CHAPTER IV.

BINARY STARS.

Double and multiple stars may be either optical or real. Optical double stars are those in which the component stars are merely apparently close together, owing to their being seen in nearly the same direction in space. Two stars may _seem_ to be close together, while, in reality, one of them may be placed at an immense distance behind the other. Just as two lighthouses at sea may, on a dark night, appear close together when viewed from a certain point, whereas they may be really miles apart. In the case of double stars it is, of course, always difficult to determine whether the apparent closeness of the stars is real or merely optical. But when, from a long series of observations of their relative position, we find that one is apparently moving round the other, we know that the stars must be comparatively close, and linked together by some physical bond of union. These most interesting objects are known to astronomers as binary or revolving double stars. The probable existence of such objects was predicted from abstract reasoning by Mitchell in the eighteenth century; but the discovery of their actual existence was made by Sir William Herschel, while engaged on an attempt to determine the distance of some of the double stars from the earth. “Instead of finding, as he expected, that annual fluctuation to and fro of one component of a double star with respect to the other—that alternate 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 cases, 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 a real motion of the stars themselves,” and measurements made during the subsequent 25 years fully proved the truth of the illustrious astronomer’s discovery. It was found that in many double stars an orbital motion round each other was evident after a number of years of careful observation of their relative positions. Unlike the planetary orbits, which are nearly circular, at least those of the larger planets of the solar system, it was found that the orbits of these double stars differ, in many cases, widely from the circular form, in some cases, indeed, approaching in shape more the orbit of a comet than a planet.

The binary stars are among the most interesting objects in the heavens. The number now known probably amounts to nearly one thousand. In most of them, however, the motion is very slow, and in only about seventy cases has the change of position, since their discovery, been sufficient to enable an orbit to be computed. In most cases the plane of the real orbit, or ellipse, described by the companion round the principal star, is inclined to the line of sight. We therefore see the orbit foreshortened into a more elongated ellipse.

The relation of the apparent ellipse—or the ellipse we see described by one star round the other—to the real ellipse will be easily understood by the following illustration. Suppose a cylinder or rod of an elliptical, not circular, section to be cut across obliquely to its axis. This oblique section will represent the _real_ orbit of a binary star, and the section at right angles to the axis, the _apparent_ orbit. The angle between these two sections will represent the inclination of the real orbit to the plane of projection, or background of the sky. In the apparent orbit, the primary star, which is assumed to be situated in one of the foci of the real ellipse, does not lie in the focus of the apparent ellipse, and from its observed position in this latter ellipse we can deduce, mathematically, the particular angle at which the oblique section must be made to agree with the observed place of the primary star, and other details respecting the real ellipse.

Savary, in 1830, was the first astronomer who attempted to compute the orbit of a binary star, namely, the star Xi Ursæ Majoris. This remarkable pair was discovered by Sir William Herschel in 1780, and as the period of revolution is about 61 years, a considerable portion of the ellipse had been described in 1830, when it was attacked by Savary. Since that year, orbits have been computed for a number of binary stars by several computers, among whom may be mentioned Sir R. Ball, Behrmann, Casey, Celoria, Doberck, Dunér, Elkin, Fritsche, Glasenapp, Sir J. Herschel, Hind, Jacob, Mädler, Mann, Schur, See, Thiele, Villarceau, and the present writer. The computation of a double star orbit is a matter of considerable trouble and difficulty, and cannot be described here. An account of the principal results arrived at by astronomers in this interesting branch of sidereal astronomy may, however, prove of interest to the general reader.

We will first consider the binary stars with short periods of revolution, which are, of course, the most interesting, and those whose orbits can be computed with greater accuracy than binaries having periods of considerable length. The binary star with the shortest period known at present seems to be the fourth magnitude star Kappa Pegasi. It was discovered as a wide double star by Sir William Herschel in 1786, the companion star being of the ninth magnitude. In August, 1880, Mr. Burnham, the famous American double star observer, examining the star with the 18½ inch refractor of the Dearborn Observatory, found the brighter star to be a very close double, with a distance between the components of only a quarter of a second of arc. A few years’ observations showed that this pair were in rapid motion round each other, and from measures up to the year 1892, Burnham finds a period of 11·37 years. A later determination by Dr. See makes the period 11·42 years, so that we may conclude that the orbit is now pretty accurately determined. The plane of the orbit is highly inclined to the line of sight. Dr. See makes the inclination 81°.

Another binary star, with a period of about the same length, is Delta Equulei, which was discovered to be a close double by Otto Struve in 1851. As in the case of Kappa Pegasi, the orbit is highly inclined to the line of sight. In the year 1887, Wrublewsky, the Russian computer, found a period of about 11½ years, with an orbit nearly circular. A new orbit was published in 1895 by Dr. See, who finds a period of 11·45 years, and an orbit agreeing fairly well with that of Wrublewsky, the orbit differing little from the circular form, and inclined to the line of sight at the high angle of 79 degrees. Burnham found only a “slight elongation” in the star with the great 36-inch telescope of the Lick Observatory in July, 1889. The distance between the components does not at any time exceed half a second of arc, so that it is always beyond the reach of all but the largest telescopes.

