Fig. 92.—The Orbit of Sirius (Professor Burnham).Fig. 92.—The Orbit of Sirius (Professor Burnham).
The fact that Sirius had not been moving uniformly was of such interest that it arrested the attention of Bessel when he discovered the irregularities in 1844. Believing, as Bessel did, that there must be some adequate cause for thesedisturbances, it was hardly possible to doubt what the cause must be. When motion is disturbed there must be force in action, and the only force that we recognise in such cases is that known as gravitation. But gravity can only act from one body to another body; so that when we seek for the derangement of Sirius by gravitation, we are obliged to suppose that there must be some mighty and massive body near Sirius. The question was taken up again by Peters and by Auwers, who were able to discover, from the irregularities of Sirius, the nature of the path of the disturbing body. They were able to show that it must revolve around Sirius in a period of about fifty years, and although they could not tell its distance from Sirius, yet they were able to point out the direction in which it must lie. Fig. 92 shows the orbit of Sirius as given by Mr. Burnham, of Yerkes Observatory.
The detection of the attendant of Sirius, and the measures which have been made thereon, enable us to determine the weight of this famous star. Let us attempt to illustrate this subject. It must, no doubt, be admitted that the numerical estimates we employ have to be received with a certain degree of caution. The companion of Sirius is a difficult object to observe, and previous to 1896 it had only been followed through an arc of 90°. We are, therefore, hardly as yet in a position to speak with absolute accuracy as to the periodic time in which the companion completes its revolution. We may, however, take this time to be fifty-two years. We also know the distance from Sirius to his companion, and we may take it to be about twenty-one times the distance from the earth to the sun. It is useful, in the first place, to compare the revolution of the companion around Sirius with the revolution of the planet Uranus around the sun. Taking the earth's distance as unity, the radius of the orbit of Uranus is about nineteen, and Uranus takes eighty-four years to accomplish a complete revolution. We have no planet in the solar system at a distance of twenty-one; but from Kepler's third law it may be shown that, if there were such a planet, its periodic time would be about ninety-nine years. We have now the necessary materials for making the comparison between themass of Sirius and the mass of the sun. A body revolving around Sirius at a certain distance completes its journey in fifty-two years. To revolve around the sun at the same distance a body should complete its journey in ninety-nine years. The quicker the body is moving the greater must be the centrifugal force, and the greater must be the attractive power of the central body. It can be shown from the principles of dynamics that the attractive power is inversely proportional to the square of the periodic time. Hence, then, the attractive power of Sirius must bear to the attractive power of the sun the proportion which the square of ninety-nine has to the square of fifty-two. As the distances are in each case supposed to be equal, the attractive powers will be proportional to the masses, and hence we conclude that the mass of Sirius, together with that of his companion, is to the mass of the sun, together with that of his planet, in the ratio of three and a half to one. We had already learned that Sirius was much brighter than the sun; now we have learned that it is also much more massive.
Before we leave the consideration of Sirius, there is one additional point of very great interest which it is necessary to consider. There is a remarkable contrast between the brilliancy of Sirius and his companion. Sirius is a star far transcending all other stars of the first magnitude, while his companion is extremely faint. Even if it were completely withdrawn from the dazzling proximity of Sirius, the companion would be only a small star of the eighth or ninth magnitude, far below the limits of visibility to the unaided eye. To put the matter in numerical language, Sirius is 5,000 times as bright as its companion, but only about twice as heavy! Here is a very great contrast; and this point will appear even more forcible if we contrast the companion of Sirius with our sun. The companion is slightly heavier than our sun; but in spite of its slightly inferior bulk, our sun is much more powerful as a light-giver. One hundred of the companions of Sirius would not give as much light as our sun! This is a result of very considerable significance. It teaches us that besides the great bodies in the universe which attract attention by their brilliancy, there are also other bodiesof stupendous mass which have but little brilliancy—probably some of them possess none at all. This suggests a greatly enhanced conception of the majestic scale of the universe. It also invites us to the belief that the universe which we behold bears but a small ratio to the far larger part which is invisible in the sombre shades of night. In the wide extent of the material universe we have here or there a star or a mass of gaseous matter sufficiently heated to be luminous, and thus to become visible from the earth; but our observation of these luminous points can tell us little of the remaining contents of the universe.
