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+The Project Gutenberg EBook of Astronomical Discovery, by Herbert Hall Turner
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Astronomical Discovery
+
+Author: Herbert Hall Turner
+
+Release Date: August 3, 2010 [EBook #33337]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK ASTRONOMICAL DISCOVERY ***
+
+
+
+
+Produced by Juliet Sutherland, Joseph Myers and the Online
+Distributed Proofreading Team at http://www.pgdp.net.
+
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+
+
+
+ASTRONOMICAL DISCOVERY
+
+
+
+
+[Illustration: 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
+
+
+                                                                    PAGE
+  CHAPTER I
+      URANUS AND EROS                                                  1
+
+  CHAPTER II
+      THE DISCOVERY OF NEPTUNE                                        38
+
+  CHAPTER III
+      BRADLEY'S DISCOVERIES OF THE ABERRATION OF LIGHT AND OF THE
+      NUTATION OF THE EARTH'S AXIS                                    86
+
+  CHAPTER IV
+      ACCIDENTAL DISCOVERIES                                         121
+
+  CHAPTER V
+      SCHWABE AND THE SUN-SPOT PERIOD                                155
+
+  CHAPTER VI
+      THE VARIATION OF LATITUDE                                      177
+
+  INDEX                                                              221
+
+
+
+
+LIST OF PLATES
+
+
+  PLATE
+
+     I. PORTRAIT OF J. C. ADAMS                        _To face page_ 22
+
+    II. PORTRAIT OF A. GRAHAM                               "    "    22
+
+   III. PORTRAIT OF U. J. LE VERRIER                        "    "    60
+
+    IV. PORTRAIT OF J. G. GALLE                             "    "    60
+
+     V. CORNER OF THE BERLIN MAP BY THE USE OF WHICH
+        GALLE FOUND NEPTUNE                                 "    "    82
+
+    VI. ASTRONOMERS ROYAL                                 _Frontispiece_
+
+   VII. GREAT COMET OF NOV. 7, 1882                   _To face page_ 122
+
+  VIII. THE OXFORD NEW STAR                                "    "    142
+
+    IX. NEBULOSITY ROUND NOVA PERSEI                       "    "    146
+
+     X. SUN-SPOTS AT GREENWICH, FEB. 18 AND 19, 1894       "    "    158
+
+    XI. SUN-SPOTS AT GREENWICH, FEB. 20 AND 21, 1894       "    "    162
+
+   XII. NUMBER OF SUN-SPOTS COMPARED WITH DAILY RANGE
+        OF MAGNETIC DECLINATION AND DAILY RANGE OF
+        MAGNETIC HORIZONTAL FORCE                          "    "    164
+
+  XIII. GREENWICH MAGNETIC CURVES, 1859-60                 "    "    166
+
+   XIV. GREENWICH MAGNETIC CURVES, 1841-1860               "    "    166
+
+    XV. SUN-SPOTS AND TURNS OF VANE                        "    "    170
+
+
+
+
+ERRATA
+
+
+  Page 133, line 27, _for_ "200 stars" _read_ "200 stars per hour."
+
+   "   145, See note on page 220.
+
+   "   146, bottom of page. This nebulosity was first discovered by Dr.
+            Max Wolf of Heidelberg. See _Astr. Nachr._ 3736.
+
+   "   181, line 17, _for_ "observation" _read_ "aberration."
+
+
+
+
+ASTRONOMICAL DISCOVERY
+
+
+
+
+CHAPTER I
+
+URANUS AND EROS
+
+
+[Sidenote: 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.
+
+[Sidenote: 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"_
+
+  Much have I travell'd in the realms of gold,
+  And many goodly states and kingdoms seen;
+  Round many western islands have I been
+  Which bards in fealty to Apollo hold.
+  Oft of one wide expanse had I been told
+  That deep-brow'd Homer ruled as his demesne;
+  Yet did I never breathe its pure serene
+  Till I heard Chapman speak out loud and bold:
+  Then felt I like some watcher of the skies
+  When a new planet swims into his ken;
+  Or like stout Cortez when with eagle eyes
+  He star'd at the Pacific--and all his men
+  Look'd at each other with a wild surmise--
+  Silent, upon a peak in Darien.
+
+[Sidenote: 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_
+
+     [Sidenote: 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."
+
+[Sidenote: Called first a comet.]
+
+[Sidenote: Other observers would not have found it at all.]
+
+At first sight this seems to be the wrong reference, for it speaks of a
+new comet, not a new planet. But it is indeed of Uranus that Herschel is
+speaking; and so little did he realise the full magnitude of his
+discovery at once, that he announced it as that of a comet; and a comet
+the object was called for some months. Attempts were made to calculate its
+orbit as a comet, and broke down; and it was only after much work of this
+kind had been done that the real nature of the object began to be
+suspected. But far more striking than this misconception is the display of
+skill necessary to detect any peculiarity in the object at all. Among a
+number of stars one seemed somewhat exceptional in size, but the
+difference was only just sufficient to awaken suspicion in a keen-eyed
+Herschel. Would any other observer have noticed the difference at all?
+Certainly several good observers had looked at the object before, and
+looked at it with the care necessary to record its position, without
+noting any peculiarity. Their observations were recovered subsequently and
+used to fix the orbit of the new planet more accurately. I shall remind
+you in the next chapter that Uranus had been observed in this way no less
+than seventeen times by first-rate observers without exciting their
+attention to anything remarkable. The first occasion was in 1690, nearly a
+century before Herschel's grand discovery, and these chance observations,
+which lay so long unnoticed as in some way erroneous, subsequently proved
+to be of the utmost value in fixing the orbit of the new planet. But there
+is even more striking testimony than this to the exceptional nature of
+Herschel's achievement. It is a common experience in astronomy that an
+observer may fail to notice in a general scrutiny some phenomenon which he
+can see perfectly well when his attention is directed to it: when a man
+has made a discovery and others are told what to look for, they often see
+it so easily that they are filled with amazement and chagrin that they
+never saw it before. Not so in the case of Uranus. At least two great
+astronomers, Lalande and Messier, have left on record their astonishment
+that Herschel could differentiate it from an ordinary star at all; for
+even when instructed where to look and what to look for, they had the
+greatest difficulty in finding it. I give a translation of Messier's
+words, which Herschel records in the paper already quoted announcing the
+discovery:--
+
+     "Nothing was more difficult than to recognise it; and I cannot
+     conceive how you have been able to return several times to this star
+     or comet; for absolutely it has been necessary to observe it for
+     several consecutive days to perceive that it was in motion."
+
+[Sidenote: 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?
+
+[Sidenote: Though this may happen at times.]
+
+[Sidenote: Name of new planet.]
+
+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. 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.
+
+     [Sidenote: _Georgium Sidus._]
+
+     "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 name _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."
+
+[Sidenote: Herschel.]
+
+This letter reminds us how long it was since a new name had been required
+for a new planet,--to find a similar occasion Herschel had to go to the
+almost prehistoric past, when the names of heroes and divinities were
+given to the planets. It is, perhaps, not unnatural that he should have
+considered an entirely new departure appropriate for a discovery separated
+by so great a length of time from the others; but his views were not
+generally accepted, especially on the Continent. Lalande courteously
+proposed the name of Herschel for the new planet, in honour of the
+discoverer, and this name was used in France; but Bode, on the other hand,
+was in favour of retaining the old practice simply, and calling the new
+planet Uranus. All three names seem to have been used for many years. Only
+the other day I was interested to see an old pack of cards, used for
+playing a parlour game of Astronomy, in which the name Herschel is used.
+The owner told me that they had belonged to his grandfather; and the date
+of publication was 1829, and the place London, so that this name was in
+common use in England nearly half a century after the actual discovery;
+though in the "English Nautical Almanac" the name "the Georgian"
+(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.)
+
+[Sidenote: 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.
+
+[Sidenote: Bode's law.]
+
+The discovery of Neptune, as we shall see, was totally different in
+character from that of Uranus. The latter may be described as the finding
+of something by an observer who was looking for anything; Neptune was the
+finding of something definitely sought for, and definitely pointed out by
+a most successful and brilliant piece of methodical work. But before that
+time several planets had been found, as the practical result of a definite
+search, although the guiding principle was such as cannot command our
+admiration to quite the same extent as in the case of Neptune. To explain
+it I must say something of the relative sizes of the orbits in which
+planets move round the sun. These orbits are, as we know, ellipses; but
+they are very nearly circles, and, excluding refinements, we may consider
+them as circles, with the sun at the centre of each, so that we may talk
+of the distance of any planet from the sun as a constant quantity without
+serious error. Now if we arrange the planetary distances in order, we
+shall notice a remarkable connection between the terms of the series. Here
+is a table showing this connection.
+
+  TABLE OF THE DISTANCES OF THE PLANETS FROM THE SUN, SHOWING "BODE'S LAW."
+
+  +----------------------------------------------------+
+  | Name of   | Distance from |     "Bode's Law"       |
+  | Planet.   | Sun, taking   | (originally formulated |
+  |           | that of Earth | by Titius, but brought |
+  |           | as 10.        | into notice by Bode).  |
+  |----------------------------------------------------|
+  | Mercury   |        4      |     4 +   0=   4       |
+  | Venus     |        7      |     4 +   3=   7       |
+  | The Earth |       10      |     4 +   6=  10       |
+  | Mars      |       15      |     4 +  12=  16       |
+  | (     )   |      ( )      |     4 +  24=  28       |
+  | Jupiter   |       52      |     4 +  48=  52       |
+  | Saturn    |       95      |     4 +  96= 100       |
+  | Uranus    |      192      |     4 + 192= 196       |
+  +----------------------------------------------------+
+
+[Sidenote: Gap in the series suggesting unknown planet.]
+
+[Sidenote: Search for it.]
+
+[Sidenote: Accidental discovery.]
+
+If we write down a series of 4's, and then add the numbers 3, 6, 12, and
+so on, each formed by doubling the last, we get numbers representing very
+nearly the planetary distances, which are shown approximately in the
+second column. But three points call for notice. Firstly, the number
+before 3 should be 1-1/2, and not zero, to agree with the rest. Secondly,
+there is a gap, or rather was a gap, after the discovery of Uranus,
+between Mars and Jupiter; and thirdly, we see that when Uranus was
+discovered, and its distance from the sun determined, this distance was
+found to fall in satisfactorily with this law, which was first stated by
+Titius of Wittenberg. This third fact naturally attracted attention. No
+explanation of the so-called "law" was known at the time; nor is any
+known even yet, though we may be said to have some glimmerings of a
+possible cause; and in the absence of such explanation it must be regarded
+as merely a curious coincidence. But the chances that we are in the
+presence of a mere coincidence diminish very quickly with each new term
+added to the series, and when it was found that Herschel's new planet
+fitted in so well at the end of the arrangement, the question arose
+whether the gap above noticed was real, or whether there was perhaps
+another planet which had hitherto escaped notice, revolving in an orbit
+represented by this blank term. This question had indeed been asked even
+before the discovery of Uranus, by Bode, a young astronomer of Berlin; and
+for fifteen years he kept steadily in view this idea of finding a planet
+to fill the vacant interval. The search would be a very arduous one,
+involving a careful scrutiny, not perhaps of the whole heavens, but of a
+considerable portion of it along the Zodiac; too great for one would-be
+discoverer single-handed; but in September 1800 Bode succeeded in
+organising a band of six German astronomers (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). 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.
+
+[Sidenote: 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.
+
+[Sidenote: 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.
+
+[Sidenote: 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_.
+
+     [Sidenote: 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."
+
+[Sidenote: Rediscovery of Ceres.]
+
+[Sidenote: Another planet found.]
+
+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. 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. 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_!
+
+[Sidenote: 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.
+
+  +---------------------------------------+
+  |Number|   Name.   | Discoverer. | Date.|
+  |---------------------------------------|
+  |   1  | Ceres     | Piazzi      | 1801 |
+  |   2  | Pallas    | Olbers      | 1802 |
+  |   3  | Juno      | Harding     | 1804 |
+  |   4  | Vesta     | Olbers      | 1807 |
+  |------|-----------|-------------|------|
+  |   5  | Astraea   | Hencke      | 1845 |
+  |   6  | Hebe      | Hencke      | 1847 |
+  |   7  | Iris      | Hind        | 1847 |
+  |   8  | Flora     | Hind        | 1847 |
+  |   9  | Metis     | Graham      | 1848 |
+  |  10  | Hygeia    | De Gasparis | 1849 |
+  |  11  | Parthenope| De Gasparis | 1850 |
+  |  12  | Victoria  | Hind        | 1850 |
+  |  13  | Egeria    | De Gasparis | 1850 |
+  +---------------------------------------+
+
+[Sidenote: Hencke's long search.]
+
+Here now is a table showing how other bodies were gradually added to this
+first list of four, but you will see that no addition was made for a long
+time. Not that the search was immediately abandoned; but being rewarded by
+no success for some years, it was gradually dropped, and the belief gained
+ground that the number of the planets was at last complete. The
+discoverers of Uranus and of these first four minor planets all died
+before any further addition was made; and it was not until the end of 1845
+that Astraea was found by an ex-postmaster of the Prussian town of
+Driessen, by name Hencke, who, in spite of the general disbelief in the
+existence of any more planets, set himself diligently to search for them,
+and toiled for fifteen long years before at length reaping his reward.
+Others then resumed the search; Hind, the observer of an English amateur
+astronomer near London, found Iris a few weeks after Hencke had been
+rewarded by a second discovery in 1847, and in the following year Mr.
+Graham at Markree in Ireland (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.
+
+[Illustration:
+
+  _By permission of Messrs. Macmillan & Co._
+  I.--J. C. ADAMS.]
+
+[Illustration:
+
+  II.--A. GRAHAM.
+  DISCOVERER OF THE NINTH MINOR PLANET (METIS).]
+
+[Sidenote: The photographic method.]
+
+You will see the great variety characterising these discoveries; some of
+them are the result of deliberate search, others have come accidentally,
+and some even contrary to expectation. Of the great majority of the
+earlier ones it may be said that enormous diligence was required for each
+discovery; to identify a planet it is necessary to have either a good map
+of the stars or to know them thoroughly, so that the map practically
+exists in the brain. We need only remember Hencke's fifteen years of
+search before success to recognise what vast stores of patience and
+diligence were required in carrying out the search. But of late years
+photography has effected a great revolution in this respect. It is no
+longer necessary to do more than set what Sir Robert Ball has called a
+"star-trap," or rather planet-trap. If a photograph be taken of a region
+of the heavens, by the methods familiar to astronomers, so that each star
+makes a round dot on the photographic plate, any sufficiently bright
+object moving relatively to the stars will make a small line or trail, and
+thus betray its planetary character. In this way most of the recent
+discoveries have been made, and although diligence is still required in
+taking the photographs, and again in identifying the objects thus found
+(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.
+
+  1801 to 1850--altogether 13 discoveries.
+  1851 to 1860--     "     49      "
+  1861 to 1870--     "     49      "
+  1871 to 1880--     "    108      "
+  1881 to 1890--     "     83      "
+  1891 to 1900--     "    180 announcements
+       In 1901       "     36      "
+        " 1902       "     50      "
+        " 1903       "     41      "
+                          ---
+                   Total  609
+
+  [_N.B._--Many of the more recent announcements turned out to refer to
+  old discoveries.]
+
+[Sidenote: 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:--
+
+  No.   Name.
+  248   Lameia
+  250   Bettina
+  261   Prymno
+  264   Libussa
+  296   Phaëtusa
+  340   Eduarda
+  341   California
+  350   Ornamenta
+  357   Ninina
+  385   Ilmatar
+  389   Industria
+  391   Ingeborg
+  433   Eros
+  443   Photographica
+  457   Alleghenia
+  462   Eriphyla
+  475   Ocllo
+  484   Pittsburghia
+  503   Evelyn
+
+[Sidenote: Bettina.]
+
+[Sidenote: The provisional letters.]
+
+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.
+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.
+
+[Sidenote: Eros.]
+
+Fortunately, however, on running through it for the fifth time, an object
+of particular interest was discovered. Most of these bodies revolve at a
+distance from the sun intermediate between that of Mars and that of
+Jupiter, but the little planet which took the symbol DQ, and afterwards
+the name of Eros, was found to have a mean distance actually less than
+that of Mars, and this gave it an extraordinary importance with respect to
+the great problem of determining the sun's distance. To explain this
+importance we must make a small digression.
+
+[Sidenote: 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.
+
+[Illustration: FIG. 1.]
+
+[Sidenote: The "Black Drop."]
+
+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. 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.
+
+[Sidenote: Failure.]
+
+These difficulties, as already stated, were known to exist; but there is a
+long interval between transits of Venus, or rather between every pair of
+such transits. After those of 1874 and 1882 there will be no more until
+2004 and 2012, so that we shall never see another; similarly, before that
+pair of the last century, there had not been any such occasion since 1761
+and 1769, and no one was alive who remembered at first hand the trouble
+which was known to exist. It was proposed to obviate the anticipated
+difficulties by careful practice beforehand; models were prepared to
+resemble as nearly as possible the expected appearances, and the times
+recorded by different observers were compared with the true time, which
+could, in this case of a model, be determined. In this way it was hoped
+that the habit of each observer, his "personal equation" as it is called,
+could be determined beforehand, and allowed for as a correction when he
+came to observe the actual transit. The result, however, was a great
+disappointment. The actual appearances were found to be totally different
+in character from those shown by the model; chiefly, perhaps, because it
+had been impossible to imitate with a model the effect of the atmosphere
+which surrounds the planet Venus. Observers trained beforehand, using
+similar instruments, and standing within a few feet of each other, were
+expected, after making due allowance for personal equation, to give the
+same instant for contact; but their observations when made were found to
+differ by nearly a minute of time, and after an exhaustive review of the
+whole material it was felt that all hope of determining accurately the
+sun's distance by this method must be given up. The following table will
+show how much was learned from the transits of Venus, and how much
+remained to be settled. They left the result in doubt over a range of
+about two million miles.
+
+     SUN'S DISTANCE, IN MILLIONS OF MILES, AS FOUND BY DIFFERENT OBSERVERS
+
+     =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 =93-1/4=
+     million (Airy, from British observations of 1874), =92-1/2= million
+     (Stone, from British observations of 1882), and =91-1/2= million
+     (Puiseux, from French observations), a range of 1-3/4 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.
+
+[Sidenote: Modern method for sun's distance.]
+
+[Sidenote: Photography.]
+
+[Sidenote: Dr. Gill's expedition to Ascension.]
+
+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. 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; 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.
+
+[Sidenote: Victoria, Iris, and Sappho.]
+
+[Sidenote: Eros.]
