ASTRONOMICAL DISCOVERY

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Astronomers Royal.

ASTRONOMICAL
DISCOVERY

BY

HERBERT HALL TURNER, D.Sc., F.R.S.

SAVILIAN PROFESSOR OF ASTRONOMY IN THE
UNIVERSITY OF OXFORD

WITH PLATES

LONDON
EDWARD ARNOLD
41 & 43 MADDOX STREET, W.
1904
(All rights reserved)

TO
EDWARD EMERSON BARNARD
ASTRONOMICAL DISCOVERER
THESE PAGES ARE INSCRIBED IN MEMORY OF
NEVER-TO-BE-FORGOTTEN DAYS SPENT WITH HIM AT THE
YERKES OBSERVATORY
OF
THE UNIVERSITY OF CHICAGO

PREFACE

The aim of the following pages is to illustrate, by the study of a few examples chosen almost at random, the variety in character of astronomical discoveries. An attempt has indeed been made to arrange the half-dozen examples, once selected, into a rough sequence according to the amount of “chance” associated with the discovery, though from this point of view Chapter IV. should come first; but I do not lay much stress upon it. There is undoubtedly an element of “luck” in most discoveries. “The biggest strokes are all luck,” writes a brother astronomer who had done me the honour to glance at a few pages, “but a man must not drop his catches. Have you ever read Montaigne’s essay ‘Of Glory’? It is worth reading. Change war and glory to discovery and it is exactly the same theme. If you are looking for a motto you will find a score in it.” Indeed even in cases such as those in Chapters V. and VI., where a discovery is made by turning over a heap of rubbish—declared such by experts and abandoned accordingly—we instinctively feel that the finding of something valuable was especially “fortunate.” We should scarcely recommend such waste material as the best hunting ground for gems.

The chapters correspond approximately to a series of six lectures delivered at the University of Chicago in August 1904, at the hospitable invitation of President Harper. They afforded me the opportunity of seeing something of this wonderful University, only a dozen years old and yet so amazingly vigorous; and especially of its observatory (the Yerkes observatory, situated eighty miles away on Lake Geneva), which is only eight years old and yet has taken its place in the foremost rank. For these opportunities I venture here to put on record my grateful thanks.

In a portion of the first chapter it will be obvious that I am indebted to Miss Clerke’s “History of Astronomy in the Nineteenth Century”; in the second to Professor R. A. Sampson’s Memoir on the Adams MSS.; in the third to Rigaud’s “Life of Bradley.” There are other debts which I hope are duly acknowledged in the text. My grateful thanks are due to Mr. F. A. Bellamy for the care with which he has read the proofs; and I am indebted for permission to publish illustrations to the Royal Astronomical Society, the Astronomer Royal, the editors of The Observatory, the Cambridge University Press, the Harvard College Observatory, the Yerkes Observatory, and the living representatives of two portraits.

H. H. TURNER.

University Observatory, Oxford,
November 9, 1904.

CONTENTS

LIST OF PLATES

ERRATA

ASTRONOMICAL DISCOVERY

CHAPTER I

URANUS AND EROS

Popular view of discovery.

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.

Keats’ lines.

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.”

Sonnet XI
On first looking into Chapman’s “Homer”

Comparison with discovery of Uranus.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

XXXII.—Account of a Comet
By Mr. Herschel, F.R.S.
(Communicated by Dr. Watson, jun., of Bath, F.R.S.)
Read April 26, 1781

Original announcement.

“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.”

Called first a comet.

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.Other observers would not have found it at all. 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.”

No “swimming into ken.”

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?

Though this may happen at times.

I must guard against a possible misconception. I do not mean to convey that astronomical discoveries are not occasionally made somewhat in the manner so beautifully pictured by Keats. Three years ago a persistent “watcher of the skies,” Dr. Anderson of Edinburgh, suddenly caught sight of a brilliant new star in Perseus; though here “flashed into his ken” would perhaps be a more suitable phrase than “swam.” And comets have been detected by a mere glance at the heavens without sensible effort or care on the part of the discoverer. But these may be fairly called exceptions; in the vast majority of cases hard work and a keen eye are necessary to make the discovery. The relative importance of these two factors of course varies in different cases; for the detection of Uranus perhaps the keen eye may be put in the first place, though we must not forget the diligent watching which gave it opportunity. Other cases of planetary discovery may be attributed more completely to diligence alone, as we shall presently see.Name of new planet. But before leaving Uranus for them I should like to recall the circumstances attending the naming of the planet. Herschel proposed to call it Georgium Sidus in honour of his patron, King George III., and as the best way of making his wishes known, wrote the following letter to the President of the Royal Society, which is printed at the beginning of the Philosophical Transactions for 1783.

A Letter from William Herschel, Esq., F.R.S.,
to Sir Joseph Banks, Bart., P.R.S.

“Sir,—By the observations of the most eminent astronomers in Europe it appears that the new star, which I had the honour of pointing out to them in March 1781, is a Primary Planet of our Solar System. A body so nearly related to us by its similar condition and situation in the unbounded expanse of the starry heavens, must often be the subject of conversation, not only of astronomers, but of every lover of science in general. This consideration then makes it necessary to give it a name whereby it may be distinguished from the rest of the planets and fixed stars.

“In the fabulous ages of ancient times, the appellations of Mercury, Venus, Mars, Jupiter, and Saturn were given to the planets as being the names of their principal heroes and divinities. In the present more philosophical era, it would hardly be allowable to have recourse to the same method, and call on Juno, Pallas, Apollo, or Minerva for a name to our new heavenly body. The first consideration in any particular event, or remarkable incident, seems to be its chronology: if in any future age it should be asked, when this last found planet was discovered? It would be a very satisfactory answer to say, ‘In the reign of King George the Third.’ As a philosopher then, the name Georgium Sidus presents itself to me, as an appellation which will conveniently convey the information of the time and country where and when it was brought to view. But as a subject of the best of kings, who is the liberal protector of every art and science; as a native of the country from whence this illustrious family was called to the British throne; as a member of that Society which flourishes by the distinguished liberality of its royal patron; and, last of all, as a person now more immediately under the protection of this excellent monarch, and owing everything to his unlimited bounty;—I cannot but wish to take this opportunity of expressing my sense of gratitude by giving the nameGeorgium Sidus. Georgium Sidus,

Georgium Sidus
——jam nunc assuesce vocari,
Virg. Georg.

to a star which (with respect to us) first began to shine under his auspicious reign.

“By addressing this letter to you, Sir, as President of the Royal Society, I take the most effectual method of communicating that name to the literati of Europe, which I hope they will receive with pleasure.—I have the honour to be, with the greatest respect, Sir, your most humble and most obedient servant,

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.Herschel. 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” (apparently preferred to Herschel’s Georgium Sidus) was being used officially after 1791, and did not disappear from that work until 1851 (published in 1847.)

Uranus finally adopted.

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.Bode’s law. 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 1½, and not zero, to agree with the rest.Gap in the series suggesting unknown planet. 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;Search for it. but in September 1800 Bode succeeded in organising a band of six German astronomers (including himself) 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 (January 1, 1801).Accidental discovery. 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 (in those days of leisurely postal service) 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.

Hegel’s forecast.

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.

The planet lost again.

The sensation caused by the news of the discovery was intensified by anxiety lest the new planet should already have been lost; for it had meanwhile travelled too close to the sun for further observation, and the only material available for calculating its orbit, and so predicting its place in the heavens at future dates, was afforded by the few observations made by Piazzi. Was it possible to calculate the orbit from such slender material? It would take too long to explain fully the enormous difficulty of this problem, but some notion of it may be obtained, by those unacquainted with mathematics, from a rough analogy. If we are given a portion of a circle, we can, with the help of a pair of compasses, complete the circle: we can find the centre from which the arc is struck, either by geometrical methods, or by a few experimental trials, and then fill in the rest of the circumference. If the arc given is large we can do this with certainty and accuracy; but if the arc is small it is difficult to make quite sure of the centre, and our drawing may not be quite accurate. Now the arc which had been described by the tiny planet during Piazzi’s observations was only three degrees; and if any one will kindly take out his watch and look at the minute marks round the dial, three degrees is just half a single minute space. If the rest of the dial were obliterated, and only this small arc left, would he feel much confidence in restoring the obliterated portion? This problem gives some idea of the difficulties to be encountered, but only even then a very imperfect one.

Gauss shows how to find it.

Briefly, the solution demanded a new mathematical method in astronomy. But difficulties are sometimes the opportunities of great men, and this particular difficulty attracted to astronomy the great mathematician Gauss, who set himself to make the best of the observation available, and produced his classical work, the Theoria Motus, which is the standard work for such calculations to the present day. May we look for a few moments at what he himself says in the preface to his great work? I venture to reproduce the following rough translation (the book being written in Latin, according to the scientific usage of the time):—

Extract from the Preface to the
Theoria Motus.

The Theoria Motus.

“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.”

These words do not explain in any way the methods introduced by Gauss, but they give us some notion of the flavour of the work.Rediscovery of Ceres. Aided by these brilliant researches, the little planet was found on the last day of the year by Von Zach at Gotha, and on the next night, independently, by Olbers at Bremen. But, before this success, there had been an arduous search, which led to a curious consequence.Another planet found. Olbers had made himself so familiar with all the small stars along the track which was being searched for the missing body, that he was at once struck by the appearance of a stranger near the spot where he had just identified Ceres. At first he thought this must be some star which had blazed up to brightness; but he soon found that it also was moving, and, to the great bewilderment of the astronomical world, it proved to be another planet revolving round the sun at a distance nearly the same as the former. This was an extraordinary and totally unforeseen occurrence. The world had been prepared for one planet; but here were two!

Hypothesis of many fragments.

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 (which had been named Ceres and Pallas) 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;Hencke’s long search. 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 (who is still living, and has only just retired from active work at the Cambridge Observatory) 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.

By permission of Messrs. Macmillan & Co.
I.—J. C. Adams.

II.—A. Graham.
DISCOVERER OF THE NINTH MINOR PLANET (METIS).

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.The photographic method. 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 (which are now very often the images of already known members of the system), 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.

[N.B.—Many of the more recent announcements turned out to refer to old discoveries.]

Scarcity of names.

