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INDEX 221

LIST OF PLATES

PLATE

ERRATA

" 145, See note on page 220.

ASTRONOMICAL DISCOVERY

URANUS AND EROS

Discovery is expected from an astronomer. The lay mind scarcely thinks of a naturalist nowadays discovering new animals, or of a chemist as finding new elements save on rare occasions; but it does think of the astronomer as making discoveries. The popular imagination pictures him spending the whole night in watching the skies from a high tower through a long telescope, occasionally rewarded by the finding of something new, without much mental effort. I propose to compare with this romantic picture some of the actual facts, some of the ways in which discoveries are really made; and if we find that the image and the reality differ, I hope that the romance will nevertheless not be thereby destroyed, but may adapt itself to conditions more closely resembling the facts.

The popular conception finds expression in the lines of Keats:--

Then felt I like some watcher of the skies When a new planet swims into his ken.

Keats was born in 1795, published his first volume of poems in 1817, and died in 1821. At the time when he wrote the discovery of planets was comparatively novel in human experience. Uranus had been found by William Herschel in 1781, and in the years 1800 to 1807 followed the first four minor planets, a number destined to remain without additions for nearly forty years. It would be absurd to read any exact allusion into the words quoted, when we remember the whole circumstances under which they were written; but perhaps I may be forgiven if I compare them especially with the actual discovery of the planet Uranus, for the reason that this was by far the largest of the five--far larger than any other planet known except Jupiter and Saturn, while the others were far smaller--and that Keats is using throughout the poem metaphors drawn from the first glimpses of "vast expanses" of land or water. Perhaps I may reproduce the whole sonnet. His friend C. C. Clarke had put before him Chapman's "paraphrase" of Homer, and they sat up till daylight to read it, "Keats shouting with delight as some passage of especial energy struck his imagination. At ten o'clock the next morning Mr. Clarke found the sonnet on his breakfast-table."

Much have I travell'd in the realms of gold, And many goodly states and kingdoms seen; Round many western islands have I been Which bards in fealty to Apollo hold. Oft of one wide expanse had I been told That deep-brow'd Homer ruled as his demesne; Yet did I never breathe its pure serene Till I heard Chapman speak out loud and bold: Then felt I like some watcher of the skies When a new planet swims into his ken; Or like stout Cortez when with eagle eyes He star'd at the Pacific--and all his men Look'd at each other with a wild surmise-- Silent, upon a peak in Darien.

Let us then, as our first example of the way in which astronomical discoveries are made, turn to the discovery of the planet Uranus, and see how it corresponds with the popular conception as voiced by Keats. In one respect his words are true to the life or the letter. If ever there was a "watcher of the skies," William Herschel was entitled to the name. It was his custom to watch them the whole night through, from the earliest possible moment to daybreak; and the fruits of his labours were many and various almost beyond belief. But did the planet "swim into his ken"? Let us turn to the original announcement of his discovery as given in the Philosophical Transactions for 1781.

PHILOSOPHICAL TRANSACTIONS, 1781

BY MR. HERSCHEL, F.R.S.

"On Tuesday the 13th of March, between ten and eleven in the evening, while I was examining the small stars in the neighbourhood of H Geminorum, I perceived one that appeared visibly larger than the rest; being struck with its uncommon magnitude, I compared it to H Geminorum and the small star in the quartile between Auriga and Gemini, and finding it to be so much larger than either of them, suspected it to be a comet.

"I was then engaged in a series of observations on the parallax of the fixed stars, which I hope soon to have the honour of laying before the Royal Society; and those observations requiring very high powers, I had ready at hand the several magnifiers of 227, 460, 932, 1536, 2010, &c., all which I have successfully used upon that occasion. The power I had on when I first saw the comet was 227. From experience I knew that the diameters of the fixed stars are not proportionally magnified with higher powers as the planets are; therefore I now put on the powers of 460 and 932, and found the diameter of the comet increased in proportion to the power, as it ought to be, on a supposition of its not being a fixed star, while the diameters of the stars to which I compared it were not increased in the same ratio. Moreover, the comet being magnified much beyond what its light would admit of, appeared hazy and ill-defined with these great powers, while the stars preserved that lustre and distinctness which from many thousand observations I knew they would retain. The sequel has shown that my surmises were well founded, this proving to be the Comet we have lately observed.