The most celebrated of all the variable stars is that known as Algol, whose position in the constellation of Perseus is shown inFig. 83. This star is conveniently placed for observation, being visible every night in our latitude, and its interesting changes can be observed without any telescopic aid. Everyone who desires to become acquainted with the great truths of astronomy should be able to recognise this star, and should have also followed it during one of its periods of change. Algol is usually a star of the second magnitude; but in a period between two and three days, or, more accurately, in an interval of 2 days 20 hours 48 minutes and 55 seconds, its brilliancy goes through a most remarkable cycle of variations. The series commences with a gradual decline of the star's brightness, which in the course of four and a half hours falls from the second magnitude down to the fourth. At this lowest stage of brightness Algol remains for about twenty minutes, and then begins to increase, until in three and a half hours it regains the second magnitude, at which it continues for about 2 days 12 hours, when the same series commences anew. It seems that the period required by Algol to go through its changes is itself subject to a slow but certain variation. We shall see in a following chapter how it has been proved that the variability of Algol is due to the occasional interposition of a dark companion which cuts off a part of the lustre of the star. All the circumstances can thus be accounted for, and even the weight and the size of Algol and its dark companion be determined.
There are, however, other classes of variable stars, the fluctuation of whose light can hardly be due to occasional obscuration by dark bodies. This is particularly the case with those variables which are generally faint, but now and then flare up for a short time, after which temporary exaltation they again sink down to their original condition. The periods of such changes are usually from six months to two years. The best known example of a star of this class was discovered more than three hundred years ago. It is situated in the constellation Cetus, a little south of the equator. This object was the earliest known case of a variable star, except the so-called temporary stars, to which we shall presently refer. The variable in Cetus received the name of Mira, or the wonderful. The period of the fluctuations of Mira Ceti is about eleven months, during the greater part of which time the star is of the ninth magnitude, and consequently invisible to the naked eye. When the proper time has arrived, its brightness begins to increase rather suddenly. It soon becomes a conspicuous object of the second or third magnitude. In this condition it remains for eight or ten days, and then declines more slowly than it rose until it is reduced to its original faintness, about three hundred days after the rise commenced.
More striking to the general observer than the ordinary variable stars are thetemporary starswhich on rare occasions suddenly make their appearance in the heavens. The most famous object of this kind was that which blazed out in the beginning of November, 1572, and which when first seen was as bright as Venus at its maximum brightness. It could, indeed, be seen in full daylight by sharp-sighted people. As far as history can tell us, no other temporary star has ever been as bright as this one. It is specially associated with the name of Tycho Brahe, for although he was not the discoverer, he made the best observations of the object, and he proved that it was at a distance comparable with that of the ordinary fixed stars. Tycho described carefully the gradual decline of the wonderful star until it disappeared from his view about the end of March, 1574, for the telescope, by which it could doubtless have been followed further, had not yetbeen invented. During the decline the colour of the object gradually changed; at first it was white, and by degrees became yellow, and in the spring of 1573 reddish, like Aldebaran. About May, 1573, we are told somewhat enigmatically that it "became like lead, or somewhat like Saturn," and so it remained as long as it was visible. What a fund of information our modern spectroscopes and other instruments would supply us with if so magnificent a star were to burst out in these modern days!
But though we have not in our own times been favoured with a view of a temporary star as splendid as the one seen by Tycho Brahe and his contemporaries, it has been our privilege to witness several minor outbursts of this kind. It seems likely that we should possess more records of temporary stars from former times if a better watch had been kept for them. That is at any rate the impression we get when we see how several of the modern stars of this kind have nearly escaped us altogether, notwithstanding the great number of telescopes which are now pointed to the sky on every clear night.
In 1866 a star of the second magnitude suddenly appeared in the constellation of the crown (Corona Borealis). It was first seen on the 12th May, and a few days afterwards it began to fade away. Argelander's maps of the northern heavens had been published some years previously, and when the position of the new star had been accurately determined, it was found that it was identical with an insignificant looking star marked on one of the maps as of the 9-1⁄2magnitude. The star exists in the same spot to this day, and it is of the same magnitude as it was prior to its spasmodic outburst in 1866. This was the first new star which was spectroscopically examined. We shall give inChapter XXIII. a short account of the features of its spectrum.
The next of these temporary bright stars, Nova Cygni, was first seen by Julius Schmidt at Athens on the 24th November, 1876, when it was between the third and fourth magnitudes, and he maintains that it cannot have beenconspicuous four days earlier, when he was looking at the same constellation. By some inadvertence the news of the discovery was not properly circulated, and the star was not observed elsewhere for about ten days, when it had already become considerably fainter. The decrease of brightness went on very slowly; in October, 1877, the star was only of the tenth magnitude, and it continued getting fainter until it reached the fifteenth magnitude; in other words, it became a minute telescopic star, and it is so still in the very same spot. As this star did not reach the first or second magnitude it would probably have escaped notice altogether if Schmidt had not happened to look at the Swan on that particular evening.