Next in order of shortness of period comes the southern binary star Zeta Sagittarii, for which an orbit was first computed in the year 1886 by the present writer, who found a period of 18·69 years. The orbit was re-computed in 1893, with the aid of recent measures by Mr. J. W. Froley, who finds a period of 17·71 years. The orbit of this star will, I think, require still further revision, but the period of about 18 years is probably not far from the truth.

Another remarkably rapid binary star is 85 Pegasi, for which Schaeberle computed a period of 22·3 years, but a later orbit by Prof. Glasenapp makes the period 17½ years, and Burnham thinks it will certainly be less than 20 years. Dr. See, however, finds a period of 24 years. The primary star is about the sixth magnitude, and the companion only the eleventh, a difference of five magnitudes, which implies that the larger star is one hundred times brighter than the companion.

Next in order of rapidity of motion we have the southern binary star 9 Argûs. For this pair, Burnham finds a period of 23·3 years, and Dr. See 22 years, the other elements of the orbit being also in close agreement. In this case also the orbit plane is highly inclined to the line of sight.

The star 42 Comæ Berenices has a period of about 25¾ years, according to Otto Struve. The orbit is remarkable from the fact that its plane passes through or nearly through the earth, and is, therefore, projected into a straight line, the companion star oscillating backwards and forwards on each side of its primary. I find that the plane of the orbit is at right angles to the general plane of the Milky Way.

The star Beta Delphini—the most southern of the four stars in the “Dolphin’s Rhomb”—is also a fast-moving binary, discovered by Burnham in 1873, for which periods have been computed of 22·97 years by Glasenapp, 26·07 years by Dubjago, 27·66 years by Dr. See, and 30·91 years by the present writer. Burnham thinks the period will prove to be about 28 years. The spectrum of the light of Beta Delphini is similar to that of our sun, so that the two bodies should be comparable in intrinsic brilliancy. From my orbit of the pair, the “hypothetical parallax” is 0·052″—that is, this is the parallax the star would have on the supposition that the combined mass of its components is equal to the mass of the sun. Now, assuming the value of the sun’s stellar magnitude which I have recently computed (_Knowledge_, June, 1895)—namely, 27·15—I find that the sun, if placed at the distance indicated for Beta Delphini, would be reduced to a star of 5·84 magnitude. As the star was measured 3·74 at Harvard, we have a difference of 2·1 magnitude, denoting that the binary—if of the same mass as the sun—must be about seven times brighter. As the spectrum is of the same type, this seems improbable, and we must conclude that the star’s parallax is more than 0·052″.

Another remarkable binary star with a comparatively short period is Zeta Herculis. This pair have now performed three complete revolutions since their discovery in 1782 by Sir William Herschel. Several orbits have been computed, but Dr. See’s period of 35 years is probably the best The companion is now not far from its maximum distance (1½ seconds) from the primary star, and is within the reach of moderate-sized telescopes. The companion is, however, rather faint, being only 6½ magnitude, while the primary star is of the third. When at their nearest, some observers have spoken of an “occultation” of one star by the other, but no real occultation ever takes place, the components never approaching within half a second of arc. The companion merely disappears owing to its faintness in telescopes of moderate power. An occultation of one component of a binary star by the other cannot take place except—as in the case of 42 Comæ—when the plane of the orbit passes through the earth.

[Illustration:

FIG. 4.—_Apparent Orbit of Zeta Herculis._ (From “Worlds of Space.”) ]

In the case of the binary star, Eta Coronæ Borealis, it was, some forty years ago, uncertain whether its period was 43 or 66 years, but now that two complete revolutions have been performed since its discovery by Sir William Herschel in 1781, the question has been finally decided in favour of the shorter period. Numerous orbits have been computed, but these by Dr. Doberck and Dr. Dunér are probably the best. Those give a period of about 41½ years. The components are nearly equal in brightness, but at their present distance are not within the reach of small telescopes.

The brilliant star Sirius is also an interesting binary star. The companion, which is relatively very faint—about tenth magnitude,—was discovered by Alvan Clark in 1862. The existence of some such disturbing body was previously suspected by astronomers, owing to observed irregularities in the proper motion of Sirius. Several orbits, giving periods of about 50 years, have been computed. Some measures in recent years, however, seemed to show that this period was somewhat too short, but a period of about 58½ years, computed by the present writer in 1889, will probably prove too long. Some few years ago, Burnham found the companion an easy object with the 36-inch refractor of the Lick Observatory, but towards the end of the year 1890 it passed beyond the power of even this giant telescope. It will probably, however, emerge very soon now from the rays of its brilliant primary.[110] Burnham finds a period of about 52 years, but the German astronomer, Auwers, who has carefully investigated the observed irregularities in the proper motion of Sirius, adheres to a period of about 49½ years. The great brilliancy of Sirius, the brightest star in the heavens, naturally suggests a sun of great size. Recent investigations, however, do not favour this idea. Assuming a parallax of 0″·39 (about a mean of the results found by Elkin and Gill), Auwers finds the mass of the system to be about three times the mass of the sun, the mass of the companion being about equal to the sun’s mass. Placed at the distance of Sirius, the sun would, I find, be reduced to a star of about 1½ magnitude. As Sirius is about 1 magnitude brighter than the zero magnitude—that is, about 2 magnitudes brighter than a standard star of the first magnitude—it follows that it is about 2½ magnitudes, or about ten times brighter than the sun would be in the same position. Its spectrum is, however, of the first type, and the star is therefore not comparable with the sun in brilliancy. The above result would indicate that stars of the first or Sirian type are intrinsically brighter than our sun.