"I have reduced all my observations upon this comet to the following tables. The first contains the measures of the gradual increase of the comet's diameter. The micrometers I used, when every circumstance is favourable, will measure extremely small angles, such as do not exceed a few seconds, true to 6, 8, or 10 thirds at most; and in the worst situations true to 20 or 30 thirds; I have therefore given the measures of the comet's diameter in seconds and thirds. And the parts of my micrometer being thus reduced, I have also given all the rest of the measures in the same manner; though in large distances, such as one, two, or three minutes, so great an exactness, for several reasons, is not pretended to."

At first sight this seems to be the wrong reference, for it speaks of a new comet, not a new planet. But it is indeed of Uranus that Herschel is speaking; and so little did he realise the full magnitude of his discovery at once, that he announced it as that of a comet; and a comet the object was called for some months. Attempts were made to calculate its orbit as a comet, and broke down; and it was only after much work of this kind had been done that the real nature of the object began to be suspected. But far more striking than this misconception is the display of skill necessary to detect any peculiarity in the object at all. Among a number of stars one seemed somewhat exceptional in size, but the difference was only just sufficient to awaken suspicion in a keen-eyed Herschel. Would any other observer have noticed the difference at all? Certainly several good observers had looked at the object before, and looked at it with the care necessary to record its position, without noting any peculiarity. Their observations were recovered subsequently and used to fix the orbit of the new planet more accurately. I shall remind you in the next chapter that Uranus had been observed in this way no less than seventeen times by first-rate observers without exciting their attention to anything remarkable. The first occasion was in 1690, nearly a century before Herschel's grand discovery, and these chance observations, which lay so long unnoticed as in some way erroneous, subsequently proved to be of the utmost value in fixing the orbit of the new planet. But there is even more striking testimony than this to the exceptional nature of Herschel's achievement. It is a common experience in astronomy that an observer may fail to notice in a general scrutiny some phenomenon which he can see perfectly well when his attention is directed to it: when a man has made a discovery and others are told what to look for, they often see it so easily that they are filled with amazement and chagrin that they never saw it before. Not so in the case of Uranus. At least two great astronomers, Lalande and Messier, have left on record their astonishment that Herschel could differentiate it from an ordinary star at all; for even when instructed where to look and what to look for, they had the greatest difficulty in finding it. I give a translation of Messier's words, which Herschel records in the paper already quoted announcing the discovery:--

"Nothing was more difficult than to recognise it; and I cannot conceive how you have been able to return several times to this star or comet; for absolutely it has been necessary to observe it for several consecutive days to perceive that it was in motion."

We cannot, therefore, fit the facts to Keats' version of them. The planet did not majestically reveal itself to a merely passive observer: rather did it, assuming the disguise of an ordinary star, evade detection to the utmost of its power; so that the keenest eye, the most alert attention, the most determined following up of a mere hint, were all needed to unmask it. But is the romance necessarily gone? If another Keats could arise and know the facts, could he not coin a newer and a truer phrase for us which would still sound as sweetly in our ears?

to a star which first began to shine under his auspicious reign.

W. HERSCHEL."

This letter reminds us how long it was since a new name had been required for a new planet,--to find a similar occasion Herschel had to go to the almost prehistoric past, when the names of heroes and divinities were given to the planets. It is, perhaps, not unnatural that he should have considered an entirely new departure appropriate for a discovery separated by so great a length of time from the others; but his views were not generally accepted, especially on the Continent. Lalande courteously proposed the name of Herschel for the new planet, in honour of the discoverer, and this name was used in France; but Bode, on the other hand, was in favour of retaining the old practice simply, and calling the new planet Uranus. All three names seem to have been used for many years. Only the other day I was interested to see an old pack of cards, used for playing a parlour game of Astronomy, in which the name Herschel is used. The owner told me that they had belonged to his grandfather; and the date of publication was 1829, and the place London, so that this name was in common use in England nearly half a century after the actual discovery; though in the "English Nautical Almanac" the name "the Georgian" was being used officially after 1791, and did not disappear from that work until 1851

It would appear to have been the discovery of Neptune, with which we shall deal in the next chapter, which led to this official change; for in the volume for 1851 is included Adams' account of his discovery with the title--

"ON THE PERTURBATIONS OF URANUS,"

and there was thus a definite reason for avoiding two names for the same planet in the same work. But Le Verrier's paper on the same topic at the same date still uses the name "Herschel" for the planet.