We are not so likely to miss seeing a new star since astronomers have pressed the photographic camera into their service. This became evident in 1892, when the last conspicuous temporary star appeared in Auriga. On the 24th January, Dr. Anderson, an astronomer in Edinburgh, noticed a yellowish star of the fifth magnitude in the constellation Auriga, and a week later, when he had compared a star-map with the heavens and made sure that the object was really a new star, he made his discovery public. In the case of this star we are able to fix fairly closely the moment when it first blazed out. In the course of the regular photographic survey of the heavens undertaken at the Harvard College Observatory (Cambridge, Massachusetts) the region of the sky where the new star appeared had been photographed on thirteen nights from October 21st to December 1st, 1891, and on twelve nights from December 10th to January 20th, 1892. On the first series of plates there was no trace of the Nova, while it was visible on the very first plate of the second series as a star of the fifth magnitude. Fortunately it turned out that Professor Max Wolf of Heidelberg, a most successful celestial photographer, had photographed the same region on the 8th December, and this photograph does not show the star, so that it cannot on that night have been as bright as the ninth magnitude. Nova Auriga must therefore have flared up suddenly between the 8th and the10th of December. According to the Harvard photographs, the first maximum of brightness occurred about the 20th of December, when the magnitude was 4-1⁄2. The decrease of the brightness was very irregular; the star fluctuated for the five weeks following the first of February between the fourth and the sixth magnitude, but after the beginning of March, 1892, the brightness declined very rapidly, and at the end of April the star was seen as an exceedingly faint one (sixteenth magnitude) with the great Lick Refractor. When this mighty instrument was again pointed to the Nova in the following August, it had risen nearly to the tenth magnitude, after which it gradually became extremely faint again, and is so still.
The temporary and the variable stars form but a very small section of the vast number of stars with which the vault of the heavens is studded. That the sun is no more than a star, and the stars are no less than suns, is a cardinal doctrine of astronomy. The imposing magnificence of this truth is only realised when we attempt to estimate the countless myriads of stars. This is a problem on which our calculations are necessarily vain. Let us, therefore, invoke the aid of the poet to attempt to express the innumerable, and conclude this chapter with the following lines of Mr. Allingham:—
"But number every grain of sand,Wherever salt wave touches land;Number in single drops the sea;Number the leaves on every tree,Number earth's living creatures, allThat run, that fly, that swim, that crawl;Of sands, drops, leaves, and lives, the countAdd up into one vast amount,And then for every separate oneOf all those, let a flamingSUNWhirl in the boundless skies, with eachIts massy planets, to outreachAll sight, all thought: for all we seeEncircled with infinity,Is but an island."
"But number every grain of sand,Wherever salt wave touches land;Number in single drops the sea;Number the leaves on every tree,Number earth's living creatures, allThat run, that fly, that swim, that crawl;Of sands, drops, leaves, and lives, the countAdd up into one vast amount,And then for every separate oneOf all those, let a flamingSUNWhirl in the boundless skies, with eachIts massy planets, to outreachAll sight, all thought: for all we seeEncircled with infinity,Is but an island."
Interesting Stellar Objects—Stars Optically Double—The Great Discovery of the Binary Stars made by Herschel—The Binary Stars describe Elliptic Paths—Why is this so important?—The Law of Gravitation—Special Double Stars—Castor—Mizar—The Coloured Double Stars—β Cygni.
Interesting Stellar Objects—Stars Optically Double—The Great Discovery of the Binary Stars made by Herschel—The Binary Stars describe Elliptic Paths—Why is this so important?—The Law of Gravitation—Special Double Stars—Castor—Mizar—The Coloured Double Stars—β Cygni.
Thesidereal heavens contain few more interesting objects for the telescope than can be found in the numerous class of double stars. They are to be counted in thousands; indeed,manythousands can be found in the catalogues devoted to this special branch of astronomy. Many of these objects are, no doubt, small and comparatively uninteresting, but some of them are among the most conspicuous stars in the heavens, such as Sirius, whose system we have already described. We shall in this brief account select for special discussion and illustration a few of the more remarkable double stars. We shall particularly notice some of those that can be readily observed with a small telescope, and we have indicated on the sketches of the constellations in a previous chapter how the positions of these objects in the heavens can be ascertained.
It had been shown by Cassini in 1678 that certain stars, which appeared to the unaided eye as single points of light, really consisted of two or more stars, so close together that the telescope was required for their separation.[36]The number of these objects was gradually increased by fresh discoveries, until in 1781 (the same year in which Herschel discovered Uranus) a list containing eighty double stars was publishedby the astronomer Bode. These interesting objects claimed the attention of Herschel during his memorable researches. The list of known doubles rapidly swelled. Herschel's discoveries are to be enumerated by hundreds, while he also commenced systematic measurements of the distance by which the stars were separated, and the direction in which the line joining them pointed. It was these measurements which ultimately led to one of the most important and instructive of all Herschel's discoveries. When, in the course of years, his observations were repeated, Herschel found that in some cases the relative position of the stars had changed. He was thus led to the discovery that in many of the double stars the components are so related that they revolve around each other. Mark the importance of this result. We must remember that the stars are suns, comparable, it may be, with our sun in magnitude; so that here we have the astonishing spectacle of pairs of suns in mutual revolution. There is nothing very surprising in the fact that movements should be observed, for in all probability every body in the universe is in motion. It is the particular character of the movement which is specially interesting and instructive.