The known number of these bodies has accordingly increased so rapidly as to become almost an embarrassment; and in one respect the embarrassment is definite, for it has become quite difficult to find names for the new discoveries. We remember with amusement at the present time that for the early discoveries there was sometimes a controversy (of the same kind as in the case of Uranus) about the exact name which a planet should have. Thus when it was proposed to call No. 12 (discovered in 1850, in London, by Mr. Hind) “Victoria,” there was an outcry by foreign astronomers that by a subterfuge the name of a reigning monarch was again being proposed for a planet, and considerable opposition was manifested, especially in America. But it became clear, as other discoveries were added, that the list of goddesses, or even humbler mythological people, would not be large enough to go round if we were so severely critical, and must sooner or later be supplemented from sources hitherto considered unsuitable; so, ultimately, the opposition to the name Victoria was withdrawn. Later still the restriction to feminine names has been broken through; one planet has been named Endymion, and another, of which we shall presently speak more particularly, has been called Eros. But before passing to him you may care to look at some of the names selected for others:—

Bettina.In connection with No. 250 there is an interesting little history. In the Observatory for 1885, page 63, appeared the following advertisement:—“Herr Palisa being desirous to raise funds for his intended expedition to observe the Total Solar Eclipse of August 1886, will sell the right of naming the minor planet No. 244 for £50.” The bright idea seems to have struck Herr Palisa, who had already discovered many planets and begun to find difficulties in assigning suitable names, that he might turn his difficulty into a source of profit in a good cause. The offer was not responded to immediately, nor until Herr Palisa had discovered two more planets, Nos. 248 and 250. He found names for two, leaving, however, the last discovered always open for a patron, and on page 142 of the same magazine for 1886 the following note informs us how his patience was ultimately rewarded:—“Minor planet No. 250 has been named ‘Bettina’ by Baron Albert de Rothschild.” I have not heard, however, that this precedent has been followed in other cases, and the ingenuity of discoverers was so much overtaxed towards the end of last century that the naming of their planets fell into arrears. Recently a Commission, which has been established to look after these small bodies generally, issued a notice that unless the naming was accomplished before a certain date it would be ruthlessly taken out of the hands of the negligent discoverers. The provisional letters.Perhaps we may notice, before passing on, the provisional system which was adopted to fill up the interval required for finding a suitable name, and required also for making sure that the planet was in fact a new one, and not merely an old one rediscovered. There was a system of numbering in existence as well as of naming, but it was unadvisable to attach even a number to a planet until it was quite certain that the discovery was new, for otherwise there might be gaps created in what should be a continuous series by spurious discoveries being struck out. Accordingly it was decided to attach at first to the object merely a letter of the alphabet, with the year of discovery, as a provisional name. The alphabet was, however, run through so quickly, and confusion was so likely to ensue if it was merely repeated, that on recommencing it the letter A was prefixed, and the symbols adopted were therefore AA, AB, AC, &c.; after completing the alphabet again, the letter B was prefixed, and so on; and astronomers began to fear that they had before them a monotonous prospect of continually adding new planets, varied by no incident more exciting than starting the alphabet over again after every score.

Fortunately, however, on running through it for the fifth time, an object of particular interest was discovered.Eros. 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.

Transit of Venus.

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.

Fig. 1.

The method may be briefly summarised thus: An observer in one part of the earth would see Venus cross the disc of the sun along a different path from that seen by another observer, as will be clear from the diagram. If the size of the earth, the distance of the sun, and the relative distance of Venus be known, it can be calculated what this difference in path will be. Now the relative distance of Venus is known with great accuracy, from observing the time of her revolution round the sun; the size of the earth we can measure by a survey; there remains, therefore, only one unknown quantity, the sun’s distance. And since from a knowledge of this we could calculate the difference in path, it is easy to invert the problem, and calculate the sun’s distance from the knowledge of the observed difference in path. Accordingly, observers were to be scattered, not merely to two, but to many stations over the face of the earth, to observe the exact path taken by Venus in transit over the sun’s disc as seen from their station; and especially to observe the exact times of beginning and ending of the transit; and, by comparison of their results, it was hoped to determine this very important quantity, the sun’s distance. It was known from previous experience that there were certain difficulties in observing very exactly the beginning and end of the transit.The “Black Drop.” There was an appearance called the “Black Drop,” which had caused trouble on previous occasions; an appearance as though the round black spot which can be seen when Venus has advanced some distance over the sun’s disc was reluctant to make the entry and clung to the edge or “limb” of the sun as it is called, somewhat as a drop of ink clings to a pen which is slowly withdrawn from an inkpot. Similarly, at the end of the transit or egress, instead of approaching the limb steadily the planet seems at the last moment to burst out towards it, rendering the estimation of the exact moment when the transit is over extremely doubtful.

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.Failure. 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

Before the Transits of Venus estimates varied between 96 million miles (Gilliss and Gould, 1856) and 91 million (Winneche, 1863), a range of 5 million miles.

The Transits of 1874 and 1882 gave results lying between 93¼ million (Airy, from British observations of 1874), 92½ million (Stone, from British observations of 1882), and 91½ million (Puiseux, from French observations), a range of 1¾ millions.

Gill’s Heliometer results all lie very near 93 millions. The observations of Mars in 1877 give about 100,000 miles over this figure: but the observations of Victoria, Iris, and Sappho, which are more trustworthy, all agree in giving about 100,000 miles less than the 93 millions.

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.

Modern method for sun’s distance.

We have said that the relative distance of Venus from the sun is accurately known from observations of the exact time of revolution. It is easy to see that these times of revolution can be measured accurately by mere accumulation. We may make an error of a few seconds in noting the time of return; but if the whole interval comprises 10 revolutions, this error is divided by 10, if 100 revolutions by 100, and so on; and by this time a great number of revolutions of all the planets (except those just discovered) have been recorded. Hence we know their relative distances with great precision; and if we can find the distance in miles of any one of them, we can find that of the sun itself, or of any other planet, by a simple rule-of-three sum. By making use of this principle many of the difficulties attending the direct determination of the sun’s distance can be avoided; for instance, since the sun’s light overpowers that of the stars, it is not easy to directly observe the place of the sun among the stars; but this is not so for the planets.Photography. We can photograph a planet and the stars surrounding it on the same plate, and then by careful measurement determine its exact position among the stars; and since this position differs slightly according to the situation of the observer on the earth’s surface, by comparing two photographs taken at stations a known distance apart we can find the distance of the planet from the earth; and hence, as above remarked, the distance of the sun and all the other members of the solar system. Or, instead of taking photographs from two different stations, we can take from the same station two photographs at times separated by a known interval. For in that interval the station will have been carried by the earth’s rotation some thousands of miles away from its former position, and becomes virtually a second station separated from the first by a distance which is known accurately when we know the elapsed time. Again, instead of taking photographs, and from them measuring the position of the planet among the stars, we may make the measurements on the planet and stars in the sky itself;Dr. Gill’s expedition to Ascension. and since in 1878, when Dr. Gill set out on his enterprise of determining the sun’s distance, photography was in its infancy as applied to astronomy, he naturally made his observations on the sky with an instrument known as a heliometer. He made them in the little island of Ascension, which is suitably situated for the purpose; because, being near the earth’s equator, it is carried by the earth’s rotation a longer distance in a given time than places nearer the poles, and in these observations for “parallax,” as they are called, it is important to have the displacement of the station as large as possible. For a similar reason the object selected among the planets must be as near the earth as possible; and hence the planet Mars, which at favourable times comes nearer to us than any other superior planet[1] then known, was selected for observation with the heliometer.

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.Victoria, Iris, and Sappho. 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.Eros. 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 (for it was also realised that a still better opportunity had occurred in 1894, though it was lost because the planet had not yet been discovered), 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.

CHAPTER II

THE DISCOVERY OF NEPTUNE

Search for definite objects.

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.

Disturbance of Uranus.

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.Suspicion of perturbing planet. 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 (Monthly Notices of the R.A.S., vol. iii., and Memoirs, vol. xvi.).

No. 1.—The Rev. T. J. Hussey to G. B. Airy.
[Extract.]

“‘Hayes, Kent, 17th November 1834.

“‘With M. Alexis Bouvard I had some conversation upon a subject I had often meditated, which will probably interest you, and your opinion may determine mine. Having taken great pains last year with some observations of Uranus, I was led to examine closely Bouvard’s tables of that planet. The apparently inexplicable discrepancies between the ancient and modern observations suggested to me the possibility of some disturbing body beyond Uranus, not taken into account because unknown. My first idea was to ascertain some approximate place of this supposed body empirically, and then with my large reflector set to work to examine all the minute stars thereabouts: but I found myself totally inadequate to the former part of the task. If I could have done it formerly, it was beyond me now, even supposing I had the time, which was not the case. I therefore relinquished the matter altogether; but subsequently, in conversation with Bouvard, I inquired if the above might not be the case: his answer was, that, as might have been expected, it had occurred to him, and some correspondence had taken place between Hansen and himself respecting it. Hansen’s opinion was, that one disturbing body would not satisfy the phenomena; but that he conjectured there were two planets beyond Uranus. Upon my speaking of obtaining the places empirically, and then sweeping closely for the bodies, he fully acquiesced in the propriety of it, intimating that the previous calculations would be more laborious than difficult; that if he had leisure he would undertake them and transmit the results to me, as the basis of a very close and accurate sweep. I have not heard from him since on the subject, and have been too ill to write. What is your opinion on the subject? If you consider the idea as possible, can you give me the limits, roughly, between which this body or those bodies may probably be found during the ensuing winter? As we might expect an eccentricity [inclination?] approaching rather to that of the old planets than of the new, the breadth of the zone to be examined will be comparatively inconsiderable. I may be wrong, but I am disposed to think that, such is the perfection of my equatoreal’s object-glass, I could distinguish, almost at once, the difference of light of a small planet and a star. My plan of proceeding, however, would be very different: I should accurately map the whole space within the required limits, down to the minutest star I could discern; the interval of a single week would then enable me to ascertain any change. If the whole of this matter do not appear to you a chimæra, which, until my conversation with Bouvard, I was afraid it might, I shall be very glad of any sort of hint respecting it.’

“My answer was in the following terms:—

No. 2.—G. B. Airy to the Rev. T. J. Hussey.
[Extract.]

“‘Observatory, Cambridge, 1834, Nov. 23.

Airy’s scepticism.

“‘I have often thought of the irregularity of Uranus, and since the receipt of your letter have looked more carefully to it. It is a puzzling subject, but I give it as my opinion, without hesitation, that it is not yet in such a state as to give the smallest hope of making out the nature of any external action on the planet ... if it were certain that there were any extraneous action, I doubt much the possibility of determining the place of a planet which produced it. I am sure it could not be done till the nature of the irregularity was well determined from several successive revolutions.’”

Although only a sentence or two have been selected from Airy’s reply (he was not yet Astronomer Royal), they are sufficient to show that the problem of finding the place of such a possible disturbing body was regarded at that time as one of extreme difficulty; and no one appears seriously to have contemplated embarking upon its solution. It was not until many years later that the solution was attempted. Of the first attempt we shall speak presently, putting it aside for the moment because it had no actual bearing on the discovery of the planet, for reasons which form an extraordinary episode of this history. The attempt which led to success dates from November 1845.Le Verrier’s papers. The great French astronomer Le Verrier, on November 10, 1845, read to the French Academy a paper on the Orbit of Uranus, considering specially the disturbances produced by Jupiter and Saturn, and showing clearly that with no possible orbit could the observations be satisfied. On June 1, 1846, followed a second paper by the same author, in which he considers all the possible explanations of the discordance, and concludes that none is admissible except that of a disturbing planet exterior to Uranus. And assuming, in accordance with Bode’s Law, that the distance of this new planet from the sun would be about double that of Uranus (and it is important to note this assumption), he proceeds to investigate the orbit of such a planet, and to calculate the place where it must be looked for in the heavens. This was followed by a third paper on August 31st, giving a rather completer discussion,Planet to be detected by disc. and arriving at the conclusion that the planet should be recognisable from its disc. This again is an important point. We remember that in the discovery of Uranus it needed considerable skill on the part of Sir William Herschel to detect the disc, to see in fact any difference between it and surrounding stars; and that other observers, even when their attention had been called to the planet, found it difficult to see this difference. It might be expected, therefore, that with a planet twice as far away (as had been assumed for the new planet) the disc would be practically unrecognisable, and as we shall presently see, this assumption was made in some searches for the planet which had been commenced even before the publication of this third paper. Le Verrier’s courageous announcement, which he deduced from a consideration of the mass of the planet, that the disc should be recognisable, led immediately to the discovery of the suspected body.Galle’s discovery of the planet. He wrote to a German astronomer, Dr. Galle (still, I am glad to say, alive and well, though now a very old man), telling him the spot in the heavens to search, and stating that he might expect to detect the planet by its appearance in this way; and the same night Dr. Galle, by comparing a star map with the heavens, found the planet.

