THE DISTANCES OF THE STARS

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CHAPTER XXI. THE DISTANCES OF THE STARS

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.

We have 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 which have 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."

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 earth[Pg 444] is 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.

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 to b is much smaller than that of a. The[Pg 445] difference 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 close[Pg 446] together, 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 the[Pg 447] pair 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.

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.[Pg 448] 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 the same comparison star as 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 the difference between 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 be more than 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 his[Pg 449] observations. 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 forming[Pg 450] his 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.

Fig. 95.—Parallax in Declination of 61 Cygni.

Perhaps it will be thought that in many cases these errors appear to have attained very undesirable dimensions. Let us, therefore, hasten to say that it was precisely for the purpose[Pg 451] of setting forth these errors that this diagram has been shown; we have to exhibit the weakness of the case no less than its strength. The errors of the observations are not, however, intrinsically so great as might at first sight be imagined. To perceive this, it is only necessary to interpret the scale on which this diagram has been drawn by comparison with familiar standards. The distance from the very top of the curve to the horizontal line denotes an angle of only four-tenths of a second. This is about the apparent diameter of a penny-piece at a distance of ten miles! We can now appraise the true magnitude of the errors which have been made. It will be noticed that no one of the dots is distant from the curve by much more than half of the height of the curve. It thus appears that the greatest error in the whole series of observations amounts to but two or three tenths of a second. This is equivalent to our having pointed the telescope to the upper edge of a penny-piece fifteen or twenty miles off, instead of to the lower edge. This is not a great blunder. A rifle team whose errors in pointing were more than a hundred times as great might still easily win every prize at Bisley.

We have entered into the history of 61 Cygni with some detail, because it is the star whose distance has been most studied. We do not say that 61 Cygni is the nearest of all the stars; it would, indeed, be very rash to assert that any particular star was the nearest of all the countless millions in the heavenly host. We certainly know one star which seems nearer than 61 Cygni; it lies in one of the southern constellations, and its name is α Centauri. This star is, indeed, of memorable interest in the history of the subject. Its parallax was first determined at the Cape of Good Hope by Henderson; subsequent researches have confirmed his observations, and the elaborate investigations of Dr. Gill have proved that the parallax of this star is about three-quarters of a second, so that it is only two-thirds of the distance of 61 Cygni.

61 Cygni arrested our attention, in the first instance, by the circumstance that it had the large proper motion of five seconds annually. We have also ascertained that the annual[Pg 452] parallax is about half a second. The combination of these two statements leads to a result of considerable interest. It teaches us that 61 Cygni must each year traverse a distance of not less than ten times the radius of the earth's orbit. Translating this into ordinary figures, we learn that this star must travel nine hundred and twenty million miles per annum. It must move between two and three million miles each day, but this can only be accomplished by maintaining the prodigious velocity of thirty miles per second. There seems to be no escape from this conclusion. The facts which we have described, and which are now sufficiently well established, are inconsistent with the supposition that the velocity of 61 Cygni is less than thirty miles per second; the velocity may be greater, but less it cannot be.

For the last hundred and fifty years we know that 61 Cygni has been moving in the same direction and with the same velocity. Prior to the existence of the telescope we have no observation to guide us; we cannot, therefore, be absolutely certain as to the earlier history of this star, yet it is only reasonable to suppose that 61 Cygni has been moving from remote antiquity with a velocity comparable with that it has at present. If disturbing influences were entirely absent, there could be no trace of doubt about the matter. Some disturbing influence, however, there must be; the only question is whether that disturbing influence is sufficient to modify seriously the assumption we have made. A powerful disturbing influence might greatly alter the velocity of the star; it might deflect the star from its rectilinear course; it might even force the star to move around a closed orbit. We do not, however, believe that any disturbing influence of this magnitude need be contemplated, and there can be no reasonable doubt that 61 Cygni moves at present in a path very nearly straight, and with a velocity very nearly uniform.

