"I spent the night of the 6th of January at Herschel's, in Datchet, near Windsor, and had the good luck to hit on a fine evening. He has his 20-foot Newtonian telescope in the open air, and mounted in his garden very simply and conveniently. It is moved by an assistant, who stands below it.... Near the instrument is a clock regulated to sidereal time.... In the room near it sits Herschel's sister, and she has Flamsteed's atlas open before her. As he gives her the word, she writes down the declination and right ascension, and the other circumstances of the observation. In this way Herschel examines the whole sky without omitting the least part. He commonly observes with a magnifying power of one hundred and fifty, and is sure that after four or five years he will have passed in review every object above our horizon. He showed me the book in which his observations up to this time are written, and I am astonished at the great number of them. Each sweep covers 2° 15' in declination, and he lets each star pass at least three times through the field of his telescope, so that it is impossible that anything can escape him. He has already found about 900 double stars, and almost as many nebulæ. I went to bed about one o'clock, and up to that time he had found that night four or five new nebulæ. The thermometer in the garden stood at 13° Fahrenheit; but, in spite of this, Herschel observes the whole night through, except that he stops every three or four hours and goes into the room for a few moments. For some years Herschel has observed the heavens every hour when the weather is clear, and this always in the open air, because he says that the telescope only performs well when it is at the same temperature as the air. He protects himself against the weather by putting on more clothing. He has an excellent constitution, and thinks about nothing else in the world but the celestial bodies. He has promised me in the most cordial way, entirely in the service of astronomy, and without thinking of his own interest, to see to the telescopes I have ordered for European observatories, and he will himself attend to the preparation of the mirrors."
"I spent the night of the 6th of January at Herschel's, in Datchet, near Windsor, and had the good luck to hit on a fine evening. He has his 20-foot Newtonian telescope in the open air, and mounted in his garden very simply and conveniently. It is moved by an assistant, who stands below it.... Near the instrument is a clock regulated to sidereal time.... In the room near it sits Herschel's sister, and she has Flamsteed's atlas open before her. As he gives her the word, she writes down the declination and right ascension, and the other circumstances of the observation. In this way Herschel examines the whole sky without omitting the least part. He commonly observes with a magnifying power of one hundred and fifty, and is sure that after four or five years he will have passed in review every object above our horizon. He showed me the book in which his observations up to this time are written, and I am astonished at the great number of them. Each sweep covers 2° 15' in declination, and he lets each star pass at least three times through the field of his telescope, so that it is impossible that anything can escape him. He has already found about 900 double stars, and almost as many nebulæ. I went to bed about one o'clock, and up to that time he had found that night four or five new nebulæ. The thermometer in the garden stood at 13° Fahrenheit; but, in spite of this, Herschel observes the whole night through, except that he stops every three or four hours and goes into the room for a few moments. For some years Herschel has observed the heavens every hour when the weather is clear, and this always in the open air, because he says that the telescope only performs well when it is at the same temperature as the air. He protects himself against the weather by putting on more clothing. He has an excellent constitution, and thinks about nothing else in the world but the celestial bodies. He has promised me in the most cordial way, entirely in the service of astronomy, and without thinking of his own interest, to see to the telescopes I have ordered for European observatories, and he will himself attend to the preparation of the mirrors."
Fig. 84.Fig. 84.—William Herschel.From an Original Picture in the Possession ofWm. Watson, M.D., F.R.S.Painted by Abbott.Engraved by Ryder.
In 1783, Herschel married an estimable lady who sympathized with his pursuits. She was the only daughter of a City magnate, so his pecuniary difficulties, such as they were (they were never very troublesome to him), came to an end. They moved now into a more commodious house at Slough. Their one son, afterwards the famous Sir John Herschel,was born some nine years later. But the marriage was rather a blow to his devoted sister: henceforth she lived in lodgings, and went over at night-time to help him observe. For it must be remarked that this family literally turned night into day. Whatever sleep they got was in the day-time. Every fine night without exception was spent in observing: and the quite incredible fierceness of the pursuit is illustrated, as strongly as it can be, by the following sentence out of Caroline's diary, at the time of the move from Datchet to Slough: "The last night at Datchet was spent in sweeping till daylight, and by the next evening the telescope stood ready for observation at Slough."
Caroline was now often allowed to sweep with a small telescope on her own account. In this way she picked up a good many nebulæ in the course of her life, and eight comets, four of which were quite new, and one of which, known since as Encke's comet, has become very famous.