It had been imagined that the proximity of the two stars forming a double must be only accidental. It was thought that amid the vast host of stars in the heavens it not unfrequently happened that one star was so nearly behind another (as seen from the earth) that when the two were viewed in the telescope they produced the effect of a double star. No doubt many of the so-called double stars are produced in this way. Herschel's discovery shows that this explanation will not always answer, but that in many cases we really have two stars close together, and in motion round their common centre of gravity.
When the measurements of the distances and the positions of double stars had been accumulated during many years, they were taken over by the mathematicians to be treated by their methods. There is one peculiarity about double star observations: they have not—they cannot have—theaccuracy which the computer of an orbit demands. If the distance between the pair of stars forming a binary be four seconds, the orbit we have to scrutinise is only as large as the apparent size of a penny-piece at the distance of one mile. It would require very careful measurement to make out the form of a penny a mile off, even with good telescopes. If the penny were tilted a little, it would appear, not circular, but oval; and it would be possible, by measuring this oval, to determine how much the penny was tilted. All this requires skilful work: the errors, viewed intrinsically, may not be great, but viewed with reference to the whole size of the quantities under consideration, they are very appreciable. We therefore find the errors of observation far more prominent in observations of this class than is generally the case when the mathematician assumes the task of discussing the labours of the observer.
The interpretation of Herschel's discovery was not accomplished by himself; the light of mathematics was turned on his observations of the binary stars by Savary, and afterwards by other mathematicians. Under their searching enquiries the errors of the measurements were disclosed, and the observations were purified from the grosser part of their inaccuracy. Mathematicians could then apply to their corrected materials the methods of enquiry with which they were familiar; they could deduce with fair precision the actual shape of the orbit of the binary stars, and the position of the plane in which that orbit is contained. The result is not a little remarkable. It has been proved that the motion of each of the stars is performed in an ellipse which contains the centre of gravity of the two stars in its focus. This has been actually shown to be true in many binary stars; it is believed to be true in all. But why is this so important? Is not motion in an ellipse common enough? Does not the earth revolve in an ellipse round the sun? And do not the planets also revolve in ellipses?
It is this very fact that elliptic motion is so common in the planets of the solar system which renders its discovery in binary stars of such importance. From what does the ellipticmotion in the solar system arise? Is it not due to the law of attraction, discovered by Newton, which states that every mass attracts every other mass with a force which varies inversely as the square of the distance? That law of attraction had been found to pervade the whole solar system, and it explained the movements of the bodies of our system with marvellous fidelity. But the solar system, consisting of the sun, and the planets, with their satellites, the comets, and a host of smaller bodies, formed merely a little island group in the universe. In the economy of this tiny cosmical island the law of gravitation reigns supreme; before Herschel's discovery we never could have known whether that law was not merely a piece of local legislation, specially contrived for the exigencies of our particular system. This discovery gave us the knowledge which we could have gained from no other source. From the binary stars came a whisper across the vast abyss of space. That whisper told us that the law of gravitation was not peculiar to the solar system. It told us the law extended to the distant shores of the abyss in which our island is situated. It gives us grounds for believing that the law of gravitation is obeyed throughout the length, breadth, and depth of the entire visible universe.
One of the finest binary stars is that known as Castor, the brighter of the two principal stars in the constellation of Gemini. The position of Castor on the heavens is indicated inFig. 86, page 418. Viewed by the unaided eye, Castor resembles a single star; but with a moderately good telescope it is found that what seems to be one star is really two separate stars, one of which is of the third magnitude, while the other is somewhat less. The angular distance of these two stars in the heavens is not so great as the angle subtended by a line an inch long viewed at a distance of half a mile. Castor is one of the double stars in which the components have been observed to possess a motion of revolution. The movement is, however, extremely slow, and the lapse of centuries will be required before a revolution is completely effected.