+
+Further, a small planet which is in appearance just like an ordinary star
+has, irrespective of this great proximity, some distinct advantages over a
+planet like Mars, which appears as a round disc, and is, moreover, of a
+somewhat reddish colour. When the distance of an object of this kind from
+a point of line such as a star is measured with the heliometer it is found
+that a certain bias, somewhat difficult to allow for with certainty, is
+introduced into the measures; and our confidence in the final results
+suffers accordingly. After his observations of Mars in 1878, Dr. David
+Gill was sufficiently impressed with this source of error to make three
+new determinations of the sun's distance, using three of the minor planets
+instead of Mars, in spite of the fact that they were sensibly farther
+away; and his choice was justified by finding that the results from these
+three different sets of observations agreed well among themselves, and
+differed slightly from that given by the observations of Mars. Hence it
+seems conclusively proved that one of these bodies is a better selection
+than Mars in any case, and the discovery of Eros, which offered the
+advantage of greater proximity in addition, was hailed as a new
+opportunity of a most welcome kind. It was seen by a little calculation
+that in the winter of 1900-1901 the planet would come very near the
+earth; not the nearest possible (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
+
+
+[Sidenote: 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.
+
+[Sidenote: 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.
+
+[Sidenote: Suspicion of perturbing planet.]
+
+It is difficult to mention an exact date for the conversion into certainty
+of the suspicion that no single orbit could be found to satisfy all the
+observations; but we may certainly regard this fact as established in
+1821, when Alexis Bouvard published some tables of the planet, and showed
+fully in the introduction that when every correction for the disturbing
+action of other planets had been applied, it was still impossible to
+reconcile the old observations with the orbit calculated from the new
+ones. The idea accordingly grew up that there might be some other body or
+bodies attracting the planet and causing these discrepancies. Here again
+it is not easy to say exactly when this notion arose, but it was certainly
+existent in 1834, as the following letter to the Astronomer Royal will
+show. I take it from his well-known "Account of some Circumstances
+historically connected with the Discovery of the Planet exterior to
+Uranus," which he gave to the Royal Astronomical Society at its first
+meeting after that famous discovery (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:--
+
+     [Sidenote: Airy's scepticism.]
+
+
+     NO. 2.--G. B. AIRY _to the_ REV. T. J. HUSSEY.
+     [_Extract._]
+
+     "'OBSERVATORY, CAMBRIDGE, _1834, Nov. 23_.
+
+     "'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.'"
+
+[Sidenote: Le Verrier's papers.]
+
+[Sidenote: Planet to be detected by disc.]
+
+[Sidenote: Galle's discovery of the planet.]
+
+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. 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, 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. 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.
+
+[Sidenote: Adams' work publicly announced.]
+
+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. 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.
+
+[Sidenote: 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.
+
+[Sidenote: Airy's "Account."]
+
+[Sidenote: "A movement of the age."]
+
+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), 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."
+
+[Sidenote: Airy under-estimated Adams' work.]
+
+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. 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_.
+
+     [Sidenote: Challis mentions Adams to Airy, and suggests Adams' visit
+     to Greenwich.]
+
+     "'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 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.
+
+     [Sidenote: 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:--
+
+        Mean distance (assumed nearly in accordance
+            with Bode's Law)                           38.4
+        Mean sidereal motion in 365.25 days             1°30'.9
+        Mean longitude, 1st October 1845              323 34
+        Longitude of perihelion                       315 55
+        Eccentricity                                  0.1610.
+        Mass (that of the sun being unity)            0.0001656.
+
+     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._
+
+                "
+        1780  +0.27
+        1783  -0.23
+        1786  -0.96
+        1789  +1.82
+        1792  -0.91
+        1795  +0.09
+        1798  -0.99
+        1801  -0.04
+        1804  +1.76
+        1807  -0.21
+        1810  +0.56
+        1813  -0.94
+        1816  -0.31
+        1819  -2.00
+        1822  +0.30
+        1825  +1.92
+        1828  +2.25
+        1831  -1.06
+        1834  -1.44
+        1837  -1.62
+        1840  +1.73
+
+     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._
+
+               "
+        1690  +44.4
+        1712  + 6.7
+        1715  - 6.8
+        1750  - 1.6
+        1753  + 5.7
+        1756  - 4.0
+        1763  - 5.1
+        1769  + 0.6
+        1771  +11.8
+
+     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_.
+
+     [Sidenote: 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."
+
+[Sidenote: 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.
+
+[Sidenote: His disappointment at Greenwich, and at Airy's question.]
+
+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.
+
+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.
+
+[Sidenote: The merits of Airy's question.]
+
+[Sidenote: The range of possibilities.]
+
+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 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.
+
+[Illustration:
+
+  III--U. J. LE VERRIER.
+  (_From a print in the possession of the Royal Astronomical Society._)]
+
+[Illustration:
+
+  IV--J. G. GALLE.
+  WHO FIRST SAW THE PLANET NEPTUNE]
+
+[Sidenote: Airy receives Le Verrier's memoir.]
+
+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, 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_.
+
+     [Sidenote: He puts the "radius-vector" question to Le Verrier, but
+     makes no mention of Adams.]
+
+     "'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. 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.
+
+[Sidenote: Airy announces the likelihood of a new planet, and suggests a
+search for it at Cambridge not having suitable telescope at Greenwich]
+
+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." 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; 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."
+
+[Sidenote: Challis undertakes the search.]
+
+[Sidenote: He finds too late that he had observed the planet.]
+
+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 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.
+
+[Sidenote: Sensation caused by the discovery.]
+
+[Sidenote: Not all _national_ jealousy.]
+
+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. 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. 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.
+
+[Sidenote: The position of Cambridge in the matter.]
+
+[Sidenote: Challis the weakest point.]
+
+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. 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; 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.
+
+[Sidenote: Curious difference between actual and supposed planet.]
+
+[Sidenote: Professor Peirce's contention that the discovery was a mere
+accident.]
+
+[Sidenote: The explanation.]
+
+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_. 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.
+
+[Sidenote: 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.
+
+[Sidenote: 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.
+
+                 I.    II.   III.    IV.    V.     VI.
+
+  Correct      1820   1835   1872   1830   1861   1856
+
+  Within ±5°  {1812   1827   1865   1813   1815   1826
+              {1827   1842   1877   1866   1871   1868
+
+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.
+
+[Sidenote: 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.
+
+     [Sidenote: The visible disc.]
+
+     "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_.
+     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."
+
+[Sidenote: 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).
+
+[Sidenote: Newcomb's criticism.]
+
+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. 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."
+
+[Sidenote: Element of good fortune.]
+
+[Sidenote: The map used by Galle.]
+
+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. 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. 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.
+
+[Illustration: V.--CORNER OF THE BERLIN MAP, BY THE USE OF WHICH GALLE
+FOUND NEPTUNE.]
+
+[Sidenote: 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
+
+
+[Sidenote: 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.
+
+[Sidenote: Bradley's birth and early life.]
+
+[Sidenote: Brief clerical career.]
+
+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. 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."
+
+[Sidenote: Learnt astronomy _not_ at Oxford, but from his uncle, James
+Pound.]
+
+[Sidenote: Pound a first-rate observer.]
+
+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. 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; 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.
+
+[Sidenote: Bradley worked with him.]
+
+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. 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.
+
+[Sidenote: The work done by Pound and Bradley.]
+
+[Sidenote: Use of very long telescopes.]
+
+[Sidenote: Reason for great length.]
+
+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. And finally, his skill
+in the management of instruments is shown by his measuring the diameter of
+the planet Venus with a telescope actually 212-1/4 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. 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.
+
+[Sidenote: Bradley appointed at Oxford, but continues to work at Wansted.]
+
+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, 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.
+
+[Sidenote: Samuel Molyneux.]
+
+[Sidenote: Attempts to find stellar parallax.]
+
+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. 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 [gamma] 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.
+
+[Sidenote: The instrument.]
+
+[Sidenote: Expected results.]
+
+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. 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. 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.
+
+[Illustration: FIG. 2.]
+
+[Sidenote: Unexpected results.]
+
+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, [gamma] 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. 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.
+
+[Sidenote: 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
+[gamma] 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.
+
+[Sidenote: Nutation?]
+
+[Sidenote: Anomalous refraction.]
+
+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 [gamma] 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
+[gamma] Draconis, the other stars included would make the same circuit,
+preceding or following [gamma] 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 [gamma] 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. 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.
+
+[Illustration: 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.
+
+[Illustration: 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.
+
+[Sidenote: Delay in finding real explanation.]
+
+[Sidenote: Bradley sets up another instrument at Wansted.]
+
+[Sidenote: Finds the right clue.]
+
+[Sidenote: A wind-vane on a boat.]
+
+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, [gamma] Draconis and the small star above
+mentioned. 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. 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. 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.
+
+[Illustration: FIG. 5.]
+
+[Sidenote: 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.
+
+[Sidenote: 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.
+
+[Sidenote: Results of discovery.]
+
+The discovery of aberration made Bradley famous at a bound. Oxford might
+well be proud of her two Savilian Professors at this time, for they had
+both made world-famous discoveries--Halley that of the periodicity of
+comets, and Bradley of the aberration of light. How different their tastes
+were and how difficult it would have been for either to do the work of the
+other! Bradley was no great mathematician, and though he was quite able to
+calculate the orbit of a comet, and carried on such work when Halley left
+it, it was probably not congenial to him. Halley, on the other hand,
+almost despised accurate observations as finicking. "Be sure you are
+correct to a minute," he was wont to say, "and the fractions do not so
+much matter." With such a precept Bradley would never have made his
+discoveries. No quantity was too small in his eyes, and no sooner was the
+explanation of aberration satisfactorily established than he perceived
+that though it would account for the main facts, it would not explain all.
+There was something left. This is often the case in the history of
+science. A few years ago it was thought that we knew the constitution of
+our air completely--oxygen, nitrogen, water vapour, and carbonic acid gas;
+but a great physicist, Lord Rayleigh, found that after extracting all the
+water and carbonic acid gas, all the oxygen and all the nitrogen, there
+was something left--a very minute residuum, which a careless experimenter
+would have overlooked or neglected, but which a true investigator like
+Lord Rayleigh saw the immense importance of. He kept his eye on that
+something left, and presently discovered a new gas which we now know as
+argon. Had he repeated the process, extracting all the argon after the
+nitrogen, he might have found by a scrutiny much more accurate still yet
+another gas, helium, which we now know to exist in extremely minute
+quantities in the air. But meantime this discovery was made in another
+way.
+
+[Sidenote: Still something to be explained.]
+
+[Sidenote: Probably nutation.]
+
+[Sidenote: His nineteen years' campaign.]
+
+When Bradley had extracted all the aberration from his observations he
+found that there was something left, another problem to be solved and some
+more thinking to be done to solve it. But he was now able to profit by his
+previous labours, and the second step was made more easily than the first.
+The residuum was not the parallax of which he had originally been in
+search, for it did not complete a cycle within the year; it was rather a
+progressive change from year to year. But there was an important clue of
+another kind. He saw that the apparent movements of all stars were in
+this case the same; and he knew that a movement of this kind can be
+referred, not to the stars themselves, but to the plumb-line from which
+their directions are measured. He had thought out the possible causes of
+such a movement of the plumb-line or of the earth itself, and had realised
+that there might be a _nutation_ which would go through a cycle in about
+nineteen years, the period in which the moon's nodes revolve. He was not
+mathematician enough to work out the cause completely, but he saw clearly
+that to trace the whole effect he must continue the observations for
+nineteen years; and accordingly he entered on this long campaign without
+any hesitation. His instrument was still that in his aunt's house at
+Wansted, where he continued to live and make the observations for a few
+years, but in 1732 he removed to Oxford, as we shall see, and he must have
+made many journeys between Wansted and Oxford in the course of the
+remaining fifteen years during which he continued to trace out the effects
+of nutation. His aunt too left Wansted to accompany Bradley to Oxford, and
+the house passed into other hands. It is to the lasting credit of the new
+occupant, Mrs. Elizabeth Williams, that the great astronomer was allowed
+to go on and complete the valuable series of observations which he had
+commenced. Bradley was not lodged in her house; he stayed with a friend
+close by on his visits to Wansted, but came freely in and out of his
+aunt's old home to make his observations. How many of us are there who
+would cheerfully allow an astronomer to enter our house at any hour of the
+night to make observations in the coal-cellar! It says much, not only for
+Bradley's fame, but for his personal attractiveness, that he should have
+secured this permission, and that there should be no record of any
+friction during these fifteen years. At the end of the whole series of
+nineteen years his conclusions were abundantly verified, and his second
+great discovery of nutation was established. Honours were showered upon
+him, and no doubt the gentle heart of Mrs. Elizabeth Williams was uplifted
+at the glorious outcome of her long forbearance.
+
+[Sidenote: Residence at Oxford.]
+
+But we may now turn for a few moments from Bradley's scientific work to
+his daily life. We have said that in 1732, after holding his professorship
+for eleven years, he first went definitely to reside in Oxford. He
+actually had not been able to afford it previously. His income was only
+£140 a year, and the statutes prevented him from holding a living: so
+that he was fain to accept Mrs. Pound's hospitable shelter. But in 1729 an
+opportunity of adding to his income presented itself, by giving lectures
+in "experimental philosophy." The observations on nutation were not like
+those on aberration: he was not occupied day and night trying to find the
+solution: he had practically made up his mind about the solution, and the
+actual observations were to go on in a quiet methodical manner for
+nineteen years, so that he now had leisure to look about him for other
+employment. Dr. Keill, who had been Professor of Astronomy before Bradley,
+had attracted large classes to lectures, not on astronomy, but on
+experimental philosophy: but had sold his apparatus and goodwill to Mr.
+Whiteside, of Christ Church, one of the candidates who were disappointed
+by Bradley's election. In 1729 Bradley purchased the apparatus from
+Whiteside, and began to give lectures in experimental philosophy. His
+discovery of aberration had made him famous, so that his classes were
+large from the first, and paid him considerable fees. Suddenly therefore
+he changed his poverty for a comfortable income, and he was able to live
+in Oxford in one of two red brick houses in New College Lane, which were
+in those days assigned to the Savilian Professors (now inhabited by New
+College undergraduates). His aunt, Mrs. Pound, to whom he was devotedly
+attached, came with him, and two of her nephews. In his time of prosperity
+Bradley was thus able to return the hospitality which had been so
+generously afforded him in times of stress.
+
+[Sidenote: Astronomer Royal at Greenwich.]
+
+[Sidenote: Letter from Earl of Macclesfield.]
+
+Before he completed his observations for nutation another great change in
+his fortunes took place. In 1742 he was elected to succeed Halley as
+Astronomer Royal. It was Halley's dying wish that Bradley should succeed
+him, and it is said that he was even willing to resign in his favour, for
+his right hand had been attacked by paralysis, and the disease was
+gradually spreading. But he died without any positive assurance that his
+wish would be fulfilled. The chief difficulty in securing the appointment
+of Bradley seems to have been that he was the obvious man for the post in
+universal opinion. "It is not only my friendship for Mr. Bradley that
+makes me so ardently wish to see him possessed of the position," wrote the
+Earl of Macclesfield to the Lord Chancellor; "it is my real concern for
+the honour of the nation with regard to science. For as our credit and
+reputation have hitherto not been inconsiderable amongst the astronomical
+part of the world, I should be extremely sorry we should forfeit it all at
+once by bestowing upon a man of inferior skill and abilities the most
+honourable, though not the most lucrative, post in the profession (a post
+so well filled by Dr. Halley and his predecessor), when at the same time
+we have amongst us a man known by all the foreign, as well as our own
+astronomers, not to be inferior to either of them, and one whom Sir Isaac
+Newton was pleased to call the best astronomer in Europe." And again, "As
+Mr. Bradley's abilities in astronomical learning are allowed and confessed
+by all, so his character in every respect is so well established, and so
+unblemished, that I may defy the worst of his enemies (if so good and
+worthy a man have any) to make even the lowest or most trifling objection
+to it."
+
+"After all," the letter goes on, "it may be said if Mr. Bradley's skill is
+so universally acknowledged, and his character so established, there is
+little danger of opposition, since no competitor can entertain the least
+hope of success against him. But, my lord, we live in an age when most men
+how little soever their merit may be, seem to think themselves fit for
+whatever they can get, and often meet with some people, who by their
+recommendations of them appear to entertain the same opinion of them, and
+it is for this reason that I am so pressing with your lordship not to lose
+any time."
+
+Such recommendations had, however, their effect: the dreaded possibility
+of a miscarriage of justice was averted, and Bradley became the third
+Astronomer Royal, though he did not resign his professorship at Oxford.
+Halley, Bradley, and Bliss, who were Astronomers Royal in succession, all
+held the appointment along with one of the Savilian professorships at
+Oxford; but since the death of Bliss in 1761, the appointment has always
+gone to a Cambridge man.
+
+[Sidenote: Instruments very defective.]
+
+When Bradley went to Greenwich, in June 1742, he was at first unable to do
+much from the wretched state in which he found the instruments. Halley was
+not a good observer: his heart was not in the work, and he had not taken
+the trouble to set the instruments right when they went wrong. The
+counterpoises of that instrument which ought to have been the best in the
+world at the time rubbed against the roof so that the telescope could
+scarcely be moved in some positions: and some of the screws were broken.
+There was no proper means of illuminating the cross-wires, and so on. With
+care and patience Bradley set all this right, and began observations. He
+had the good fortune to secure the help of his nephew, John Bradley, as
+assistant, and the companionship seems to have been as happy as that
+previous one of James Bradley and his uncle Pound. John Bradley was able
+to carry on the observations when his uncle was absent in Oxford, and the
+work the two got through together in the first year is (in the words of
+Bradley's biographer Rigaud) "scarcely to be credited." The transit
+observations occupy 177 folio pages, and no less than 255 observations
+were taken on one night. And at the same time, it must be remembered,
+Bradley was still carrying on his nutation observations at Wansted, still
+lecturing at Oxford, and not content with all this, began a course of
+experiments on the length of the seconds' pendulum. Truly a giant for hard
+work!
+
+[Sidenote: New instruments.]
+
+But, in spite of his care in setting them right, the instruments in the
+Observatory were found to be hopelessly defective. The history of the
+instruments at the Royal Observatory is a curious one. When Flamsteed was
+appointed the first Astronomer Royal he was given the magnificent salary
+of £100 a year, and no instruments to observe with. He purchased some
+instruments with his own money, and at his death they were claimed by his
+executors. Hence Halley, the second Astronomer Royal, found the
+Observatory totally unprovided in this respect. He managed to persuade the
+nation to furnish the funds for an equipment; but Halley, though a man of
+great ability in other ways, did not know a good instrument from a bad
+one; so that Bradley's first few years at the Observatory were wasted
+owing to the imperfection of the equipment. When this was fully realised
+he asked for funds to buy new instruments, and such was the confidence
+felt in him that he got what he asked for without much difficulty. More
+than £1000, a large sum for those days, was spent under his direction,
+the principal purchases being two quadrants for observation of the
+position of the stars, one to the north and the other to the south. With
+these quadrants, which represented the perfection of such apparatus at
+that time, Bradley made that long and wonderful series of observations
+which is the starting-point of our knowledge of the movements of the
+stars. The instruments are still in the Royal Observatory, the more
+important of the two in its original position as Bradley mounted it and
+left it.