The work they got through between them is something astonishing. He made with his own hands 430 parabolic mirrors for reflecting telescopes, besides a great number of complete instruments. He was forty-two when he began contributing to the Royal Society; yet before he died he had sent them sixty-nine long and elaborate treatises. One of these memoirs is a catalogue of 1000 nebulæ. Fifteen years after he sends in another 1000; and some years later another 500. He also discovered 806 double stars, which he proved were really corrected from the fact that they revolved round each other (p. 309). He lived to see some of them perform half a revolution. For him the stars were not fixed: they moved slowly among themselves. He detected their proper motions. He passed the whole northern firmament in review four distinct times; counted the stars in 3,400 gauge-fields, and estimated the brightness of hundreds of stars. He also measured as accurately ashe could their proper motions, devising for this purpose the method which still to this day remains in use.
And what is the outcome of it all? It is not Uranus, nor the satellites, nor even the double stars and the nebulæ considered as mere objects: it is the beginning of a science of the stars.
Fig. 85.Fig. 85.—Caroline Herschel.From a Drawing from Life, byGeorge Müller, 1847.
Hitherto the stars had only been observed for nautical and practical purposes. Their times of rising and southing and setting had been noted; they had been treated as a clock or piece of dead mechanism, and as fixed points of reference. All the energies of astronomers had gone out towards the solar system. It was the planets that had beenobserved. Tycho had observed and tabulated their positions. Kepler had found out some laws of their motion. Galileo had discovered their peculiarities and attendants. Newton and Laplace had perceived every detail of their laws.
But for the stars—the old Ptolemaic system might still have been true. They might still be mere dots in a vast crystalline sphere, all set at about one distance, and subservient to the uses of the earth.
Herschel changed all this. Instead of sameness, he found variety; instead of uniformity of distance, limitless and utterly limitless fields and boundless distances; instead of rest and quiescence, motion and activity; instead of stagnation, life.
Fig. 86.Fig. 86.—The double-double star ε Lyræ as seen under three different powers.
Yes, that is what Herschel discovered—the life and activity of the whole visible universe. No longer was our little solar system to be the one object of regard, no longer were its phenomena to be alone interesting to man. With Herschel every star was a solar system. And more than that: he found suns revolving round suns, at distances such as the mind reels at, still obeying the same law of gravitation as pulls an apple from a tree. He tried hard to estimate the distance of the stars from the earth, but there he failed: it was too hopeless a problem. It was solved some time after his death by Bessel, and the distances ofmany stars are now known but these distances are awful and unspeakable. Our distance from the sun shrinks up into a mere speck—the whole solar system into a mere unit of measurement, to be repeated hundreds of thousands of times before we reach the stars.
Yet their motion is visible—yes, to very accurate measurement quite plain. One star, known as 61 Cygni, was then and is now rushing along at the rate of 100 miles every second. Not that you must imagine that this makes any obvious and apparent change in its position. No, for all ordinary and practical purposes they are still fixed stars; thousands of years will show us no obvious change; "Adam" saw precisely the same constellations as we do: it is only by refined micrometric measurement with high magnifying power that their flight can be detected.
But the sun is one of the stars—not by any means a specially large or bright one; Sirius we now know to be twenty times as big as the sun. The sun is one of the stars: then is it at rest? Herschel asked this question and endeavoured to answer it. He succeeded in the most astonishing manner. It is, perhaps, his most remarkable discovery, and savours of intuition. This is how it happened. With imperfect optical means and his own eyesight to guide him, he considered and pondered over the proper motion of the stars as he had observed it, till he discovered a kind of uniformity running through it all. Mixed up with irregularities and individualities, he found that in a certain part of the heavens the stars were on the whole opening out—separating slowly from each other; on the opposite side of the heavens they were on the average closing up—getting slightly nearer to each other; while in directions at right angles to this they were fairly preserving their customary distances asunder.
Now, what is the moral to be drawn from such uniformity of behaviour among unconnected bodies? Surely that this part of their motion is only apparent—that it is we who are moving. Travelling over a prairie bounded by a belt oftrees, we should see the trees in our line of advance opening out, and those behind closing up; we should see in fact the same kind of apparent motion as Herschel was able to detect among the stars: the opening out being most marked near the constellation Hercules. The conclusion is obvious: the sun, with all its planets, must be steadily moving towards a point in the constellation Hercules. The most accurate modern research has been hardly able to improve upon this statement of Herschel's. Possibly the solar system may ultimately be found to revolve round some other body, but what that is no one knows. All one can tell is the present direction of the majestic motion: since it was discovered it has continued unchanged, and will probably so continue for thousands of years.
Fig. 87.Fig. 87.—Old drawing of the cluster in Hercules.
And, finally, concerning the nebulæ. These mysterious objects exercised a strong fascination for Herschel, andmany are the speculations he indulges in concerning them. At one time he regards them all as clusters of stars, and the Milky Way as our cluster; the others he regards as other universes almost infinitely distant; and he proceeds to gauge and estimate the shape of our own universe or galaxy of suns, the Milky Way.