The discovery of Neptune, as we shall see, was totally different in character from that of Uranus. The latter may be described as the finding of something by an observer who was looking for anything; Neptune was the finding of something definitely sought for, and definitely pointed out by a most successful and brilliant piece of methodical work. But before that time several planets had been found, as the practical result of a definite search, although the guiding principle was such as cannot command our admiration to quite the same extent as in the case of Neptune. To explain it I must say something of the relative sizes of the orbits in which planets move round the sun. These orbits are, as we know, ellipses; but they are very nearly circles, and, excluding refinements, we may consider them as circles, with the sun at the centre of each, so that we may talk of the distance of any planet from the sun as a constant quantity without serious error. Now if we arrange the planetary distances in order, we shall notice a remarkable connection between the terms of the series. Here is a table showing this connection.

TABLE OF THE DISTANCES OF THE PLANETS FROM THE SUN, SHOWING "BODE'S LAW."

If we write down a series of 4's, and then add the numbers 3, 6, 12, and so on, each formed by doubling the last, we get numbers representing very nearly the planetary distances, which are shown approximately in the second column. But three points call for notice. Firstly, the number before 3 should be 1-1/2, and not zero, to agree with the rest. Secondly, there is a gap, or rather was a gap, after the discovery of Uranus, between Mars and Jupiter; and thirdly, we see that when Uranus was discovered, and its distance from the sun determined, this distance was found to fall in satisfactorily with this law, which was first stated by Titius of Wittenberg. This third fact naturally attracted attention. No explanation of the so-called "law" was known at the time; nor is any known even yet, though we may be said to have some glimmerings of a possible cause; and in the absence of such explanation it must be regarded as merely a curious coincidence. But the chances that we are in the presence of a mere coincidence diminish very quickly with each new term added to the series, and when it was found that Herschel's new planet fitted in so well at the end of the arrangement, the question arose whether the gap above noticed was real, or whether there was perhaps another planet which had hitherto escaped notice, revolving in an orbit represented by this blank term. This question had indeed been asked even before the discovery of Uranus, by Bode, a young astronomer of Berlin; and for fifteen years he kept steadily in view this idea of finding a planet to fill the vacant interval. The search would be a very arduous one, involving a careful scrutiny, not perhaps of the whole heavens, but of a considerable portion of it along the Zodiac; too great for one would-be discoverer single-handed; but in September 1800 Bode succeeded in organising a band of six German astronomers for the purpose of conducting this search. They divided the Zodiac into twenty-four zones, and were assigning the zones to the different observers, when they were startled by the news that the missing planet had been accidentally found by Piazzi in the constellation Taurus. The discovery was made somewhat dramatically on the first evening of the nineteenth century . Piazzi was not looking for a planet at all, but examining an error made by another astronomer; and in the course of this work he recorded the position of a star of the eighth magnitude. Returning to it on the next night, it seemed to him that it had slightly moved westwards, and on the following night this suspicion was confirmed. Remark that in this case no peculiar appearance in the star suggested that it might be a comet or planet, as in the case of the discovery of Uranus. We are not unfair in ascribing the discovery to pure accident, although we must not forget that a careless observer might easily have missed it. Piazzi was anything but careless, and watched the new object assiduously till February 11th, when he became dangerously ill; but he had written, on January 23rd, to Oriani of Milan, and to Bode at Berlin on the following day. These letters, however, did not reach the recipients until April 5th and March 20th respectively; and we can imagine the mixed feelings with which Bode heard that the discovery which he had contemplated for fifteen years, and for which he was just about to organise a diligent search, was thus curiously snatched from him.

More curious still must have seemed the intelligence to a young philosopher of Jena named Hegel, who has since become famous, but who had just imperilled his future reputation by publishing a dissertation proving conclusively that the number of the planets could not be greater than seven, and pouring scorn on the projected search of the half-dozen enthusiasts who were proposing to find a new planet merely to fill up a gap in a numerical series.