A beautiful double star can be readily identified in theconstellation of Ursa Major (seeFig. 80, page 410). It is known as Mizar, and is the middle star (ζ) of the three which form the tail. In the close neighbourhood of Mizar is the small star Alcor, which can be readily seen with the unaided eye; but when we speak of Mizar as a double star, it is not to be understood that Alcor is one of the components of the double. Under the magnifying power of the telescope Alcor is seen to be transferred a long way from Mizar, while Mizar itself is split up into two suns close together. These components are of the second and the fourth magnitudes respectively, and as the apparent distance is nearly three times as great as in Castor, they are observed with facility even in a small telescope. This is, indeed, the best double star in the heavens for the beginner to commence his observations upon. We cannot, however, assert that Mizar is a binary, inasmuch as observations have not yet established the existence of a motion of revolution. Still less are we able to say whether Alcor is also a member of the same group, or whether it may not merely be a star which happens to fall nearly in the line of vision. Recent spectroscopic observations have shown that the larger component of Mizar is itself a double, consisting of a pair of suns so close together that there is not the slightest possibility of their ever being seen separately by the most powerful telescope in the world.
A pleasing class of double stars is that in which we have the remarkable phenomenon of colours, differing in a striking degree from the colours of ordinary stars. Among the latter we find, in the great majority of cases, no very characteristic hue; some are, however, more or less tinged with red, some are decidedly ruddy, and some are intensely red. Stars of a bluish or greenish colour are much more rare,[37]and when a star of this character does occur, it is almost invariably as one of a pair which form a double. The other star of the double is sometimes of the same hue, but more usually it is yellow or ruddy.
One of the loveliest of these objects, which lies within reach of telescopes of very moderate pretensions, is that found in the constellation of the Swan, and known as β Cygni (Fig. 91). This exquisite object is composed of two stars. The larger, about the third magnitude, is of a golden-yellow, or topaz, colour; the smaller, of the sixth magnitude, is of a light blue. These colours are nearly complementary, but still there can be no doubt that the effect is not merely one of contrast. That these two stars are both tinged with the hues we have stated can be shown by hiding each in succession behind a bar placed in the field of view. It has also been confirmed in a very striking manner by spectroscopic investigation; for we see that the blue star has experienced a special absorption of the red rays, while the more ruddy light of the other star has arisen from the absorption of the blue rays. The contrast of the colours in this object can often be very effectively seen by putting the eye-piece out of focus. The discs thus produced show the contrast of colours better than when the telescope exhibits merely two stellar points.
Such are a few of these double and multiple stars. Their numbers are being annually augmented; indeed, one observer—Mr. Burnham, formerly on the staff of the Lick Observatory, and now an observer in the Yerkes Observatory—has added by his own researches more than 1,000 new doubles to the list of those previously known.
The interest in this class of objects must necessarily be increased when we reflect that, small as the stars appear to be in our telescopes, they are in reality suns of great size and splendour, in many cases rivalling our own sun, or, perhaps, even surpassing him. Whether these suns have planets attending upon them we cannot tell; the light reflected from the planet would be utterly inadequate to the penetration of the vast extent of space which separates us from the stars. If there be planets surrounding these objects, then, instead of a single sun, such planets will be illuminated by two, or, perhaps, even more suns. What wondrous effects of light and shade must be the result! Sometimes both suns will beabove the horizon together, sometimes only one sun, and sometimes both will be absent. Especially remarkable would be the condition of a planet whose suns were of the coloured type. To-day we have a red sun illuminating the heavens, to-morrow it would be a blue sun, and, perhaps, the day after both the red sun and the blue sun will be in the firmament together. What endless variety of scenery such a thought suggests! There are, however, grave dynamical reasons for doubting whether the conditions under which such a planet would exist could be made compatible with life in any degree resembling the life with which we are familiar. The problem of the movement of a planet under the influence of two suns is one of the most difficult that has ever been proposed to mathematicians, and it is, indeed, impossible in the present state of analysis to solve with accuracy all the questions which it implies. It seems not at all unlikely that the disturbances of the planet's orbit would be so great that it would be exposed to vicissitudes of light and of temperature far transcending those experienced by a planet moving, like the earth, under the supreme control of a single sun.
Sounding-line for Space—The Labours of Bessel—Meaning of Annual Parallax—Minuteness of the Parallactic Ellipse Illustrated—The Case of 61 Cygni—Different Comparison Stars used—The Proper Motion of the Star—Struve's Investigations—Can they be Reconciled?—Researches at Dunsink—Conclusion obtained—Accuracy which such Observations admit Examined—The Proper Motion of 61 Cygni—The Permanence of the Sidereal Heavens—The New Star in Cygnus—Its History—No Appreciable Parallax—A Mighty Outburst of Light—The Movement of the Solar System through Space—Herschel's Discovery—Journey towards Lyra—Probabilities.