Sirius is about 11 magnitudes brighter than its faint companion. This makes the light of Sirius about 25,000 times the light of the small star. If, therefore, the two bodies were of the same intrinsic brilliancy, their diameters would be in the ratio of 158·5 to 1, and if of the same density, the mass of Sirius would be nearly five million times the mass of the companion! But, according to Auwers’ calculations, the companion’s mass is about one-half that of its primary. The two bodies must, therefore, be differently constituted, and, indeed, the companion must be nearly a dark body. It has been suggested that the companion may possibly shine by reflected light from Sirius; but this I have shown elsewhere to be quite impossible.[111] Even with a diameter equal to that of the sun, I find that with reflected light only it would be quite invisible in all parts of its orbit, even with the great Lick telescope. It must, therefore, shine with inherent light of its own, and it seems probable that it is a large body, cooling down and approaching the complete extinction of its light. If Sirius has any planets revolving round it—like those of our solar system—they must for ever remain invisible in our largest telescopes. This remark, of course, applies to all the fixed stars, single and double. They may possibly have attendant families of planets, like our sun, but if so, the fact can never be ascertained by direct observation. I find that the plane of the orbit of Sirius is at right angles to the general plane of the Milky Way.

[Illustration:

FIG. 5.—_Apparent Orbit of the Companion of Sirius._

(From “Old and New Astronomy.”) ]

The star Zeta Cancri is a well-known triple star, the close pair revolving in a period of about 60 years. Nearly two revolutions have now been completed since its discovery by Sir William Herschel in 1781. All three stars probably form a connected system, but the motion of the third star round the binary pair is very slow and irregular. The motion of this interesting system has recently been investigated by Professor Seeliger, and he comes to the conclusion that, to make the observations agree with calculation, it is necessary to assume that the third star is in reality a very close double, the components of which revolve round their centre of gravity in about 17½ years, and both round the known binary pair. If this be so, we have here a remarkable quadruple pair; but it must be added that all efforts with large telescopes to see the companion star double have failed, and that the existence of the fourth star rests only on theory. Burnham, in 1889, using a power of 1500, failed to see any other component.

Another interesting binary star is Xi Ursæ Majoris. As already stated, this was the first pair for which an orbit was computed. More than a complete revolution has now been performed since its discovery by Sir William Herschel in 1780. The period has, therefore, been well determined, and seems to be about 60 years. Although the components are not near their maximum distance at present, they are still within the reach of moderate telescopes, the distance being about 1¾ seconds, and the magnitudes of the components, not very unequal, about 4 and 5.

The bright southern star, Alpha Centauri, the nearest of all the fixed stars to the earth, so far as is known at present, is also a remarkable binary star. It seems to have been first noticed as a double star by Richaud in 1690. Several orbits have been computed, ranging from about 75 to 88½ years, but recent calculations by Mr. A. W. Roberts and Dr. See make the period about 81 years, which agrees closely with Dr. Elkin’s period of 80⅓ years. Combining Dr. Gill’s parallax of 0″·76 with Elkin’s elements, I find the sum of the masses nearly twice the mass of our sun, and the mean distance between the components about 23 times the earth’s distance from the sun, or somewhat greater than the distance between the sun and Uranus. Dr. Doberck finds a period of about 79 years, and assuming a parallax of 0″·75, he finds the mean distance between the components 24·6 times the earth’s distance from the sun; and he points out that if we suppose that their diameter does not differ much from that of our sun, each component “would appear from the other as a mere star to unaided vision, the distance being too great to show a disc.”[112] From a recent investigation of the proper motion and position of Alpha Centauri, Mr. A. W. Roberts finds that the masses of the components are nearly equal, and the combined mass equal to twice the mass of our sun, a conclusion in close agreement with the result found above from the orbit. According to Dr. Gill, the difference in brightness of the two components is 1·25 magnitude, and Professor Bailey makes their photometric magnitudes 0·50 and 1·75. As this difference would make the brighter component over three times brighter than the companion, it follows that its surface must be much brighter, and Mr. Roberts concludes that the companion has proceeded “some distance on the down track from a sun to an ordinary planet.” Assuming my value of the sun’s stellar magnitude (about 27), I find that the sun, if placed at the distance of Alpha Centauri, would appear of about the same brightness as the star does to us. As, according to Professor Pickering, the spectrum of Alpha Centauri is of the second or solar type, it would seem that in mass, brightness, and physical condition, the star closely resembles our sun.