+
+[Sidenote: Work at Greenwich.]
+
+It seems needless to mention his work as Astronomer Royal, but I will give
+quite briefly a summary of what he accomplished, and then recall a
+particular incident, which shows how far ahead of his generation his
+genius for observation placed him. The summary may be given as follows.
+We owe to Bradley--
+
+1. A better knowledge of the movements of Jupiter's satellites.
+
+2. The orbits of several comets calculated directly from his own
+observations, when such work was new and difficult.
+
+3. Experiments on the length of the pendulum.
+
+4. The foundation of our knowledge of the refraction of our atmosphere.
+
+5. Considerable improvements in the tables of the moon, and the promotion
+of the method for finding the longitude by lunar distances.
+
+6. The proper equipment of our national Observatory with instruments, and
+the use of these to form the basis of our present knowledge of the
+positions and motions of the stars.
+
+Many men would consider any one of these six achievements by itself a
+sufficient title to fame. Bradley accomplished them all in addition to his
+great discoveries of aberration and nutation.
+
+[Sidenote: Might have found variation of latitude.]
+
+And with a little more opportunity he might have added another great
+discovery which has shed lustre on the work of the last decade. We said
+earlier in this chapter that the axis of the earth may move in one or two
+ways. Either it may point to a different star, remaining fixed relatively
+to the earth, as in the nutation which Bradley discovered; or it may
+actually change its position in the earth. This second kind of movement
+was believed until twenty years ago not to exist appreciably; but the
+work of Küstner and Chandler led to the discovery that it did exist, and
+its complexities have been unravelled, and will be considered in the sixth
+chapter. Now a century and a half ago Bradley was on the track of this
+"variation of latitude." His careful observations actually showed the
+motion of the pole, as Mr. Chandler has recently demonstrated; and,
+moreover, Bradley himself noticed that there was something unexplained.
+Once again there was a _residuum_ after (first) aberration and (next)
+nutation had been extracted from the observations; and with longer life he
+might have explained this residuum, and added a third great discovery to
+the previous two. Or another coming after him might have found it; but
+after the giant came men who could not tread in his footsteps, and the
+world waited 150 years before the discrepancy was explained.
+
+[Sidenote: Oxford's tardy recognition of Bradley.]
+
+The attitude of our leading universities towards science and scientific
+men is of sufficient importance to justify another glance at the relations
+between Bradley and Oxford. We have seen that Oxford's treatment of
+Bradley was not altogether satisfactory. She left him to learn astronomy
+as he best could, and he owes no teaching to her. She made him Professor
+of Astronomy, but gave him no observatory and a beggarly income which he
+had to supplement by giving lectures on a different subject. But when he
+had disregarded these discouragements and made a name for himself, Oxford
+took her share in recognition. He was created D.D. by diploma in 1742; and
+when his discovery of nutation was announced in 1748, and produced
+distinctions and honours of all kinds from over the world, we are told
+that "amidst all these distinctions, wide as the range of modern science,
+and permanent as its history, there was one which probably came nearer his
+heart, and was still more gratifying to his feeling than all. Lowth
+(afterwards Bishop of London), a popular man, an elegant scholar, and
+possessed of considerable eloquence, had in 1751 to make his last speech
+in the Sheldonian Theatre at Oxford as Professor of Poetry. In recording
+the benefits for which the University was indebted to its benefactors, he
+mentioned the names of those whom Sir Henry Savile's foundation had
+established there: 'What men of learning! what mathematicians! we owe to
+Savile, Briggs, Wallis, Halley; to Savile we owe Greaves, Ward, Wren,
+Gregory, Keill, and one whom I will not name, for posterity will ever have
+his name on its lips.' Bradley was himself present; there was no one in
+the crowded assembly on whom the allusion was lost, or who did not feel
+the truth and justice of it; all eyes were turned to him, while the walls
+rung with shouts of heartfelt affection and admiration; it was like the
+triumph of Themistocles at the Olympic games."
+
+[Sidenote: The study of "residual phenomena."]
+
+These words of Rigaud indicate the fame deservedly acquired by an earnest
+and simple-minded devotion to science: but can we learn anything from the
+study of Bradley's work to guide us in further research? The chief lessons
+would seem to be that if we make a series of careful observations, we
+shall probably find some deviation from expectation: that we must follow
+up this clue until we have found some explanation which fits the facts,
+not being discouraged if we cannot hit upon the explanation at once, since
+Bradley himself was puzzled for several years: that after finding one
+_vera causa_, and allowing for the effect of it, the observations may show
+traces of another which must again be patiently hunted, even though we
+spend nineteen years in the chase: and that again we may have to leave the
+complete rectification of the observations to posterity. But though we may
+admit the general helpfulness of these directions, and that this patient
+dealing with residual phenomena seems to be a method capable of frequent
+application, we cannot deduce any universal principle of procedure from
+them: witness the difficulty of dealing with meteorological observations,
+for instance. It is not always possible to find any orderly arrangement of
+the residuals which will give us a clue to start with. When such an
+arrangement is manifested, we must certainly follow up the clue; it would
+almost seem that no expense should be prohibitive, since it is impossible
+to foresee the importance of the result.
+
+
+
+
+CHAPTER IV
+
+ACCIDENTAL DISCOVERIES
+
+
+[Sidenote: The Oxford new star found during work on Astrographic Chart.]
+
+In reviewing various types of astronomical discovery I have laid some
+stress upon the fact that they are, generally speaking, far from being
+accidental in character. A new planet does not "swim into our ken," at any
+rate not usually, but is found only after diligent search, and then only
+by an investigator of acute vision, or other special qualifications. But
+this is, of course, not always the case. Some discoveries are made by the
+merest accident, as we have had occasion to remark incidentally in the
+case of the minor planets; and for the sake of completeness it is
+desirable to include among our types at least one case of such accidental
+discovery. As, however, the selection is a little invidious, I may perhaps
+be pardoned for taking the instance from my own experience, which happens
+to include a case where one of those remarkable objects called "new stars"
+walked deliberately into a net spread for totally different objects. There
+is the further reason for choosing this instance: that it will afford me
+the opportunity of saying something about the special research in which we
+were actually engaged, the work of mapping out the heavens by
+photography, or, as it has been called, the Astrographic Chart--a great
+scheme of international co-operation by which it is hoped to leave as a
+legacy for future centuries a record of the state of the sky in our age.
+Such a record cannot be complete; for however faint the stars included, we
+know that there are fainter stars which might have been included had we
+given longer exposures to the plates. Nor can it be in other ways final or
+perfect; however large the scale, for instance, on which the map is made,
+we can imagine the scale doubled or increased many-fold. But the map will
+be a great advance on anything that has hitherto been made, and some
+account of it will therefore no doubt be of interest.
+
+[Sidenote: Origin of the chart.]
+
+We may perhaps begin with a brief historical account of the enterprise.
+Photographs of the stars were taken many years ago, but only by a few
+enthusiasts, and with no serious hope of competing with eye observations
+of the sky. The old wet-plate photography was, in fact, somewhat unsuited
+to astronomical purposes; to photograph faint objects a long exposure is
+necessary, and the wet plate may dry up before the exposure is
+concluded--nay, even before it is commenced, if the observer has to wait
+for passing clouds--and therefore it may be said that the successful
+application of photography to astronomy dates from the time when the dry
+plate was invented; when it became possible to expose a plate in the
+telescope for hours, or by accumulation even for days. The dry plate
+remains sensitive for a long period, and if it is desired to extend an
+exposure beyond the limits of one night, it is quite easy to close up
+the telescope and return to the operations again on the next fine night;
+and so on, if not perhaps indefinitely, at any rate so long as to
+transcend the limits of human patience up to the present.
+
+[Illustration:
+
+  VII.--GREAT COMET OF NOV. 7TH, 1882
+  (_From a photograph taken at the Royal Observatory, Cape of Good Hope._)]
+
+[Sidenote: Comet of 1882.]
+
+[Sidenote: Stars shown on the pictures.]
+
+But to consider our particular project. We may assign, perhaps, the date
+1882 as that in which it first began to take shape. In that year there was
+a magnificent bright comet, the last really large comet which we, in the
+Northern Hemisphere, have had the good fortune to see. Some of us, of
+course, were not born at that time, and perhaps others who were alive may
+nevertheless not have seen that comet; for it kept somewhat uncomfortably
+early morning hours, and I can well remember myself feeling rather more
+resentment than gratitude to the man who waked me up about four o'clock to
+see it. Many observations were of course made of this interesting visitor,
+and what specially concerns us is that at the Cape of Good Hope some
+enterprising photographers tried to photograph it. They tried in the first
+instance with ordinary cameras, and soon found--what any astronomer could
+have told them--that the movement of the earth, causing an apparent
+movement of the comet and the stars in the opposite direction, frustrated
+their efforts. The difficulties of obtaining pictures of moving objects
+are familiar to all photographers. A "snap-shot" might have met the
+difficulty, but the comet was scarcely bright enough to affect the plate
+with a short exposure. Ultimately Dr. David Gill, the astronomer at the
+Cape Observatory, invited one of the photographers to strap his camera to
+one of the telescopes at the Observatory, a telescope which could be
+carried round by clockwork in the usual way, so as to counteract the
+earth's motion, and in effect to keep the comet steadily in view, as
+though it were at rest. As a consequence, some very beautiful and
+successful pictures of the comet were obtained, and on them a large number
+of stars were also shown. They were, as I have said, not by any means the
+first pictures of stars obtained by photography, but they represented in
+facility and in success so great an advance upon what had been formerly
+obtained that they attracted considerable attention. They were sent to
+Europe and stimulated various workers to further experiments.
+
+[Sidenote: The brothers Henry begin work.]
+
+[Sidenote: Conference of 1887.]
+
+The late Dr. Common in England, an amateur astronomer, began that
+magnificent pioneer work in astronomical photography which soon brought
+him the Gold Medal of the Royal Astronomical Society for his photographs
+of nebulæ. But the most important result for our purpose was produced in
+France. There had been started many years before by the French astronomer
+Chacornac a series of star maps round the Zodiac similar in intention to
+the Berlin maps which figured in the history of the discovery of Neptune.
+Chacornac died before his enterprise was very far advanced, and the work
+was taken up by two brothers, Paul and Prosper Henry, who followed
+Chacornac in adopting for the work the laborious method of eye
+observation of each individual star. They proceeded patiently with the
+work on these lines; but when they came to the region where the Zodiac is
+crossed by the Milky Way, and the number of stars in a given area
+increases enormously, they found the labour so great as to be practically
+prohibitive, and were in doubt how to deal with the difficulty. It was at
+this critical moment that these comet photographs, showing the stars so
+beautifully, suggested the alternative of mapping the stars
+photographically. They immediately set to work with a trial lens, and
+obtained such encouraging results that they proceeded themselves to make a
+larger lens of the same type; this again was satisfactory, and the idea
+naturally arose of extending to the whole heavens the scheme which they
+had hitherto intended only for the Zodiac, a mere belt of the heavens. But
+this rendered the enterprise too large for a single observatory. It became
+necessary to obtain the co-operation of other observatories, and with this
+end in view an International Conference was summoned to meet in Paris in
+1887 to consider the whole project. There were delegates from, if not all
+nations, at any rate a considerable number:--
+
+  France            20
+  British Empire     8
+  Germany            6
+  Russia             3
+  Holland            3
+  U.S. America       3
+  Austria            2
+  Sweden             2
+  Denmark            2
+  Belgium            1
+  Italy              1
+  Spain              1
+  Switzerland        1
+  Portugal           1
+  Brazil             1
+  Argentine Republic 1
+
+[Sidenote: Choice of instrument.]
+
+[Sidenote: Expense of "doublet."]
+
+[Sidenote: Advantages of reflector.]
+
+[Sidenote: Refractor chosen.]
+
+The Conference had a number of very important questions to discuss, for
+knowledge of the photographic method and its possibilities was at that
+time in its infancy. There was, for instance, the question whether all the
+instruments need be of the same pattern, and if so what that pattern
+should be. The first of these questions was settled in the affirmative, as
+we might expect; in the interests of uniformity it was desirable that the
+maps should be as nearly similar as possible. The second question was not
+so easy; there were at least three different types of instruments which
+might be used. First of all, there was the photographic lens, such as is
+familiar to all who have used an ordinary camera, consisting of two lenses
+with a space between; though since each of these lenses is itself made up
+of two, we should more correctly say four lenses in all. It was with a
+lens of this kind that the comet pictures had been taken at the Cape of
+Good Hope, and it might seem the safest plan to adopt what had been shown
+to be capable of such good work. But there was this difficulty; the
+pictures of the comet were on a very small scale, and taken with a small
+lens; a much larger lens was required for the scheme now under
+contemplation, and when there are four separate lenses to be made, each
+with two surfaces to polish, and each requiring a perfectly sound clear
+piece of glass, it will be obvious that the difficulties of making a large
+compound lens of this kind are much greater, and the expense much more
+serious than in the case of a single lens, or even a pair. It was this
+question of expense which had led the brothers Henry to experiment with a
+different kind of instrument, in which only one pair of lenses was used
+instead of two. Their instrument was, in fact, very similar to the
+ordinary telescope, excepting that they were bound to make their lenses
+somewhat different in shape in order to bring to focus the rays of light
+suitable for photography, which are not the same as those suitable for eye
+observation with the ordinary telescope. Dr. Common, again, had used a
+third kind of instrument, mainly with the view of reducing the necessary
+expense still further, or, perhaps, of increasing the size of the
+instrument for the same expense. His telescope had no lens at all, but a
+curved mirror instead, the mirror being made of glass silvered on the face
+(not on the back as in the ordinary looking-glass). In this case there is
+only one surface to polish instead of four, as in the Henrys' telescope,
+or eight, as in the case of the photographic doublet; and, moreover, since
+the rays of light are reflected from the surface of the glass, and do not
+pass _through_ it at all, the internal structure of the glass is not so
+strictly important as in the other cases. Hence the reflector is a very
+cheap instrument, and it is, moreover, quite free from some difficulties
+attached to the other instruments. No correction for rays of light of
+different colours is required, since all rays of whatever colour come to
+the same focus automatically. These advantages of the reflector were so
+considerable as to almost outweigh one well-known disadvantage, which is,
+however, not very easily expressed in words. The reflector might be
+described as an instrument with a temper; sometimes it gives excellent
+results, but at others _something_ seems to be wrong, though the worried
+observer does not exactly know what. Long experience and patience are
+requisite to humour the instrument and get the best results from it, and
+it was felt that this uncertainty was sufficient to disqualify the
+instrument for the serious piece of routine work contemplated in mapping
+the heavens. Accordingly the handier and more amiable instrument with
+which the brothers Henry had done such good work was selected as the
+pattern to be adopted.
+
+[Sidenote: Doublet would have been better.]
+
+It is curious that at the Conference of 1887 nothing at all was said about
+the type of instrument first mentioned (the "doublet lens"), although a
+letter was written in its favour by Professor Pickering of Harvard College
+Observatory. Since that time we have learnt much of its advantages, and it
+is probable that if the Conference were to meet now they might arrive at a
+different decision; but at that time they were, to put it briefly,
+somewhat afraid of an instrument which seemed to promise, if anything, too
+well, especially in one respect. With the reflector and the refractor it
+had been found that the field of good images was strictly limited. The
+Henrys' telescope would not photograph an area of the sky greater in
+extent than 2° in diameter at any one time, and the reflector was more
+limited still; within this area the images of the stars were good, and it
+had been found that their places were accurately represented. Now the
+"doublet" seemed to be able to show much larger areas than this with
+accuracy, but no one had been able to test the accuracy to see whether it
+was sufficient for astronomical purposes; and although no such feeling was
+openly expressed or is on record, I think there is no doubt that a feeling
+existed of general mistrust of an instrument which seemed to offer such
+specious promises. Whatever the reason, its claims were passed over in
+silence at the Conference, and the safer line (as it was then thought) of
+adopting as the type the Henrys' instrument, was taken.
+
+[Sidenote: The eighteen observatories.]
+
+This was perhaps the most important question settled at the Conference,
+and the answers to many of the others naturally followed. The size of the
+plates, for instance, was settled automatically. The question down to what
+degree of faintness should stars be included, resolved itself into the
+equivalent question, What should be the length of time during which the
+plates were exposed? Then, again, the question, What observatories should
+take part in the work? became simply this: What observatories could
+afford to acquire the instruments of this new pattern and get other funds
+for carrying out the work specified? It was ultimately found that eighteen
+observatories were able to obtain the apparatus and funds, though
+unfortunately three of the eighteen have since found it impossible to
+proceed. The following is the original list, and in brackets are added the
+names of three other observatories which in 1900 undertook to fill the
+places of the defaulters.
+
+  OBSERVATORIES CO-OPERATING FOR THE ASTROGRAPHIC CHART.
+
+  +----------------------+------------+----------+
+  |    Observatory.      |  Zones of  |  Number  |
+  |                      |Declination.|of Plates.|
+  +----------------------+------------+----------+
+  |Greenwich             |+90° to +65°|   1149   |
+  |Rome                  |+64°  " +55°|   1140   |
+  |Catania               |+54°  " +47°|   1008   |
+  |Helsingfors           |+46°  " +40°|   1008   |
+  |Potsdam               |+39°  " +32°|   1232   |
+  |Oxford                |+31°  " +25°|   1180   |
+  |Paris                 |+24°  " +18°|   1260   |
+  |Bordeaux              |+17°  " +11°|   1260   |
+  |Toulouse              |+10°  " + 5°|   1080   |
+  |Algiers               |+ 4°  " - 2°|   1260   |
+  |San Fernando          |- 3°  " - 9°|   1260   |
+  |Tacubaya              |-10°  " -16°|   1260   |
+  |Santiago (Monte Video)|-17°  " -23°|   1260   |
+  |La Plata (Cordoba)    |-24°  " -31°|   1360   |
+  |Rio (Perth, Australia)|-32°  " -40°|   1376   |
+  |Cape of Good Hope     |-41°  " -51°|   1512   |
+  |Sydney                |-52°  " -64°|   1400   |
+  |Melbourne             |-65°  " -90°|   1149   |
+  +----------------------+------------+----------+
+
+[Sidenote: Sky covered twice.]