Later on, however, he pictures to himself the nebulæ as nascent suns: solar systems before they are formed. Some he thinks have begun to aggregate, while some are still glowing gas.
Fig. 88.Fig. 88.—Old drawing of the Andromeda nebula.
He likens the heavens to a garden in which there are plants growing in all manner of different stages: some shooting, some in leaf, some in flower, some bearing seed, some decaying; and thus at one inspection we have before us the whole life-history of the plant.
Just so he thinks the heavens contain worlds, some old, some dead, some young and vigorous, and some in the act of being formed. The nebulæ are these latter, and the nebulous stars are a further stage in the condensation towards a sun.
And thus, by simple observation, he is led towards something very like the nebular hypothesis of Laplace; and his position, whether it be true or false, is substantially the same as is held to-day.
Fig. 89.Fig. 89.—The great nebula in Orion.
Weknownow that many of the nebulæ consist of innumerable isolated particles and may be spoken of as gas. We know that some are in a state of whirling motion. We know also that such gas left to itself will slowly as it cools condense and shrink, so as to form a central solid nucleus; and also, if it were in whirling motion, that it would send off rings from itself, and that these rings could break up into planets. In two familiar cases the ring hasnot yet thus aggregated into planet or satellite—the zone of asteroids, and Saturn's ring.
The whole of this could not have been asserted in Herschel's time: for further information the world had to wait.
These are the problems of modern astronomy—these and many others, which are the growth of this century, aye, and the growth of the last thirty or forty, and indeed of the last ten years. Even as I write, new and very confirmatory discoveries are being announced. The Milky Waydoesseem to have some affinity with our sun. And the chief stars of the constellation of Orion constitute another family, and are enveloped in the great nebula, now by photography perceived to be far greater than had ever been imagined.
What is to be the outcome of it all I know not; but sure I am of this, that the largest views of the universe that we are able to frame, and the grandest manner of its construction that we can conceive, are certain to pale and shrink and become inadequate when confronted with the truth.
Bode's Law.—Write down the series 0, 3, 6, 12, 24, 48, &c.; add 4 to each, and divide by 10; you get the series:
·4·71·01·62·85·210·019·638·8MercuryVenusEarthMars——JupiterSaturnUranus——
numbers which very fairly represent the distances of the then known planets from the sun in the order specified.
Ceres was discovered on the 1st of January, 1801, by Piazzi; Pallas in March, 1802, by Olbers; Juno in 1804, by Harding; and Vesta in 1807, by Olbers. No more asteroids were discovered till 1845, but there are now several hundreds known. Their diameters range from 500 to 20 miles.
Neptune was discovered from the perturbations of Uranus by sheer calculation, carried on simultaneously and independently by Leverrier in Paris, and Adams in Cambridge. It was first knowingly seen by Galle, of Berlin, on the 23rd of September, 1846.
Upto the time of Herschel, astronomical interest centred on the solar system. Since that time it has been divided, and a great part of our attention has been given to the more distant celestial bodies. The solar system has by no means lost its interest—it has indeed gained in interest continually, as we gain in knowledge concerning it; but in order to follow the course of science it will be necessary for us to oscillate to and fro, sometimes attending to the solar system—the planets and their satellites—sometimes extending our vision to the enormously more distant stellar spaces.
Those who have read the third lecture in Part I. will remember the speculation in which Kepler indulged respecting the arrangements of the planets, the order in which they succeeded one another in space, and the law of their respective distances from the sun; and his fanciful guess about the five regular solids inscribed and circumscribed about their orbits.
The rude coincidences were, however, accidental, and he failed to discover any true law. No thoroughly satisfactory law is known at the present day. And yet, if the nebular hypothesis or anything like it be true, there must be some law to be discovered hereafter, though it may be a very complicated one.
An empirical relation is, however, known: it was suggested by Tatius, and published by Bode, of Berlin, in 1772. It is always known as Bode's law.
Bode's law asserts that the distance of each planet is approximately double the distance of the inner adjacent planet from the sun, but that the rate of increase is distinctly slower than this for the inner ones; consequently a better approximation will be obtained by adding a constant to each term of an appropriate geometrical progression. Thus, form a doubling series like this, 1½, 3, 6, 12, 24, &c. doubling each time; then add 4 to each, and you get a series which expresses very fairly the relative distances of the successive planets from the sun, except that the number for Mercury is rather erroneous, and we now know that at the other extreme the number for Neptune is erroneous too.I have stated it in the notes above in a form calculated to give the law every chance, and a form that was probably fashionable after the discovery of Uranus; but to call the first term of the doubling series 0 is evidently not quite fair, though it puts Mercury's distance right. Neptune's distance, however, turns out to be more nearly 30 times the earth's distance than 38·8. The others are very nearly right: compare column D of the table preceding Lecture III. onp. 57, with the numbers in the notes onp. 294.