To two points to which I have specially called attention in this brief summary—namely, the preliminary assumption that the planet would be, according to Bode’s Law, twice as far away as Uranus; secondly, the confident assertion that it would have a visible disc—I will ask you to add, thirdly, that it was found by the aid of a star map, for this map played an important part in the further history to which we shall now proceed. It may naturally be supposed that the announcement of the finding of a planet in this way, the calculation of its place from a belief in the universal action of the great Law of Gravitation, the direction to an eminent observer to look in that place for a particular thing, and his immediate success,—this extraordinary combination of circumstances caused a profound sensation throughout not only the astronomical, but the whole world; and this sensation was greatly enhanced by the rumour which had begun to gather strength that, but for some unfortunate circumstances, the discovery might have been made even earlier and as a consequence of totally independent calculations made by a young Cambridge mathematician, J. C. Adams.Adams’ work publicly announced. Some of you are doubtless already familiar with the story in its abridged form, for it has been scattered broadcast through literature. In England it generally takes the form of emphasising the wickedness or laziness of the Astronomer Royal who, when told where to look for a planet, neglected his obvious duty, so that in consequence another astronomer who made the calculation much later and gave a more virtuous observer the same directions where to look, obtained for France the glory of a discovery which ought to have been retained in England. There is no doubt that Airy’s conduct received a large amount of what he called “savage abuse.” When the facts are clearly stated I think it will be evident that many of the harsh things said of him were scarcely just, though at the same time it is also difficult to understand his conduct at two or three points of the history, even as explained by himself.

Facts undoubted.

There is fortunately no doubt whatever about any of the facts. Airy himself gave a very clear and straightforward account of them at the time, for which more credit is due to him than he commonly receives; and since the death of the chief actors in this sensational drama they have been naturally again ransacked, with the satisfactory result that there is practically no doubt about any of the facts. As to the proper interpretations of them there certainly may be wide differences of opinion, nor does this circumstance detract from their interest. It is almost impossible to make a perfectly colourless recital of them, nor is it perhaps necessary to do so. I will therefore ask you to remember in what I now say that there is almost necessarily an element of personal bias, and that another writer would probably give a different colouring. Having said this, I hope I may speak quite freely as the matter appears in my personal estimation.

Airy’s “Account.”

Airy’s account was, as above stated, given to the Royal Astronomical Society at their first meeting (after the startling announcement of the discovery of the new planet), on November 13, 1846, and I have already quoted an extract from it. He opens with a tribute to the sensational character of the discovery, and then states that although clearly due to two individuals (namely, Le Verrier and Galle),“A movement of the age.” it might also be regarded as to some extent the consequence of a movement of the age. His actual words are these: “The principal steps in the theoretical investigations have been made by one individual, and the published discovery of the planet was necessarily made by one individual. To these persons the public attention has been principally directed; and well do they deserve the honours which they have received, and which they will continue to receive. Yet we should do wrong if we considered that these two persons alone are to be regarded as the authors of the discovery of this planet. I am confident that it will be found that the discovery is a consequence of what may properly be called a movement of the age; that it has been urged by the feeling of the scientific world in general, and has been nearly perfected by the collateral, but independent labours, of various persons possessing the talents or powers best suited to the different parts of the researches.”

I have quoted these words as the first point at which it is difficult to understand Airy’s conduct in excluding from them all specific mention of Adams, knowing as he did the special claims which entitled him to such mention; claims indeed which he proceeded immediately to make clear.Airy under-estimated Adams’ work. It seems almost certain that Airy entirely under-estimated the value of Adams’ work throughout. But this will become clearer as we proceed. The “account” takes the form of the publication of a series of letters with occasional comments. Airy was a most methodical person, and filed all his correspondence with great regularity. It was jestingly said of him once that if he wiped his pen on a piece of blotting-paper, he would date the blotting-paper and file it for reference. The letters reproduced in this “account” are still in the Observatory at Greenwich, pinned together just as Airy left them; and in preparing his “account” it was necessary to do little else than to have them copied out and interpolate comments. From two of them I have already quoted to show how difficult the enterprise of finding an exterior planet from its action on Uranus was considered in 1834. To these may be added the following sentence from No. 4, dated 1837. “If it be the effect of any unseen body,” writes Airy to Bouvard, “it will be nearly impossible ever to find out its place.” But the first letter which need concern us is No. 6, and it is only necessary to explain that Professor Challis was the Professor of Astronomy at Cambridge, and in charge of the Cambridge Observatory, in which offices he had succeeded Airy himself on his leaving Cambridge for Greenwich some eight years earlier.

No. 6.—Professor Challis to G. B. Airy.
[Extract.]

“‘Cambridge Observatory, Feb. 13, 1844.

Challis mentions Adams to Airy,

“‘A young friend of mine, Mr. Adams of St. John’s College, is working at the theory of Uranus, and is desirous of obtaining errors of the tabular geocentric longitudes of this planet, when near opposition, in the years 1818-1826, with the factors for reducing them to errors of heliocentric longitude. Are your reductions of the planetary observations so far advanced that you could furnish these data? and is the request one which you have any objection to comply with? If Mr. Adams may be favoured in this respect, he is further desirous of knowing, whether in the calculation of the tabular errors any alterations have been made in Bouvard’s Tables of Uranus besides that of Jupiter’s mass.’

“My answer to him was as follows:—

No. 7.—G. B. Airy to Professor Challis.
[Extract.]

“‘Royal Observatory, Greenwich, 1844, Feb. 15.

“‘I send all the results of the observations of Uranus made with both instruments (that is, the heliocentric errors of Uranus in longitude and latitude from 1754 to 1830, for all those days on which there were observations, both of right ascension and of polar distance). No alteration is made in Bouvard’s Tables of Uranus except in increasing the two equations which depend on Jupiter by ¹⁄50 part. As constants have been added (in the printed tables) to make the equations positive, and as ¹⁄50 part of the numbers in the tables has been added, ¹⁄50 part of the constants has been subtracted from the final results.’

“Professor Challis in acknowledging the receipt of these, used the following expressions:—

No. 8.—Professor Challis to G. B. Airy.
[Extract.]

“‘Cambridge Observatory, Feb. 16, 1844.

“‘I am exceedingly obliged by your sending so complete a series of tabular errors of Uranus.... The list you have sent will give Mr. Adams the means of carrying on in the most effective manner the inquiry in which he is engaged.’

“The next letter shows that Mr. Adams has derived results from these errors.

No. 9.—Professor Challis to G. B. Airy.

“‘Cambridge Observatory, Sept. 22, 1845.

“‘My friend Mr. Adams (who will probably deliver this note to you) has completed his calculations respecting the perturbation of the orbit of Uranus by a supposed ulterior planet,and suggests Adams’ visit to Greenwich. and has arrived at results which he would be glad to communicate to you personally, if you could spare him a few moments of your valuable time. His calculations are founded on the observations you were so good as to furnish him with some time ago; and from his character as a mathematician, and his practice in calculation, I should consider the deductions from his premises to be made in a trustworthy manner. If he should not have the good fortune to see you at Greenwich, he hopes to be allowed to write to you on this subject.’

“On the day on which this letter was dated, I was present at a meeting of the French Institute. I acknowledged it by the following letter:—

No. 10.—G. B. Airy to Professor Challis.

“‘Royal Observatory, Greenwich, 1845, Sept. 29.

“‘I was, I suppose, on my way from France, when Mr. Adams called here; at all events, I had not reached home, and therefore, to my regret, I have not seen him. Would you mention to Mr. Adams that I am very much interested with the subject of his investigations, and that I should be delighted to hear of them by letter from him?’

“On one of the last days of October 1845, Mr. Adams called at the Royal Observatory, Greenwich, in my absence and left the following important paper:—

No. 11.—J. C. Adams, Esq., to G. B. Airy.

Adams’ announcement of the new planet.

“‘According to my calculations, the observed irregularities in the motion of Uranus may be accounted for by supposing the existence of an exterior planet, the mass and orbit of which are as follows:—

For the modern observations I have used the method of normal places, taking the mean of the tabular errors, as given by observations near three consecutive oppositions, to correspond with the mean of the times; and the Greenwich observations have been used down to 1830: since which, the Cambridge and Greenwich observations, and those given in the Astronomische Nachrichten, have been made use of. The following are the remaining errors of mean longitude:—

Observation—Theory.

The error for 1780 is concluded from that for 1781 given by observation, compared with those of four or five following years, and also with Lemonnier’s observations in 1769 and 1771.

“‘For the ancient observations, the following are the remaining errors:—

Observation—Theory.

The errors are small, except for Flamsteed’s observation of 1690. This being an isolated observation, very distant from the rest, I thought it best not to use it in forming the equations of condition. It is not improbable, however, that this error might be destroyed by a small change in the assumed mean motion of the planet.’

“I acknowledged the receipt of this paper in the following terms:—

No. 12.—G. B. Airy to J. C. Adams, Esq.

“‘Royal Observatory, Greenwich, 1845, Nov. 5.

Airy’s inquiry about the “radius vector.”

“‘I am very much obliged by the paper of results which you left here a few days since, showing the perturbations on the place of Uranus produced by a planet with certain assumed elements. The latter numbers are all extremely satisfactory: I am not enough acquainted with Flamsteed’s observations about 1690 to say whether they bear such an error, but I think it extremely probable.

“‘But I should be very glad to know whether this assumed perturbation will explain the error of the radius vector of Uranus. This error is now very considerable, as you will be able to ascertain by comparing the normal equations, given in the Greenwich observations for each year, for the times before opposition with the times after opposition.’

“I have before stated that I considered the establishment of this error of the radius vector of Uranus to be a very important determination. I therefore considered that the trial, whether the error of radius vector would be explained by the same theory which explained the error of longitude, would be truly an experimentum crucis. And I waited with much anxiety for Mr. Adams’ answer to my query. Had it been in the affirmative, I should at once have exerted all the influence which I might possess, either directly, or indirectly through my friend Professor Challis, to procure the publication of Mr. Adams’ theory.

“From some cause with which I am unacquainted, probably an accidental one, I received no immediate answer to this inquiry. I regret this deeply, for many reasons.”

Adams’ silence.