+
+In the list is also shown the total number of plates that were to be taken
+by each observatory. When once the size of the plates had been settled,
+it was a straightforward matter to divide up the sky into the proper
+number of regions necessary to cover it completely, not only without gaps
+between the plates, but with actually a small overlap of contiguous
+plates. And more than this, it was decided that the whole sky should be
+completely covered _twice over_. It was conceivable that a question might
+arise whether an apparent star image on a plate was, on the one hand, a
+dust speck, or, on the other hand, a planet, or perhaps a variable or new
+star. By taking two different plates at slightly different times,
+questions of this kind could be settled; and to make the check more
+independent it was decided that the plates should not be exactly repeated
+on the same portion of sky, but that in the second series the centre of a
+plate should occupy the point assigned to the corner of a plate in the
+first series.
+
+[Sidenote: Times of exposure.]
+
+Then there came the important question of time of exposure, which involved
+a long debate between those who desired the most modest programme possible
+consistent with efficiency, and those enthusiasts who were anxious to
+strain the programme to the utmost limits attainable. Ultimately it was
+resolved to take two series of plates; one series of long exposure which
+was set in the first instance at 10 minutes, then became 15, then 30, then
+40, and has by some enterprising observers been extended to 1-1/2 hours;
+the other a series of short exposures which have been generally fixed at
+6 minutes. Thus instead of covering the sky twice, it was decided to cover
+it in all four times, and the number of plates assigned to each
+observatory in the above list must be regarded as doubled by this new
+decision. And further still, on the series of short-exposure plates it was
+decided to add to the exposure of six minutes another one of three
+minutes, having slightly shifted the telescope between the two so that
+they should not be superimposed; and later still, a third exposure of
+twenty seconds was added to these. It would take too long to explain here
+the reasons for these details, but it will be clear that the general
+result of the discussion was to extend the original programme
+considerably, and render the work even more laborious than it had appeared
+at the outset.
+
+[Sidenote: Measurement of plates.]
+
+[Sidenote: The réseau.]
+
+[Sidenote: The microscope.]
+
+[Sidenote: Reversal of plates.]
+
+[Sidenote: Personal equation.]
+
+When all these plates have been taken, the work is by no means finished;
+indeed, it is only just commencing. There remains the task of measuring
+accurately on each of the short-exposure plates the positions of the stars
+which it represents, numbering on the average some 300 or 400; so that for
+instance at Oxford the total number of stars measured on the twelve
+hundred plates is nearly half a million. These are not all separate stars;
+for the sky is represented twice over, and there is also the slight
+overlap of contiguous plates; but the number of actual separate stars
+measured at this one observatory is not far short of a quarter of a
+million, and it has taken nearly ten years to make the measurements, with
+the help of three or four measurers trained for the purpose. To render the
+measures easy, a network or réseau of cross lines is photographed on each
+plate by artificial light after it has been exposed to the stars, so that
+on development these cross lines and the stars both appear. We can see at
+a glance the approximate position of a star by counting the number of the
+space from left to right and from top to bottom in which it occurs; and we
+can also estimate the fraction of a space in addition to the whole number;
+but it is necessary for astronomical purposes to estimate this fraction
+with the greatest exactness. The whole numbers are already given with
+great exactness by the careful ruling of the cross lines, which can be
+spaced with extraordinary perfection. To measure the fraction, we place
+the plate under a microscope in the eye-piece of which there is a finally
+divided cross scale; the centre of the cross is placed over a star image,
+and then it is noted where the lines of the réseau cut the cross scale. In
+this way the position of the image of a star is read off with accuracy,
+and after a little practice with considerable rapidity. It has been found
+at Oxford that under favourable conditions the places of nearly 200 stars
+per hour can be recorded in this way by a single measurer, if he has some
+one to write down for him the numbers he calls out. This is only one form
+of measuring apparatus; there are others in which, instead of a scale in
+the eye-piece, micrometer screws are used to measure the fractions; but
+the general principle in all these instruments is much the same, and the
+rate of work is not very different; while to the minor advantages and
+disadvantages of the different types there seems no need here to refer.
+One particular point, however, is worth noting. After a plate has been
+measured, it is turned round completely, so that left is now right, and
+top is now bottom, and the measurements are repeated. This repetition has
+the advantage first of all of checking any mistakes. When a long piece of
+measuring or numerical work of any kind is undertaken there are invariably
+moments when the attention seems to wander, and some small error is the
+result. But there are also certain errors of a systematic character
+similar to those denoted by the term "personal equation," which has found
+its way into other walks of life. In the operation of placing a cross
+exactly over the image of a star, different observers would show slight
+differences of habit; one might place it a little more to the right than
+another. But when the plate is turned round the effect of this habit on
+the measure is exactly reversed, and hence if we take the mean of the two
+measures any personal habit of this kind is eliminated. It has been found
+by experience that such personal habits are much smaller for measures of
+this kind than for those to which we have long been accustomed in
+observations made by eye on the stars themselves. The troubles from
+"personal equation" have been much diminished by the photographic method,
+and certain peculiarities of the former method have been clearly exhibited
+by the comparison. For instance, it has gradually become clear that with
+eye observations personal equation is not a constant quantity, but is
+different for stars of different brightness. When observing the transit of
+a bright star the observer apparently records an instant definitely
+earlier than in recording the transit of a faint one; and this peculiarity
+seems to be common to the large majority of observers, which is perhaps
+the reason why it was not noticed earlier. But when positions of the stars
+determined in this way are compared with their positions measured on the
+photographic plates, the peculiarity is made clearly manifest. For
+example, at Oxford, our first business after making measurements is to
+compare them with visual observations on a limited number of the brighter
+stars made at Cambridge about twenty years ago. (About 14,000 stars were
+observed at Cambridge, and we are dealing with ten times that number.) The
+comparison shows that the Cambridge observations are affected with the
+following systematic errors:--
+
+    If stars of magnitude 10 are observed correctly,
+  then   "        "        9        "     0.10 secs. too early
+         "        "        8        "     0.16        "
+         "        "        7        "     0.19        "
+         "        "        6        "     0.21        "
+         "        "        5        "     0.23        "
+
+[Sidenote: Main object of the work.]
+
+This may serve as an illustration of various incidental results which are
+already flowing from the enormous and laborious piece of work which, as
+far as the University Observatory at Oxford is concerned, we have just
+completed, though some of the other colleagues are not so far advanced.
+But the main results will not appear just yet. The work must be repeated,
+and the positions of the stars just obtained must be compared with those
+which they will be found to occupy at some future date, in order to see
+what kind of changes are going on in the heavens. Whether this future date
+shall be one hundred years hence, or fifty, or ten, or whether we should
+begin immediately to repeat what has been done, is a matter not yet
+decided, and one which requires some little consideration.
+
+[Sidenote: The concluding year.]
+
+I have said perhaps enough to give you a general idea of the work on which
+we have been engaged at Oxford for the last ten years. Ten years ago it
+seemed to stretch out in front of us rather hopelessly; the pace we were
+able to make seemed so slow in view of the distance to be covered. We felt
+rather like the schoolboy who has just returned to school and sees the
+next holidays as a very remote prospect, and we solaced ourselves much in
+the same way as he does, by making a diagram representing the total number
+of plates to be dealt with and crossing off each one as it was finished,
+just as he sometimes crosses off the days still remaining between him and
+the prospective holidays. It was pleasant to watch the growth of the
+number of crosses on this diagram, and by the end of the year 1902 we had
+the satisfaction of seeing very little blank space remaining. Now, up to
+this point it had not much mattered whether any particular plate was
+secured in any particular year, or in a subsequent year, so long as there
+were always sufficient plates to keep us occupied in measuring them. But
+it then became a matter of importance to secure each plate at the proper
+time of year; for the sun, as we know, travels round the Zodiac among the
+stars, obliterating by his radiance a large section of the sky for a
+period of some months, and in this way a particular region of the heavens
+is apt to "run into daylight," as the observatory phrase goes, and ceases
+to be available for photography during several months, until the sun is
+again far enough away to allow of the particular region being seen at
+night.
+
+[Sidenote: A disappointment.]
+
+[Sidenote: A curious plate.]
+
+[Sidenote: A strange object.]
+
+[Sidenote: A new star?]
+
+Roughly speaking then, if a plate which should be taken in February is not
+secured in this month owing to bad weather, the proper time for taking it
+will not occur again until the following February; and when there was a
+fair prospect of finishing our work in 1903, it became important to secure
+each plate at the proper time in that year. Hence we were making special
+efforts to utilise to the full any fine night that Providence sent in our
+way, and on such occasions it is clearly an economy, if not exactly to
+"make hay while the sun shines," at any rate to take plates vigorously
+while the sun is _not_ shining and the night is fine; leaving the
+development of them until the daytime. There is, of course, the risk that
+the whole night's work may in this way be lost owing to some fault in the
+plates, which might have been detected if some of them were immediately
+developed. Perhaps in the early days of our work it would have been
+reckless or foolish to neglect this little precaution; but we had for
+years been accustomed to rely upon the excellence of the plates without
+finding our trust betrayed; and the sensitiveness of the plates had
+increased rather than diminished as time went on. Hence it will be readily
+understood that when one fatal morning we developed a series of some
+thirty plates, and found that owing to some unexplained lack of
+sensitiveness they were all unsuitable for our purpose, it came as a most
+unwelcome and startling surprise. It was, of course, necessary to make
+certain that there was no oversight, that the developer was not at fault,
+and that the weather had not been treacherous. All such possibilities were
+carefully considered before communication with the makers of the plates,
+but it ultimately became clear that there had been some unfortunate
+failure in sensitiveness, and that it would be necessary to repeat the
+work with opportunities restricted by the intervening lapse of time.
+However, disappointments from this or similar causes are not unknown in
+astronomical work; and we set about this repetition with as little loss of
+time and cheerfulness as was possible. Under the circumstances, however,
+it seemed desirable to examine carefully whether anything could be saved
+from the wreck--whether any of the plates could be admitted as _just_
+coming up to the minimum requirements. And I devoted a morning to this
+inquiry. In the course of it I came across one plate which certainly
+seemed worth an inclusion among our series from the point of view of the
+number of stars shown upon it. It seemed quite rich in stars, perhaps even
+a little richer than might have been expected. On inquiry I was told that
+this was not one of the originally condemned plates, but one which had
+been taken since the failure in sensitiveness of the plates had been
+detected; was from a new and specially sensitive batch with which the
+courteous makers had supplied us; but though there were certainly a
+sufficient number of stars upon the plate, owing to some unexplained cause
+the telescope had been erroneously pointed, and the region taken did not
+correspond to the region required. To investigate the cause of the
+discrepancy I thereupon took down from our store of plates the other one
+of the same region which had been rejected for insufficiency of stars, and
+on comparing the two it was at once evident that there was a strange
+object on the plate taken later of the two, a bright star or other
+heavenly body, which was not on the former plate. I have explained that by
+repeating the exposure more than once, it is easily possible to recognise
+whether a mark upon the plate is really a celestial body or is an
+accidental blot or dust speck, and there was no doubt that this was the
+image of some strange celestial body. It might, of course, be a new
+planet, or even an old one which had wandered into the region; but a few
+measures soon showed that it was not in movement. The measures consisted
+in comparing the separation of the three exposures with the separation of
+the corresponding exposures of obvious stars, for the exposures were not,
+of course, simultaneous, and if the body were a planet and had moved in
+the interval between them, this would be made manifest on measuring the
+separations. No such movements could be detected; and the possibilities
+were thus restricted to two. So far as we knew the object was a star, but
+might be either a star of the class known as _variable_ or of that known
+as _new_. In the former case it would become bright and faint at more or
+less regular intervals, and might possibly have been already catalogued;
+for the number of these bodies already known amounts to some hundreds.
+Search being made in the catalogues, no entry of it was found, though it
+still might be one of this class which had hitherto escaped detection. Or
+it might be a "new star," one of those curious bodies which blaze up quite
+suddenly to brightness and then die away gradually until they become
+practically invisible. The most famous perhaps of these is the star which
+appeared in 1572, and was so carefully observed by Tycho Brahé; but such
+apparitions are rare, and altogether we have not records as yet of a score
+altogether; so that in this latter case the discovery would be of much
+greater interest than in the former. In either event it was desirable to
+inform other observers as soon as possible of the existence of a strange
+body; already some time had elapsed since the plate had been taken, March
+16th, for the examination of which I have spoken was not made until March
+24th. Accordingly, a telegram was at once despatched to the Central Office
+at Kiel, which undertakes to distribute such information all over the
+world, and a few post-cards were sent to observers close at hand who might
+be able to observe the star the same night. Certain observations with the
+spectroscope soon made it clear that the object was really a "new star."
+
+[Sidenote: The discovery accidental.]
+
+[Sidenote: Mrs. Fleming's discoveries.]
+
+This, therefore, is the discovery which we made at Oxford: as you will
+see, in an entirely accidental manner, during the course of a piece of
+work in which it was certainly never contemplated. Its purely accidental
+nature is sufficiently illustrated by the fact that if the plates
+originally supplied by the makers had been of the proper quality, the
+plate which led to the discovery would never have been taken. If the
+plates exposed in February had been satisfactory, we should have been
+content, and should not have repeated the exposure on March 16th. Again I
+can testify personally how purely accidental it was that the examination
+was made on March 24th to see whether anything could be saved, as I have
+said, from the wreck. The idea came casually into my mind as I was walking
+through the room and saw the neat pile of rejected plates; and one may
+fairly call it an accidental impulse. This new star is not, however, the
+first of such objects to have been discovered "accidentally"; many of the
+others were found just as much by chance, though a notable exception must
+be made of those discovered at the Harvard Observatory, which are the
+result of a deliberate search for such bodies by the careful examination
+of photographic plates. Mrs. Fleming, who spends her life in such work,
+has had the good fortune to detect no less than six of these wonderful
+objects as the reward of her laborious scrutiny; and she is the _only_
+person who has thus found new stars by photography until this accidental
+discovery at Oxford. The following is a complete list of new stars
+discovered to date:--
+
+  LIST OF NEW STARS.
+
+  +----------------------------------------------+
+  |Ref. No.| Constellation. | Year.| Discoverer. |
+  +----------------------------------------------+
+  |   1    | Cassiopeia     | 1572 | Tycho Brahé.|
+  |   2    | Cygnus         | 1600 | Janson.     |
+  |   3    | Ophiuchus      | 1604 | Kepler.     |
+  |   4    | Vulpecula      | 1670 | Anthelm.    |
+  |   5    | Ophiuchus      | 1848 | Hind.       |
+  |   6    | Scorpio        | 1860 | Auwers.     |
+  |   7    | Corona Borealis| 1866 | Birmingham. |
+  |   8    | Cygnus         | 1876 | Schmidt.    |
+  |   9    | Andromeda      | 1885 | Hartwig.    |
+  |  10    | Perseus        | 1887 | Fleming.    |
+  |  11    | Auriga         | 1891 | Anderson.   |
+  |  12    | Norma          | 1893 | Fleming.    |
+  |  13    | Carina         | 1895 | Fleming.    |
+  |  14    | Centaurus      | 1895 | Fleming.    |
+  |  15    | Sagittarius    | 1898 | Fleming.    |
+  |  16    | Aquila         | 1899 | Fleming.    |
+  |  17    | Perseus        | 1901 | Anderson.   |
+  |  18    | Gemini         | 1903 | At Oxford.  |
+  +----------------------------------------------+
+
+[Illustration:
+
+  MARCH 1, 1903      MARCH 14, 1903
+  VIII.--THE OXFORD NEW STAR.
+
+  A PAIR OF PHOTOGRAPHS TAKEN AT THE HARVARD COLLEGE OBSERVATORY BEFORE
+  AND AFTER ITS APPEARANCE
+
+  (_The arrow indicates the place of the new star. It will be seen that
+  the left-hand picture though it shews fainter stars than the other, has
+  not a trace of the new star._)]
+
+[Sidenote: Dr. Anderson.]
+
+[Sidenote: Nova Persei.]
+
+Generally these stars have been noted by eye observation, as in the case
+of the two found by Dr. Anderson of Edinburgh. In these cases also we may
+say that deliberate search was rewarded; for Dr. Anderson is probably the
+most assiduous "watcher of the skies" living, though he seldom uses a
+telescope; sometimes he uses an opera-glass, but usually the naked eye. He
+describes himself as an "Astrophil" rather than as an astronomer. "I love
+the stars," he says; "and whenever they are shining, I must be looking."
+And so on every fine night he stands or sits at his open study window
+gazing at the heavens. I believe he was just about to leave them for his
+bed, near 3 A.M. on the night of February 21, 1901, when, throwing a last
+glance upward, he suddenly saw a brilliant star in the constellation
+Perseus. His first feeling was actually one of disappointment, for he felt
+sure that this object must have been there for some time past without his
+knowing of it, and he grudged the time lost when he might have been
+regarding it. More in a spirit of complaint than of inquiry, he made his
+way to the Royal Observatory at Edinburgh next day to hear what they had
+to say about it, though he found it difficult to approach the subject. He
+first talked about the weather, and the crops, and similar topics of
+general interest; and only after some time dared he venture a casual
+reference to the "new portent in the heavens." Seeing his interlocutor
+look somewhat blank, he ventured a little farther, and made a direct
+reference to the new star in Perseus; and then found to his astonishment,
+as also to his great delight, that he was the first to bring news of it.
+The news was soon communicated to other observers; all the telescopes of
+the world were soon trained upon it; and this wonderful "new star of the
+new century" has taught us more of the nature of these extraordinary
+bodies than all we knew before.
+
+[Sidenote: Records previous to discovery.]
+
+[Sidenote: Was Nova Geminorum previously shining faintly?]
+
+[Sidenote: The suspicion negatived.]
+
+Perhaps I may add a few remarks on one or two features of these bodies.
+Firstly, let us note that Professor Pickering of Harvard is now able to
+make a most important contribution to the _former_ history of these
+objects--that is to say, their history preceding their actual detection.
+We remember that, after Uranus had been discovered, it was found that
+several observers had long before recorded its place unknowingly; and
+similarly Professor Pickering and his staff have usually photographed
+other new objects unknowingly. There are on the shelves at Harvard vast
+stores of photographs, so many that they are unable to examine them when
+they have been taken; but once any object of interest has been discovered,
+it is easy to turn over the store and examine the particular plates which
+may possibly show it at an earlier date. In this way it was found that Dr.