Bode's law asserts that the distance of each planet is approximately double the distance of the inner adjacent planet from the sun, but that the rate of increase is distinctly slower than this for the inner ones; consequently a better approximation will be obtained by adding a constant to each term of an appropriate geometrical progression. Thus, form a doubling series like this, 1½, 3, 6, 12, 24, &c. doubling each time; then add 4 to each, and you get a series which expresses very fairly the relative distances of the successive planets from the sun, except that the number for Mercury is rather erroneous, and we now know that at the other extreme the number for Neptune is erroneous too.
I have stated it in the notes above in a form calculated to give the law every chance, and a form that was probably fashionable after the discovery of Uranus; but to call the first term of the doubling series 0 is evidently not quite fair, though it puts Mercury's distance right. Neptune's distance, however, turns out to be more nearly 30 times the earth's distance than 38·8. The others are very nearly right: compare column D of the table preceding Lecture III. onp. 57, with the numbers in the notes onp. 294.
The discovery of Uranus a few years afterwards, in 1781, at 19·2 times the earth's distance from the sun, lent greatéclâtto the law, and seemed to establish its right to be regarded as at least a close approximation to the truth.
The gap between Mars and Jupiter, which had often been noticed, and which Kepler filled with a hypothetical planet too small to see, comes into great prominence by this law of Bode. So much so, that towards the end of last century an enthusiastic German, von Zach, after some search himself for the expected planet, arranged a committee of observing astronomers, or, as he termed it, a body of astronomical detective police, to begin a systematic search for this missing subject of the sun.
Fig. 90.Fig. 90.—Planetary orbits to scale; showing the Asteroidal region between Jupiter and Mars. (The orbits of satellites are exaggerated.)
In 1800 the preliminaries were settled: the heavens near the zodiac were divided into twenty-four regions, each of which was intrusted to one observer to be swept. Meanwhile, however, quite independently of these arrangements in Germany, and entirely unknown to this committee, a quiet astronomer in Sicily, Piazzi, was engaged in making a catalogue of the stars. His attention was directed to a certain region in Taurus by an error in a previous catalogue, which contained a star really non-existent.
In the course of his scrutiny, on the 1st of January, 1801, he noticed a small star which next evening appeared to have shifted. He watched it anxiously for successive evenings, and by the 24th of January he was quite sure he had got hold of some moving body, not a star: probably, he thought, a comet. It was very small, only of the eighth magnitude; and he wrote to two astronomers (one of them Bode himself) saying what he had observed. He continued to observe till the 11th of February, when he was attacked by illness and compelled to cease.
His letters did not reach their destination till the end of March. Directly Bode opened his letter he jumped to the conclusion that this must be the missing planet. But unfortunately he was unable to verify the guess, for the object, whatever it was, had now got too near the sun to be seen. It would not be likely to be out again before September, and by that time it would be hopelessly lost again, and have just as much to be rediscovered as if it had never been seen.
Mathematical astronomers tried to calculate a possible orbit for the body from the observations of Piazzi, but the observed places were so desperately few and close together. It was like having to determine a curve from three points close together. Three observations ought to serve,[27]but if they are taken with insufficient interval between them it is extremely difficult to construct the whole circumstances of the orbit from them. All the calculations gave different results, and none were of the slightest use.
The difficulty as it turned out was most fortunate. It resulted in the discovery of one of the greatest mathematicians, perhaps the greatest, that Germany has ever produced—Gauss. He was then a young man of twenty-five, eking out a living by tuition. He had invented but not published several powerful mathematical methods (one of them now known as "the method of least squares"), and he applied them to Piazzi's observations. He was thus able to calculate an orbit, and to predict a place where, by the end of the year, the planet should be visible. On the 31st of December of that same year, very near the place predicted by Gauss, von Zach rediscovered it, and Olbers discovered it also the next evening. Piazzi called it Ceres, after the tutelary goddess of Sicily.
Its distance from the sun as determined by Gauss was 2·767 times the earth's distance. Bode's law made it 2·8. It was undoubtedly the missing planet. But it was only one hundred and fifty or two hundred miles in diameter—the smallest heavenly body known at the time of its discovery. It revolves the same way as other planets, but the plane of its orbit is tilted 10° to the plane of the ecliptic, which was an exceptionally large amount.