Here we may leave Airy’s “account” for a few moments to consider the reason why he received no answer. Adams was a very shy and retiring young man, and very sensitive; though capable of a great resolution, and of enormous perseverance in carrying it out. We know (what is not indicated in the above account), how steadily he had kept in view the idea of solving this great problem. It was characteristic of him that as early as 1841 he had formed a resolution to undertake it, although at the time he was not able to enter upon its accomplishment. The following memorandum, which is still in existence, having been found among his papers after his death, records these facts:

“1841, July 3. Formed a design, in the beginning of this week, of investigating, as soon as possible after taking my degree, the irregularities in the motion of Uranus, which were as yet unaccounted for: in order to find whether they may be attributed to the action of an undiscovered planet beyond it, and if possible thence to determine the elements of its orbit, &c., approximately, which would probably lead to its discovery.”

Accordingly, “as soon as possible after taking his degree” he embarked upon the enterprise, and the first solution was made in the long vacation of 1843, assuming the orbit of the unknown planet to be a circle with a radius equal to twice the mean distance of Uranus from the sun (an assumption which, as we have seen, was also made by Le Verrier). Having satisfied himself that there was a good general agreement between his results and the observations, Adams began a more complete solution; indeed from first to last he made no less than six separate solutions, the one which he announced to Airy in the above letter being the fourth. Hence he had already done an enormous amount of work on the problem, and was in his own mind so justly convinced of the correctness and value of his results that he was liable to forget that others had not had the same opportunity of judging of their completeness; and he was grievously disappointed when his announcement was not received with full confidence.

His disappointment at Greenwich,

But perhaps it should first be stated that by a series of mischances Adams had been already much disappointed at the failure of his attempts to see the Astronomer Royal on his visits to Greenwich. This does not seem to have been exactly Airy’s fault; he was, as may well be supposed, an extremely busy man, and was much occupied at the time on a question of great practical importance, at the direct request of the Government, namely, the settling of the proper gauge for railways throughout the country. The first time Adams called to see him, he was actually in London sitting on the Committee which dealt with this question, and Adams was asked to call later; when the visit was repeated, Airy was unfortunately at dinner (and it may be added that his hours for dinner were somewhat peculiar), and the butler, acting somewhat in the manner of his kind, protected his master’s dinner by sending away one whom he doubtless regarded as a troublesome visitor. There is, as I have said, little doubt about any of the facts, and it seems well established that Airy himself did not learn of Adams’ visits until afterwards, and it would scarcely be just to blame him for a servant’s oversight. But Adams had left the paper above reproduced, and Airy with his business-like habits ultimately proceeded to deal with it; he wrote the answer given above asking Adams a definite question, filed a copy of it with the original letter, and then dismissed the matter from his thoughts until the reply from Adams, which he confidently expected should again bring it under notice.

and at Airy’s question.

This further disappointment was, however, too much for Adams; he regarded the question put by Airy as having so obvious an answer that it was intended as an evasion, though this was far from being the case. Airy was thoroughly in earnest about his question, though it must be admitted that a more careful study of the problem would have shown him that it was unnecessary. Later, when he learnt of Le Verrier’s researches, he put the same question to him, and received a polite but very clear answer, showing that the suggested test was not an experimentum crucis as he supposed. But Adams did not feel equal to making this reply; he shrank into his shell and solaced himself only by commencing afresh another solution of the problem which had so engrossed his life at that time.

The merits of Airy’s question.

I have heard severe or contemptuous things said about this question by those who most blame Airy. Some of them have no hesitation in accusing him of intellectual incompetence: they say that it was the question of a stupid man. I think that in the first place they forget the difference between a deliberate error of judgement and a mere consequence of insufficient attention. But there is even more than this to be said in defence of the question. The “error of radius vector” came before Airy in an entirely independent way, and as an entirely independent phenomenon, from the “error of longitude,” and there was nothing unnatural in regarding it as requiring independent explanation. It is true that, as the event proved, a mere readjustment of the orbit of Uranus got rid of this error of radius vector (this was substantially Le Verrier’s answer to Airy’s question); but we must not judge of what was possible before the event in the light of what we now know.The range of possibilities. The original possibilities were far wider, though we have forgotten their former extent now that they have been narrowed down by the discovery. If a sentry during war time hears a noise in a certain direction, he may be compelled to make the assumption that it is the movement of an enemy; and if he fires in that direction and kills him, and thus saves his own army from destruction, he is deservedly applauded for the success which attends his action. But it does not follow that the assumption on which he acted was the only possible one. Or, to take a more peaceful illustration, in playing whist it sometimes becomes apparent that the game can only be won if the cards lie in a certain way; and a good player will thereupon assume that this is the fact, and play accordingly. Adams and Le Verrier played to win the game on the particular assumption that the disturbance of Uranus was due to an external planet revolving at a distance from the sun about twice that of Uranus; and won it; and we applaud them for doing so. But it is easy to imagine a rearrangement of the cards with which they would have lost it; and Airy’s question simply meant that he was alive to these wider possibilities, and did not see the need for attempting to win the game in that particular way.

One such alternative possibility has already been mentioned. “Hansen’s opinion was, that one disturbing body would not satisfy the phenomena; but he conjectured that there were two planets beyond Uranus.” Another conceivable alternative is that there was some change in the law of gravitation at the distance of Uranus, which, it must be remembered, is twice as great as that of any planet previously known. Or some wandering body might have passed close enough to Uranus to change its orbit somewhat suddenly. We now know, for instance, that the swarm of meteorites which gives rise to the well-known “November meteors” must have passed very close to Uranus in A.D. 126, assuming that neither the planet nor the swarm have been disturbed in any unknown manner in the meantime. It is to this encounter that we owe the introduction of this swarm to our solar system: wandering through space, they met Uranus, and were swept by his attraction into an orbit round the sun. Was there no reaction upon Uranus himself? The probabilities are that the total mass of the swarm was so small as to affect the huge planet inappreciably; but who was to say that some other swarm of larger mass, or other body, might not have approached near Uranus at some date between 1690 and 1845, and been responsible at any rate in part for the observed errors? These are two or three suppositions from our familiar experience; and there are, of course, limitless possibilities beyond. Which is the true scientific attitude, to be alive to them all, or to concentrate attention upon one?

But we are perhaps wandering too far from the main theme. It is easy to do so in reviewing this extraordinary piece of history, for at almost every point new possibilities are suggested.

III—U. J. Le Verrier.
(From a print in the possession of the Royal Astronomical Society.)

IV—J. G. Galle.
WHO FIRST SAW THE PLANET NEPTUNE

We must return, however, to Airy’s “account.” We reached the point where he had written to Adams (on November 5, 1845), asking his question about the radius vector, and received no reply; and there the matter remained, so far as he was concerned,Airy receives Le Verrier’s memoir. until the following June, when Le Verrier’s memoir reached him; and we will let him give his own version of the result.

“This memoir reached me about the 23rd or 24th of June. I cannot sufficiently express the feeling of delight and satisfaction which I received from it. The place which it assigned to the disturbing planet was the same, to one degree, as that given by Mr. Adams’ calculations, which I had perused seven months earlier. To this time I had considered that there was still room for doubt of the accuracy of Mr. Adams’ investigations; for I think that the results of algebraic and numerical computations, so long and so complicated as those of an inverse problem of perturbations, are liable to many risks of error in the details of the process: I know that there are important numerical errors in the Mécanique Céleste of Laplace; in the Théorie de la Lune of Plana; above all, in Bouvard’s first tables of Jupiter and Saturn; and to express it in a word, I have always considered the correctness of a distant mathematical result to be a subject rather of moral than of mathematical evidence. But now I felt no doubt of the accuracy of both calculations, as applied to the perturbation in longitude. I was, however, still desirous, as before, of learning whether the perturbation in radius vector was fully explained. I therefore addressed to M. Le Verrier the following letter:—

No. 13.—G. B. Airy to M. Le Verrier.

“‘Royal Observatory, Greenwich, 1846, June 26.

He puts the “radius-vector” question to Le Verrier,

“‘I have read, with very great interest, the account of your investigations on the probable place of a planet disturbing the motions of Uranus, which is contained in the Compte Rendu de l’Académie of June 1; and I now beg leave to trouble you with the following question. It appears, from all the later observations of Uranus made at Greenwich (which are most completely reduced in the Greenwich Observations of each year, so as to exhibit the effect of an error either in the tabular heliocentric longitude, or the tabular radius vector), that the tabular radius vector is considerably too small. And I wish to inquire of you whether this would be a consequence of the disturbance produced by an exterior planet, now in the position which you have indicated?’”

There is more of the letter, but this will suffice to show that he wrote to Le Verrier in the same way as to Adams, and, as already stated, received a reply dated three or four days later. But the rest of the letter contains no mention of Adams, and thus arises a second difficulty in understanding Airy’s conduct.but makes no mention of Adams. It seems extraordinary that when he wrote to Le Verrier he made no mention of the computations which he had previously received from Adams; or that he should not have written to Adams, and made some attempt to understand his long silence, now that, as he himself states, he “felt no doubt of the accuracy of both calculations.” The omission may have been, and probably was, mere carelessness or forgetfulness; but he could hardly be surprised if others mistook it for deliberate action.

Airy announces the likelihood of a new planet,

However, attention had now been thoroughly attracted to the near possibility of finding the planet. On June 29, 1846, there was a special meeting of the Board of Visitors of Greenwich Observatory, and Airy incidentally mentioned to them this possibility. The impression produced must have been definite and deep; for Sir John Herschel, who was present, was bold enough to say on September 10th following to the British Association assembled at Southampton: “We see it (the probable new planet) as Columbus saw America from the shores of Spain. Its movements have been felt trembling along the far-reaching line of our analysis with a certainty hardly inferior to that of ocular demonstration.”and suggests a search for it at Cambridge Airy discussed the matter with Professor Challis (who, it will be remembered, had originally written to him on behalf of Adams), suggesting that he should immediately commence a search for the supposed planet at Cambridge. It may be asked why Airy did not commence this search himself at Greenwich, and the answer is that he had no telescope which he regarded as large enough for the purpose. The Royal Observatory at Greenwich has always been, and is now, better equipped in some respects than any other observatory, as might be expected from its deservedly great reputation; but to possess the largest existing telescope has never been one of its ambitions. The instruments in which it takes most pride are remarkable for their steadiness and accuracy rather than for their size;not having suitable telescope at Greenwich and at that time the best telescope possessed by the observatory was not, in Airy’s opinion, large enough to detect the planet with certainty. In this opinion we now know that he was mistaken; but, again, we must not judge his conduct before the event in the light of what we have since discovered. It may be recalled here that it was not until Le Verrier’s third paper, published on August 31, that he (Le Verrier) emphatically pointed out that the new planet might be of such a size as to have a sensible disc; and it was this remark which led immediately to its discovery. Until this was so decisively stated, it must have seemed exceptionally improbable; for we saw in the last chapter how diligently the Zodiac had been swept in the search for minor planets,—how, for instance, Hencke had searched for fifteen years without success; and it might fairly be considered that if there were a fairly bright object (such as Neptune has since been found to be) it would have been discovered earlier. Hence Airy not unreasonably considered it necessary to spread his net for very small objects. On July 9 he wrote to Professor Challis as follows:—

No. 15.—G. B. Airy to Professor Challis.

“The Deanery, Ely, 1846, July 9.