+Anderson's new star had been visible only for a few days before its
+discovery, there being no trace of it on earlier plates. Similarly, in
+the case of the new star found at Oxford, plates taken on March 1st and
+6th, fifteen days and ten days respectively before the discovery-plate of
+March 16th, showed the star. But, in this particular instance, greater
+interest attaches to two still earlier plates taken elsewhere, and with
+exposures much longer than any available at Harvard. One had been obtained
+at Heidelberg by Dr. Max Wolf, and another at the Yerkes Observatory of
+Chicago University, by Mr. Parkhurst; and on both there appeared to be a
+faint star of about the fourteenth or fifteenth magnitude, in the place
+subsequently occupied by the Nova; and the question naturally arose, Was
+this the object which ultimately blazed up and became the new star? To
+settle this point, it was necessary to measure its position, with
+reference to neighbouring stars, with extreme precision; and here it was
+unfortunate that the photographs did not help us as much as they might,
+for they were scarcely capable of being measured with the requisite
+precision. The point was an important one, because if the identity of the
+Nova with this faint star could be established, it would be the second
+instance of the kind; but so far as they went, measurements of the
+photographs were distinctly against the identity. Such was the conclusion
+of Mr. Parkhurst from his photograph alone; and it was confirmed by
+measures made at Oxford on copies of both plates, which were kindly sent
+there for the purpose. The conclusion seemed to be that there was a faint
+star _very near_, but _not at_, the place of the new star; and it was
+therefore probable that, although this faint star was temporarily
+invisible from the brightness of the adjacent Nova, as the latter became
+fainter (in the way with which we have become familiar in the case of new
+stars), it might be possible to see the two stars alongside each other.
+This critical observation was ultimately made by the sharp eyes of
+Professor Barnard, aided by the giant telescope of the Yerkes Observatory;
+and it seems clear therefore that the object which blazed up to become the
+Nova of 1903 could not have previously been so bright as a faint star of
+the fourteenth magnitude. Although this is merely a negative conclusion,
+it is an important one in the history of these bodies.
+
+[Sidenote: Nebula round Nova Persei.]
+
+[Sidenote: Its changes.]
+
+[Sidenote: Due to travelling illumination.]
+
+The second point to which I will draw your attention is from the history
+of the other Nova just mentioned--Dr. Anderson's New Star of 1901. In this
+instance it is not the history previous to discovery, but what followed
+many months after discovery, that was of engrossing interest; and again
+Yerkes Observatory, with its magnificent equipment, played an important
+part in the drama. When, with its giant reflecting telescope, photographs
+were taken of the region of Nova Persei after it had become comparatively
+faint, it was found that there was an extraordinarily faint nebulosity
+surrounding the star. Repeating the photographs at intervals, it was
+found that this nebulosity was rapidly changing in shape. "Rapidly" is, of
+course, a relative term, and a casual inspection of two of the photographs
+might not convey any impression of rapidity; it is only when we come to
+consider the enormous distance at which the movements, or apparent
+movements, of the nebulæ must be taking place that it becomes clear how
+rapid the changes must be. It was not possible to determine this distance
+with any exactness, but limits to it could be set, and it seemed probable
+that the velocity of the movement was comparable with that of light. The
+conclusion suggested itself that the velocity might actually be identical
+with that of light, in which case what we saw was not the movement of
+actual matter, but merely that of illumination, travelling from point to
+point of matter already existing.
+
+[Illustration:
+
+  SEPT. 20, 1901   NOV. 13, 1901
+  IX--NEBULOSITY ROUND NOVA PERSEI
+  (_From photographs taken at the Yerkes Observatory by G. W. Ritchey._)]
+
+
+[Sidenote: When did it all happen?]
+
+An analogy from the familiar case of sound may make clearer what is meant.
+If a loud noise is made in a large hall, we hear echoes from the walls.
+The sound travels with a velocity of about 1100 feet per second, reaches
+the walls, is reflected back from them, and returns to us with the same
+velocity. From the interval occupied in going and returning we could
+calculate the distance of the walls. The velocity of light is so enormous
+compared with that of sound that we are usually quite unable to observe
+any similar phenomenon in the case of light. If we strike a match in the
+largest hall, all parts of it are illuminated so immediately that we
+cannot possibly realise that there was really an interval between the
+striking of the match, the travelling of the light to the walls, and its
+return to our eyes. The scale of our terrestrial phenomenon is far too
+small to render this interval perceptible. But those who accept the theory
+above mentioned regarding the appearances round Nova Persei (although
+there are some who discredit it) believe that we have in this case an
+illustration of just this phenomenon of light echoes, on a scale large
+enough to be easily visible. They think that, surrounding the central star
+which blazed up so brightly in February 1901, there was a vast dark
+nebula, of which we had no previous knowledge, because it was not shining
+with any light of its own. When the star blazed up, the illumination
+travelled from point to point of this dark nebula and lighted it up; but
+the size of the nebula was so vast that, although the light was travelling
+with the enormous velocity of 200,000 miles per second, it was not until
+months afterwards that it reached different portions of this nebula; and
+we accordingly got news of the existence of this nebula some months after
+the news reached us of the central conflagration, whatever it was. Remark
+that all we can say is that the news of the nebula reached us _some months
+later_ than that of the outburst. The actual date when either of the
+actual things happened, we have as yet no means of knowing; it may have
+been hundreds or even thousands of years ago that the conflagration
+actually occurred of which we got news in February 1901, the light having
+taken all that time to reach us from that distant part of space; and the
+light reflected from the nebula was following it on its way to us all
+these years at that same interval of a few months.
+
+[Sidenote: An objection.]
+
+Now, let me refer before leaving this point to the chief objection which
+has been urged against this theory. It has been maintained that the
+illumination would necessarily appear to travel outwards from the centre
+with an approach to uniformity, whereas the observed rate of travel is not
+uniform, and has been even towards the centre instead of away from it;
+which would seem as though portions of the nebula more distant from the
+centre were lighted up sooner than those closer to it. By a simple
+illustration from our solar system, we shall see that these curious
+anomalies may easily be explained. Let us consider for simplicity two
+planets only, say the Earth and Saturn. We know that Saturn travels round
+the sun in an orbit which is ten times larger than the orbit of the earth.
+Suppose now that the sun were suddenly to be extinguished; light takes
+about eight minutes to travel from the sun to the earth, and consequently
+we should not get news of the extinction for some eight minutes; the sun
+would appear to us to still go on shining for eight minutes after he had
+really been extinguished. Saturn being about ten times as far away from
+the sun, the news would take eighty minutes to reach Saturn; and from the
+earth we should see Saturn shining more[3] than eighty minutes after the
+sun had been extinguished, although we ourselves should have lost the
+sun's light after eight minutes. I think we already begin to see
+possibilities of curious anomalies; but they can be made clearer than
+this. Instead of imagining an observer on the earth, let us suppose him
+removed to a great distance away in the plane of the two orbits; and let
+us suppose that the sun is now lighted up again as suddenly as the new
+star blazed up in February 1901. Then such an observer would first see
+this blaze in the centre; eight minutes afterwards the illumination would
+reach the earth, a little speck of light near the sun would be
+illuminated, just as we saw a portion of the dark nebula round Nova Persei
+illuminated; eighty minutes later another speck, namely, Saturn, would
+begin to shine. But now, would Saturn necessarily appear to the distant
+observer to be farther away from the sun than the earth was? Looking at
+the diagram, we can see that if Saturn were at S{1} then it would present
+this natural appearance of being farther away from the sun than the earth;
+but it might be at S{2} or S{3}, in which case it would seem to be nearer
+the sun, and the illumination would seem to travel inwards towards the
+central body instead of outwards. Without considering other cases in
+detail, it will be tolerably clear that almost any anomalous appearance
+might be explained by choosing a suitable arrangement of the nebulous
+matter which we suppose lighted up by the explosion of Nova Persei.
+Another objection urged against the theory I have sketched is that the
+light reflected from such a nebula would be so feeble that it would not
+affect our photographic plates. This depends upon various assumptions
+which we have no time to notice here; but I think we may say that there is
+certainly room for the acceptance of the theory.
+
+[Illustration: FIG. 6.]
+
+[Sidenote: Did the nebula cause the outburst?]
+
+Now, if this dark nebula was previously existing in this way all round the
+star which blazed up, the question naturally arises whether the nebula had
+anything to do with the conflagration. Was there previously a star, either
+so cold or so distant as not to be shining with appreciable light, which,
+travelling through space, encountered this vast nebula, and by the
+friction of the encounter was suddenly rendered so luminous as to outshine
+a star of the first magnitude? The case of meteoric stones striking our
+own atmosphere seems to suggest such a possibility. These little stones
+are previously quite cold and invisible, and are travelling in some way
+through space, many of them probably circling round our sun. If they
+happen in their journey to encounter our earth, even the extremely tenuous
+atmosphere, so thin that it will scarcely bend the rays of light
+appreciably, even this is sufficient by its friction to raise the stones
+to a white heat, so that they blaze up into the falling stars with which
+we are familiar. This analogy is suggested, but we must be cautious in
+accepting it; for we know so very little of the nature of nebulæ such as
+that of which we have been speaking. But in any case, a totally new series
+of phenomena have been laid open to our study by those wonderful
+photographs taken at the Yerkes Observatory and the Lick Observatory in
+the few years which the present century has as yet run.
+
+[Sidenote: Importance of new stars]
+
+One thing is quite certain: we must lose no opportunity of studying such
+stars as may appear, and no diligence spent in discovering them at the
+earliest possible moment is thrown away. We have only known up to the
+present, as already stated, less than a score of them, and of these many
+have told us but little; partly because they were only discovered too late
+(after they had become faint), and partly because the earlier ones could
+not be observed with the spectroscope, which had not then been invented.
+It seems clear that in the future we must not allow accident to play so
+large a part in the discovery of these objects; more must be done in the
+way of deliberate search. Although we know beforehand that this will
+involve a vast amount of apparently useless labour, that months and years
+must be spent in comparing photographic plates, or portions of the sky
+itself, with one another without detecting anything remarkable, it will
+not be the first time that years have been cheerfully spent in such
+searches without result. We need only recall Hencke's fifteen years of
+fruitless search, before finding a minor planet, to realise this fact.
+
+[Sidenote: Superposition of plates.]
+
+[Sidenote: The stereo-comparator.]
+
+One thing of importance may be done; we may improve our methods of making
+the search, so as to economise labour, and several successful attempts
+have already been made in this direction. The simplest plan is to
+superpose two photographs taken at different dates, so that the stars on
+one lie very close to those on the other; then if an image is seen to be
+unpaired we _may_ have found a new star, though of course the object may
+be merely a planet or a variable. The superposition of the plates may be
+either actual or virtual. A beautiful instrument has been devised on the
+principle of the stereoscope for examining two plates placed side by side,
+one with each eye. We know that in this way two photographs of the same
+object from different points of view will appear to coalesce, and at the
+same time to give an appearance of solidity to the object or landscape,
+portions of which will seem to stand out in front of the background.
+Applying this principle to two photographs of stars, what happens is this:
+if the stars have all remained in the same positions exactly, the two
+pictures will seem to us to coalesce, and the images all to lie on a flat
+background; but if in the interval between the exposures of the two plates
+one of the stars has appreciably moved or disappeared, it will seem, when
+looked at with this instrument, to stand out in front of this background,
+and is accordingly detected with comparatively little trouble. This new
+instrument, to which the name Stereo-comparator has been given, promises
+to be of immense value in dredging the sky for strange bodies in the
+future. I am glad to say that a generous friend has kindly presented the
+University Observatory at Oxford with one of these beautiful instruments,
+which have been constructed by Messrs. Zeiss of Jena after the skilful
+designs of Dr. Pulfrich. Whether we shall be able to repeat by deliberate
+search the success which mere accident threw in our way remains to be
+seen.
+
+
+
+
+CHAPTER V
+
+SCHWABE AND THE SUN-SPOT PERIOD
+
+
+[Sidenote: Discoveries contrary to expectation.]
+
+In preceding chapters we have reviewed discoveries, some of which have
+been made as a result of a deliberate search, and others accidentally in
+the course of work directed to a totally different end; but so far we have
+not considered a case in which the discoverer entered upon an enterprise
+from which he was positively dissuaded.
+
+[Sidenote: Nothing expected from spots.]
+
+In the next chapter we shall come across a very striking instance of this
+type; but even in the discovery that there was a periodicity in the solar
+spots, with which I propose to deal now, Herr Schwabe began his work in
+the face of deterrent opinions from eminent men. His definite announcement
+was first made in 1843, though he had himself been convinced some years
+earlier. In 1857 the Royal Astronomical Society awarded him their gold
+medal for the discovery; and in the address delivered on the occasion the
+President commenced by drawing attention to this very fact, that
+astronomers who had expressed any opinions on the subject had been
+uniformly and decidedly against the likelihood of there being anything
+profitable in the study of the solar spots. I will quote the exact words
+of the President, Mr. Manuel Johnson, then Radcliffe Observer at Oxford.
+
+     "It was in 1826 that Heinrich Schwabe, a gentleman resident in
+     Dessau, entered upon those researches which are now to engage our
+     attention. I am not aware of the motive that induced him--whether any
+     particular views had suggested themselves to his own mind--or whether
+     it was a general desire of investigating, more thoroughly than his
+     predecessors had done, the laws of a remarkable phenomenon, which it
+     had long been the fashion to neglect. He could hardly have
+     anticipated the kind of result at which he has arrived; at the same
+     time we cannot imagine a course of proceeding better calculated for
+     its detection, even if his mind had been prepared for it, than that
+     which he has pursued from the very commencement of his career.
+     Assuredly if he entertained such an idea, it was not borrowed from
+     the authorities of the last century, to whom the solar spots were
+     objects of more attention than they have been of late years.
+
+     "'Nulla constanti temporum lege apparent aut evanescunt,' says Keill
+     in 1739.--_Introduct. ad Physic. Astronom._, p. 253.
+
+     "'Il est manifest par ce que nous venons de rapporter qu'il n'y a
+     point de règle certaine de leur formation, ni de leur nombre et de
+     leur figure,' says Cassini II. in 1740.--_Elém d'Astron._, vol. i. p.
+     82.
+
+     "'Il semble qu'elles ne suivent aucune loi dans leur apparitions,'
+     says Le Monnier in 1746.--_Instit. Astron._, p. 83.
+
+     "'Solar spots observe no regularity in their shape, magnitude,
+     number, or in the time of their appearance or continuance,' says Long
+     in 1764.--_Astron._, vol. ii. p. 472.
+
+     "'Les apparitions des tâches du soleil n'ont rien de regulier,' says
+     Lalande in 1771.--_Astron._, vol. iii. § 3131, 2nd edit.
+
+     "And Delambre's opinion may be inferred from a well-known passage in
+     the third volume of his 'Astronomy' (p. 20), published in 1814, where
+     treating of the solar spots he says, 'Il est vrai qu'elles sont plus
+     curieuses que vraiment utiles.'"[4]
+
+It will thus be evident that Herr Schwabe had the courage to enter upon a
+line of investigation which others had practically condemned as likely to
+lead nowhere, and that his discovery was quite contrary to expectation. It
+is a lesson to us that not even the most unlikely line of work is to be
+despised; for the outcome of Schwabe's work was the first step in the
+whole series of discoveries which have gradually built up the modern
+science of Solar Physics, which occupies so deservedly large a part of the
+energies of, for instance, the great observatory attached to the
+University of Chicago.
+
+[Sidenote: Schwabe's announcement.]
+
+It has been our practice to recall the actual words in which the
+discoverer himself stated his discovery, and I will give the original
+modest announcement of Schwabe, though for convenience of those who do not
+read German I will attempt a rough translation. He had communicated year
+by year the results of his daily counting of the solar spots to the
+_Astronomische Nachrichten_, and after he had given ten years' results in
+this way he collected them together, but he made no remark on the curious
+sequence which they undoubtedly showed at that time. Waiting patiently six
+years for further material, in 1843 he ventured to make his definite
+announcement as follows:--"From my earlier observations, which I have
+communicated annually to this journal, there was manifest already a
+certain periodicity of sun-spots; and the probability of this being really
+the case is confirmed by this year's results. Although I gave in volume 15
+the total numbers of groups for the years 1826-1837, nevertheless I will
+repeat here a complete series of all my observations of sun-spots, giving
+not only the number of groups, but also the number of days of observation,
+and further the days when the sun was free from spots. The number of
+groups alone will not in itself give sufficient accuracy for determination
+of a period, since I have convinced myself that when there are a large
+number of sun-spots the number will be reckoned somewhat too small, and
+when few sun-spots, the number somewhat too large; in the first case
+several groups are often counted together in one, and in the second it is
+easy to divide a group made up of two component parts into two separate
+groups. This must be my excuse for repeating the early catalogue, as
+follows:--
+
+  +---------------------------------------------+
+  | Year.| Number of |  Days free |   Days of   |
+  |      |  Groups.  | from Spots.| Observation.|
+  |---------------------------------------------|
+  | 1826 |    118    |     22     |     277     |
+  | 1827 |    161    |      2     |     273     |
+  | 1828 |    225    |      0     |     282     |
+  | 1829 |    199    |      0     |     244     |
+  | 1830 |    190    |      1     |     217     |
+  |---------------------------------------------|
+  | 1831 |    149    |      3     |     239     |
+  | 1832 |     84    |     49     |     270     |
+  | 1833 |     33    |    139     |     267     |
+  | 1834 |     51    |    120     |     273     |
+  | 1835 |    173    |     18     |     244     |
+  |---------------------------------------------|
+  | 1836 |    272    |      0     |     200     |
+  | 1837 |    333    |      0     |     168     |
+  | 1838 |    282    |      0     |     202     |
+  | 1839 |    162    |      0     |     205     |
+  | 1840 |    152    |      3     |     263     |
+  |---------------------------------------------|
+  | 1841 |    102    |     15     |     283     |
+  | 1842 |     68    |     64     |     307     |
+  | 1843 |     34    |    149     |     324     |
+  |(1844)|    (52)   |  (111)     |    (320)    |
+  +---------------------------------------------+
+
+"If we now compare together the number of groups, and the days free from
+spots, we find that the sun-spots have a period of about ten years, and
+that for about five years they are so numerous that during this period few
+days, if any, are free from spots. The sequel must show whether this
+period is constant, whether the minimum activity of the sun in producing
+spots lasts for one or two years, and whether this activity increases more
+quickly than it decreases."
+
+[Illustration:
+
+  FEB. 18, 1894.   FEB. 19, 1894.
+
+  X.--PHOTOGRAPHS OF THE SUN TAKEN AT THE ROYAL OBSERVATORY, GREENWICH,
+  SHEWING SUNSPOTS.]
+
+[Sidenote: Attracted little attention, until eight years later.]
+
+This brief announcement is all that the discoverer says upon the subject;
+and it is perhaps not remarkable that it attracted very little attention,
+especially when we remember that it related to a matter which the
+astronomical world had agreed to put aside as unprofitable and not worth
+attention. Next year, in giving his usual paper on the spots for 1844 he
+recurs to the subject in the following sentence: "The periodicity of spots
+of about ten years which was indicated in my summary published last year,
+is confirmed by this year's observations." I have added in brackets to the
+table above reproduced the numbers for 1844 subsequently given, and it
+will be seen how nearly they might have been predicted.
