its orbit. On that account the star will appear to us to take more time in moving through that half of its orbit than it really does. Exactly the contrary takes place on the other half; for the light will take less and less time to arrive at the earth in proportion as the star approaches nearer to us; and therefore it will seem to move through this half of its orbit in less time than it really does. This circumstance furnishes the means of finding the absolute breadth of the orbit in miles, and from that the true distance of the star from the earth. For, since the greatest and least distances of the satellite star from the earth differ by the breadth of its orbit, the time which the star takes to move from the nearest to the remotest point of its orbit is greater than it ought to be by the whole time its light takes to cross the orbit, and the period of moving through the other half is exactly as much less. Hence the difference between the observed times of these two semi-revolutions of the star is equal to twice the time that its light employs to cross its orbit; and, as we know the velocity of light, the diameter of the orbit may be found in miles, and from that its whole dimensions; for the position of the orbit with regard to us is known by observation, as well as the place, inclination, and apparent magnitude of its major axis, or, which is the same thing, the angle under which it is seen from the earth. Since, then, three things are known in this great triangle, namely, the base or major axis of the orbit in miles, the angle opposite to it at the earth, and the angle it makes with the visual ray, the distance of the satellite star from the earth may be found by the most simple of calculations. The merit of having first proposed this very ingenious method of finding the distance of the stars is due to M. Savary; but, unfortunately, it is not of general application, as it depends upon the position of the orbit, and a long time must elapse before observation can furnish data, since the shortest period of any revolving star that we know of is 30 years. Still the distances of a vast number of stars may ultimately be made out in this way; and, as one important discovery almost always leads to another, their masses may thus be weighed against that of the earth or sun.