Sounding-line for Space—The Labours of Bessel—Meaning of Annual Parallax—Minuteness of the Parallactic Ellipse Illustrated—The Case of 61 Cygni—Different Comparison Stars used—The Proper Motion of the Star—Struve's Investigations—Can they be Reconciled?—Researches at Dunsink—Conclusion obtained—Accuracy which such Observations admit Examined—The Proper Motion of 61 Cygni—The Permanence of the Sidereal Heavens—The New Star in Cygnus—Its History—No Appreciable Parallax—A Mighty Outburst of Light—The Movement of the Solar System through Space—Herschel's Discovery—Journey towards Lyra—Probabilities.
Wehave long known the dimensions of the solar system with more or less accuracy. Our knowledge includes the distances of the planets and the comets from the sun, as well as their movements. We have also considerable knowledge of the diameters and the masses of many of the different bodies which belong to the solar system. We have long known, in fact, many details of the isolated group nestled together under the protection of the sun. The problem for consideration in the present chapter involves a still grander survey than is required for measures of our solar system. We propose to carry the sounding-line across the vast abyss which separates the group of bodies closely associated about our sun from the other stars which are scattered through the realms of space. For centuries the great problem of star distance has engaged the attention of those who have studied the heavens. It would be impossible to attempt here even an outline of the various researches which have been made on the subject. In the limited survey which we can make, we must glance first at the remarkable speculative efforts which have been directed to the problem, and then we shall refer to those labours whichhave introduced the problem into the region of accurate astronomy.
No attempt to solve the problem of the absolute distances of the stars was successful until many years after Herschel's labours were closed. Fresh generations of astronomers, armed with fresh appliances, have for many years pursued the subject with unremitting diligence, but for a long time the effort seemed hopeless. The distances of the stars were so great that they could not be ascertained until the utmost refinements of mechanical skill and the most elaborate methods of mathematical calculation were brought to converge on the difficulty. At last it was found that the problem was beginning to yield. A few stars have been induced to disclose the secret of their distance. We are able to give some answer to the question—How far are the stars? though it must be confessed that our reply up to the present moment is both hesitating and imperfect. Even the little knowledge which has been gained possesses interest and importance. As often happens in similar cases, the discovery of the distance of a star was made independently about the same time by two or three astronomers. The name of Bessel stands out conspicuously in this memorable chapter of astronomy. Bessel proved (1840) that the distance of the star known as 61 Cygni was a measurable quantity. His demonstration possessed such unanswerable logic that universal assent could not be withheld. Almost simultaneously with the classical labours of Bessel we have Struve's measurement of the distance of Vega, and Henderson's determination of the distance of the southern star α Centauri. Great interest was excited in the astronomical world by these discoveries, and the Royal Astronomical Society awarded its gold medal to Bessel. It appropriately devolved on Sir John Herschel to deliver the address on the occasion of the presentation of the medal: that address is a most eloquent tribute to the labours of the three astronomers. We cannot resist quoting the few lines in which Sir John said:—
"Gentlemen of the Royal Astronomical Society,—I congratulate you and myself that we have lived to see the great and hitherto impassable barrier to our excursion into the sidereal universe, that barrier against which we have chafed so long and so vainly—æstuantes angusto limite mundi—almost simultaneously overleaped at three different points. It is the greatest and most glorious triumph which practical astronomy has ever witnessed. Perhaps I ought not to speak so strongly; perhaps I should hold some reserve in favour of the bare possibility that it may be all an illusion, and that future researches, as they have repeatedly before, so may now fail to substantiate this noble result. But I confess myself unequal to such prudence under such excitement. Let us rather accept the joyful omens of the time, and trust that, as the barrier has begun to yield, it will speedily be effectually prostrated."
"Gentlemen of the Royal Astronomical Society,—I congratulate you and myself that we have lived to see the great and hitherto impassable barrier to our excursion into the sidereal universe, that barrier against which we have chafed so long and so vainly—æstuantes angusto limite mundi—almost simultaneously overleaped at three different points. It is the greatest and most glorious triumph which practical astronomy has ever witnessed. Perhaps I ought not to speak so strongly; perhaps I should hold some reserve in favour of the bare possibility that it may be all an illusion, and that future researches, as they have repeatedly before, so may now fail to substantiate this noble result. But I confess myself unequal to such prudence under such excitement. Let us rather accept the joyful omens of the time, and trust that, as the barrier has begun to yield, it will speedily be effectually prostrated."
Before proceeding further, it will be convenient to explain briefly how the distance of a star can be measured. The problem is one of a wholly different character from that of the sun's distance, which we have already discussed in these pages. The observations for the determination of stellar parallax are founded on the familiar truth that the earth revolves around the sun. We may for our present purpose assume that the earth revolves in a circular path. The centre of that path is at the centre of the sun, and the radius of the path is 92,900,000 miles. Owing to our position on the earth, we observe the stars from a point of view which is constantly changing. In summer the earth is 185,800,000 miles distant from the position which it occupied in winter. It follows that the apparent positions of the stars, as projected on the background of the sky, must present corresponding changes. We do not now mean that the actual positions of the stars are really displaced. The changes are only apparent, and while oblivious of our own motion, which produces the displacements, we attribute the changes to the stars.