+
+[Sidenote: Other phenomena sympathetic and others not.]
+
+Still the subject attracted little attention. Turning over the leaves of
+the journal at random, I came across the annual report of the Astronomer
+Royal of England, printed at length. But in it there is no reference to
+this discovery, which opened up a line of work now strongly represented in
+the annual programme of the Royal Observatory at Greenwich. Mr. Johnson
+remarks that the only person who had taken it up was Julius Schmidt, who
+then resided near Hamburg. But Schwabe went on patiently accumulating
+facts; and in 1851 the great Von Humboldt in the third volume of his
+_Cosmos_, drew attention to the discovery, which was accordingly for the
+first time brought into general notice. It will be seen that there are not
+many facts of general interest relating to the actual discovery beyond the
+courage with which the work was commenced in a totally unpromising
+direction, and the scant attention it received after being made for us. We
+may admit that interest centres chiefly in the tremendous consequences
+which flowed from it. We now recognise that many other phenomena are bound
+up with this waxing and waning of the solar spots. We might be prepared
+for a sympathy in phenomena obviously connected with the sun itself; but
+it was an unexpected and startling discovery that magnetic phenomena on
+the earth had also a sympathetic relation with the changes in sun-spots,
+and it is perhaps not surprising that when once this connection of solar
+and terrestrial phenomena was realised, various attempts have been made to
+extend it into regions where we cannot as yet allow that it has earned a
+legitimate right of entry. We have heard of the weather and of Indian
+famines occurring in cycles identical with the sun-spot cycle; and it is
+obvious how tremendously important it would be for us if this were found
+to be actually the case. For we might in this way predict years of
+possible famine and guard against them; or if we could even partially
+foretell the kind of weather likely to occur some years hence, we might
+take agricultural measures accordingly. The importance of the connection,
+if only it could be established, is no doubt the reason which has misled
+investigators into laying undue stress on evidence which will not bear
+close scrutiny. For the present we must say decidedly that no case has
+been made out for paying serious attention to the influence of sun-spots
+on weather. Nevertheless, putting all this aside, there is quite enough of
+first-rate importance in the sequel to Schwabe's discovery.
+
+[Sidenote: Greenwich sun records.]
+
+[Sidenote: The sun's rotation.]
+
+Let us review the facts in order. Most of us, though we may not have had
+the advantage of seeing an actual sun-spot through a telescope, have seen
+drawings or photographs of spots. There is a famous drawing made by James
+Nasmyth (of steam-hammer fame), in July, 1864, which is of particular
+interest, because at that time Nasmyth was convinced--and he convinced
+many others with him--that the solar surface was made up of a
+miscellaneous heap of solid bodies in shape like willow leaves, or grains
+of rice, thrown together almost at random, and the drawing was made by him
+to illustrate this idea. Comparing a modern photograph with it, we see
+that there is something to be said for Nasmyth's view, which attracted
+much attention at the time and occasioned a somewhat heated controversy.
+But since the invention of the spectroscope it has become quite obsolete;
+it probably does not correspond in any way to the real facts. But instead
+of looking at pictures which have been enlarged to show the detailed
+structure in and near a spot, we will look at a series of pictures of
+the whole sun taken on successive days at Greenwich in which the spots are
+necessarily much smaller, but which show the behaviour of the spots from
+day to day. (See Plates X. and XI.) From the date at the foot of each it
+will be seen that they gradually cross the disc of the sun (a fact first
+discovered by Galileo in 1610), showing that the sun rotates on an axis
+once in about every twenty-five days. There are many interesting facts
+connected with this rotation; especially that the sun does not rotate as a
+solid body, the parts near the (Sun's) Equator flowing quicker than those
+nearer the Poles; but for the present we cannot stop to dwell upon them.
+What interests us particularly is the history, not from day to day, but
+from year to year, as Schwabe has already given it for a series of years.
+
+[Illustration:
+
+  FEB. 20, 1894.   FEB. 21, 1894.
+
+  XI.--PHOTOGRAPHS OF THE SUN TAKEN AT THE ROYAL OBSERVATORY, GREENWICH,
+  SHEWING SUNSPOTS]
+
+[Sidenote: Wolf's numbers.]
+
+[Sidenote: Greenwich areas.]
+
+[Sidenote: Magnetic fluctuations.]
+
+When it became generally established that this periodicity existed, Rudolf
+Wolf of Zurich collected the facts about sun-spots from the earliest
+possible date, and represented this history by a series of numbers which
+are still called Wolf's Sun-Spot Numbers. You will see from the diagram
+the obvious rise and fall for eleven years,--not ten years, as Schwabe
+thought, but just a little over eleven years. The facts are, however,
+given more completely by the work done at the Royal Observatory at
+Greenwich. It is part of the regular daily work of that Observatory to
+photograph the sun at least twice. Many days are of course cloudy or wet,
+so that photographs cannot be obtained; but there are available
+photographs similarly taken in India or in Mauritius, where the weather is
+more favourable, and from these the gaps are so well filled up that very
+few days, if any, during the whole year are left without some photograph
+of the sun's surface. On these photographs the positions and the areas of
+the spots are carefully measured under a microscope, and the results when
+submitted to certain necessary calculations are published year by year. It
+is clearly a more accurate estimate of the spottedness of the sun to take
+the total _area_ of all the spots rather than their mere _number_, for in
+the latter case a large spot and a small one count equally. Hence the
+Greenwich records will perhaps give us an even better idea of the
+periodicity than Wolf's numbers. Now, at the same observatory magnetic
+observations are also made continuously. If a magnet be suspended freely
+we are accustomed to say that it will point to the North Pole; but this is
+only very roughly true. In the first place, it is probably well known to
+you that there is a considerable deviation from due north owing to the
+fact that the magnetic North Pole is not the same as the geographical
+North Pole; but this for the present need not concern us. What does
+concern us is, that if the needle is hung up and left long enough to come
+to rest, it does not then remain steadily at rest, but executes slow and
+small oscillations backwards and forwards, up and down, throughout the
+day; repeating nearly the same oscillations on the following day, but at
+the same time gradually changing its behaviour so as to oscillate
+differently in summer and winter. These changes are very small, and would
+pass unnoticed by the naked eye; but when carefully watched through a
+telescope, or better still, when photographed by some apparatus which will
+at the same time magnify them, they can be rendered easily visible. When
+the history of these changes is traced it is seen at once that there is a
+manifest connection with the cycle of sun-spot changes; for instance, if
+we measure the range of swing backwards and forwards during the day and
+take the average for all the days in the year, and then compare this with
+the average number of sun-spots, we shall see that the averages rise and
+fall together. Similarly we may take the up and down swing, find the
+average amount of it throughout the year, and again we shall find that
+this corresponds very closely with the average number of sun-spots.
+
+[Illustration: PLATE XII. NUMBER OF SUNSPOTS (Wolf) Compared with DAILY
+RANGE of MAGNETIC DECLINATION & DAILY RANGE of MAGNETIC HORZL. FORCE
+(as observed at Greenwich.)]
+
+[Sidenote: Daily curves.]
+
+[Sidenote: Difference between summer and winter, and between sun-spot
+maximum and minimum.]
+
+[Sidenote: Cause unknown.]
+
+But perhaps the most striking way to exhibit the sympathy is to combine
+different variations of the needle into one picture. And first we must
+remark that there is another important variation of the earth's magnetic
+action which we have not yet considered. We have mentioned the swing of
+the needle to and fro, and the swing up and down, and these correspond to
+changes in the _direction_ of the force of attraction on the needle. But
+there may be also changes in _intensity_ of this action; the pull may be a
+little stronger or a little weaker than before, and these variations are
+not represented by any actual movement of the needle, though they can be
+measured by proper experiments. We can, however, imagine them represented
+by a movement of the end of the needle if we suppose it made of elastic
+material, so that it would lengthen when the force was greater and
+contract slightly when the force was less. If a pencil were attached to
+the end of such an elastic needle so as to make a mark on a sheet of
+paper, and if for a moment we exclude the up and down movements, the
+pencil would describe during the day a curve on the paper, as the end of
+the needle swung backwards and forwards with the change in direction, and
+moved across the direction of swing with the change in intensity. Now when
+curves of this kind are described for a day in each month of the year,
+there is a striking difference between the forms of them. During the
+summer months they are, generally speaking, comparatively large and open,
+and during the winter months they are small and close. This change in form
+is seen by a glance at Plate XIII., which gives the curves throughout the
+whole of one year. Let us now, instead of forming a curve of this kind for
+each month, form a single average curve for the whole year; and let us
+further do this for a series of years. (Plate XIV.) We see that the curves
+change from year to year in a manner very similar to that in which they
+change from month to month in any particular year, and the law of change
+is such that in years when there are many sun-spots we get a large open
+curve similar to those found in the summer, while for years when there are
+few sun-spots we get small close curves very like those in the winter.
+Hence we have two definite conclusions suggested: firstly, that the
+changes of force are sympathetic with the changes in the sun-spots; and
+secondly, that times of maximum sun-spots correspond to summer, and times
+of minimum to winter. And here I must admit that this is about as far as
+we have got at present in the investigation of this relationship. _Why_
+the needle behaves in this way we have as yet only the very vaguest ideas;
+suggestions of different kinds have certainly been put forward, but none
+of them as yet can be said to have much evidence in favour of its being
+the true one. For our present purpose, however, it is sufficient to note
+that there is this very real connection, and that consequently Schwabe's
+sun-spot period may have a very real importance with regard to changes in
+our earth itself.
+
+[Illustration:
+
+  GREENWICH MAGNETIC CURVES
+  1859-60
+  PLATE XIII.
+  GREENWICH MAGNETIC CURVES FOR APRIL 1841-1860]
+
+[Sidenote: Illustration of spurious connection.]
+
+But I may perhaps repeat the word of caution already uttered against
+extending without sufficient evidence this notion of the influence of
+sun-spots to other phenomena, such as weather. A simple illustration will
+perhaps serve better than a long argument to show both the way in which
+mistakes have been made and the way in which they can be seen to be
+mistakes. There is at the Royal Observatory at Greenwich an instrument for
+noting the direction of the wind, the essential part being an ordinary
+wind-vane, the movements of which are automatically recorded on a sheet of
+paper. As the wind shifts from north to east the pencil moves in one
+direction, and when it shifts back again towards the north the pencil
+moves in the reverse way. But sometimes the wind shifts continuously from
+north to east, south, west, and back to north again, the vane making a
+complete revolution; and this causes the pencil to move continuously in
+one direction, until when the vane has come to north again, the pencil is
+far away from the convenient place of record; on such occasions it is
+often necessary to replace it by hand. Then again, the vane may turn in
+the opposite direction, sending the pencil inconveniently to the other
+side of the record. During the year it is easy to count the number of
+complete changes of wind in either direction, and subtracting one number
+from the other, we get the excess of complete revolutions of the vane in
+one direction over that in the other. Now if these rather arbitrary
+numbers are set down year by year, or plotted in the shape of a diagram,
+we get a curve which may be compared with the sun-spot curve, and during a
+period of no less than sixteen years--from 1858 to 1874--there was a
+remarkable similarity between the two diagrams. From this evidence _alone_
+it might fairly be inferred that the sun-spots had some curious effect
+upon the weather at Greenwich, traceable in this extraordinary way in the
+changes of the wind. But the particular way in which these changes are
+recorded is so arbitrary that we should naturally feel surprise if there
+was a real connection between the two phenomena; and fortunately there
+were other records preceding these years and following them which enabled
+us to test the connection further, and it was found, as we might naturally
+expect, that it was not confirmed. On looking at diagrams (Plate XV.) for
+the periods before and after, no similarity can be traced between the
+sun-spot curve and the wind-vane curve, and we infer that the similarity
+during the period first mentioned was entirely accidental. This shows that
+we must be cautious in accepting, from a limited amount of evidence, a
+connection between two phenomena as real and established; for it may be
+purely fortuitous. We may particularly remark that it is desirable to have
+repetitions through several complete periods instead of one alone. It is
+possible to reduce to mathematical laws the rules for caution in this
+matter; and much useful work has already been done in this direction by
+Professor Schuster of Manchester and others, though as yet too little
+attention has been paid to their rules by investigators naturally eager to
+discover some hitherto unthought-of connection between phenomena.
+
+[Sidenote: Faculæ follow spots and the chromosphere.]
+
+With this example of the need for caution, we may return to phenomena of
+which we can certainly say that they vary sympathetically with the
+sun-spots. Roughly speaking, the whole history of the sun seems to be
+bound up with them. Besides these dark patches which we call spots (which,
+by the way, are not really dark but only less bright than the surrounding
+part of the disc), there are patches brighter than the rest which have
+been called faculæ. With ordinary telescopes, either visual or
+photographic, these can generally only be detected near the edge of the
+sun's disc; but even with this limitation it can easily be established
+that the faculæ vary in number and size from year to year much in the same
+way as the spots, and this conclusion is amply confirmed by the beautiful
+method of observing the faculæ with the new instrument designed by
+Professor Hale of the Yerkes Observatory. With this instrument, called a
+spectroheliograph, it is possible to photograph the faculæ in all parts of
+the sun's disc, and thus to obtain a much more complete history of them,
+and there is no doubt whatever of their variation sympathetically with the
+spots. Nor is there any doubt about similar variations in other parts of
+the sun which we cannot see _at all_ with ordinary telescopes, except on
+the occasions when the sun is totally eclipsed. Roughly speaking, these
+outlying portions of the sun consist of two kinds, the chromosphere and
+the corona, the former looking like an irregular close coating of the
+ordinary sun, and the latter like a pearly halo of light extending to
+many diameters of the sun's disc, but not with any very regular form.
+
+[Illustration: PLATE XV. SMOOTHED SUNSPOT CURVE (WOLF) COMPARED WITH THE
+NUMBER OF TURNS MADE IN EACH YEAR BY THE OSLER ANEMOMETER VANE OF THE
+ROYAL OBSERVATORY, GREENWICH (THE EXCESS OF THE DIRECT TURNS (D) OVER THE
+RETROGRADE TURNS (R) OR _VICE VERSA_.)
+
+THE UPPER CURVE IS IN EACH CASE THE SUNSPOT CURVE, THE LOWER THE VANE
+CURVE. THE BREAK IN 1882 IN THE VANE CURVE IS DUE TO THE OMISSION OF
+EVIDENTLY ACCIDENTAL TURNS FROM THAT DATE.]
+
+The chromosphere, from which shoot out the prominences or "red flames,"
+can now be observed without an eclipse if we employ the beautiful
+instrument above-mentioned, the spectroheliograph; and Professor Hale has
+succeeded in photographing spots, faculæ, and prominences all on the same
+plate. But although many have made the attempt (and Professor Hale,
+perhaps, a more determined attempt than any man living), no one has yet
+succeeded in obtaining any picture or evidence of the existence of the
+corona excepting on the occasion of a total solar eclipse.
+
+[Sidenote: Eclipses of sun.]
+
+[Sidenote: Total eclipses rare.]
+
+Now these occasions are very rare. There are two or three eclipses of the
+sun every year, but they are generally of the kind known as partial; when
+the moon does indeed come between us and the sun to some extent, but only
+cuts off a portion of his light--a clean-cut black disc is seen to
+encroach more or less on the surface of the sun. Most of us have had an
+opportunity of seeing a partial eclipse, probably more than once; but few
+have seen a total eclipse. For this the moon must come with great
+exactness centrally between us and the sun; and the spot where this
+condition is fulfilled completely only covers a few hundred miles of the
+earth's surface at one moment. As the earth turns round, and as the moon
+revolves in its orbit, this patch from which the sun is totally eclipsed
+travels over the earth's surface, marking out a track some thousands of
+miles in length possibly, but still not more than 200 miles wide; and in
+order to see the sun totally eclipsed even on the rare occasions when it
+is possible at all (for, as already remarked, in the majority of cases the
+eclipse is only partial), we must occupy some station in this narrow belt
+or track, which often tantalisingly passes over either the ocean or some
+regions not easily accessible to civilised man. Moreover, if we travel to
+such favoured spots the whole time during which the sun is totally
+eclipsed cannot exceed a few minutes, and hence observations are made
+under rather hurried and trying conditions. In these modern days of
+photography it is easier to take advantage of these precious moments than
+it used to be when there was only the eye and memory of an excited
+observer to rely upon. It is perhaps not surprising that some of the
+evidence collected on these earlier occasions was conflicting; but
+nowadays the observers, generally speaking, direct their energies in the
+first place to mounting accurately in position photographic apparatus of
+different kinds, each item of it specially designed to settle some
+particular problem in the most feasible way; secondly, to rehearsing very
+carefully the exact programme of exposures necessary during the critical
+few minutes; and finally, to securing these photographs with as few
+mistakes as possible when the precious moments actually arrive. Even then
+the whole of their efforts are quite likely to be rendered unavailing by a
+passing cloud; and bitter is the disappointment when, after travelling
+thousands of miles, and spending months in preparation, the whole
+enterprise ends in nothing owing to some caprice of the weather.
+
+[Sidenote: Corona follows spots.]
+
+Hence it will easily be imagined that our knowledge of the corona, the
+part of the sun which we can still only study on occasions of a total
+solar eclipse, advances but slowly. During the last twenty years there has
+been altogether scarcely half-an-hour available for this research, though
+it may fairly be said that the very best possible use has been made of
+that half-hour. And, what is of importance for our immediate purpose, it
+has gradually been established by comparing the photographs of one eclipse
+with those of another, that the corona itself undergoes distinct changes
+in form in the same period which governs the changes of sun-spots. When
+there are many sun-spots the corona spreads out in all directions from the
+edge of the sun's disc; when there are few sun-spots the corona extends
+very much further in the direction of the sun's equator, so that at
+sun-spot minimum there is an appearance of two huge wings. Although the
+evidence is necessarily collected in a scrappy manner, by this time there
+is sufficient to remove this relationship out of the region of mere
+suspicion, and to give it a well-established place in our knowledge of the
+sun's surroundings.
+
+[Sidenote: Corona may influence magnets.]
+
+Now the corona of the sun may be compared to some rare animal which we
+only see by paying a visit to some distant land, and may consider
+ourselves even then fortunate to get a glimpse of; and it might be thought
+that the habits of such an animal are not likely to be of any great
+importance in our everyday life. But so far from this being the case in
+regard to the corona, it is more than possible that the knowledge of its
+changes may be of vital interest to us. I have already said that, as yet,
+we have no satisfactory account of the reason why changes in sun-spots
+seem to influence changes in our magnets on the earth; but one of the
+theories put forward in explanation, and one by no means the least
+plausible, is that this influence may come, not from the sun-spots
+themselves, but from some other solar phenomenon which varies in sympathy
+with them; and in particular that it may come from the corona. These wings
+which reach out at sun-spot minimum can be seen to extend a considerable
+distance, and there is no reason to suppose that they actually cease at
+the point where they become too faint for us to detect them further; they
+may extend quite as far as the earth itself and even beyond; and they may
+be of such a nature as to influence our magnets. As the earth revolves
+round the sun it may sometime plunge into them, to emerge later and pass
+above or below them; as again the wings spread themselves at sun-spot
+minimum and seem to shrink at maximum, so our magnets may respond by
+sympathetic though very small vibrations. Hence it is quite possible that
+the corona is directly influencing the magnetic changes on the earth.