We next come to another very interesting binary star, known to astronomers as 70 Ophiuchi. It is a very fine double star, the magnitudes of the components being about 4 and 6, and the colours yellow and orange. More than a complete revolution has now been described by the components since its discovery by Sir William Herschel in 1779. Numerous orbits have been computed with periods ranging from 73¾ to 98 years. An orbit computed by the present writer, in 1888, gave a period of 87·84 years, and this was confirmed in 1894 by Burnham, who found a period of 87·85 years. A subsequent investigation by Schur gives a period of 88·356 years. My orbit, combined with Krüger’s parallax of 0″·162, give for the combined mass of the components 2·777 times the mass of the sun, and the distance between them 27·777 times the earth’s distance from the sun, or somewhat less than the distance of Neptune from the sun. Schur has, however, recently found a parallax of 0″·286, which would reduce the mass of the system, and also the distance between the components. Recent observations show that the companion is now in advance of the theoretical position indicated by Schur’s orbit, and Dr. See thinks that the observed irregularities in the orbital motion of the pair indicate the existence of a third body, and that either the primary star or the companion, probably the latter, is a very close binary star. Careful search, however, for a third body, made with large telescopes, have failed to reveal its existence, and so the matter remains in suspense. Placed at the distance indicated by Krüger’s parallax, I find that our sun would be reduced to a star of about magnitude 3½, which shows that the sun and star are of about equal brightness. The spectrum is of the solar type, according to Vogel. I find that the plane of the orbit is at right angles to the plane of the Milky Way.

The star Gamma, in Corona Borealis, is a close and difficult binary star. Dr. Doberck finds a period of 95½ years, and Celoria about 85¼. As in the case of 42 Comæ, the plane of the orbit nearly passes through the earth, and the apparent orbit is, consequently, nearly a straight line. I find that the plane of the orbit is at right angles to the plane of the Milky Way.

The star Xi Scorpii is a remarkable triple star, like Zeta Cancri, the magnitudes of the components being about 4½, 5, and 7½. The components of the close pair have described a complete revolution since their discovery by Sir William Herschel in 1780. Dr. Doberck finds a period of about 96 years, and Schorr 105 years. The real orbit is nearly circular, but owing to its high inclination, about 70°, the apparent orbit is a very elongated ellipse. All three stars have a common proper motion through space, and, probably, form one system, but the motion of the third star is very slow, and its period of revolution must be several hundred years.

[Illustration:

APPARENT ORBIT OF 70 OPHIUCHI, COMPUTED BY J. E. GORE (1888).

(_Showing positions of companion star in different years._)

(From “The Scenery of the Heavens.”) ]

The star ο^2, or 40 Eridani, is another interesting object. It is a star of about 4½ magnitude, with a distant ninth magnitude companion, which is a double and binary star. It is sometimes stated that the bright star is the binary, but this is quite incorrect; the large star is single—at least, as far as is known at present. An orbit for the binary pair was computed, in 1886, by the present writer, who found a period of 139 years; but Burnham, using later observations, finds a period of 180 years. A physical connexion may possibly exist between the binary pair and the bright star, as both have the same common motion through space, but the angular motion, if any, is very slow. Professor Asaph Hall found a parallax of about one-fifth of a second of arc, and this, combined with Burnham’s orbit, gives the combined mass of the binary pair about two-thirds of the sun’s mass, a result which seems remarkable, for the sun, placed at the distance indicated by Hall’s parallax would, I find, shine as a star of about the third magnitude, or considerably brighter than the principal star of 40 Eridani. Owing to the faintness of the binary pair, the nature of its spectrum has not been determined. Computed by a well-known formula, its “relative brightness”—that is, its brightness compared with that of other binaries—is very small.

A very famous binary star is that known to astronomers as Gamma Virginis. Its history is a very interesting one. It lies close to the celestial equator, about one degree to the south and about fifteen degrees to the north-west of the bright star Spica (Alpha of the same constellation), with which it forms the stem of a Y-shaped figure, formed by the brightest stars of the constellation Virgo, or the Virgin, Gamma being at the junction of the two upper branches. The brightness of Gamma Virginis is a little greater than an average star of the third magnitude. Photometric measures made at Oxford and Harvard Observatories agree closely, and make its brightness about 2·7 magnitude—that is to say, rather nearer the third than the second magnitude. Variation of light has, however, been suspected in one or both components, and this question of light variation will be considered further on. The Persian astronomer, Al-Sûfi, in his description of the heavens, written in the tenth century, rates it of the third magnitude, and describes it as “the third of the stars of _al-auvâ_, which is a mansion of the moon,” the first and second stars of this “mansion” being Beta and Eta Virginis, the fourth star Delta, and the fifth Epsilon, these five stars forming the two upper branches of the Y-shaped figure above referred to. Gamma was called _Zawiyah-al-auvâ_, “the corner of the barkers!” perhaps from its position in the figure, which formed the thirteenth Lunar Mansion of the old astrologers. It was also called _Porrima_ and _Postvarta_ in the old calendars. These ancient names of the stars are curious, and their origin doubtful.