Very soon, a more surprising discovery followed. Olbers, while searching for Ceres, had carefully mapped the part of the heavens where it was expected; and in March, 1802, he saw in this place a star he had not previously noticed. In two hours he detected its motion, and in a month he sent his observations to Gauss, who returned as answer the calculated orbit. It was distant 2·67, like Ceres, and was a little smaller, but it had a very excentric orbit: its plane being tilted 34½°, an extraordinary inclination. This was called Pallas.
Olbers at once surmised that these two planets were fragments of a larger one, and kept an eager look out for other fragments.
In two years another was seen, in the course of charting the region of the heavens traversed by Ceres and Pallas. It was smaller than either, and was called Juno.
In 1807 the persevering search of Olbers resulted in the discovery of another, with a very oblique orbit, which Gauss named Vesta. Vesta is bigger than any of the others, being five hundred miles in diameter, and shines like a star of the sixth magnitude. Gauss by this time had become so practised in the difficult computations that he worked out the complete orbit of Vesta within ten hours of receiving the observational data from Olbers.
For many weary years Olbers kept up a patient and unremitting search for more of these small bodies, or fragments of the large planet as he thought them; but his patience went unrewarded, and he died in 1840 without seeing or knowing of any more. In 1845 another was found, however, in Germany, and a few weeks later two others by Mr. Hind in England. Since then there seems no end to them; numbers have been discovered in America, where Professors Peters and Watson have made a specialty of them, and have themselves found something like a hundred.
Vesta is the largest—its area being about the same as that of Central Europe, without Russia or Spain—and the smallest known is about twenty miles in diameter, or with a surface about the size of Kent. The whole of them together do not nearly equal the earth in bulk.
The main interest of these bodies to us lies in the question, What is their history? Can they have been once a single planet broken up? or are they rather an abortive attempt at a planet never yet formed into one?
The question is notentirelysettled, but I can tell you which way opinion strongly tends at the present time.
Imagine a shell travelling in an elliptic orbit round theearth to suddenly explode: the centre of gravity of all its fragments would continue moving along precisely the same path as had been traversed by the centre of the shell before explosion, and would complete its orbit quite undisturbed. Each fragment would describe an orbit of its own, because it would be affected by a different initial velocity; but every orbit would be a simple ellipse, and consequently every piece would in time return through its starting-point—viz. the place at which the explosion occurred. If the zone of asteroids had a common point through which they all successively passed, they could be unhesitatingly asserted to be the remains of an exploded planet. But they have nothing of the kind; their orbits are scattered within a certain broad zone—a zone everywhere as broad as the earth's distance from the sun, 92,000,000 miles—with no sort of law indicating an origin of this kind.
It must be admitted, however, that the fragments of our supposed shell might in the course of ages, if left to themselves, mutually perturb each other into a different arrangement of orbits from that with which they began. But their perturbations would be very minute, and moreover, on Laplace's theory, would only result in periodic changes, provided each mass were rigid. It is probable that the asteroids were at one time not rigid, and hence it is difficult to say what may have happened to them; but there is not the least reason to believe that their present arrangement is derivable in any way from an explosion, and it is certain that an enormous time must have elapsed since such an event if it ever occurred.
It is far more probable that they never constituted one body at all, but are the remains of a cloudy ring thrown off by the solar system in shrinking past that point: a small ring after the immense effort which produced Jupiter and his satellites: a ring which has aggregated into a multitude of little lumps instead of a few big ones. Such an event is not unique in the solar system;there is a similar ring round Saturn. At first sight, and to ordinary careful inspection, this differs from the zone of asteroids in being a solid lump of matter, like a quoit. But it is easy to show from the theory of gravitation, that a solid ring could not possibly be stable, but would before long get precipitated excentrically upon the body of the planet. Devices have been invented, such as artfully distributed irregularities calculated to act as satellites and maintain stability; but none of these things really work. Nor will it do to imagine the rings fluid; they too would destroy each other. The mechanical behaviour of a system of rings, on different hypotheses as to their constitution, has been worked out with consummate skill by Clerk Maxwell; who finds that the only possible constitution for Saturn's assemblage of rings is a multitude of discrete particles each pursuing its independent orbit. Saturn's ring is, in fact, a very concentrated zone of minor asteroids, and there is every reason to conclude that the origin of the solar asteroids cannot be very unlike the origin of the Saturnian ones. The nebular hypothesis lends itself readily to both.
The interlockings and motions of the particles in Saturn's rings are most beautiful, and have been worked out and stated by Maxwell with marvellous completeness. His paper constituted what is called "The Adams Prize Essay" for 1856. Sir George Airy, one of the adjudicators (recently Astronomer-Royal), characterized it as "one of the most remarkable applications of mathematics to physics that I have ever seen."
There are several distinct constituent rings in the entire Saturnian zone, and each perturbs the other, with the result that they ripple and pulse in concord. The waves thus formed absorb the effect of the mutual perturbations, and prevent an accumulation which would be dangerous to the persistence of the whole.