“You know that I attach importance to the examination of that part of the heavens in which there is ... reason for suspecting the existence of a planet exterior to Uranus. I have thought about the way of making such examination, but I am convinced that (for various reasons, of declination, latitude of place, feebleness of light, and regularity of superintendence) there is no prospect whatever of its being made with any chance of success, except with the Northumberland telescope.

“Now, I should be glad to ask you, in the first place, whether you could make such an examination?

“Presuming that your answer would be in the negative, I would ask, secondly, whether, supposing that an assistant were supplied to you for this purpose, you would superintend the examination?

“You will readily perceive that all this is in a most unformed state at present, and that I am asking these questions almost at a venture, in the hope of rescuing the matter from a state which is, without the assistance that you and your instruments can give, almost desperate. Therefore I should be glad to have your answer, not only responding simply to my questions, but also entering into any other considerations which you think likely to bear on the matter.

“The time for the said examination is approaching near.”

Challis undertakes the search.

Professor Challis did not require an assistant, but determined to undertake the work himself, and devised his own plan of procedure; but he also set out on the undertaking with the expectation of a long and arduous search. No such idea as that of finding the planet on the first night ever entered his head. For one thing, he had no map of the region to be examined, for although the map used by Galle had been published, no copy of it had as yet reached Cambridge, and Professor Challis had practically to construct a map for himself. In these days of photography to make such a map is a simple matter, but at that time the process was terribly laborious. “I get over the ground very slowly,” he wrote on September 2nd to Airy, “thinking it right to include all stars to 10-11 magnitude; and I find that to scrutinise thoroughly in this way the proposed portion of the heavens will require many more observations than I can take this year.” With such a prospect, it is not surprising that one night’s observations were not even compared with the next; there would be a certain economy in waiting until a large amount of material had been accumulated, and then making the comparisons all together, and this was the course adopted. But when Le Verrier’s third paper, with the decided opinion that the planet would be bright enough to be seen by its disc, ultimately reached Professor Challis, it naturally gave him an entirely different view of the possibilities;He finds too late that he had observed the planet. he immediately began to compare the observations already made, and found that he had observed the planet early in August. But it was now too late to be first in the field, for Galle had already made his announcement of discovery. Writing to Airy on October 12, Challis could only lament that after four days’ observing the planet was in his grasp, if only he had examined or mapped the observations, and if he had not delayed doing so until he had more observations to reduce, and if he had not been very busy with some comet observations. Oh! these terrible ifs which come so often between a man and success! The third of them is a peculiarly distressing one, for it represents that eternal conflict between one duty and another, which is so constantly recurring in scientific work. Shall we finish one piece of work now well under way, or shall we attend to something more novel and more attractive? Challis thought his duty lay in steadily completing the comet observations already begun. We saw in the last lecture how the steady pursuit of the discovery of minor planets, a duty which had become tedious and apparently led nowhere, suddenly resulted in the important discovery of Eros. But Challis was not so fortunate in electing to plod along the beaten track; he would have done better to leave it. There is no golden rule for the answer; we must be guided in each case by the special circumstances, and the dilemma is consequently a new one on every occasion, and perhaps the more trying with each repetition.

Such are briefly the events which led to the discovery of Neptune, which was made in Germany by direction from France, when it might have been made in Cambridge alone. The incidents created a great stir at the time.Sensation caused by the discovery. The “Account” of them, as read by Airy to the Royal Astronomical Society on November 13, 1846, straightforward and interesting though it was, making clear where he had himself been at fault, nevertheless stirred up angry passions in many quarters, and chiefly directed against Airy himself. Cambridge was furious at Airy’s negligence, which it considered responsible for costing the University a great discovery; and others were equally irate at his attempting to claim for Adams some of that glory which they considered should go wholly to Le Verrier.Not all national jealousy. But it may be remarked that feeling was not purely national. Some foreigners were cordial in their recognition of the work of Adams, while some of those most eager to oppose his claims were found in this country. In their anxiety to show that they were free from national jealousy, scientific men went almost too far in the opposite direction.

Airy’s conduct was certainly strange at several points, as has already been remarked. One cannot understand his writing to Le Verrier in June 1846 without any mention of Adams. He could not even momentarily have forgotten Adams’ work; for he tells us himself how he noticed the close correspondence of his result with that of Le Verrier: and had he even casually mentioned this fact in writing to the latter, it would have prepared the way for his later statement. But we can easily understand the unfavourable impression produced by this statement after the discovery had been made, when there had been no previous hint on the subject at all.The position of Cambridge in the matter. Of those who abused him Cambridge had the least excuse; for there is no doubt that with a reasonably competent Professor of Astronomy in Cambridge, she need not have referred to Airy at all. It would not seem to require any great amount of intelligence to undertake to look in a certain region for a strange object if one is in possession of a proper instrument. We have seen that Challis had the instrument, and when urged to do so was equal to the task of finding the planet; but he was a man of no initiative, and the idea of doing so unless directed by some authority never entered his head. He had been accustomed for many years to lean rather helplessly upon Airy, who had preceded him in office at Cambridge. For instance, when appointed to succeed him, and confronted with the necessity of lecturing to students, he was so helpless that he wrote to implore Airy to come back to Cambridge and lecture for him;Challis the weakest point. and this was actually done, Airy obtaining leave from the Government to leave his duties at Greenwich for a time in order to return to Cambridge, and show Challis how to lecture. Now it seems to me that this helplessness was the very root of all the mischief of which Cambridge so bitterly complained. I claimed at the outset the privilege of stating my own views, with which others may not agree: and of all the mistakes and omissions made in this little piece of history, the most unpardonable and the one which had most serious consequences seems to me to be this: that Challis never made the most casual inquiry as to the result of the visit to Greenwich which he himself had directed Adams to make. I am judging him to some extent by default; because I assume the facts from lack of evidence to the contrary: but it seems practically certain that after sending this young man to see Airy on this important topic, Challis thereupon washed his hands of all responsibility so completely that he never even took the trouble to inquire on his return, “Well! how did you get on? What did the Astronomer Royal say?” Had he put this simple question, which scarcely required the initiative of a machine, and learnt in consequence, as he must have done, that the sensitive young man thought Airy’s question trivial, and did not propose to answer it, I think we might have trusted events to right themselves. Even Challis might have been trusted to reply, “Oh! but you must answer the Astronomer Royal’s question: you may think it stupid, but you had better answer it politely, and show him that you know what you are about.” It is unprofitable to pursue speculation further; this did not happen, and something else did. But I have always felt that my old University made a scapegoat of the wrong man in venting its fury upon Airy, when the real culprit was among themselves, and was the man they had themselves chosen to represent astronomy. He was presumably the best they had; but if they had no one better than this, they should not have been surprised, and must not complain, if things went wrong. If a University is ambitious of doing great things, it must take care to see that there are men of ability and initiative in the right places. This is a most difficult task in any case, and we require all possible incentives towards it. To blink the facts when a weak spot is mercilessly exposed by the loss of a great opportunity is to lose one kind of incentive, and perhaps not the least valuable.

Curious difference between actual and supposed planet.

Let us now turn to some curious circumstances attending this remarkable discovery of a planet by mathematical investigation, of which there are several. The first is, that although Neptune was found so near the place where it was predicted, its orbit, after discovery, proved to be very different from that which Adams and Le Verrier had supposed. You will remember that both calculators assumed the distance from the sun, in accordance with Bode’s Law, to be nearly twice that of Uranus. The actual planet was found to have a mean distance less than this by 25 per cent., an enormous quantity in such a case. For instance, if the supposed planet and the real were started round the sun together, the real planet would soon be a long way ahead of the other, and the ultimate disturbing effect of the two on Uranus would be very different. To explain the difference, we must first recall a curious property of such disturbances. When two planets are revolving, so that one takes just twice or three times, or any exact number of times, as long to revolve round the sun as the other, the usual mathematical expressions for the disturbing action of one planet on the other would assign an infinite disturbance, which, translated into ordinary language, means that we must start with a fresh assumption, for this state of things cannot persist. If the period of one were a little longer than this critical value, some of the mathematical expressions would be of contrary sign from those corresponding to a period a little shorter.Professor Peirce’s contention that the discovery was a mere accident.
The explanation. Now it is curious that the supposed planet and the real had orbits on opposite sides of a critical value of this kind, namely, that which would assign a period of revolution for Neptune exactly half that of Uranus; and it was pointed out in America by Professor Peirce that the effect of the planet imagined by Adams and Le Verrier was thus totally different from that of Neptune. He therefore declared that the mathematical work had not really led to the discovery at all; but that it had resulted from mere coincidence, and this opinion—somewhat paradoxical though it was—found considerable support. It was not replied to by Adams until some thirty years later, when a short reply was printed in Liouville’s Journal. The explanation is this: the expressions considered by Professor Peirce are those representing the action of the planet throughout an indefinite past, and did not enter into the problem, which would have been precisely the same if Neptune had been suddenly created in 1690; while, on the other hand, if Neptune had existed up till 1690 (the time when Uranus was first observed, although unknowingly), and then had been destroyed, there would have been no means of tracing its previous existence. In past ages it had no doubt been perturbing the orbit of Uranus, and had effected large changes in it; but if it had then been suddenly destroyed, we should have had no means of identifying these changes. There might have been instead of Neptune another planet, such as that supposed by Adams and Le Verrier; and its action in all past time would have been very different from that of Neptune, as is properly represented in the mathematical expressions which Professor Peirce considered. In consequence the orbit of Uranus in 1690 would have been very different from the orbit as it was actually found; but in either case the mathematicians Adams and Le Verrier would have had to take it as they found it; and the disturbing action which they considered in their calculations was the comparatively small disturbance which began in 1690 and ended in 1846. During this limited number of years the disturbance of the planet they imagined, although not precisely the same as that of Neptune, was sufficiently like it to give them the approximate place of the planet.

Still it is somewhat bewildering to look at the mathematical expressions for the disturbances as used by Adams and Le Verrier, when we can now compare with them the actual expressions to which they ought to correspond; and one may say frankly that there seems to be no sort of resemblance. Recently a memorial of Adams’ work has been published by the Royal Astronomical Society; they have reproduced in their Memoirs a facsimile of Adams’ MS. containing the “first solution,” which he made in 1843 in the Long Vacation after he had taken his degree, and which would have given the place of Neptune at that time with an error of 15°. In an introduction describing the whole of the MSS., written by Professor R. A. Sampson of Durham, it is shown how different the actual expressions for Neptune’s influence are from those used by Adams, and it is one of the curiosities of this remarkable piece of history that some of them seem to be actually in the wrong direction; and others are so little alike that it is only by fixing our attention resolutely on the considerations above mentioned that we can realise that the analytical work did indeed lead to the discovery of the planet.

Suggested elementary method for finding Neptune illusory.

A second curiosity is that a mistaken idea should have been held by at least one eminent man (Sir J. Herschel), to the effect that it would have been possible to find the place of the planet by a much simpler mathematical calculation than that actually employed by Adams or Le Verrier. In his famous “Outlines of Astronomy” Sir John Herschel describes a simple graphical method, which he declares would have indicated the place of the planet without much trouble. Concerning it I will here merely quote Professor Sampson’s words:—

“The conclusion is drawn that Uranus arrived at a conjunction with the disturbing planet about 1822; and this was the case. Plausible as this argument may seem, it is entirely baseless. For the maximum of perturbations depending on the eccentricities has no relation to conjunction, and the others which depend upon the differences of the mean motions alone are of the nature of forced oscillations, and conjunction is not their maximum or stationary position, but their position of most rapid change.”