The fact that Gamma Virginis really consists of two stars very close together seems to have been discovered by the famous astronomer, Bradley, in 1718. He recorded the position of the components by stating that the line joining them was then exactly parallel to a line joining Alpha and Delta of the same constellation. This was, of course, only a rough method of measurement, and the position thus found by Bradley being probably more or less erroneous, has given much trouble to computers of the orbit described by the component stars round each other, or, rather, round their common centre of gravity. Bradley does not give the apparent distance between the component stars; but we may conclude from the orbit, which is now well determined, that they were then at nearly their greatest possible distance apart. It is curious that between Bradley’s time and 1794, the star was on several occasions occulted by the moon; but none of the observers refer to its duplicity. It was again measured by Cassini in 1720, by Tobias Mayer in 1756, and by Sir William Herschel in 1780. These measures showed that the distance between the components was steadily diminishing, and that the position angle of the two stars was also decreasing. This decrease in the position angle—measured from the north round by the east, south, and west, from 0 to 360°—shows that the apparent orbital motion is what is called retrograde, or in the direction of the hands of a clock, direct or “planetary motion” being in the opposite direction. The star was again measured by Sir John Herschel and South in the years 1822–38, by Struve in the same years, and by Dawes and other observers from 1831 to the present time. The recorded measures are very numerous, and have enabled computers to determine the orbit with considerable accuracy. The rapid decrease in the apparent distance from 1780–1834 indicated that the apparent orbit is very elongated, and that possibly the two stars might “close up” altogether, and appear as a single star even in telescopes of considerable power. This actually occurred in the year 1836, or, at least, the stars were then so close together that the most powerful telescopes of that day failed to show Gamma Virginis as anything but a single star. Of course, it would not have been beyond the reach of the giant telescopes of our day. From the year 1836 the pair began to open out again, and at present the distance is again approaching a maximum. It is now within the reach of small telescopes, and forms a fine telescopic object with a moderate-sized instrument.

The general character of the orbital motion may be described as follows:—In 1718, at the time of Bradley’s observation, the companion star was to the north-west of the primary star; it then gradually moved towards the west and south, and in 1836, when at its minimum distance, it was to the south-east. From that date it again turned towards the north, and at present it is north-west of the primary star, and not far from the position found by Bradley in 1718.

The first to attempt a calculation of the orbit described by this remarkable pair of suns was Sir John Herschel, who in the year 1831 found a period of about 513 years. In 1833, he re-calculated the orbit, and found nearly 629 years. We now know that both these periods are much too long; but the data then available were insufficient for the calculation of an accurate orbit. From these results Herschel predicted that “the latter end of the year 1833, or the beginning of the year 1834, will witness one of the most striking phenomena which sidereal astronomy has yet afforded, _viz._, the perihelion passage of one star round another, with the immense angular velocity of between 60° and 70° per annum, that is to say, of a degree in five days. As the two stars will then, however, be within little more than half a second of each other, and as they are both large and nearly equal, none but the very finest telescopes will have any chance of showing this magnificent phenomenon. The prospect, however, of witnessing a visible and measurable change in the state of an object so remote, in a time so short, may reasonably be expected to call into action the most powerful instrumental means which can be brought to bear on it.” This prediction was not verified until the year 1836, when the pair “closed up out of all telescopic reach,” except at the Dorpat Observatory, where a magnifying power of 848 still showed an elongation in the telescopic disc of the star. The orbit found by Sir John Herschel was a tolerably elongated ellipse, with its longer axis lying north-east and south-west. This was not quite correct, for we now know that this axis lies north-west and south-east, and that the apparent orbit is much more elongated than Sir John Herschel at first supposed. This was soon recognised by Herschel himself, and he came to the conclusion that he and other computers had been misled by Bradley’s observation in 1718. He then rejected this early, and evidently faulty, observation, and using the measures up to 1845, he found a period of about 182 years, which we now know to be near the truth. The orbit was also computed by the famous German astronomer, Mädler, who found periods of 145, 157, and 169 years; by Hind, 141 years; by Henderson, 143 years; by Jacob, 133½, 157½ and 171 years; by Adams, 174 years; by Flammarion, 175 years; and by Admiral Smyth, 148 and 178 years. All these periods, we now know, are too small. Fletcher found 184½ years, and Thiele 185 years. Two orbits were computed by Dr. Doberck, in recent years, with periods of 180½ and 179½ years; but very recently (1895) the orbit has been re-computed by Dr. See, and he finds a period of 194 years. A comparison of the observed and computed positions shows, he thinks, that his elements are the most exact yet determined for any binary star.

The apparent orbit of the pair is a very elongated ellipse, and as Admiral Smyth said, “more like a comet’s than a planet’s.” The real ellipse has a very high eccentricity, nearly 0·9—indeed, the greatest of all the known binary stars, and not much less than that of Halley’s comet

As I said above, the variability of the light of one or both components of Gamma Virginis has been strongly suspected. So far back as 1851 and 1852, O. Struve paid particular attention to this point. His observations in these years show that sometimes the component stars were exactly equal in brilliancy, and sometimes the southern star—the one generally taken as the primary—was from 0·2 to 0·7 magnitude brighter than the other. There seems to be little doubt that some variation really takes place in the relative brightness of the pair. This is clearly indicated by the measures of position angle. For example, in the year 1886, Professor Hall recorded the position as 154·9, evidently measuring from the northern star as the brightest of the two; while, in 1887, Schiaparelli gives 334°·2—or about 180° more—thus indicating that he considered the _southern_ star as the primary, or brighter, of the pair. Burnham found 153°·4 in 1889, and Dr. See 332°·50 in 1891. This is also shown by earlier measures, for Otto Struve found the southern star half a magnitude brighter than the other on April 3, 1852, while on April 29 of the same year he found them “perfectly equal.” He thought the variation was about 0·7 of a magnitude, but that the climate of Poulkova, where he observed, was not suitable for such observations. This variation is very interesting, and the question should be thoroughly investigated with a good telescope.