On the diagram in Fig. 93 is an ellipse with certain months—viz., January, April, July, October—marked upon its circumference. This ellipse may be regarded as a miniature picture of the earth's orbit around the sun. In January the earthis at the spot so marked; in April it has moved a quarter of the whole journey; and so on round the whole circle, returning to its original position in the course of one year. When we look from the position of the earth in January, we see the star A projected against the point of the sky marked 1. Three months later the observer with his telescope is carried round to April; but he now sees the star projected to the position marked 2. Thus, as the observer moves around the whole orbit in the annual revolution of the earth, so the star appears to move round in an ellipse on the background of the sky. In the technical language of astronomers, we speak of this as the parallactic ellipse, and it is by measuring the major axis of this ellipse that we determine the distance of the star from the sun. Half of this major axis, or, what comes to the same thing, the angle which the radius of the earth's orbit subtends as seen from the star, is called the star's "annual parallax."
Fig. 93.—The Parallactic Ellipse.Fig. 93.—The Parallactic Ellipse.
The figure shows another star,B, more distant from the earth and the solar system generally than the star previously considered. This star also describes an elliptic path. We cannot, however, fail to notice that the parallactic ellipse belonging toBis much smaller than that ofA. Thedifference in the sizes of the ellipses arises from the different distances of the stars from the earth. The nearer the star is to the earth the greater is the ellipse, so that the nearest star in the heavens will describe the largest ellipse, while the most distant star will describe the smallest ellipse. We thus see that the distance of the star is inversely proportional to the size of the ellipse, and if we measure the angular value of the major axis of the ellipse, then, by an exceedingly simple mathematical manipulation, the distance of the star can be expressed as a multiple of a radius of the earth's orbit. Assuming that radius to be 92,900,000 miles, the distance of the star is obtained by simple arithmetic. The difficulty in the process arises from the fact that these ellipses are so small that our micrometers often fail to detect them.
How shall we adequately describe the extreme minuteness of the parallactic ellipses in the case of even the nearest stars? In the technical language of astronomers, we may state that the longest diameter of the ellipse never subtends an angle of more than one and a half seconds. In a somewhat more popular manner, we would say that one thousand times the major axis of the very largest parallactic ellipse would not be as great as the diameter of the full moon. For a still more simple illustration, let us endeavour to think of a penny-piece placed at a distance of two miles. If looked at edgeways it will be linear, if tilted a little it would be elliptic; but the ellipse would, even at that distance, be greater than the greatest parallactic ellipse of any star in the sky. Suppose a sphere described around an observer, with a radius of two miles. If a penny-piece were placed on this sphere, in front of each of the stars, every parallactic ellipse would be totally concealed.
The star in the Swan known as 61 Cygni is not remarkable either for its size or for its brightness. It is barely visible to the unaided eye, and there are some thousands of stars which are apparently larger and brighter. It is, however, a very interesting example of that remarkable class of objects known as double stars. It consists of two nearly equal stars closetogether, and evidently connected by a bond of mutual attraction. The attention of astronomers is also specially directed towards the star by its large proper motion. In virtue of that proper motion, the two components are carried together over the sky at the rate of five seconds annually. A proper motion of this magnitude is extremely rare, yet we do not say it is unparalleled, for there are some few stars which have a proper motion even more rapid; but the remarkable duplex character of 61 Cygni, combined with the large proper motion, render it an unique object, at all events, in the northern hemisphere.
When Bessel proposed to undertake the great research with which his name will be for ever connected, he determined to devote one, or two, or three years to the continuous observations of one star, with the view of measuring carefully its parallactic ellipse. How was he to select the object on which so much labour was to be expended? It was all-important to choose a star which should prove sufficiently near to reward his efforts by exhibiting a measurable parallax. Yet he could have but little more than surmise and analogy as a guide. It occurred to him that the exceptional features of 61 Cygni afforded the necessary presumption, and he determined to apply the process of observation to this star. He devoted the greater part of three years to the work, and succeeded in discovering its distance from the earth.
Since the date of Sir John Herschel's address, 61 Cygni has received the devoted and scarcely remitted attention of astronomers. In fact, we might say that each succeeding generation undertakes a new discussion of the distance of this star, with the view of confirming or of criticising the original discovery of Bessel. The diagram here given (Fig. 94) is intended to illustrate the recent history of 61 Cygni.