+
+[Sidenote: Possible importance of corona.]
+
+But it may be urged that these changes are so slight as to be merely of
+scientific interest. That may be true to-day, but who will be bold enough
+to say that it will be true to-morrow? If we are thinking of practical
+utility alone, we may remember that two great forces of Nature which we
+have chained into the service of man, steam and electricity, put forth
+originally the most feeble manifestations, which might readily have been
+despised as valueless; but by careful attention to proper conditions
+results of overwhelming practical importance have been obtained from these
+forces, which might have been, and for many centuries were, neglected as
+too trivial to be worth attention. Recently the world has been startled by
+the discovery of new elements, such as radium, whose very existence was
+only detected by a triumph of scientific acuteness in investigation, and
+yet which promise to yield influences on our lives which may overwhelm in
+importance all that has gone before. And similarly it may be that these
+magnetic changes, when properly interpreted or developed, may become of an
+importance in the future out of all proportion to the attention which they
+have hitherto attracted. Hence, although perhaps sufficient has already
+been established to show the immense consequences which flow from
+Schwabe's remarkable discovery of the periodicity in solar spots, we may
+be as yet only on the threshold of its real value.
+
+From what little causes great events spring! How little can Schwabe have
+realised, when he began to point his modest little telescope at the sun,
+and to count the number of spots--the despised spots which he had been
+assured were of no interest and exhibited no laws, and were generally
+unprofitable--that he was taking the first step in the invention of the
+great science of Solar Physics!--a science which is, I am glad to say,
+occupying at the present moment so much of the attention, not only of the
+great Yerkes Observatory, but of many other observatories scattered over
+the globe.
+
+
+
+
+CHAPTER VI
+
+THE VARIATION OF LATITUDE
+
+
+If we should desire to classify discoveries in order of merit, we must
+undoubtedly give a high place to those which are made under direct
+discouragements. In the last chapter we saw that Schwabe entered upon his
+work under conditions of this kind, it being the opinion of experienced
+astronomers who had looked at the facts that there was nothing of interest
+to be got by watching sun-spots. In the present chapter I propose to deal
+with a discovery made in the very teeth of the unanimous opinion of the
+astronomical world by an American amateur, Mr. S. C. Chandler of Cambridge
+(Massachusetts). It is my purpose to allow him to himself explain the
+steps of this discovery by giving extracts from the magnificent series of
+papers which he contributed to the _Astronomical Journal_ on the subject
+in the years 1891-94, but it may help in the understanding of these
+extracts if I give a brief summary of the facts. And I will first explain
+what is meant by the "Variation of Latitude."
+
+[Sidenote: Latitude.]
+
+[Sidenote: Precession.]
+
+We are all familiar with the existence of a certain star in the heavens
+called the Pole Star, and we know that at any particular place it is seen
+constantly in the north at a definite height above the horizon, which is
+the latitude of the place. When watched carefully with a telescope it is
+found to be not absolutely stationary, but to describe a small circle in
+the heavens day by day, or rather night by night. These simple facts are
+bound up with the phenomenon of the earth's rotation in this way: the axis
+about which it is rotating points to the centre of that little circle, and
+any change in the position of the axis can therefore be determined by
+observing these motions of the Pole Star. Such changes may be of two
+kinds: firstly, we might find that the size of the circle increased or
+diminished, and this would mean that the earth's axis was pointing farther
+away from the Pole Star or nearer to it--pointing, that is to say, in a
+different direction in space. This actually happens (as has been known for
+some thousands of years) owing to the phenomenon called "precession"; the
+circle described by our Pole Star is at present getting a little smaller,
+but it will ultimately increase in size, and after thousands of years
+become so large that the Pole Star will entirely lose its character as a
+steady guide to the North.
+
+[Sidenote: Change of latitude.]
+
+[Sidenote: Twenty years ago disbelieved.]
+
+Secondly (and this is what more immediately concerns us), the centre of
+the circle may alter its position and be no longer at the same height
+above the horizon of any given place. This would mean that the earth's
+axis was shifting _in the earth itself_--that the North Pole which our
+explorers go to seek is not remaining in the same place. That it does not
+change appreciably in position we know from familiar experience; our
+climates, for instance, would suffer considerably if there were any large
+changes. But astronomers are concerned with minute changes which would not
+have any appreciable effect on climate, and the question has long been
+before them whether, putting aside large movements, there were any minute
+variations in position of the North Pole. Twenty years ago the answer to
+this question would have been given decidedly in the negative; it was
+considered as certain that the North Pole did not move at all within the
+limits of our most refined astronomical observations. Accepted theory
+seemed to indicate that any movements must in any case recur after a
+period of ten months, and careful discussion of the observations showed
+that there was no oscillation in such a period. Now we know that the
+theory itself was wrong, or rather was founded upon a mistaken assumption;
+and that the facts when properly examined show clearly a distinct movement
+of the North Pole, not a very large one, for all its movements take place
+within the area occupied by a moderate-sized room, but still a movement
+easily measurable by astronomical observations, and Mr. Chandler was the
+first to point out the law of these movements, and very possibly the first
+to suspect them.
+
+[Sidenote: Chandler's papers.]
+
+With these few words of explanation I will let Mr. Chandler tell his own
+story. His first paper appeared in the _Astronomical Journal_ in November
+1891, and is courageously headed, "On the Variation of Latitude"--I say
+courageously, because at that time it was believed that the latitude did
+_not_ vary, and Mr. Chandler himself was only in possession of a small
+portion of the facts. They unravelled themselves as he went forward; but
+he felt that he had firm hold of the end of the thread, and he faced the
+world confidently in that belief. He begins thus:--
+
+     [Sidenote: First signs of change.]
+
+     "In the determination of the latitude of Cambridge[5] with the
+     Almucantar, about six years and a half ago, it was shown that the
+     observed values, arranged according to nights of observation,
+     exhibited a decided and curious progression throughout the series,
+     the earlier values being small, the later ones large, and the range
+     from November 1884 to April 1885 being about four-tenths of a second.
+     There was no known or imaginable instrumental or personal cause for
+     this phenomenon, yet the only alternative seemed to be an inference
+     that the latitude had actually changed. This seemed at the time too
+     bold an inference to place upon record, and I therefore left the
+     results to speak for themselves. The subsequent continuation of the
+     series of observations to the end of June 1885 gave a maximum about
+     May 1, while the discussion of the previous observations from May to
+     November 1884 gave a minimum about September 1, indicating a range of
+     0".7 within a half-period of about seven months."
+
+Mr. Chandler then gives some figures in support of these statements,
+presenting them with the clearness which is so well marked a feature of
+the whole series of papers, and concludes this introductory paper as
+follows:--
+
+     "It thus appears that the apparent change in the latitude of
+     Cambridge is verified by this discussion of more abundant material.
+     The presumption that it is real, on this determination alone, would
+     justify further inquiry.
+
+     [Sidenote: Confirmed in Europe.]
+
+     "Curiously enough Dr. Küstner, in his determination of the
+     aberration from a series of observations coincident in time with
+     those of the Almucantar, came upon similar anomalies, and his
+     results, published in 1888, furnish a counterpart to those which I
+     had pointed out in 1885. The verification afforded by the recent
+     parallel determinations at Berlin, Prague, Potsdam, and Pulkowa,
+     which show a most surprising and satisfactory accordance, as to the
+     character of the change, in range and periodicity, with the
+     Almucantar results, has led me to make further investigations on the
+     subject. They seem to establish the nature of the law of those
+     changes, and I will proceed to present them in due order."
+
+The second paper appeared on November 23, and opens with the following
+brief statement of his general results at that time:--
+
+     [Sidenote: 427 days' period.]
+
+     "Before entering upon the details of the investigations spoken of in
+     the preceding number, it is convenient to say that the general result
+     of a preliminary discussion is to show a revolution of the earth's
+     pole in a period of 427 days, from west to east, with a radius of
+     thirty feet, measured at the earth's surface. Assuming provisionally,
+     for the purpose of statement, that this is a motion of the north pole
+     of the principal axis of inertia about that of the axis of rotation,
+     the direction of the former from the latter lay towards the Greenwich
+     meridian about the beginning of the year 1890. This, with the period
+     of 427 days, will serve to fix approximately the relative positions
+     of these axes at any other time, for any given meridian. It is not
+     possible at this stage of the investigation to be more precise, as
+     there are facts which appear to show that the rotation is not a
+     perfectly uniform one, but is subject to secular change, and perhaps
+     irregularities within brief spaces of time."
+
+[Sidenote: Contrary to received views.]
+
+It is almost impossible, now that we have become familiar with the ideas
+conveyed in this paragraph, to understand, or even fully to remember, the
+impression produced by them at the time; the sensation caused in some
+quarters, and the ridicule excited in others. They were in flat
+contradiction to all accepted views; and it was believed that these views
+were not only theoretically sound, but had been matured by a thorough
+examination of observational evidence. The only period in which the
+earth's pole could revolve was believed to be ten mouths; and here was Mr.
+Chandler proclaiming, apparently without any idea that he was
+contradicting the laws of dynamics, that it was revolving in fourteen
+months! The radius of its path had been found to be insensible by careful
+discussion of observations, and now he proclaimed a sensible radius o£
+thirty feet. Finally, he had the audacity to announce a _variable_ period,
+to which there was nothing at all corresponding in the mathematical
+possibilities. This was the bitterest pill of all. Even after Professor
+Newcomb had shown us how to swallow the other two, he could not recommend
+any attempt at the third, as we shall presently see; and Mr. Chandler was
+fain ultimately to gild it a little before it could be gulped.
+
+[Sidenote: Pulkowa puzzle solved, also Washington.]
+
+But this is anticipating, and it is our intention to follow patiently the
+evidence adduced in support of the above statements, made with such
+splendid confidence to a totally disbelieving world. Mr. Chandler first
+examines the observations of Dr. Küstner of Berlin, quoted at the end of
+his last paper, and shows how well they are suited by the existence of a
+variation in the latitude of 427 days; and that this new fact is
+added--when the Cambridge (U.S.A.) latitudes were the smallest those of
+Berlin were the largest, and _vice versâ_, as would clearly be the case if
+the phenomenon was due to a motion of the earth's pole; for if it moved
+nearer America it must move further from Europe. He then examines a long
+series of observations made in the years 1864-1873 at Pulkowa, near St.
+Petersburg, and again finds satisfactory confirmation of his law of
+variation. Now it had long been known that there was something curious
+about these observations, but no one could tell what it was. The key
+offered by Mr. Chandler fitted the lock exactly, and the anomalies which
+had been a puzzle were removed. This was in itself a great triumph; but
+there was another to come, which we may let Mr. Chandler describe in his
+own words:--
+
+     "In 1862 Professor Hubbard began a series of observations of [a]
+     Lyræ at the Washington Observatory with the prime vertical transit
+     instrument, for the purpose of determining the constants of
+     aberration and nutation and the parallax of the star. The methods of
+     observation and reduction were conformed to those used with such
+     success by W. Struve. After Hubbard's death the series was continued
+     by Professors Newcomb, Hall, and Harkness until the beginning of
+     1867. Professor Hall describes these observations as the most
+     accurate determinations of declination ever made at the Naval
+     Observatory. The probable error of a declination from a single
+     transit was ±0".141, and judging from the accidental errors, the
+     series ought to give trustworthy results. Upon reducing them,
+     however, it was found that some abnormal source of error existed,
+     which resulted in anomalous values of the aberration-constant in the
+     different years, and a negative parallax in all. A careful
+     verification of the processes of reduction failed to discover the
+     cause of the trouble, and Professor Hall says that the results must
+     stand as printed, and that probably some annual disturbance in the
+     observations or the instrument occurred, which will never be
+     explained, and which renders all deductions from them uncertain. The
+     trouble could not be connected with personal equation, the anomalies
+     remaining when the observations of the four observers who took part
+     were separately treated. Nor, as Professor Hall points out, will the
+     theoretical ten-month period in the latitude furnish the explanation.
+
+     "It is manifest, however, that if the 427-day period exists, its
+     effect ought to appear distinctly in declination-measurements of such
+     high degree of excellence as these presumably were, and, as I hope
+     satisfactorily to show, actually are. When this variation is taken
+     into account the observations will unquestionably vindicate the high
+     expectations entertained with regard to them by the accomplished and
+     skilful astronomers who designed and carried them out."
+
+[Sidenote: Direction of revolution of Pole.]
+
+[Sidenote: Example of results.]
+
+From this general account I am excluding technical details and figures,
+and unfortunately a great deal is thereby lost. We lose the sense of
+conviction which the long rows of accordant figures force upon us, and we
+lose the opportunities of admiring both the astonishing amount of work
+done and the beautiful way in which the material is handled by a master.
+But I am tempted to give one very small illustration of the numerical
+results from near the end of the paper. After discussing the Washington
+results, and amply fulfilling the promise made in the preceding extract,
+Mr. Chandler compares them with the Pulkowa results, and shows that the
+Earth's Pole must be revolving from west to east, and not from east to
+west. And then he writes down a simple formula representing this motion,
+and compares his formula with the observations. He gives the results in
+seconds of arc, but for the benefit of those not familiar with
+astronomical measurements we may readily convert these into feet; and in
+the following tables are shown the distances of the Earth's Pole _in feet_
+from its average position,[6] as observed at Washington and at Pulkowa,
+and the same distances calculated according to the formula which Mr.
+Chandler was able to write down at this early stage. The signs + and - of
+course indicate opposite directions of displacement:--
+
+  WASHINGTON.
+
+  _Deviation of Pole._
+
+  +-------------------------------------+
+  |     Date.     | Observed.| Formula. |
+  |-------------------------------------|
+  | 1864, Dec. 28 | -28 feet | -23 feet |
+  | 1865, Mar. 19 | - 1  "   | -12  "   |
+  |  "    June  1 | +15  "   | +12  "   |
+  |  "    Aug. 11 | +22  "   | +23  "   |
+  |  "    Oct.  9 | +11  "   | +15  "   |
+  |  "    Dec. 13 | -17  "   | - 6  "   |
+  +-------------------------------------+
+
+
+  PULKOWA.
+
+  _Deviation of Pole._
+
+  +-------------------------------------+
+  |     Date.     | Observed.| Formula. |
+  |-------------------------------------|
+  | 1865, July 25 | -18 feet | -12 feet |
+  |   "   Sept. 9 | + 3  "   | + 3  "   |
+  |   "   Nov. 22 | +26  "   | +22  "   |
+  | 1866, Feb. 22 | +18  "   | +13  "   |
+  |   "   June  4 | -11  "   | -18  "   |
+  |   "   July 17 | -16  "   | -23  "   |
+  +-------------------------------------+
+
+Of course the figures are not exact in every case, but they are never many
+feet wrong; and it may well be imagined that it is a difficult thing to
+deduce, even from the most refined observations, the position of the
+earth's pole to within a foot. The difficulty is exactly the same as that
+of measuring the length of an object 300 miles away to within an inch!
+
+Mr. Chandler winds up his second paper thus:--
+
+     "We thus find that the comparison of the simultaneous series at
+     Pulkowa and Washington, 1863-1867, leads to the same conclusion as
+     that already drawn from the simultaneous series at Berlin and
+     Cambridge, 1884-1885. The direction of the polar motion may therefore
+     be looked upon as established with a large degree of probability.
+
+     "In the next paper I will present the results derived from PETERS,
+     STRUVE, BRADLEY, and various other series of observations, after
+     which the results of all will be brought to bear upon the
+     determination of the best numerical values of the constants
+     involved."
+
+[Sidenote: Bradley's observations.]
+
+[Sidenote: Latitude varied in twelve months then.]
+
+The results were not, however, presented in this order. In the next paper,
+which appeared on December 23, 1891, Mr. Chandler begins, with the work of
+Bradley, the very series of observations at Kew and Wansted which led to
+the discoveries of aberration and nutation, and which we considered in the
+third chapter. He first shows that, notwithstanding the obvious accuracy
+of the observations, there is some unexplained discordance. The very
+constant of aberration which Bradley discovered from them differs by
+half-a-second of arc from our best modern determinations. Attempts have
+been made to ascribe the discordance to changes in the instrument, but Mr.
+Chandler shows that such changes, setting aside the fact that Bradley
+would almost certainly have discovered them, will not fit in with the
+facts. The facts, when analysed with the skill to which we have become
+accustomed, are that there is a periodic swing in the results _with a
+period of about a year_, and not fourteen months, as before, "a result so
+curious," as he admits, that "if we found no further support, it might
+lead us to distrust the above reasoning, and throw us back to the
+possibility that, after all, BRADLEY'S observations may have been vitiated
+by some kind of annual instrumental error. But it will abundantly appear,
+when I have had the opportunity to print the deductions from all the other
+series of observations down to the present time, that the inference of an
+increase in the period of polar revolution is firmly established by their
+concurrent testimony." We shall presently return to this curious result,
+which might well have dismayed a less determined researcher than Mr.
+Chandler, but which only led him on to renewed exertions.
+
+The results obtained from Bradley's observations may be put in the form
+of a diagram thus:--
+
+[Illustration: FIG. 7.]
+
+It will be seen that the maxima and minima fall in the spring and autumn,
+and this fact alone seemed to show that the effect could not be due to
+temperature, for we should expect the greatest effect in that case in
+winter and summer. It could not be due to the parallax of the stars for
+which Bradley began his search, for stars in different quarters of the
+heavens would then be differently affected, and this was not the case.
+"There remains," concluded Mr. Chandler after full discussion, "the only
+natural conclusion of an actual displacement of the zenith, in other
+words, a change of latitude." And he concludes this paper with the
+following fine passage:--
+
+     "So far, then, as the results of this incomparable series of
+     observations at Kew and Wansted, considered by themselves alone, can
+     now be stated, the period of the polar rotation at that epoch appears
+     to have been probably somewhat over a year, and certainly shorter by
+     about two months than it is at the present time. The range of the
+     variation was apparently in the neighbourhood of a second of arc, or
+     considerably larger than that shown by the best modern observations.
+
+     [Sidenote: Bradley's greatness.]