As the distance of Gamma Virginis from the earth has not been determined, it is not possible to calculate the actual dimensions of the orbit and the mass of the system. If we assume that the combined mass of the components is equal to the sun’s mass, I find from Dr. See’s orbit that the “hypothetical parallax” would be 0·119″, implying a distance of 1,733,319 times the sun’s distance from the earth. If, however, we suppose that the mass of each of the components is equal to the sun’s mass, or the mass of the system double that of the sun—perhaps a more probable supposition—I find that the parallax would be about one-tenth of a second, denoting a distance of 2,062,650 times the sun’s distance from the earth. Placed at this last distance, the sun would, I find, be reduced to a star of about 4½ magnitude, or about 1¾ magnitudes fainter than Gamma Virginis appears to us. This difference implies that, supposing each of the component stars of the binary to have a mass equal to the sun’s mass, their combined light is about five times greater than the sun would emit if placed at the same distance, and as the components are nearly equal in brightness, each of them would be 2½ times brighter than the sun. According to Vogel, the star’s light gives a spectrum of the first or Sirian type, but according to the Draper “Catalogue of Stellar Spectra,” the spectrum is of the solar type. If the spectrum is of the first type, its brilliancy is easily explained; for, as I have shown elsewhere, the Sirian stars, are intrinsically much brighter in proportion to their mass than those of the solar type. But if its spectrum is of the solar type, it is not so easy to explain its brilliancy. Computing by a well-known formula, I find its relative brightness is nearly five times greater than that of Xi Ursæ Majoris, the spectrum of which is of the solar type. If, to account for its brilliancy, we assume that the star is nearer to the earth than the parallax assumed above would imply, then the mass of the system must be less than the mass of our sun. As we have seen above, doubling the supposed mass increased the distance; so, on the other hand, if we diminish the distance, we must diminish the mass also. Thus, if we reduce the distance to one-half, we must reduce the mass to one-eighth of the sun’s mass. A distance of one-third would give a mass of ¹⁄₂₇th, and a distance of one-fourth would imply a mass only ¹⁄₆₄th of the sun’s mass. To reduce the sun to the same brightness as Gamma Virginis, it should be removed to a distance indicated by a parallax of one-tenth of a second multiplied by the square root of five, or 0·223″. If, however, the star’s parallax were so much as this, it is probable that it would have been detected and measured long ago. In the case of the binary star Castor, I find from the orbit and a small parallax found by Johnson (about one-fifth of a second) that its mass is only ¹⁄₁₉th of the sun’s mass, but in this case the spectrum is of the Sirian type, and stars of this type are very bright in proportion to their mass. The colours of the components of Gamma Virginis, which are very similar to those of Castor—white or pale yellow—would suggest that they may belong to the same type.

Another interesting binary star is Eta Cassiopeiæ. The components are about 4 and 7½ magnitude, and the pair have described a considerable portion of their orbit since its discovery in 1779 by Sir William Herschel, the distance diminishing from about 11 seconds to 4¾. Periods ranging from 149 to 222½ years have been found by different computers. The most recent computation makes it about 196 years. Assuming a parallax of 0·154″ found by Struve, the mass of the system will be from 5¾ to 10¾ times the mass of the sun, according to the length of the period we assume. A much larger parallax of 0″·3743 was, however, found by Schweizer and Socoloff, which would considerably reduce the mass, and recently a still larger parallax of 0″·465 has been found by photography, which, with Grüber’s elements of the orbit, would reduce the mass of the system to ⅙th of that of the sun.

The bright star Gamma Leonis, situated in the well-known “Sickle in Leo,” is also a binary star, but only a small portion of the orbit has been described since its discovery by Sir William Herschel in 1782. Dr. Doberck finds a period of 407 years. It is remarkable for its very high “relative brightness,” which is curious, as its spectrum is of the solar type. This pair forms a fine object for a small telescope.

The star known as 12 Lyncis is a triple star, the components being 5, 6, and 7½ magnitude. The close pair form a binary system, for which an orbit has been computed by the present writer, who finds a period of about 486 years. Sir John Herschel predicted in 1823 that the angular motion of the pair would “bring the three stars into a straight line in 57 years.” This prediction was fulfilled in 1887, when measures by Tarrant showed that the stars were then exactly in a straight line.

[Illustration:

FIG. 7.—_Triple Stars._

(From “Scenery of the Heavens.”) ]

The bright star Castor is a famous double star, and has been known since the year 1718, when it was observed by Bradley and Pond. It was also observed by Maskelyne in 1759, and frequently by Sir William Herschel from 1799 to 1803. Numerous orbits have been computed, with periods ranging from 199 years by Mädler, and 1,001 years by Doberck. Wilson found a period of about 983 years, and Thiele about 997 years, so that the longest period would seem to be nearest the truth. According to a somewhat doubtful parallax found by Johnson, the distance of Castor from the earth is about double that of Sirius. With this distance, and Doberck’s elements of the orbit, I find that the mass of the system of Castor is only ¹⁄₁₉th of the sun’s mass, a result which would imply that the components are masses of glowing gas! The spectrum of Sirius is of the first, or Sirian, type, another example of the great brilliancy of stars of this type. Quite recently (1896), Dr. Bélopolsky has found, with the spectroscope, that the brighter component is a close binary star with a dark companion, like Algol. The period of revolution is about 3 days, and the relative orbital velocity about 20¾ miles a second. Dr. Bélopolsky’s observations show that the system is receding from the earth at the rate of about 4½ miles per second. Assuming the bright and dark companion to be of equal mass, and hence the absolute orbital velocity of each one half the relative velocity found by Bélopolsky, I find that, if the orbit is circular, the distance between the components is about 85,400 miles, or slightly less than the sun’s diameter, and their combined mass about ¹⁄₈₇th of the sun’s mass. This result would imply a still smaller mass for the whole system of Castor than that found from the orbit of the two bright components, but tends strongly to confirm the opinion already expressed, that the components of this remarkable system are merely masses of glowing gas. Assuming that all three components are of equal mass, the combined mass of the system would be ¹⁄₅₈th of the sun’s mass. From this result we can easily compute the stars’ parallax, which, from Dr. Doberck’s orbit, I find to be 0″·2873, a quantity which might be measured by the photographic method.