The only effect of gravitational perturbation and of collisions is gradually to broaden out the whole ring, enlargingits outer and diminishing its inner diameter. But if there were any frictional resistance in the medium through which the rings spin, then other effects would slowly occur, which ought to be looked for with interest. So complete and intimate is the way Maxwell works out and describes the whole circumstances of the motion of such an assemblage of particles, and so cogent his argument as to the necessity that they must move precisely so, and no otherwise, else the rings would not be stable, that it was a Cambridge joke concerning him that he paid a visit to Saturn one evening, and made his observations on the spot.
The total number of stars in the heavens visible to a good eye is about 5,000. The total number at present seen by telescope is about 50,000,000. The number able to impress a photographic plate has not yet been estimated; but it is enormously greater still. Of those which we can see in these latitudes, about 14 are of the first magnitude, 48 of the second, 152 of the third, 313 of the fourth, 854 of the fifth, and 2,010 of the sixth; total, 3,391.
The quickest-moving stars known are a double star of the sixth magnitude, called 61 Cygni, and one of the seventh magnitude, called Groombridge 1830. The velocity of the latter is 200 miles a second. The nearest known stars are 61 Cygni and α Centauri. The distance of these from us is about 400,000 times the distance of the sun. Their parallax is accordingly half a second of arc. Sirius is more than a million times further from us than our sun is, and twenty times as big; many of the brightest stars are at more than double this distance. The distance of Arcturus is too great to measure even now. Stellar parallax was first securely detected in 1838, by Bessel, for 61 Cygni. Bessel was born in 1784, and died in 1846, shortly before the discovery of Neptune.
The stars are suns, and are most likely surrounded by planets. One planet belonging to Sirius has been discovered. It was predicted by Bessel, its position calculated by Peters, and seen by Alvan Clark in 1862. Another predicted one, belonging to Procyon, has not yet been seen.
A velocity of 5 miles a second could carry a projectile right round the earth. A velocity of 7 miles a second would carry it away from the earth, and round the sun. A velocity of 27 miles a second would carry a projectile right out of the solar system never to return.
Wewill now leave the solar system for a time, and hastily sketch the history of stellar astronomy from the time of Sir William Herschel.
You remember how greatly Herschel had changed the aspect of the heavens for man,—how he had found that none of the stars were really fixed, but were moving in all manner of ways: some of this motion only apparent, much of it real. Nevertheless, so enormously distant are they, that if we could be transported back to the days of the old Chaldæan astronomers, or to the days of Noah, we should still see the heavens with precisely the same aspect as they wear now. Only by refined apparatus could any change be discoverable in all those centuries. For all practical purposes, therefore, the stars may still be well called fixed.
Another thing one may notice, as showing their enormous distances, is that from every planet of the solar system the aspect of the heavens will be precisely the same. Inhabitants of Mars, or Jupiter, or Saturn, or Uranus, will see exactly the same constellations as we do. The whole dimensions of the solar system shrink up into a speck when so contemplated. And from the stars none of the planetary orbs of our system are visible at all; nothing but the sun is visible, and that merely as a twinkling star, brighter than some, but fainter than many others.
The sun and the stars are one. Try to realize this distinctly, and keep it in mind. I find it often difficult to drive this idea home. After some talk on the subject a friendly auditor will report, "the lecturer then described the stars, including that greatest and most magnificent of all stars, the sun." It would be difficult more completely to misapprehend the entire statement. When I say the sun is one of the stars, I mean one among the others; we are a long way from them, they are a long way from each other. They need be no more closely packed among each other than we are closely packed among them; except that some of them are double or multiple, and we are not double.
It is highly desirable to acquire an intimate knowledge of the constellations and a nodding acquaintance with their principal stars. A description of their peculiarities is dull and uninteresting unless they are at least familiar by name. A littlevivâ vocehelp to begin with, supplemented by patient night scrutiny with a celestial globe or star maps under a tent or shed, is perhaps the easiest way: a very convenient instrument for the purpose of learning the constellations is the form of map called a "planisphere," because it can be made to show all the constellations visible at a given time at a given date, and no others. The Greek alphabet also is a thing that should be learnt by everybody. The increased difficulty in teaching science owing to the modern ignorance of even a smattering of Greek is becoming grotesque. The stars are named from their ancient grouping into constellations, and by the prefix of a Greek letter to the larger ones, and of numerals to the smaller ones. The biggest of all have special Arabic names as well. The brightest stars are called of "the first magnitude," the next are of "the second magnitude," and so on. But this arrangement into magnitudes has become technical and precise, and intermediate or fractional magnitudes are inserted. Those brighter than the ordinary first magnitude are therefore now spoken of as of magnitude ½, for instance, or ·6, which is rather confusing. Small telescopic stars are often only named by their numbers in some specified catalogue—a dull but sufficient method.Here is a list of the stars visible from these latitudes, which are popularly considered as of the first magnitude. All of them should be familiarly recognized in the heavens, whenever seen.Star.Constellation.SiriusCanis majorProcyonCanis minorRigelOrionBetelgeuxOrionCastorGeminiPolluxGeminiAldebaranTaurusArcturusBoötesVegaLyraCapellaAurigaRegulusLeoAltairAquilaFomalhautSouthern FishSpicaVirgoα Cygni is a little below the first magnitude. So, perhaps, is Castor. In the southern heavens, Canopus and α Centauri rank next after Sirius in brightness.