"Some ideas had occurred to me on this subject in September 1801, at a time when I was occupied on something quite different; ideas which seemed to contribute to the solution of the great problem of which I have spoken. In such cases it often happens that, lest we be too much Distracted From the Attractive Investigation On Which We Are Engaged, We Allow Associations Of Ideas Which, If More Closely Examined, Might Prove Extraordinarily Fruitful, To Perish From Neglect. Perchance These Same Idea-lets of Mine Would Have Met With This Fate, If They Had Not Most Fortunately Lighted Upon a Time Than Which None Could Have Been Chosen More Favourable For Their Preservation and Development. For About The Same Time a Rumour Began To Be Spread Abroad Concerning a New Planet Which Had Been Detected On January 1st of That Year at the Observatory Of Palermo; and Shortly Afterwards the Actual Observations Which Had Been Made Between January 1st And February 11th by the Renowned Philosopher Piazzi Were Published. Nowhere in All The Annals of Astronomy Do We Find Such an Important Occasion; and Scarcely Is It Possible To Imagine a More Important Opportunity for Pointing Out, As Emphatically As Possible, the Importance Of That Problem, As at the Moment When Every Hope of Re-discovering, Among the Innumerable Little Stars of Heaven, That Mite of a Planet Which Had Been Lost To Sight for Nearly a Year, Depended Entirely on an Approximate Knowledge Of Its Orbit, Which Must Be Deduced From Those Scanty Observations. Could I Ever Have Had A Better Opportunity for Trying Whether Those Idea-lets Of Mine Were of Any Practical Value Than If I Then Were To Use Them for the Determination Of The Orbit of Ceres, a Planet Which, in the Course of those forty-one days, had described around the earth an arc of no more than three degrees? and, after a year had passed, required to be tracked out in a region of the sky far removed from its original position? The first application of this method was made in the month of October 1801, and the first clear night, when the planet was looked for by the help of the ephemeris I had made, revealed the truant to the observer. Three new planets found since then have supplied fresh opportunities for examining and proving the efficacy and universality of this method.

"Now a good many astronomers, immediately after the rediscovery of Ceres, desired me to publish the methods which had been used in my calculations. There were, however, not a few objections which prevented me from gratifying at that moment these friendly solicitations, viz. other business, the desire of treating the matter more fully, and more especially the expectation that, by continuing to devote myself to this research, I should bring the different portions of the solution of the problem to a more perfect pitch of universality, simplicity, and elegance. As my hopes have been justified, I do not think there is any reason for repenting of my delay. For the methods which I had repeatedly applied from the beginning admitted of so many and such important variations, that scarcely a vestige of resemblance remains between the method by which formerly I had arrived at the orbit of Ceres and the practice which I deal with in this work. Although indeed it would be alien to my intention to write a complete history about all these researches which I have gradually brought to even greater perfection, yet on many occasions, especially whenever I was confronted by some particularly serious problem, I thought that the first methods which I employed ought not to be entirely suppressed. Nay, rather, in addition to the solutions of the principal problems, I have in this work followed out many questions which presented themselves to me, in the course of a long study of the motions of the heavenly bodies in conic sections, as being particularly worthy of attention, whether on account of the neatness of the analysis, or more especially by reason of their practical utility. Yet I have always given the greater care to subjects which I have made my own, merely noticing by the way well-known facts where connection of thought seemed to demand it."

The thought occurred to Olbers that they were perhaps fragments of a single body which had been blown to pieces by some explosion, and that there might be more of the pieces; and he therefore suggested as a guide for finding others that, since by the known laws of gravitation, bodies which circle round the sun return periodically to their starting-point, therefore all these fragments would in due course return to the point in the heavens where the original planet had exploded. Hence the search might be most profitably conducted in the neighbourhood of the spot where the two first fragments had already been found. We now have good reason to believe that this view is a mistaken one, but nevertheless it was apparently confirmed by the discovery of two more bodies of the same kind, which were called Juno and Vesta; the second of these being found by Olbers himself after three years' patient work in 1807. Hence, although the idea of searching for a more or less definitely imagined planet was not new, although Bode had conceived it as early as 1785, and organised a search on this plan, three planets were actually found before the first success attending a definite search. Ceres, as already remarked, was found by a pure accident; and the same may be said of Pallas and Juno, though it may fairly be added that Pallas was actually contrary to expectation.

MINOR PLANETS, 1801 TO 1850.

Here now is a table showing how other bodies were gradually added to this first list of four, but you will see that no addition was made for a long time. Not that the search was immediately abandoned; but being rewarded by no success for some years, it was gradually dropped, and the belief gained ground that the number of the planets was at last complete. The discoverers of Uranus and of these first four minor planets all died before any further addition was made; and it was not until the end of 1845 that Astraea was found by an ex-postmaster of the Prussian town of Driessen, by name Hencke, who, in spite of the general disbelief in the existence of any more planets, set himself diligently to search for them, and toiled for fifteen long years before at length reaping his reward. Others then resumed the search; Hind, the observer of an English amateur astronomer near London, found Iris a few weeks after Hencke had been rewarded by a second discovery in 1847, and in the following year Mr. Graham at Markree in Ireland found Metis; and from that time new discoveries have been added year by year, until the number of planets now known exceeds 500, and is steadily increasing.