Professor Sampson goes on to show that a more elaborate discussion seems quite as unpromising; and he concludes that the refinements employed were not superfluous, although it seems now clear that a different mode of procedure might have led more certainly to the required conclusion.

The evil influence of Bode’s Law.

For the third curious point is that both calculators should have adhered so closely to Bode’s Law. If they had not had this guiding principle it seems almost certain that they would have made a better approximation to the place of the planet, for instead of helping them it really led them astray. We have already remarked that if two planets are at different distances from the sun, however slight, and if they are started in their revolution together, they must inevitably separate in course of time, and the amount of separation will ultimately become serious. Thus by assuming a distance for the planet which was in error, however slight, the calculators immediately rendered it impossible for themselves to obtain a place for the planet which should be correct for more than a very brief period. Professor Sampson has given the following interesting lists of the dates at which Adams’ six solutions gave the true place of the planet and the intervals during which the error was within 5° either way.

Now the date at which it was most important to obtain the correct place was 1845 or thereabouts when it was proposed to look for the planet; but no special precaution seems to have been taken by either investigator to secure any advantage for this particular date. Criticising the procedure after the event (and of course this is a very unsatisfactory method of criticism), we should say that it would have been better to make several assumptions as regards the distance instead of relying upon Bode’s Law; but no one, so far as I know, has ever taken the trouble to write out a satisfactory solution of the problem as it might have been conducted. Such a solution would be full of interest, though it could only have a small weight in forming our estimation of the skill with which the problem was solved in the first instance.

Le Verrier’s erroneous limits.

Fourthly, we may notice a very curious point. Le Verrier went to some trouble not only to point out the most likely place for the planet, but to indicate limits outside which it was not necessary to look. This part of his work is specially commented upon with enthusiasm by Airy, and I will reproduce what he says. It is rather technical perhaps, but those who cannot follow the mathematics will be able to appreciate the tone of admiration.

“M. Le Verrier then enters into a most ingenious computation of the limits between which the planet must be sought. The principle is this: assuming a time of revolution, all the other unknown quantities may be varied in such a manner that though the observations will not be so well represented as before, yet the errors of observation will be tolerable. At last, on continuing the variation of elements, one error of observation will be intolerably great. Then, by varying the elements in another way, we may at length make another error of observation intolerably great; and so on. If we compute, for all these different varieties of elements, the place of the planet for 1847, its locus will evidently be a discontinuous curve or curvilinear polygon. If we do the same thing with different periodic times, we shall get different polygons; and the extreme periodic times that can be allowed will be indicated by the polygons becoming points. These extreme periodic times are 207 and 233 years. If now we draw one grand curve, circumscribing all the polygons, it is certain that the planet must be within that curve. In one direction, M. Le Verrier found no difficulty in assigning a limit; in the other he was obliged to restrict it, by assuming a limit to the eccentricity. Thus he found that the longitude of the planet was certainly not less than 321°, and not greater than 335° or 345°, according as we limit the eccentricity to 0.125 or 0.2. And if we adopt 0.125 as the limit, then the mass will be included between the limits 0.00007 and 0.00021; either of which exceeds that of Uranus. The visible disc.From this circumstance, combined with a probable hypothesis as to the density, M. Le Verrier concluded that the planet would have a visible disk, and sufficient light to make it conspicuous in ordinary telescopes.

“M. Le Verrier then remarks, as one of the strong proofs of the correctness of the general theory, that the error of radius vector is explained as accurately as the error of longitude. And finally, he gives his opinion that the latitude of the disturbing planet must be small.

“My analysis of this paper has necessarily been exceedingly imperfect, as regards the astronomical and mathematical parts of it; but I am sensible that, in regard to another part, it fails totally. I cannot attempt to convey to you the impression which was made on me by the author’s undoubting confidence in the general truth of his theory, by the calmness and clearness with which he limited the field of observation, and by the firmness with which he proclaimed to observing astronomers, ‘Look in the place which I have indicated, and you will see the planet well.’ Since Copernicus declared that, when means should be discovered for improving the vision, it would be found that Venus had phases like the moon, nothing (in my opinion) so bold, and so justifiably bold, has been uttered in astronomical prediction. It is here, if I mistake not, that we see a character far superior to that of the able, or enterprising, or industrious mathematician; it is here that we see the philosopher.”

Peirce’s views of the limits.

But now this process of limitation was faulty and actually misleading. Let us compare what is said about it by Professor Peirce a little later.

“Guided by this principle, well established, and legitimate, if confined within proper limits, M. Le Verrier narrowed with consummate skill the field of research, and arrived at two fundamental propositions, namely:—

“1st. That the mean distance of the planet cannot be less than 35 or more than 37.9. The corresponding limits of the time of sidereal revolution are about 207 and 233 years.

“2nd. ‘That there is only one region in which the disturbing planet can be placed in order to account for the motions of Uranus; that the mean longitude of this planet must have been, on January 1, 1800, between 243° and 252°.’

“‘Neither of these propositions is of itself necessarily opposed to the observations which have been made upon Neptune, but the two combined are decidedly inconsistent with observation. It is impossible to find an orbit, which, satisfying the observed distance and motion, is subject to them. If, for instance, a mean longitude and time of revolution are adopted according with the first, the corresponding mean longitude in 1800 must have been at least 40° distant from the limits of the second proposition. And again, if the planet is assumed to have had in 1800 a mean longitude near the limits of the second proposition, the corresponding time of revolution with which its motions satisfy the present observations cannot exceed 170 years, and must therefore be about 40 years less than the limits of the first proposition.’

“Neptune cannot, then, be the planet of M. Le Verrier’s theory, and cannot account for the observed perturbations of Uranus under the form of the inequalities involved in his analysis”—(Proc. Amer. Acad. I., 1846-1848, p. 66).

At the time when Professor Peirce wrote, the orbit of Neptune was not sufficiently well determined to decide whether one of the two limitations might not be correct, though he could see that they could not both be right, and we now know that they are both wrong. The mean distance of Neptune is 30, which does not lie between 35 and 37.9; and the longitude in 1800 was 225°, which does not lie between 243° and 252°. The ingenious process which Airy admired and which Peirce himself calls “consummately skilful” was wrong in principle.Newcomb’s criticism. As Professor Newcomb has said, “the error was the elementary one that, instead of considering all the elements simultaneously variable, Le Verrier took them one at a time, considering the others as fixed, and determining the limits between which each could be contained on this hypothesis. No solver of least square equations at the present day ought to make such a blunder. Of course one trouble in Le Verrier’s demonstration, had he attempted a rigorous one, would have been the impossibility of forming the simultaneous equations expressive of possible variations of all the elements.”

The account of Le Verrier’s limits by Professor Peirce, though it exhibits the error with special clearness, is a little unfair to Le Verrier in one point. If, instead of taking the limits for the date 1800, we take them for 1846 (when the search for Neptune was actually made), we shall find that they do include the actual place of the planet, as Airy found. The erroneous mean motion of Le Verrier’s planet allowed of his being right at one time and wrong at another; and Airy examined the limits under favourable conditions, which explains his enthusiasm. But we can scarcely wonder that Professor Peirce came to the conclusion that the planet discovered was not the one pointed out by Le Verrier, and had been found by mere accident.Element of good fortune. And all these circumstances inevitably contribute to a general impression that the calculators had a large element of good fortune to thank for their success. Nor need we hesitate to make this admission, for there is an element of good fortune in all discoveries. To look no further than this—if a man had not been doing a particular thing at a particular time, as he might easily not have been, most discoveries would never have been made. If Sir William Herschel had not been looking at certain small stars for a totally different purpose he would never have found Uranus; and no one need hesitate to admit the element of chance in the finding of Neptune.The map used by Galle. It is well illustrated by a glance at the map which, as has been remarked, Galle used to compare with the sky on the night when he made the actual discovery. The planet was found down near the bottom corner of the map, and since the limits assigned for its place might easily have varied a few degrees one way or the other, it might easily have been off the map; in which case, it is probable that the search would not have been successful, or at any rate that success would have been delayed.

[Larger Image]

V.—Corner of the Berlin Map, by the use of which Galle found Neptune.

Every one made mistakes.

Thus, it is a most remarkable feature of the discovery of Neptune that mistakes were made by almost every one concerned, however eminent. Airy made a mistake in regarding the question of the Radius Vector as of fundamental importance; Sir J. Herschel was wrong in describing an elementary method which he considered might have found the planet; Professor Peirce was wrong in supposing that the actual and the supposed planet were essentially different in their action on Uranus; Le Verrier was wrong in assigning limits outside which it was not necessary to look when the actual planet was outside them; Adams was more or less wrong in thinking that the eccentricity of the new planet could be found from the material already at disposal of man. Both Adams and Le Verrier gave far too much importance to Bode’s Law.

To review a piece of history of this kind and note the mistakes of such men is certainly comforting, and need not in any way lessen our admiration. In the case of the investigators themselves, much may be set down to excitement in the presence of a possible discovery. Professor Sampson has provided us with a small but typical instance of this fact. When Adams had carried through all his computations for finding Neptune, and was approaching the actual place of the planet, he, “who could carry through fabulous computations without error,” for the first time wrote down a wrong figure. The mistake was corrected upon the MS., “probably as soon as made,” but no doubt betrays the excitement which the great worker could not repress at this critical moment. There is a tradition that, similarly, when the mighty Newton was approaching the completion of his calculations to verify the Law of Gravitation, his excitement was so great that he was compelled to assign to a friend the task of finishing them.

Finally, we may remark how the history of the discovery of Neptune again illustrates the difficulty of formulating any general principles for guiding scientific work. Sometimes it is well to follow the slightest clue, however imperfectly understood; at other times we shall do better to refuse such guidance. Bode’s Law pointed to the existence of minor planets, and might conceivably have helped in finding Uranus: but by trusting to it in the case of Neptune, the investigators were perilously near going astray. Sometimes it is better to follow resolutely the work in hand whatever it may be, shutting one’s ears to other calls; but Airy and Challis lost their opportunities by just this course of action. The history of science is full of such contradictory experiences; and the only safe conclusion seems to be that there are no general rules of conduct for discovery.

CHAPTER III

BRADLEY’S DISCOVERIES OF THE ABERRATION OF LIGHT AND OF THE NUTATION OF THE EARTH’S AXIS

Biographical method adopted.

In examining different types of astronomical discovery, we shall find certain advantages in varying to some extent the method of presentation. In the two previous chapters our opportunities for learning anything of the life and character of those who made the discoveries have been slight; but I propose to adopt a more directly biographical method in dealing with Bradley’s discoveries, which are so bound up with the simple earnestness of his character that we could scarcely appreciate their essential features properly without some biographical study. But the record of his life apart from his astronomical work is not in any way sensational; indeed it is singularly devoid of incident. He had not even a scientific quarrel. There was scarcely a man of science of that period who had not at least one violent quarrel with some one, save only Bradley, whose gentle nature seems to have kept him clear of them all. Judged by ordinary standards his life was uneventful: and yet it may be doubted whether, to him who lived it, that life contained one dull moment. Incident came for him in his scientific work: in the preparation of apparatus, the making of observations, above all in the hard-thinking which he did to get at the clue which would explain them; and after reviewing his biography,[2] I think we shall be inclined to admit that if ever there was a happy life, albeit one of unremitting toil, it was that of James Bradley.