With reference to the colours of the components of binary stars, the following relation between colour and relative brightness has been established[113]:—

(1.) When the magnitudes of the components are equal, or approaching equality, the colours are generally the same, or similar.

(2.) When the magnitudes of the components differ considerably, there is also a considerable difference in colour.

A new class of binary stars has been discovered within the last few years by means of the spectroscope. These have been called “spectroscopic binaries,” and the brighter component of Castor, referred to above, is an example of the class. They are supposed to consist of two component stars, so close together that the highest powers of the largest telescopes fail to show them as anything but single stars. Indeed, the velocities indicated by the spectroscope show that they must be so close that the components must for ever remain invisible by the most powerful telescopes which could ever be constructed by man. In some of these remarkable objects, the doubling of the spectral lines indicates that the components are both bright bodies, but in others, as in Algol, the lines are merely shifted from their normal position, not doubled, thus denoting that one of the components is a dark body. In either case, the motion in the line of sight can be measured by the spectroscope, and we can, therefore, calculate the actual dimensions of the system in miles, and thence its mass in terms of the sun’s mass, although the star’s distance from the earth remains unknown. Judging, however, from the brightness of the star, and the character of its spectrum, we can make an estimate of its probable distance from the earth.

Let us first take the case of Algol. This famous variable star has, according to the Draper catalogue, a spectrum of the Sirian type. It may, therefore, be comparable with that brilliant star in intrinsic brightness and density. Assuming the mass of Sirius at 2·20 times the mass of the sun, as found by Auwers, and that of the brighter component of Algol at four-ninths of the sun’s mass, as given by Vogel,[114] I find that for the _same distance_ Sirius would be about 2·8 times brighter than Algol. But photometric measures show that Sirius is about 22 times brighter than Algol, from which it follows—since light varies inversely as the square of the distance—that Algol is 2·77 times further from the earth. Assuming the parallax of Sirius at 0·39″, this would give for the parallax of Algol O·14″, or a journey for light of about 23 years. From the dimensions of the system, as given by Vogel—about 3,230,000 miles from centre to centre of the components—this parallax would give an apparent distance between the components of less than ¹⁄₂₀₀th of a second, a quantity much too small to be visible in our largest telescopes, or probably in any telescope which man can ever construct From a consideration of irregularities in the proper motion of Algol and in the period of its light changes, Dr. Chandler infers the existence of a third dark body and a parallax of 0·07″. As this is exactly one-half the parallax found above, it implies a distance just double of what I have found, and would, of course, indicate that Algol is intrinsically four times brighter than Sirius. This greater brilliancy would suggest greater heat, and would agree with its small density, which, from its diameter, as given by Vogel—1,061,000 miles—I find to be only one-third of that of water.

Let us now consider the case of Beta Aurigæ, which spectroscopic observations show to be a close binary star with a period of about four days, and a distance between the components of about eight millions of miles. This period and distance imply that the mass of the system is about five times that of the sun. As in this case the spectral lines are doubled at regular intervals of two days, and not merely shifted, as in the case of Algol, we may conclude that both the components are bright bodies, and we may not be far wrong in supposing that they are of equal mass, each having 2½ times the mass of the sun. As the spectrum of Beta Aurigæ is of the same type as Sirius, we may compare it with that star, as we did in the case of Algol. Assuming the same density and intrinsic brightness for both Beta Aurigæ and Sirius, I find that Beta Aurigæ should be about twice as bright as Sirius. Now, according to the Oxford photometric measures, Sirius is 2·89 magnitudes, or 14·32 times brighter than Beta Aurigæ. Hence it follows that the distance of Beta Aurigæ should be about 5½ times greater than the distance of Sirius. Hence, assuming the parallax of Sirius at 0″·39, that of Beta Aurigæ should be about 0″·061. From actual measures of the parallax of Beta Aurigæ, made by the late Prof. Pritchard at Oxford, he found, from two companion stars, a mean parallax of 0″·062, a result in remarkably close agreement with that computed above from a consideration of the star’s mass and light, compared with that of Sirius. As the actual distance between the components of Beta Aurigæ is equal to the sun’s diameter divided by 11·625, we have the maximum angular separation between the components equal to 0″·062 divided by 11·625, or about ¹⁄₂₀₀th of a second, or nearly the same as in the case of Algol.