You will see the great variety characterising these discoveries; some of them are the result of deliberate search, others have come accidentally, and some even contrary to expectation. Of the great majority of the earlier ones it may be said that enormous diligence was required for each discovery; to identify a planet it is necessary to have either a good map of the stars or to know them thoroughly, so that the map practically exists in the brain. We need only remember Hencke's fifteen years of search before success to recognise what vast stores of patience and diligence were required in carrying out the search. But of late years photography has effected a great revolution in this respect. It is no longer necessary to do more than set what Sir Robert Ball has called a "star-trap," or rather planet-trap. If a photograph be taken of a region of the heavens, by the methods familiar to astronomers, so that each star makes a round dot on the photographic plate, any sufficiently bright object moving relatively to the stars will make a small line or trail, and thus betray its planetary character. In this way most of the recent discoveries have been made, and although diligence is still required in taking the photographs, and again in identifying the objects thus found , the tedious scrutiny with the eye has become a thing of the past.

TABLE SHOWING THE NUMBER OF MINOR PLANETS DISCOVERED IN EACH DECADE SINCE 1850.

No. Name. 248 Lameia 250 Bettina 261 Prymno 264 Libussa 296 Pha?tusa 340 Eduarda 341 California 350 Ornamenta 357 Ninina 385 Ilmatar 389 Industria 391 Ingeborg 433 Eros 443 Photographica 457 Alleghenia 462 Eriphyla 475 Ocllo 484 Pittsburghia 503 Evelyn

Fortunately, however, on running through it for the fifth time, an object of particular interest was discovered. Most of these bodies revolve at a distance from the sun intermediate between that of Mars and that of Jupiter, but the little planet which took the symbol DQ, and afterwards the name of Eros, was found to have a mean distance actually less than that of Mars, and this gave it an extraordinary importance with respect to the great problem of determining the sun's distance. To explain this importance we must make a small digression.

About the middle of the last century our knowledge of the sun's distance was very rough, as may be seen from the table on p. 32; but there were in prospect two transits of Venus, in 1874 and 1882, and it was hoped that these would give opportunities of a special kind for the measurement of this important quantity, which lies at the root of all our knowledge of the exact masses and dimensions of not only the sun, but of the planets as well.

These difficulties, as already stated, were known to exist; but there is a long interval between transits of Venus, or rather between every pair of such transits. After those of 1874 and 1882 there will be no more until 2004 and 2012, so that we shall never see another; similarly, before that pair of the last century, there had not been any such occasion since 1761 and 1769, and no one was alive who remembered at first hand the trouble which was known to exist. It was proposed to obviate the anticipated difficulties by careful practice beforehand; models were prepared to resemble as nearly as possible the expected appearances, and the times recorded by different observers were compared with the true time, which could, in this case of a model, be determined. In this way it was hoped that the habit of each observer, his "personal equation" as it is called, could be determined beforehand, and allowed for as a correction when he came to observe the actual transit. The result, however, was a great disappointment. The actual appearances were found to be totally different in character from those shown by the model; chiefly, perhaps, because it had been impossible to imitate with a model the effect of the atmosphere which surrounds the planet Venus. Observers trained beforehand, using similar instruments, and standing within a few feet of each other, were expected, after making due allowance for personal equation, to give the same instant for contact; but their observations when made were found to differ by nearly a minute of time, and after an exhaustive review of the whole material it was felt that all hope of determining accurately the sun's distance by this method must be given up. The following table will show how much was learned from the transits of Venus, and how much remained to be settled. They left the result in doubt over a range of about two million miles.

SUN'S DISTANCE, IN MILLIONS OF MILES, AS FOUND BY DIFFERENT OBSERVERS

It became necessary, therefore, to look to other methods; and before the second transit of 1882 was observed, an energetic astronomer, Dr. David Gill, had already put into operation the method which may be now regarded as the standard one.

And now it will be seen why the discovery of the little planet Eros was important, for Mars was no longer the known planet capable of coming nearest to us; it had been replaced by this new arrival.