Bradley’s birth and early life.

He was born at Sherbourn, in Gloucestershire, in 1693. We know little of his boyhood except that he went to the Grammar School at Northleach, and that the memory of this fact was preserved at the school in 1832 when Rigaud was writing his memoir. [The school is at present shut up for want of funds to carry it on; and all inquiries I have made have failed to elicit any trace of this memory.] Similarly we know little of his undergraduate days at Oxford, except that he entered as a commoner at Balliol in 1710, took his B.A. in the regular course in 1714, and his M.A. in 1717. As a career he chose the Church, being ordained in 1719, and presented to the vicarage of Bridstow in Monmouthshire; but he only discharged the duties of vicar for a couple of years, for in 1721 he returned to Oxford as Professor of Astronomy, an appointment which involved the resignation of his livings; and so slight was this interruption to his career as an astronomer that we may almost disregard it, and consider him as an astronomer from the first.Brief clerical career. But to guard against a possible misconception, let me say that Bradley entered on a clerical career in a thoroughly earnest spirit; to do otherwise would have been quite foreign to his nature. When vicar of Bridstow he discharged his duties faithfully towards that tiny parish, and moreover was so active in his uncle’s parish of Wansted that he left the reputation of having been curate there, although he held no actual appointment. And thirty years later, when he was Astronomer Royal and resident at Greenwich, and when the valuable vicarage of Greenwich was offered to him by the Chancellor of the Exchequer, he honourably refused the preferment, “because the duty of a pastor was incompatible with his other studies and necessary engagements.”

Learnt astronomy not at Oxford,

But now let us turn to Bradley’s astronomical education. I must admit, with deep regret, that we cannot allow any of the credit of it to Oxford. There was a great astronomer in Oxford when Bradley was an undergraduate, for Edmund Halley had been appointed Savilian Professor of Geometry in 1703, and had immediately set to work to compute the orbits of comets, which led to his immortal discovery that some of these bodies return to us again and again, especially the one which bears his name—Halley’s Comet—and returns every seventy-five years, being next expected about 1910. But there is no record that Bradley came under Halley’s teaching or influence as an undergraduate. In later years the two men knew each other well, and it was Halley’s one desire towards the close of his life that Bradley should succeed him as Astronomer Royal at Greenwich; a desire which was fulfilled in rather melancholy fashion, for Halley died without any assurance that his wish would be gratified. But Bradley got no astronomical teaching at Oxford either from Halley or others.but from his uncle, James Pound. The art of astronomical observation he learnt from his maternal uncle, the Rev. James Pound, Rector of Wansted, in Essex. He is the man to whom we owe Bradley’s training and the great discoveries which came out of it. He was, I am glad to say, an Oxford man too; very much an Oxford man; for he seems to have spent some thirteen years there migrating from one Hall to another. His record indeed was such as good tutors of colleges frown upon; for it was seven years before he managed to take a degree at all; and he could not settle to anything. After ten years at Oxford he thought he would try medicine; after three years more he gave it up and went out in 1700 as chaplain to the East Indies. But he seems to have been a thoroughly lovable man, for news was brought of him four years later that he had a mind to come home, but was dissuaded by the Governor saying that “if Dr. Pound goes, I and the rest of the Company will not stay behind.” Soon afterwards the settlement was attacked in an insurrection, and Pound was one of the few who escaped with his life, losing however all the property he had gradually acquired. He returned to England in 1706, and was presented to the living of Wansted; married twice, and ended his days in peace and fair prosperity in 1724. Such are briefly the facts about Bradley’s uncle, James Pound;Pound a first-rate observer. but the most important of all remains to be told—that somehow or other he had learnt to make first-rate astronomical observations, how or when is not recorded; but in 1719 he was already so skilled that Sir Isaac Newton made him a present of fifty guineas for some observations; and repeated the gift in the following year; and even three years before this we find Halley writing to ask for certain observations from Mr. Pound.

With this excellent man Bradley used frequently to stay. To his nephew he seems to have been more like a father than an uncle. When his nephew had smallpox in 1717, he nursed him through it; and he supplemented from his own pocket the scanty allowance which was all that Bradley’s own father could afford. But what concerns us most is that he fostered, if he did not actually implant, a love of astronomical observation in his nephew.Bradley worked with him. The two worked together, entering their observations one after the other on the same paper; and it was to the pair of them together, rather than to the uncle alone, that Newton made his princely presents, and Halley wrote for help in his observations. There seems to be no doubt that the uncle and nephew were about this time the best astronomical observers in the world. There was no rivalry between them, and therefore there is no need to discuss whether the partnership was one of equal merit on both sides; but it is interesting to note that it probably was. The ability of Pound was undoubted; many were keenly desirous that he, and not his nephew, should be elected to the Oxford Chair in 1721, but he felt unequal to the duties at his advanced age. On the other hand, when Bradley lost his uncle’s help, there was no trace of faltering in his steps to betray previous dependence on a supporting or guiding hand. He walked erect and firm, and trod paths where even his uncle might not have been able to follow.

The work done by Pound and Bradley.

A few instances will suffice to show the kind of observations made by this notable firm of Pound and Bradley. They observed the positions of the fixed stars and nebulæ: these being generally the results required by Halley and Newton. They also observed the places of the planets among the stars, and especially the planet Mars, and determined its distance from the Earth by the method of parallax, thus anticipating the modern standard method of finding the Sun’s distance; and though with their imperfect instruments they did not obtain a greater accuracy than 1 in 10, still this was a great advance on what had been done before, and excited the wonder and admiration of Halley. They also paid some attention to double stars, and did a great deal of work on Jupiter’s satellites. We might profitably linger over the records of these early years, which are full of interest, but we must press on to the time of the great discoveries, and we will dismiss them with brief illustrations of three points: Bradley’s assiduity, his skill in calculation, and his wonderful skill in the management of instruments. Of his assiduity an example is afforded by his calculations of the orbits of two comets which are still extant. One of them fills thirty-two pages of foolscap, and the other sixty; and it must be remembered that the calculations themselves were quite novel at that time. Of his skill in calculation, apart from his assiduity, we have a proof in a paper communicated to the Royal Society rather later (1726), where he determines the longitudes of Lisbon and New York from the eclipses of Jupiter’s satellites, using observations which were not simultaneous, and had therefore to be corrected by an ingenious process which Bradley devised expressly for this purpose.Use of very long telescopes. And finally, his skill in the management of instruments is shown by his measuring the diameter of the planet Venus with a telescope actually 212¼ feet in length. It is difficult for us to realise in these days what this means; even the longest telescope of modern times does not exceed 100 feet in length, and it is mounted so conveniently with all the resources of modern engineering, in the shape of rising floors, &c., that the management of it is no more difficult than that of a 10-foot telescope. But Bradley had no engineering appliances beyond a pole to hold up one end of the telescope and his own clever fingers to work the other; and he managed to point the unwieldy weapon accurately to the planet, and measure the diameter with an exactness which would do credit to modern times.Reason for great length. A few words of explanation may be given why such long telescopes were used at all. The reason lay in the difficulty of getting rid of coloured images, due to the composite character of white light. Whenever we use a single lens to form an image, coloured fringes appear. Nowadays we know that by making two lenses of different kinds of glass and putting them together, we can practically get rid of these coloured fringes; but this discovery had not been made in Bradley’s time. The only known ways of dealing with the evil then were to use a reflecting telescope like Newton and Gregory, or if a lens was used, to make one of very great focal length; and hence the primary necessity for these very long telescopes. They had another advantage in producing a large image, or they would probably have given way to the reflector. This advantage is gradually bringing them back into use, and perhaps in the eclipse of 1905 we may use a telescope as long as Bradley’s; but we shall not use it as he did in any case. It will be laid comfortably flat on the ground, and the rays of light reflected into it by a coelostat.

Bradley appointed at Oxford,

In 1721 Bradley was appointed to the Savilian Professorship of Astronomy at Oxford, vacant by the death of Dr. John Keill. Once it became clear that there was no chance of securing his uncle for this position, Bradley himself was supported enthusiastically by all those whose support was worth having, especially by the Earl of Macclesfield, who was then Lord Chancellor; by Martin Foulkes, who was afterwards the President of the Royal Society; and by Sir Isaac Newton himself. He was accordingly elected on October 31, 1721, and forthwith resigned his livings. His resignation of the livings was necessitated by a definite statute of the University relating to the Professorship, and not by the existence of any very onerous duties attaching to it; indeed such duties seem to have been conspicuously absent,but continues to work at Wansted. and after Bradley’s election he passed more time than ever with his uncle in Wansted, making the astronomical observations which both loved; for there was not the vestige of an observatory in Oxford. His uncle’s death in 1724 interrupted the continuity of these joint observations, and by an odd accident prepared the way for Bradley’s great discovery. He was fain to seek elsewhere that companionship in his work which had become so essential to him, and his new friend gave a new bent to his observations.

Samuel Molyneux.

Samuel Molyneux was a gentleman of fortune much attached to science, and particularly to astronomy, who was living about this time at Kew. He was one of the few, moreover, who are not content merely to amuse themselves with a telescope, but had the ambition to do some real earnest work, and the courage to choose a problem which had baffled the human race for more than a century. The theory of Copernicus, that the earth moved round the sun, necessitated a corresponding apparent change in the places of the stars, one relatively to another; and it was a standing difficulty in the way of accepting this theory that no such change could be detected. In the old days before the telescope it was perhaps easy to understand that the change might be too small to be noticed, but the telescope had made it possible to measure changes of position at least a hundred times as small as before, and still no “parallax,” as the astronomical term goes, could be found for the stars. The observations of Galileo, and the measures of Tycho Brahé, as reduced to systematic laws by Kepler, and finally by the great Newton, made it clear that the Copernican theory was true: but no one had succeeded in proving its truth in this particular way.Attempts to find stellar parallax. Samuel Molyneux must have been a man of great courage to set himself to try to crack this hard nut; and we can understand the attraction which his enterprise must have had for Bradley, who had just lost the beloved colleague of many courageous astronomical undertakings. His co-operation seems to have been welcomed from the first; his help was invited and freely given in setting up the instrument, and he fortunately had the leisure to spend considerable time at Kew making the observations with Molyneux, just as he had been wont to observe with his uncle.

I must now briefly explain what these observations were. There is a bright star γ Draconis, which passes almost directly overhead in the latitude of London. Its position is slowly changing owing to the precession of the equinoxes, but for two centuries it has been, and is still, under constant observation by London astronomers owing to this circumstance, that it passes directly overhead, and so its position is practically undisturbed by the refraction of our atmosphere.