As the distance of 61 Cygni from the sun is forty billions of miles, and its velocity is thirty miles a second, it is easy to find how long the star would take to accomplish a journey equal to its distance from the sun. The time required will be about 40,000 years. In the last 400,000 years[Pg 453] 61 Cygni will have moved over a distance ten times as great as its present distance from the sun, whatever be the direction of motion. This star must therefore have been about ten times as far from the earth 400,000 years ago as it is at present. Though this epoch is incredibly more remote than any historical record, it is perhaps not incomparable with the duration of the human race; while compared with the vast lapse of geological time, such periods seem trivial and insignificant. Geologists have long ago repudiated mere thousands of years; they now claim millions, and many millions of years, for the performance of geological phenomena. If the earth has existed for the millions of years which geologists assert, it becomes reasonable for astronomers to speculate on the phenomena which have transpired in the heavens in the lapse of similar ages. By the aid of our knowledge of star distances, combined with an assumed velocity of thirty miles per second, we can make the attempt to peer back into the remote past, and show how great are the changes which our universe seems to have undergone.

In a million years 61 Cygni will apparently have moved through a distance which is twenty-five times as great as its present distance from the sun. Whatever be the direction in which 61 Cygni is moving—whether it be towards the earth or from the earth, to the right or to the left, it must have been about twenty-five times as far off a million years ago as it is at present; but even at its present distance 61 Cygni is a small star; were it ten times as far it could only be seen with a good telescope; were it twenty-five times as far it would barely be a visible point in our greatest telescopes.

The conclusions arrived at with regard to 61 Cygni may be applied with varying degrees of emphasis to other stars. We are thus led to the conclusion that many of the stars with which the heavens are strewn are apparently in slow motion. But this motion though apparently slow may really be very rapid. When standing on the sea-shore, and looking at a steamer on the distant horizon, we can hardly notice that the steamer is moving. It is true that by looking again in a few minutes we can detect a change in its place; but[Pg 454] the motion of the steamer seems slow. Yet if we were near the steamer we would find that it was rushing along at the rate of many miles an hour. It is the distance which causes the illusion. So it is with the stars: they seem to move slowly because they are very distant, but were we near them, we could see that in the majority of cases their motions are a thousand times as fast as the quickest steamer that ever ploughed the ocean.

It thus appears that the permanence of the sidereal heavens, and the fixity of the constellations in their relative positions, are only ephemeral. When we rise to the contemplation of such vast periods of time as the researches of geology disclose, the durability of the constellations vanishes! In the lapse of those stupendous ages stars and constellations gradually dissolve from view, to be replaced by others of no greater permanence.

It not unfrequently happens that a parallax research proves abortive. The labour has been finished, the observations are reduced and discussed, and yet no value of the parallax can be obtained. The distance of the star is so vast that our base-line, although it is nearly two hundred millions of miles long, is too short to bear any appreciable ratio to the distance of the star. Even from such failures, however, information may often be drawn.

Let me illustrate this by an account derived from my own experience at Dunsink. We have already mentioned that on the 24th November, 1876, a well-known astronomer—Dr. Schmidt, of Athens—noticed a new bright star of the third magnitude in the constellation Cygnus. On the 20th of November Nova Cygni was invisible. Whether it first burst forth on the 21st, 22nd, or 23rd no one can tell; but on the 24th it was discovered. Its brilliancy even then seemed to be waning; so, presumably, it was brightest at some moment between the 20th and 24th of November. The outbreak must thus have been comparatively sudden, and we know of no cause which would account for such a phenomenon more simply than a gigantic collision. The decline in the brilliancy was much more tardy than its growth, and[Pg 455] more than a fortnight passed before the star relapsed into insignificance—two or three days (or less) for the rise, two or three weeks for the fall. Yet even two or three weeks was a short time in which to extinguish so mighty a conflagration. It is comparatively easy to suggest an explanation of the sudden outbreak; it is not equally easy to understand how it can have been subdued in a few weeks. A good-sized iron casting in one of our foundries takes nearly as much time to cool as sufficed to abate the celestial fires in Nova Cygni!

On this ground it seemed not unreasonable to suppose that perhaps Nova Cygni was not really a very extensive conflagration. But, if such were the case, the star must have been comparatively near to the earth, since it presented so brilliant a spectacle and attracted so much attention. It therefore appeared a plausible object for a parallax research; and consequently a series of observations were made some years ago at Dunsink. I was at the time too much engaged with other work to devote very much labour to a research which might, after all, only prove illusory. I simply made a sufficient number of micrometric measurements to test whether a large parallax existed. It has been already pointed out how each star appears to describe a minute parallactic ellipse, in consequence of the annual motion of the earth, and by measurement of this ellipse the parallax—and therefore the distance—of the star can be determined. In ordinary circumstances, when the parallax of a star is being investigated, it is necessary to measure the position of the star in its ellipse on many different occasions, distributed over a period of at least an entire year. The method we adopted was much less laborious. It was sufficiently accurate to test whether or not Nova Cygni had a large parallax, though it might not have been delicate enough to disclose a small parallax. At a certain date, which can be readily computed, the star is at one end of the parallactic ellipse, and six months later the star is at the other end. By choosing suitable times in the year for our observations, we can measure the star in those two positions when it is most deranged by parallax.[Pg 456] It was by observations of this kind that I sought to detect the parallax of Nova Cygni. Its distance from a neighbouring star was carefully measured by the micrometer at the two seasons when, if parallax existed, those distances should show their greatest discrepancy; but no certain difference between these distances could be detected. The observations, therefore, failed to reveal the existence of a parallactic ellipse—or, in other words, the distance of Nova Cygni was too great to be measured by observations of this kind.