Further, a small planet which is in appearance just like an ordinary star has, irrespective of this great proximity, some distinct advantages over a planet like Mars, which appears as a round disc, and is, moreover, of a somewhat reddish colour. When the distance of an object of this kind from a point of line such as a star is measured with the heliometer it is found that a certain bias, somewhat difficult to allow for with certainty, is introduced into the measures; and our confidence in the final results suffers accordingly. After his observations of Mars in 1878, Dr. David Gill was sufficiently impressed with this source of error to make three new determinations of the sun's distance, using three of the minor planets instead of Mars, in spite of the fact that they were sensibly farther away; and his choice was justified by finding that the results from these three different sets of observations agreed well among themselves, and differed slightly from that given by the observations of Mars. Hence it seems conclusively proved that one of these bodies is a better selection than Mars in any case, and the discovery of Eros, which offered the advantage of greater proximity in addition, was hailed as a new opportunity of a most welcome kind. It was seen by a little calculation that in the winter of 1900-1901 the planet would come very near the earth; not the nearest possible , but still the nearest approach which would occur for some thirty years; and extensive, though somewhat hasty, preparations were made to use it to the fullest advantage. Photography had now become established as an accurate method of making measurements of the kind required; and all the photographic telescopes which could be spared were pressed into the service, and diligently photographed the planet and surrounding stars every fine night during the favourable period. The work of measuring and reducing these photographs involves an enormous amount of labour, and is even yet far from completed, but we know enough to expect a result of the greatest value. More than this we have not time to say here about this great problem, but it will have been made clear that just when astronomers were beginning to wonder whether it was worth while continuing the monotonous discovery of new minor planets by the handful, the 433rd discovery also turned out to be one of the greatest importance.

To canons for the advantageous prosecution of research, if we care to make them, we may therefore add this--that there is no line of research, however apparently unimportant or monotonous, which we can afford to neglect. Just when we are on the point of relinquishing it under the impression that the mine is exhausted, we may be about to find a nugget worth all our previous and future labour. This rule will not, perhaps, help us very much in choosing what to work at; indeed, it is no rule at all, for it leaves us the whole field of choice unlimited. But this negative result will recur again and again as we examine the lessons taught by discoveries: there seem to be no rules at all. Whenever we seem to be able to deduce one from an experience, some other experience will flatly contradict it. Thus we might think that the discovery of Eros taught us to proceed patiently with a monotonous duty, and not turn aside to more novel and attractive work; yet it is often by leaving what is in hand and apparently has first claim on our attention that we shall do best, and we shall learn in the next chapter how a failure thus to turn flexibly aside was repented.

THE DISCOVERY OF NEPTUNE

In the last chapter we saw that the circumstances under which planets were discovered varied considerably. Sometimes the discoveries were not previously expected, occurring during a general examination of the heavens, or a search for other objects; and, on one occasion at least, the discovery may be said to have been even contrary to expectation, though, as the existence of a number of minor planets began to be realised, there have also been many cases where the discovery has been made as the result of a definite and deliberate search. But the search cannot be said to have been inspired by any very clear or certain principle: for the law of Bode, successful though it has been in indicating the possible existence of new planets, cannot, as yet, be said to be founded upon a formulated law of nature. We now come, however, to a discovery made in direct interpretation of Newton's great law of gravitation--the discovery of Neptune from its observed disturbance of Uranus. I will first briefly recall the main facts relating to the actual discovery.

After Uranus had been discovered and observed sufficiently long for its orbit to be calculated, it was found that the subsequent position of the planet did not always agree with this orbit; and, more serious than this, some early observations were found which could not be reconciled with the later ones at all. It is a wonderful testimony to the care and sagacity of Sir William Herschel, as was remarked in the last chapter, that Uranus was found to have been observed, under the mistaken impression that it was an ordinary star, by Flamsteed, Lemonnier, Bradley, and Mayer, all observers of considerable ability. Flamsteed's five observations dated as far back as 1690, 1712, and 1715; observations by others were in 1748, 1750, 1753, 1756, and so on up to 1771, and the body of testimony was so considerable that there was no room for doubt as to the irreconcilability of the observations with the orbit, such as might have been the case had there been only one or two, possibly affected with some errors.

It is difficult to mention an exact date for the conversion into certainty of the suspicion that no single orbit could be found to satisfy all the observations; but we may certainly regard this fact as established in 1821, when Alexis Bouvard published some tables of the planet, and showed fully in the introduction that when every correction for the disturbing action of other planets had been applied, it was still impossible to reconcile the old observations with the orbit calculated from the new ones. The idea accordingly grew up that there might be some other body or bodies attracting the planet and causing these discrepancies. Here again it is not easy to say exactly when this notion arose, but it was certainly existent in 1834, as the following letter to the Astronomer Royal will show. I take it from his well-known "Account of some Circumstances historically connected with the Discovery of the Planet exterior to Uranus," which he gave to the Royal Astronomical Society at its first meeting after that famous discovery .

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