When Bessel engaged in his labours, the pair of stars forming the double were at the point indicated on the diagram by the date 1838. The next epoch occurred fifteen years later, when Otto Struve undertook his researches, and thepair of stars had by that time moved to the position marked 1853. Finally, when the same object was more recently observed at Dunsink Observatory, the pair had made still another advance, to the position indicated by the date 1878. Thus, in forty years this double star had moved over an arc of the heavens upwards of three minutes in length. The actual path is, indeed, more complicated than a simple rectilinear movement. The two stars which form the double have a certain relative velocity, in consequence of their mutual attraction. It will not, however, be necessary to take this into account, as the displacement thus arising in the lapse of a single year is far too minute to produce any inconvenient effect on the parallactic ellipse.
Fig. 94.—61 Cygni and the Comparison Stars.Fig. 94.—61 Cygni and the Comparison Stars.
The case of 61 Cygni is, however, exceptional. It is one of our nearest neighbours in the heavens. We can never find its distance accurately to one or two billions of miles; but still we have a consciousness that an uncertainty amounting to twenty billions is too large a percentage of the whole.We shall presently show that we believe Struve was right, yet it does not necessarily follow that Bessel was wrong. The apparent paradox can be easily explained. It would not be easily explained if Struve had used thesame comparison staras Bessel had done; but Struve's comparison star was different from either of Bessel's, and this is probably the cause of the discrepancy. It will be recollected that the essence of the process consists of the comparison of the small ellipse made by the distant star with the larger ellipse made by the nearer star. If the two stars were at the same distance, the process would be wholly inapplicable. In such a case, no matter how near the stars were to the earth, no parallax could be detected. For the method to be completely successful, the comparison star should be at least eight times as far as the principal star. Bearing this in mind, it is quite possible to reconcile the measures of Bessel with those of Struve. We need only assume that Bessel's comparison stars are about three times as far as 61 Cygni, while Struve's comparison star is at least eight or ten times as far. We may add that, as the comparison stars used by Bessel are brighter than that of Struve, there really is a presumption that the latter is the most distant of the three.
We have here a characteristic feature of this method of determining parallax. Even if all the observations and the reductions of a parallax series were mathematically correct, we could not with strict propriety describe the final result as the parallax of one star. It is only thedifferencebetween the parallax of the star and that of the comparison star. We can therefore only assert that the parallax sought cannot be less than the quantity determined. Viewed in this manner, the discrepancy between Struve and Bessel vanishes. Bessel asserted that the distance of 61 Cygni could not bemorethan sixty billions of miles. Struve did not contradict this—nay, he certainly confirmed it—when he showed that the distance could not be more than forty billions.
Nearly half a century has elapsed since Struve made hisobservations. Those observations have certainly been challenged; but they are, on the whole, confirmed by other investigations. In a critical review of the subject Auwers showed that Struve's determination is worthy of considerable confidence. Yet, notwithstanding this authoritative announcement, the study of 61 Cygni has been repeatedly resumed. Dr. Brünnow, when Astronomer Royal of Ireland, commenced a series of observations on the parallax of 61 Cygni, which were continued and completed by the present writer, his successor. Brünnow chose a fourth comparison star (marked on the diagram), different from any of those which had been used by the earlier observers. The method of observing which Brünnow employed was quite different from that of Struve, though the filar micrometer was used in both cases. Brünnow sought to determine the parallactic ellipse by measuring the difference in declination between 61 Cygni and the comparison star.[38]In the course of a year it is found that the difference in declination undergoes a periodic change, and from that change the parallactic ellipse can be computed. In the first series of observations I measured the difference of declination between the preceding star of 61 Cygni and the comparison star; in the second series I took the other component of 61 Cygni and the same comparison star. We had thus two completely independent determinations of the parallax resulting from two years' work. The first of these makes the distance forty billions of miles, and the second makes it almost exactly the same. There can be no doubt that this work supports Struve's determination in correction of Bessel's, and therefore we may perhaps sum up the present state of our knowledge of this question by saying that the distance of 61 Cygni is much nearer to the forty billions of miles which Struve found than to the sixty billions which Bessel found.[39]
It is desirable to give the reader the means of forminghis own opinion as to the quality of the evidence which is available in such researches. The diagram in Fig. 95 here shown has been constructed with this object. It is intended to illustrate the second series of observations of difference of declination which I made at Dunsink. Each of the dots represents one night's observations. The height of the dot is the observed difference of declination between 61 (B) Cygni and the comparison star. The distance along the horizontal line—or the abscissa, as a mathematician would call it—represents the date. These observations are grouped more or less regularly in the vicinity of a certain curve. That curve expresses where the observations should have been, had they been absolutely perfect. The distances between the dots and the curve may be regarded as the errors which have been committed in making the observations.