The bright star Spica has also been found by the spectroscope to be a close binary star. Vogel finds a period of four days with a distance between the components of about 6¼ millions of miles, and assuming that the components have equal mass and are moving in a circular orbit, he finds the mass of the system about 2·6 times the mass of our sun. This would give each of the components 1·3 times the mass of the sun, and it follows that the light of Spica—which gives a spectrum of the Sirian type—should, for equal distances, exceed that of Sirius about 1·4 times. Now, the photometric measures at Oxford show that Sirius is 1·91 magnitude, or 5·8 times brighter than Spica. Hence it follows that the distance of Spica should be 2·85 times the distance of Sirius. This would make the parallax of Spica about 0″·137. So far as I know, a measurable parallax has not yet been found for this star. Brioschi, in 1819–20, observing with a vertical circle of four inches aperture, found a negative parallax, which would imply that its parallax is too small to be measurable. Still, the above result would seem to indicate that its parallax might be measurable by the photographic method. The parallax found above would imply that the maximum distance between the components of Spica would not exceed ⅒th of a second, a quantity much too small to be detected by the most powerful telescopes. In addition to its orbital motion, Vogel finds that Spica is approaching the sun at the rate of over 9 miles per second.

We now come to Zeta Ursæ Majoris (Mizar), which has also a spectrum of the Sirian type, and which the spectroscopic measures indicate is a close binary star with a period of about 104 days, and a combined mass equal to forty times the mass of the sun. Proceeding as before, we find that the light of Mizar should be about 8·7 times that of Sirius. But the photometric measures show that Sirius is about three magnitudes, or about sixteen times brighter than Mizar. Hence the distance of Mizar should be nearly twelve times the distance of Sirius. This gives for the parallax of Mizar about 0″·033. Klinkerfues found a parallax of 0″·0429 to 0″·0477, which does not differ widely from the above result. As the velocity of the orbital motion shown by the spectroscope indicates a distance between the components of about 143 millions of miles, or about the distance of Mars from the sun, it follows that the maximum distance between the components would be 0″032, multiplied by 1½ or 0″·048, a quantity beyond the reach of our present telescopes.

The well-known variable star, Delta Cephei, has recently been added to the list of “spectroscopic binaries.” From observations with the great 30-inch refractor of the Pulkowa Observatory in the summer of 1894, M. Bélopolsky finds that the star is probably a very close double, the companion being a nearly, or wholly, dark body, as in the case of Algol, and the orbit a very eccentric one. The observed variation of light indicates, however, that there is no eclipse, as occurs in Algol, so that the fluctuations in the light of Delta Cephei are probably due to some other cause. The spectrum of the star is of the solar type, so that in this respect it differs from the other spectroscopic binaries referred to above. The observations show that the system is approaching the sun at the rate of about 15 miles a second. Spectroscopic observations also suggest that the well-known variable star Beta Lyræ may also consist of two close companions. Further details respecting these observations will be given in the next chapter.

From a recent investigation of the proper motion of the star Tau Virginis, Dr. Fritz Cohen thinks it is probably a close binary, the companion star of which has not yet been detected.

It should be mentioned that in the case of Beta Aurigæ, Spica, Zeta Ursæ Majoris, and Castor, as there is no variation of light, as in Algol, the plane of the orbit is probably inclined to the line of sight. This would have the effect of increasing the computed mass of the system, and thus diminishing the calculated parallax. As the above calculations have been made on the assumption that the plane of the orbit passes through the earth, it follows that the computed parallax is a maximum, and that these remarkable objects may be really further from the earth than even the minute parallaxes found above would indicate. As the parallaxes of the nearest stars, such as Alpha Centauri, 61 Cygni, Sirius, and some other stars, are considerably greater than those found above, it would seem that our solar system is not situated in a region of binary stars, and that these wonderful objects lie beyond our immediate neighbourhood. It is also remarkable that, with the exception of Delta Cephei, they have all spectra of the Sirian type, including those Algol variables whose spectra have been examined.

By the aid of the parallaxes computed above, we can easily calculate the relative brightness of the sun compared with that of the spectroscopic binaries. Assuming that the sun is 27 magnitudes brighter than the Zero magnitude, or 28 magnitudes brighter than a standard star of the first magnitude, and taking the parallax of Algol as 0″·07, I find that the sun, placed at the distance indicated by this parallax, would be reduced to a star of 5·35 magnitude, or about three magnitudes fainter than Algol, which implies that Algol is about 15½ times brighter than our sun. In the case of Beta Aurigæ, if the sun were placed at the distance indicated by the parallax of 0″·061, it would be reduced to a star of 5·65 magnitude, or about 3·7 magnitudes fainter than Beta Aurigæ, which would imply that Beta Aurigæ is about thirty times brighter than the sun. In the case of Spica we have the sun reduced to a star of about the fourth magnitude, or about three magnitudes fainter than Spica, indicating that Spica is, like Algol, about 15½ times brighter than the sun, although the mass of Spica is only 2·6 times the mass of the sun. Finally, in the case of Mizar, we have the sun reduced to a star of about the seventh, or about five magnitudes fainter than Mizar, indicating that Mizar is no less than one hundred times brighter than our sun. These results show the great relative brilliancy of stars with a Sirian spectrum, when compared with that of the sun, a consideration which has already been arrived at from other considerations.