It is highly desirable to acquire an intimate knowledge of the constellations and a nodding acquaintance with their principal stars. A description of their peculiarities is dull and uninteresting unless they are at least familiar by name. A littlevivâ vocehelp to begin with, supplemented by patient night scrutiny with a celestial globe or star maps under a tent or shed, is perhaps the easiest way: a very convenient instrument for the purpose of learning the constellations is the form of map called a "planisphere," because it can be made to show all the constellations visible at a given time at a given date, and no others. The Greek alphabet also is a thing that should be learnt by everybody. The increased difficulty in teaching science owing to the modern ignorance of even a smattering of Greek is becoming grotesque. The stars are named from their ancient grouping into constellations, and by the prefix of a Greek letter to the larger ones, and of numerals to the smaller ones. The biggest of all have special Arabic names as well. The brightest stars are called of "the first magnitude," the next are of "the second magnitude," and so on. But this arrangement into magnitudes has become technical and precise, and intermediate or fractional magnitudes are inserted. Those brighter than the ordinary first magnitude are therefore now spoken of as of magnitude ½, for instance, or ·6, which is rather confusing. Small telescopic stars are often only named by their numbers in some specified catalogue—a dull but sufficient method.
Here is a list of the stars visible from these latitudes, which are popularly considered as of the first magnitude. All of them should be familiarly recognized in the heavens, whenever seen.
Star.Constellation.SiriusCanis majorProcyonCanis minorRigelOrionBetelgeuxOrionCastorGeminiPolluxGeminiAldebaranTaurusArcturusBoötesVegaLyraCapellaAurigaRegulusLeoAltairAquilaFomalhautSouthern FishSpicaVirgo
α Cygni is a little below the first magnitude. So, perhaps, is Castor. In the southern heavens, Canopus and α Centauri rank next after Sirius in brightness.
Fig. 91.Fig. 91.—Diagram illustrating Parallax.
The distances of the fixed stars had, we know, been a perennial problem, and many had been the attempts to solve it. All the methods of any precision have depended on the Copernican fact that the earth in June was 184 million miles away from its position in December, and that accordingly the grouping and aspect of the heavens should be somewhat different when seen from so different a point of view. An apparent change of this sort is called generally parallax;theparallax of a star being technically defined as the angle subtended at the star by the radius of the earth's orbit: that is to say, the angle EσS; where E is the earth, S the sun, and σ a star (Fig. 91).
Plainly, the further off σ is, the more nearly parallel willthe two lines to it become. And the difficulty of determining the parallax was just this, that the more accurately the observations were made, the more nearly parallel did those lines become. The angle was, in fact, just as likely to turn out negative as positive—an absurd result, of course, to be attributed to unavoidable very minute inaccuracies.
For a long time absolute methods of determining parallax were attempted; for instance, by observing the position of the star with respect to the zenith at different seasons of the year. And many of these determinations appeared to result in success. Hooke fancied he had measured a parallax for Vega in this way, amounting to 30" of arc. Flamsteed obtained 40" for γ Draconis. Roemer made a serious attempt by comparing observations of Vega and Sirius, stars almost the antipodes of each other in the celestial vault; hoping to detect some effect due to the size of the earth's orbit, which should apparently displace them with the season of the year. All these fancied results however, were shown to be spurious, and their real cause assigned, by the great discovery of the aberration of light by Bradley.