It is certain that if Nova Cygni had been one of the nearest stars these observations would not have been abortive. We are therefore entitled to believe that Nova Cygni must be at least 20,000,000,000,000 miles from the solar system; and the suggestion that the brilliant outburst was of small dimensions must, it seems, be abandoned. The intrinsic brightness of Nova Cygni, when at its best, cannot have been greatly if at all inferior to the brilliancy of our sun himself. If the sun were withdrawn from us to the distance of Nova Cygni, it would seemingly have dwindled down to an object not more brilliant than the variable star. How the lustre of such a stupendous object declined so rapidly remains, therefore, a mystery not easy to explain. Have we not said that the outbreak of brilliancy in this star occurred between the 20th and the 24th of November, 1876? It would be more correct to say that the tidings of that outbreak reached our system at the time referred to. The real outbreak must have taken place at least three years previously. Indeed, at the time that the star excited such commotion in the astronomical world here, it had already relapsed again into insignificance.

In connection with the subject of the present chapter we have to consider a great problem which was proposed by Sir William Herschel. He saw that the stars were animated by proper motion; he saw also that the sun is a star, one of the countless host of heaven, and he was therefore led to propound the stupendous question as to whether the sun, like the other stars which are its peers, was also in motion. Consider all that this great question involves. The sun has[Pg 457] around it a retinue of planets and their attendant satellites, the comets, and a host of smaller bodies. The question is, whether all this superb system is revolving around the sun at rest in the middle, or whether the whole system—sun, planets, and all—is not moving on bodily through space.

Herschel was the first to solve this noble problem; he discovered that our sun and the splendid retinue by which it is attended are moving in space. He not only discovered this, but he ascertained the direction in which the system was moving, as well as the approximate velocity with which that movement was probably performed. It has been shown that the sun and his system is now hastening towards a point of the heavens near the constellation Lyra. The velocity with which the motion is performed corresponds to the magnitude of the system; quicker than the swiftest rifle-bullet that was ever fired, the sun, bearing with it the earth and all the other planets, is now sweeping onwards. We on the earth participate in that motion. Every half hour we are something like ten thousand miles nearer to the constellation of Lyra than we should have been if the solar system were not animated by this motion. As we are proceeding at this stupendous rate towards Lyra, it might at first be supposed that we ought soon to get there; but the distances of the stars in that neighbourhood seem not less than those of the stars elsewhere, and we may be certain that the sun and his system must travel at the present rate for far more than a million years before we have crossed the abyss between our present position and the frontiers of Lyra. It must, however, be acknowledged that our estimate of the actual speed with which our solar system is travelling is exceedingly uncertain, but this does not in the least affect the fact that we are moving in the direction first approximately indicated by Herschel (see Chapter XXIII.).

It remains to explain the method of reasoning which Herschel adopted, by which he was able to make this great discovery. It may sound strange to hear that the detection of the motion of the sun was not made by looking at the sun; all the observations of the luminary itself with all the telescopes in the world would never tell us of that motion,[Pg 458] for the simple reason that the earth, whence our observations must be made, participates in it. A passenger in the cabin of a ship usually becomes aware that the ship is moving by the roughness of the sea; but if the sea be perfectly calm, then, though the tables and chairs in the cabin are moving as rapidly as the ship, yet we do not see them moving, because we are also travelling with the ship. If we could not go out of the cabin, nor look through the windows, we would never know whether the ship was moving or at rest; nor could we have any idea as to the direction in which the ship was going, or as to the velocity with which that motion was performed.

The sun, with his attendant host of planets and satellites, may be likened to the ship. The planets may revolve around the sun just as the passengers may move about in the cabin, but as the passengers, by looking at objects on board, can never tell whither the ship is going, so we, by merely looking at the sun, or at the other planets or members of the solar system, can never tell if our system as a whole is in motion.