It was therefore thought at the time that, there being no disturbance from refraction, the disturbance from precession being accurately known, and there being nothing else to disturb the position but “parallax” (the apparent shift due to the earth’s motion which it was desirable to find), this star ought to be a specially favourable object for the determination of parallax. Indeed it had been announced many years before by Hooke that its parallax had been found; but his observations were not altogether satisfactory, and it was with a view of either confirming them or seeing what was wrong with them that Molyneux and Bradley started their search. They set up a much more delicate piece of apparatus than Hooke had employed.The instrument. It was a telescope 24 feet long pointed upwards to the star, and firmly attached to a large stack of brick chimneys within the house. The telescope was not absolutely fixed, for the lower end could be moved by a screw so as to make it point accurately to the star, and a plumb-line showed how far it was from the vertical when so pointing. Hence if the star changed its position, however slightly, the reading of this screw would show the change.Expected results. Now, before setting out on the observations, the observers knew what to expect if the star had a real parallax; that is to say, they knew that the star would seem to be farthest south in December, farthest north in June, and at intermediate positions in March and September; though they did not know how much farther south it would appear in December than in June—this was exactly the point to be decided.

Fig. 2.

The reason of this will be clear from [Fig. 2]. [Remark, however, that this figure and the corresponding figure 4 do not represent the case of Bradley’s star, γ Draconis: another star has been chosen which simplifies the diagram, though the principle is essentially the same.] Let A B C D represent the earth’s orbit, the earth being at A in June, at B in September, and so on, and let K represent the position of the star on the line D B. Then in March and September it will be seen from the earth in the same direction, namely, D B K; but the directions in which it is seen in June and December, viz. A K and C K, are inclined in opposite ways to this line. The farther away the star is, the less will this inclination or “parallax” be; and the star is actually so far away that the inclination can only be detected with the utmost difficulty: the lines C K and A K are sensibly parallel to D B K. But Bradley did not know this; it was just this point which he was to examine, and he expected the greatest inclination in one direction to be in December. Accordingly when a few observations had been made on December 3, 5, 11, and 12 it was thought that the star had been caught at its most southerly apparent position, and might be expected thereafter to move northwards, if at all.Unexpected results. But when Bradley repeated the observation on December 17, he found to his great surprise that the star was still moving southwards. Here was something quite new and unexpected, and such a keen observer as Bradley was at once on the alert. He soon found that the changes in the position of the star were of a totally unexpected character. Instead of the extreme positions being occupied in June and December, they were occupied in March and September, just midway between these. And the range in position was quite large, about 40″—not a quantity which could have been detected in the days before telescopes, but one which was unmistakable with an instrument of the most moderate measuring capacity.

Tentative explanations.

What, then, was the cause of this quite unforeseen behaviour on the part of the star? The first thought of the observers was that something might be wrong with their instrument, and it was carefully examined, but without result. The next was that the apparent movement was in the plumb-line, the line of reference. If the whole earth, instead of carrying its axis round the sun in a constant direction, were to be executing an oscillation, then all our plumb-lines would oscillate, and when the direction of a star like γ Draconis was compared with that of the plumb-line it would seem to vary, owing actually to the variation in the plumb-line. The earth might have a motion of this kind in two ways, which it will be necessary for us to distinguish, and the adopted names for them are “nutation of the axis” and “variation of latitude” respectively. In the case of nutation the North Pole remains in the same geographical position, but points to a different part of the heavens. The “variation of latitude,” on the other hand, means that the North Pole wanders about on the earth itself. We shall refer to the second phenomenon more particularly in the sixth chapter.

Nutation?

But it was the first kind of change, the nutation, which Bradley suspected; and very early in the series of observations he had already begun to test this hypothesis. If it was not the star, but the earth and the plumb-line, which were in motion, then other stars ought to be affected. The telescope had been deliberately restricted in its position to suit γ Draconis; but since the stars circle round the Pole, if we draw a narrow belt in the heavens with the Pole as centre, and including γ Draconis, the other stars included would make the same circuit, preceding or following γ Draconis by a constant interval. Most of them would be too faint for observation with Bradley’s telescope; but there was one bright enough to be observed, which also came within its limited range, and it was promptly put under surveillance when a nutation of the earth’s axis was suspected. Careful watching showed that it was not affected in the same way as γ Draconis, and hence the movement could not be in the plumb-line. Was there, then, after all, some effect of the earth’s atmosphere which had been overlooked? We have already remarked that since the star passes directly overhead there should be practically no refraction; and this assumption was made by Molyneux and Bradley in choosing this particular star for observation. It follows at once, if we assume that the atmosphere surrounds the earth in spherical layers.Anomalous refraction. But perhaps this was not so? Perhaps, on the contrary, the atmosphere was deformed by the motion of the earth, streaming out behind her like the smoke of a moving engine? No possibility must be overlooked if the explanation of this puzzling fact was to be got at.

Fig. 3.

The way in which a deformation of the atmosphere might explain the phenomenon is best seen by a diagram. First, it must be remarked that rays of light are only bent by the earth’s atmosphere, or “refracted,” if they enter it obliquely.

If the atmosphere were of the same density throughout, like a piece of glass, then a vertical ray of light, A B (see [Fig. 3]), entering the atmosphere at B would suffer no bending or refraction, and a star shining from the direction A B would be seen truly in that direction from C. But an oblique ray, D E, would be bent on entering the atmosphere at E along the path EF, and a star shining along D E would appear from F to be shining along the dotted line G E F. The atmosphere is not of the same density throughout, but thins out as we go upwards from the earth; and in consequence there is no clear-cut surface, B E, and no sudden bending of the rays as at E: they are gradually bent at an infinite succession of imaginary surfaces. But it still remains true that there is no bending at all for vertical rays; and of oblique rays those most oblique are most bent.

Fig. 4.

Now, suppose the atmosphere of the earth took up, owing to its revolution round the sun, an elongated shape like that indicated in diagram 4, and suppose the star to be at a great distance away to the right of the diagram. When the earth is in the position labelled “June,” the light would fall vertically on the nose of the atmosphere at A, and there would be no refraction. Similarly in “December” the light would fall at C on the stern, also vertically, and there would be no refraction. [The rays from the distant star in December are to be taken as sensibly parallel to those received in June, notwithstanding that the earth is on the opposite side of the sun, as was remarked on p. 98.] But in March and September the rays would strike obliquely on the sides of the supposed figure, and thus be bent in opposite directions, as indicated by the dotted lines; and the extreme positions would thus occur in March and September, as had been observed. The explanation thus far seems satisfactory enough.

But we have assumed the star to lie in the plane of the earth’s orbit; and the stars under observation by Bradley did not lie in this plane, nor did they lie in directions equally inclined to it. Making the proper allowance for their directions, it was found impossible to fit in the facts with this hypothesis, which had ultimately to be abandoned.

Delay in finding real explanation.

It is remarkable to find that two or three years went by before the real explanation of this new phenomenon occurred to Bradley, and during this time he must have done some hard thinking. We have all had experience of the kind of thinking if only in the guessing of conundrums. We know the apparent hopelessness of the quest at the outset: the racking of our brains for a clue, the too frequent despair and “giving it up,” and the simplicity of the answer when once it is declared. But with scientific conundrums the expedient of “giving it up” is not available. We must find the answer for ourselves or remain in ignorance; and though we may feel sure that the answer when found will be as simple as that to the best conundrum, this expected simplicity does not seem to aid us in the search. Bradley was not content with sitting down to think: he set to work to accumulate more facts. Molyneux’s instrument only allowed of the observation of two stars, γ Draconis and the small star above mentioned.Bradley sets up another instrument at Wansted. Bradley determined to have an instrument of his own which should command a wider range of stars; and by this time he was able to return to his uncle’s house at Wansted for this purpose. His uncle had been dead for two or three years, and the memory of the loss was becoming mellowed with time. His uncle’s widow was only too glad to welcome back her nephew, though no longer to the old rectory, and she allowed him to set up a long telescope, even though he cut holes in her floor to pass it through. The object-glass end was out on the roof and the eye end down in the coal cellar; and accordingly in this coal cellar Bradley made the observations which led to his immortal discovery. He had a list of seventy stars to observe, fifty of which he observed pretty regularly. It may seem odd that he did not set up this new instrument at Oxford, but we find from an old memorandum that his professorship was not bringing him in quite £140 a year, and probably he was glad to accept his aunt’s hospitality for reasons of economy. By watching these different stars he gradually got a clear conception of the laws of aberration. The real solution of the problem, according to a well-authenticated account, occurred to him almost accidentally.Finds the right clue. We all know the story of the apple falling and setting Newton to think about the causes of gravitation. It was a similarly trivial circumstance which suggested to Bradley the explanation which he had been seeking for two or three years in vain. In his own words, “at last, when he despaired of being able to account for the phenomena which he had observed, a satisfactory explanation of them occurred to him all at once when he was not in search of it.” He accompanied a pleasure party in a sail upon the river Thames. The boat in which they were was provided with a mast which had a vane at the top of it. It blew a moderate wind, and the party sailed up and down the river for a considerable time.A wind-vane on a boat. Dr. Bradley remarked that every time the boat put about the vane at the top of the boat’s mast shifted a little, as if there had been a slight change in the direction of the wind. He observed this three or four times without speaking; at last he mentioned it to the sailors, and expressed his surprise that the wind should shift so regularly every time they put about. The sailors told him that the wind had not shifted, but that the apparent change was owing to the change in the direction of the boat, and assured him that the same thing invariably happened in all cases. This accidental observation led him to conclude that the phenomenon which had puzzled him so much was owing to the combined motion of light and of the earth. To explain exactly what is meant we must again have recourse to a diagram; and we may also make use of an illustration which has become classical.

Fig. 5.

Analogy of rain.

If rain is falling vertically, as represented by the direction A B; and if a pedestrian is walking horizontally in the direction C D, the rain will appear to him to be coming in an inclined direction, E F, and he will find it better to tilt his umbrella forwards. The quicker his pace the more he will find it advisable to tilt the umbrella. This analogy was stated by Lalande before the days of umbrellas in the following words: “Je suppose que, dans un temps calme, la pluie tombe perpendiculairement, et qu’on soit dans une voiture ouverte sur le devant; si la voiture est en repos, on ne reçoit pas la moindre goutte de pluie; si la voiture avance avec rapidité, la pluie entre sensiblement, comme si elle avoit pris une direction oblique.” Lalande’s example, modified to suit modern conditions, has been generally adopted by teachers, and in examinations candidates produce graphic pictures of the stationary, the moderate-paced, and the flying, possessors of umbrellas.

Aberration.

Applying it to the phenomenon which it is intended to illustrate, if light is being received from a star by an earth, travelling across the direction of the ray, the telescope (which in this case represents the umbrella) must be tilted forward to catch the light. Now on reference to [Fig. 4] it will be seen that the earth is travelling across the direction of rays from the star in March and September; and in opposite directions in the two cases. Hence the telescope must be tilted a little, in opposite directions, to catch the light; or, in other words, the star will appear to be farthest south in March, farthest north in September. And so at last the puzzle was solved, and the solution was found, as so often happens, to be of the simplest kind; so simple when once we know, and so terribly hard to imagine when we don’t! It may comfort us in our struggles with minor problems to reflect that Bradley manfully stuck to his problem for two or three years. It was probably never out of his thoughts, waking or sleeping; when at work it was the chief object of his labours, and when on a pleasure party he was ready to catch at the slightest clue, in the motion of a wind-vane on a boat, which might help him to the solution.

Results of discovery.