After this discovery it was possible to watch for still outstanding very minute discrepancies; and so the problem of stellar parallax was attacked with fresh vigour by Piazzi, by Brinkley, and by Struve. But when results were obtained, they were traced after long discussion to age and gradual wear of the instrument, or to some other minute inaccuracy. The more carefully the observation was made, the more nearly zero became the parallax—the more nearly infinite the distance of the stars. The brightest stars were the ones commonly chosen for the investigation, and Vega was a favourite, because, going near the zenith, it was far removed from the fluctuating and tiresome disturbances of atmospheric refraction. The reason bright stars were chosen was because they were presumably nearer than the others; and indeed a rough guess at their probabledistance was made by supposing them to be of the same size as the sun, and estimating their light in comparison with sunlight. By this confessedly unsatisfactory method it had been estimated that Sirius must be 140,000 times further away than the sun is, if he be equally big. We now know that Sirius is much further off than this; and accordingly that he is much brighter, perhaps sixty times as bright, though not necessarily sixty times as big, as our sun. But even supposing him of the same light-giving power as the sun, his parallax was estimated as 1"·8, a quantity very difficult to be sure of in any absolute determination.
Relative methods were, however, also employed, and the advantages of one of these (which seems to have been suggested by Galileo) so impressed themselves upon William Herschel that he made a serious attempt to compass the problem by its means. The method was to take two stars in the same telescopic field and carefully to estimate their apparent angular distance from each other at different seasons of the year. All such disturbances as precession, aberration, nutation, refraction, and the like, would affect them both equally, and could thus be eliminated. If they were at the same distance from the solar system, relative parallax would, indeed, also be eliminated; but if, as was probable, they were at different distances, then they would apparently shift relatively to one another, and the amount of shift, if it could be observed, would measure, not indeed the distance of either from the earth, but their distance from each other. And this at any rate would be a step. It might be completed by similarly treating other stars in the same field, taking them in pairs together. A bright and a faint star would naturally be suitable, because their distances were likely to be unequal; and so Herschel fixed upon a number of doublets which he knew of, containing one bright and one faint component. For up to that time it had been supposed that such grouping in occasional pairs or triplets was chance coincidence, the two being opticallyforeshortened together, but having no real connection or proximity. Herschel failed in what he was looking for, but instead of that he discovered the real connection of a number of these doublets, for he found that they were slowly revolving round each other. There are a certain number of merely optical or accidental doublets, but the majority of them are real pairs of suns revolving round each other.
This relative method of mapping micrometrically a field of neighbouring stars, and comparing their configuration now and six months hence, was, however, the method ultimately destined to succeed; and it is, I believe, the only method which has succeeded down to the present day. Certainly it is the method regularly employed, at Dunsink, at the Cape of Good Hope, and everywhere else where stellar parallax is part of the work.
Between 1830 and 1840 the question was ripe for settlement, and, as frequently happens with a long-matured difficulty, it gave way in three places at once. Bessel, Henderson, and Struve almost simultaneously announced a stellar parallax which could reasonably be accepted. Bessel was a little the earliest, and by far the most accurate. His, indeed, was the result which commanded confidence, and to him the palm must be awarded.
He was largely a self-taught student, having begun life in a counting-house, and having abandoned business for astronomy. But notwithstanding these disadvantages, he became a highly competent mathematician as well as a skilful practical astronomer. He was appointed to superintend the construction of Germany's first great astronomical observatory, that of Königsberg, which, by his system, zeal, and genius, he rapidly made a place of the first importance.
Struve at Dorpat, Bessel at Königsberg, and Henderson at the Cape of Good Hope—all of them at newly-equipped observatories—were severally engaged at the same problem.
But the Russian and German observers had the advantageof the work of one of the most brilliant opticians—I suppose the most brilliant—that has yet appeared: Fraunhofer, of Munich. An orphan lad, apprenticed to a maker of looking-glasses, and subject to hard struggles and privations in early life, he struggled upwards, and ultimately became head of the optical department of a Munich firm of telescope-makers. Here he constructed the famous "Dorpat refractor" for Struve, which is still at work; and designed the "Königsberg heliometer" for Bessel. He also made a long and most skilful research into the solar spectrum, which has immortalized his name. But his health was broken by early trials, and he died at the age of thirty-nine, while planning new and still more important optical achievements.
A heliometer is the most accurate astronomical instrument for relative measurements of position, as a transit circle is the most accurate for absolute determinations. It consists of an equatorial telescope with object-glass cut right across, and each half movable by a sliding movement one past the other, the amount by which the two halves are dislocated being read off by a refined method, and the whole instrument having a multitude of appendages conducive to convenience and accuracy. Its use is to act as a micrometer or measurer of small distances.[28]Each half of the object-glass gives a distinct image, which may be allowed to coincide or may be separated as occasion requires. If it be the components of a double star that are being examined, each component will in general be seen double, so that four images will be seen altogether; but by careful adjustment it will be possible to arrange that one image of each pair shall be superposed on or coincide with each other, in which case only three images are visible; the amount of dislocation of the halves of the object-glass necessary to accomplishthis is what is read off. The adjustment is one that can be performed with extreme accuracy, and by performing it again and again with all possible modifications, an extremely accurate determination of the angular distance between the two components is obtained.