The conditions of a perfectly uniform movement along a perfectly calm sea are not often fulfilled on the waters with which we are acquainted, but the course of the sun and his system is untroubled by any disturbance, so that the majestic progress is conducted with absolute uniformity. We do not feel the motion; and as all the planets are travelling with us, we can get no information from them as to the common motion by which the whole system is animated.

The passengers are, however, at once apprised of the ship's motion when they go on deck, and when they look at the sea surrounding them. Let us suppose that their voyage is nearly accomplished, that the distant land appears in sight, and, as evening approaches, the harbour is discerned into which the ship is to enter. Let us suppose that the harbour has, as is often the case, a narrow entrance, and that its mouth is indicated by a lighthouse on each side. When the harbour is still a long way off, near the horizon, the two lights are seen close together, and now that the evening has closed in, and the night has become quite dark, these two lights are all[Pg 459] that remain visible. While the ship is still some miles from its destination the two lights seem close together, but as the distance decreases the two lights seem to open out; gradually the ship gets nearer, while the lights are still opening, till finally, when the ship enters the harbour, instead of the two lights being directly in front, as at the commencement, one of the lights is passed by on the right hand, while the other is similarly found on the left. If, then, we are to discover the motion of the solar system, we must, like the passenger, look at objects unconnected with our system, and learn our own motion by their apparent movements. But are there any objects in the heavens unconnected with our system? If all the stars were like the earth, merely the appendages of our sun, then we never could discover whether we were at rest or whether we were in motion: our system might be in a condition of absolute rest, or it might be hurrying on with an inconceivably great velocity, for anything we could tell to the contrary. But the stars do not belong to the system of our sun; they are, rather, suns themselves, and do not recognise the sway of our sun, as this earth is obliged to do. The stars will, therefore, act as the external objects by which we can test whether our system is voyaging through space.

With the stars as our beacons, what ought we to expect if our system be really in motion? Remember that when the ship was approaching the harbour the lights gradually opened out to the right and left. But the astronomer has also lights by which he can observe the navigation of that vast craft, our solar system, and these lights will indicate the path along which he is borne. If our solar system be in motion, we should expect to find that the stars were gradually spreading away from that point in the heavens towards which our motion tends. This is precisely what we do find. The stars in the constellations are gradually spreading away from a central point near the constellation of Lyra, and hence we infer that it is towards Lyra that the motion of the solar system is directed.

There is one great difficulty in the discussion of this question. Have we not had occasion to observe that the stars[Pg 460] themselves are in actual motion? It seems certain that every star, including the sun himself as a star, has each an individual motion of its own. The motions of the stars as we see them are partly apparent as well as partly real; they partly arise from the actual motion of each star and partly from the motion of the sun, in which we partake, and which produces an apparent motion of the star. How are these to be discriminated? Our telescopes and our observations can never effect this decomposition directly. To accomplish the analysis, Herschel resorted to certain geometrical methods. His materials at that time were but scanty, but in his hands they proved adequate, and he boldly announced his discovery of the movement of the solar system.

So astounding an announcement demanded the severest test which the most refined astronomical resources could suggest. There is a certain powerful and subtle method which astronomers use in the effort to interpret nature. Bishop Butler has said that probability is the guide of life. The proper motion of a star has to be decomposed into two parts, one real and the other apparent. When several stars are taken, we may conceive an infinite number of ways into which the movements of each star can be so decomposed. Each one of these conceivable divisions will have a certain element of probability in its favour. It is the business of the mathematician to determine the amount of that probability. The case, then, is as follows:—Among all the various systems one must be true. We cannot lay our finger for certain on the true one, but we can take that which has the highest degree of probability in its favour, and thus follow the precept of Butler to which we have already referred. A mathematician would describe his process by calling it the method of least squares. Since Herschel's discovery, one hundred years ago, many an astronomer using observations of hundreds of stars has attacked the same problem. Mathematicians have exhausted every refinement which the theory of probabilities can afford, but only to confirm the truth of that splendid theory which seems to have been one of the flashes of Herschel's genius.

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This book is part of the public domain. Robert S. Ball (2008). The Story of the Heavens. Urbana, Illinois: Project Gutenberg. Retrieved October 2022 https://www.gutenberg.org/cache/epub/27378/pg27378-images.html

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