+
+     "Before taking leave of these observations for the present I cannot
+     forbear to speak of the profound impression which a study of them
+     leaves upon the mind, and the satisfaction which all astronomers must
+     feel in recognising that, besides its first fruits of the phenomena
+     of aberration and nutation, we now owe also our first knowledge of
+     the polar motion to this same immortal work of Bradley. Its
+     excellence, highly appreciated as it has been, has still been
+     hitherto obscured by the presence of this unsuspected phenomenon.
+     When divested of its effects, the wonderful accuracy of this work
+     must appear in a finer light, and our admiration must be raised to
+     higher pitch. Going back to it after one hundred and sixty years
+     seems indeed like advancing into an era of practical astronomy more
+     refined than that from which we pass. And this leads to a suggestion
+     worthy of serious practical consideration--whether we can do better
+     in the future study of the polar rotation, than again to avail
+     ourselves of Bradley's method, without endangering its elegant
+     simplicity and effectiveness by attempts at improvement, other than
+     supplying certain means of instrumental control which would without
+     doubt commend themselves to his sagacious mind.
+
+     [Sidenote: Other puzzles explained.]
+
+     "In the next article Bradley's later observations at Greenwich, the
+     results of which are not so distinct, will be discussed; and also
+     those of Brinkley at Dublin, 1808-13 and 1818-22. This will bring
+     again to the surface one of the most interesting episodes in
+     astronomical history, the spirited and almost acrimonious dispute
+     between Brinkley and Pond with regard to stellar parallaxes. I hope
+     to show that the hitherto unsolved enigma of Brinkley's singular
+     results finds its easy solution in the fact of the polar motion. The
+     period of his epoch appears to have been about a year, and its range
+     more than a second. Afterwards will follow various discussions
+     already more or less advanced towards completion. These include
+     Bessel's observations at Königsberg, 1820-24, with the Reichenbach
+     circle, and in 1842-44 with the Repsold circle; the latitudes derived
+     from the polar-point determinations of Struve and Mädler with the
+     Dorpat circle, 1822-38; Struve's observations for the determination
+     of the aberration; Peters' observations of _Polaris_, 1841-43, with
+     the vertical-circle; the results obtained from the reflex zenith-tube
+     at Greenwich, 1837-75, whose singular anomalies can be referred in
+     large part to our present phenomenon, complicated with instrumental
+     error, to which until now they have been exclusively attributed; the
+     Greenwich transit-circle results, 1851-65, in which case, however, a
+     similar complication and the large accidental errors of observation
+     seem to frustrate efforts to get any pertinent results; the Berlin
+     prime-vertical observations of Weyer and Brünnow, 1845-46, in which I
+     hope to show that the parallax of [beta] _Draconis_ derived from them
+     is simply a record of the change of latitude; the conflicting
+     latitude determinations at Cambridge, England; the Washington
+     observation of _Polaris_ and other close Polars, 1866-87, with the
+     transit-circle; also those at Melbourne, 1863-84, a portion of which
+     have already been drawn upon in the last number of the _Journal_,
+     and some others. While the list is a considerable one, I shall be
+     able to compress the statement of results for many of the series into
+     a short space.
+
+     [Sidenote: Provisional nature of results.]
+
+     "In connection with this synopsis of the scope of the investigations,
+     one or two particulars may be of interest, which at the present
+     writing seem to foreshadow the probable outcome. I beg, however, that
+     the statement will be regarded merely as a provisional one. First,
+     while the period is manifestly subject to change, as has already once
+     or twice been intimated, I have hitherto failed in tracing the
+     variations to any regular law, expressible in a numerical formula.
+     Indeed, the general impression produced by a study of these changes
+     in the length of the period is that the cause which produces them
+     operates capriciously to a certain degree, although the average
+     effect for a century has been to diminish the velocity of the
+     revolution of the pole. How far this impression is due to the
+     uncertainty of the observations, and to the complication of the
+     phenomenon with other periodical changes of a purely instrumental
+     kind, I cannot say. Almost all of the series of any extent which have
+     been examined, have the peculiarity that they manifest the
+     periodicity quite uniformly and distinctly for a number of years,
+     then for a while obscurely. In some cases, however, what at first
+     appears to be an objective irregularity proves not to be so by
+     comparison with overlapping series at other observatories.
+
+     "Another characteristic which has struck my attention, although
+     somewhat vaguely, is that the variations in the length of the period
+     seem to go hand in hand with simultaneous alterations in the
+     amplitude of the rotation; the shorter periods being apparently
+     associated with the larger coefficients for the latter. The
+     verification of these surmises awaits a closer comparative scrutiny,
+     the opportunity for which will come when the computations are in a
+     more forward state. If confirmed, these observations will afford a
+     valuable touchstone, in seeking for the cause of a phenomenon which
+     now seems to be at variance with the accepted laws of terrestrial
+     rotation."
+
+[Sidenote: Reception of discovery.]
+
+Let us now for a few moments turn aside from the actual research to see
+how the announcement was received. It would be ungracious to reprint here
+any of the early statements of incredulity which found their way into
+print, especially in Germany. But the first note of welcome came from
+Simon Newcomb, in the same number of the _Astronomical Journal_ as the
+paper just dealt with, and the following extract will indicate both the
+difficulties felt in receiving Mr. Chandler's results and the way in which
+Newcomb struck at the root of them.
+
+     [Sidenote: Newcomb's explanation.]
+
+     "Mr. Chandler's remarkable discovery, that the apparent variations in
+     terrestrial latitudes may be accounted for by supposing a revolution
+     of the axis of rotation of the earth around that of figure, in a
+     period of 427 days, is in such disaccord with the received theory of
+     the earth's rotation that at first I was disposed to doubt its
+     possibility. But I am now able to point out a _vera causa_ which
+     affords a complete explanation of this period. Up to the present time
+     the treatment of this subject has been this: The ratio of the moment
+     of inertia of the earth around its principal axis to the mean of the
+     other two principal moments, admits of very accurate determination
+     from the amount of precession and nutation. This ratio involves what
+     we might call, in a general way, the solid ellipticity of the earth,
+     or the ellipticity of a homogeneous spheroid having the same moments
+     of inertia as the earth.
+
+     "When the differential equations of the earth's rotation are
+     integrated, there appear two arbitrary constants, representing the
+     position of any assigned epoch of the axis of rotation relative to
+     that of figure. Theory then shows that the axis of rotation will
+     revolve round that of figure, in a period of 306 days, and in a
+     direction from west toward east. The attempts to determine the value
+     of these constants have seemed to show that both are zero, or that
+     the axes of rotation and figure are coincident. Several years since,
+     Sir William Thomson published the result of a brief computation from
+     the Washington Prime-Vertical observations of [alpha] Lyrae which I
+     made at his request and which showed a coefficient 0".05. This
+     coefficient did not exceed the possible error of the result; I
+     therefore regarded it as unreal.
+
+     [Sidenote: The forgotten assumption.]
+
+     "The question now arises whether Mr. Chandler's result can be
+     reconciled with dynamic theory. I answer that it can, because the
+     theory which assigns 306 days as the time of revolution is based on
+     the hypothesis that the earth is an absolutely rigid body. But, as a
+     matter of fact, the fluidity of the ocean plays an important part in
+     the phenomenon, as does also the elasticity of the earth. The
+     combined effect of this fluidity and elasticity is that if the axis
+     of rotation is displaced by a certain amount, the axis of figure
+     will, by the changed action of the centrifugal force, be moved
+     toward coincidence with the new axis of rotation. The result is, that
+     the motion of the latter will be diminished in a corresponding ratio,
+     and thus the time of revolution will be lengthened. An exact
+     computation of the effect is not possible without a knowledge of the
+     earth's modulus of elasticity. But I think the result of
+     investigation will be that the rigidity derived from Mr. Chandler's
+     period is as great as that claimed by Sir William Thomson from the
+     phenomena of the tides."
+
+[Sidenote: But Chandler's work still mistrusted.]
+
+This was very satisfactory. Professor Newcomb put his finger on the
+assumption which had been made so long ago that it had been forgotten: and
+the lesson is well worth taking to heart, for it is not the first time
+that mistaken confidence in a supposed fact has been traced to some
+forgotten preliminary assumption: and we must be ever ready to cast our
+eyes backward over all our assumptions, when some new fact seems to
+challenge our conclusions. It might further be expected that this
+discovery of the way in which theory had been defective would as a
+secondary consequence inspire confidence in the other conclusions which
+Mr. Chandler had arrived at in apparent contradiction to theory; or at
+least suggest the suspension of judgment. But Professor Newcomb did not
+feel that this was possible in respect of the _change_ of period, from
+about twelve months in Bradley's time to fourteen months in ours. We have
+seen that Mr. Chandler himself regarded this as a "curious result"
+requiring confirmation: but since the confirmation was forthcoming, he
+stated it with full confidence, and drew the following remarks from
+Professor Newcomb in July 22, 1892:--
+
+     "The fact of a periodic variation of terrestrial latitudes, and the
+     general law of that variation, have been established beyond
+     reasonable doubt by the observations collected by Mr. Chandler. But
+     two of his minor conclusions, as enumerated in No. 3 of this volume,
+     do not seem to me well founded. They are--
+
+     "1. That the period of the inequality is a variable quantity.
+
+     "2. That the amplitude of the inequality has remained constant for
+     the last half century."
+
+Professor Newcomb proceeds to give his reasons for scepticism, which are
+too technical in character to reproduce here. But I will quote the
+following further sentence from his paper:--
+
+     "The question now arises how far we are entitled to assume that the
+     period must be invariable. I reply that, perturbations aside, any
+     variation of the period is in such direct conflict with the laws of
+     dynamics that we are entitled to pronounce it impossible. But we know
+     that there are perturbations, and I do not see how one can doubt
+     that they have so acted as to increase the amplitude of the variation
+     since 1840."
+
+[Sidenote: Chandler's reply.]
+
+In other words, while recognising that there may be a way of reconciling
+one of the "minor" conclusions with theory, Professor Newcomb considers
+that in this case the other must go. Mr. Chandler's answer will speak for
+itself. It was delayed a little in order that he might present an immense
+mass of evidence in support of his conclusions, and was ultimately printed
+on August 23, 1892.
+
+     "The material utilised in the foregoing forty-five series aggregates
+     more than thirty-three thousand observations. Of these more than
+     one-third were made in the southern hemisphere, a fact which we owe
+     principally to Cordoba. It comprises the work of seventeen
+     observatories (four of them in the southern hemisphere) with
+     twenty-one different instruments, and by nine distinct methods of
+     observation. Only three of the series (XXI., XXV., and XXXV.), and
+     these among the least precise intrinsically, give results
+     contradictory of the general law developed in No. 267. This degree of
+     general harmony is indeed surprising when the evanescent character of
+     the phenomenon under investigation is considered.
+
+     "The reader has now before him the means for independent scrutiny of
+     the material on which the conclusions already drawn, and those which
+     are to follow, are based. The space taken in the printing may seem
+     unconscionable, but I hope this will be charged to the extent of the
+     evidence collected, and not to diffuseness or the presentation of
+     needless detail; for I have studiously sought to compress the form of
+     statement without omitting anything essential for searching
+     criticism. That it was important to do this is manifest, since the
+     conclusions, if established, overthrow the existing theory of the
+     earth's rotation, as I have pointed out on p. 21. I am neither
+     surprised nor disconcerted, therefore, that Professor Newcomb should
+     hesitate to accept some of these conclusions on the ground (_A. J._,
+     No. 271) that they are in such conflict with the laws of dynamics
+     that we are entitled to pronounce them impossible. He has been so
+     considerate and courteous in his treatment of my work thus far, that
+     I am sure he will not deem presumptuous the following argument in
+     rebuttal.
+
+     [Sidenote: He "put aside all teachings of theory," and "is not
+     dismayed."]
+
+     "It should be said, first, that in beginning these investigations
+     last year, I deliberately put aside all teachings of theory, because
+     it seemed to me high time that the facts should be examined by a
+     purely inductive process; that the nugatory results of all attempts
+     to detect the existence of the Eulerian period probably arose from a
+     defect of the theory itself; and that the entangled condition of the
+     whole subject required that it should be examined afresh by processes
+     unfettered by any preconceived notions whatever. The problem which I
+     therefore proposed to myself was to see whether it would not be
+     possible to lay the numerous ghosts--in the shape of numerous
+     discordant residual phenomena pertaining to determinations of
+     aberration, parallaxes, latitudes, and the like--which had heretofore
+     flitted elusively about the astronomy of precision during the
+     century; or to reduce them to tangible form by some simple consistent
+     hypothesis. It was thought that if this could be done, a study of the
+     nature of the forces, as thus indicated, by which the earth's
+     rotation is influenced, might lead to a physical explanation of them.
+
+     "Naturally, then, I am not much dismayed by the argument of conflict
+     with dynamic laws, since all that such a phrase means must refer
+     merely to the existent state of the theory at any given time. When
+     the 427-day period was propounded, it was as inconsistent with known
+     dynamic law as the variation of it now appears to be. Professor
+     Newcomb's own happy explanation has already set aside the first
+     difficulty, as it would appear, and advanced the theory by an
+     important step. Are we so sure yet of a complete knowledge of all the
+     forces at work as to exclude the chance of a _vera causa_ for the
+     second?"
+
+[Sidenote: Faraday's words.]
+
+There is a splendid ring of resolution about these words. Let us compare
+them with a notable utterance of Faraday:--
+
+     "The philosopher should be a man willing to listen to every
+     suggestion, but determined to judge for himself. He should not be
+     biassed by appearances; have no favourite hypothesis; be of no
+     school; and in doctrine have no master. He should not be a respecter
+     of persons, but of things. Truth should be his primary object. If to
+     these qualities be added industry, he may indeed hope to walk within
+     the veil of the temple of Nature."
+
+[Sidenote: Chandler's other work at this time.]
+
+[Sidenote: His ultimate satisfactory solution.]
+
+[Sidenote: Interference of two waves.]
+
+Tested by this severe standard, Mr. Chandler fails in no particular, least
+of all in that of industry. The amount of work he got through about this
+time was enormous, for besides the main line of investigation, of which we
+have only had after all a mere glimpse, he had been able to turn aside to
+discuss a subsidiary question with Professor Comstock; he had examined
+with great care some puzzling characteristics in the variability of stars;
+he computed some comet ephemerides; and he was preparing a new catalogue
+of variable stars--a piece of work involving the collection and
+arrangement of great masses of miscellaneous material. Yet within a few
+months after replying as above to Professor Newcomb's criticism, he was
+able to announce that he had found the key to the new puzzle, and that
+"theory and observation were again brought into complete accord." We will
+as before listen to the account of this new step in his own words, but a
+slight preliminary explanation may help those unaccustomed to the
+terminology. The polar motion was found to be compounded of _two_
+independent motions, both periodic, but having different periods. Now, the
+general results of such a composition are well known in several different
+branches of physics, especially in the theory of sound. If two notes of
+nearly the same pitch be struck at the same time, we hear the resultant
+sound alternately swell and die away, because the vibrations caused by the
+two notes are sometimes going in the same direction, and after an interval
+are going exactly in opposite directions. Diagrammatically we should
+represent the vibrations by two waves, as below; the upper wave goes
+through its period seven and a half times between A and D, the lower only
+six times; and it is easily seen that at A and C the waves are
+sympathetic, at B and D antipathetic. At A and C the compound vibration
+would be doubled; at B and D reduced to insensibility. The point is so
+important that perhaps a numerical illustration of it will not be
+superfluous. The waves are now represented by rows of figures as below.
+The first series recurs after every 6, the second after every 7.
+
+[Illustration: FIG. 8.]
+
+  First Wave      1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1
+  Second Wave     1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3
+                  -------------------------------------------------------------
+  Combined Effect 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5 5 5 5 5 5 6 6 6 4 4 4
+                  Great disturbance.                      Calm.
+  -----------------------------------------------------------------------------
+
+  First Wave      2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2
+  Second Wave     4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3
+                  -------------------------------------------------------------
+
+  Combined Effect 6 7 7 5 3 3 5 7 8 6 4 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5
+                                    Great disturbance.
+
+[Sidenote: Illustration from ocean travel.]
+
+Adding the two rows together, the oscillations at first reinforce one
+another and we get numbers ranging from 2 to 8 instead of from 1 to 4; but
+one wave gains on the other, until it is rising when the other is falling,
+and the numbers add up to a steady series of 5's. It will be seen that
+there are no less than seven consecutive 5's, and all the variation seems
+to have disappeared. But presently the waves separate again, and the
+period of great disturbance recurs; it will be seen that in the "combined
+effect" the numbers repeat exactly after the 42nd term. Now those
+unfamiliar with the subject may not be prepared for the addition of one
+physical wave to another, as though they were numbers, but the analogy is
+perfect. Travellers by some of the fast twin-screw steamers have had
+unpleasant occasion to notice this phenomenon, when the engineer does not
+run the two screws precisely at the same speed; there come times when the
+ship vibrates violently, separated by periods of comparative stillness.
+Instances from other walks of life may recur to the memory when once
+attention is called to the general facts; but enough has been said to
+explain the point numbered (2) in the subjoined statement. To understand
+the rest, we must remember that if the two waves are not equal in
+"amplitude," _i.e._ if the backward and forward motion is not the same in
+both, they cannot annul one another, but the greater will always
+predominate. Those interested in following the matter further should have
+no difficulty in constructing simple examples to illustrate such points.
+We will proceed to give Mr. Chandler's statements:--
+
+     [Sidenote: Chandler's final formulæ.]
+
+     "We now come upon a new line of investigation. Heretofore, as has
+     been seen, the method has been to condense the results of each series
+     of observations into the interval comprised by a single period, then
+     to determine the mean epoch of minimum and the mean range for each
+     series, and, finally, by a discussion of these quantities, to
+     establish the general character of the law of the rotation of the
+     pole. It is now requisite to analyse the observations in a different
+     way, and discover whether the deviations from the general provisional
+     law, in the last column of Table II., are real, and also in what
+     manner the variation of the period is brought about. The outcome of
+     this discussion, which is to be presented in the present paper, is
+     extremely satisfactory. The real nature of the phenomenon is most
+     distinctly revealed, and may be described as follows:--
+
+     "1. The observed variation of the latitude is the resultant curve
+     arising from two periodic fluctuations superposed upon each other.
+     The first of these, and in general the more considerable, has a
+     period of about 427 days, and a semi-amplitude of about 0".12. The
+     second has an annual period with a range variable between 0".04 and
+     0".20 during the last half-century. During the middle portion of this
+     interval, roughly characterised as between 1860 and 1880, the value
+     represented by the lower limit has prevailed, but before and after
+     those dates, the higher one. The minimum and maximum of this annual
+     component of the variation occur at the meridian of Greenwich, about
+     ten days before the vernal and autumnal equinoxes respectively, and
+     it becomes zero just before the solstices.
+
+     "2. As the resultant of these two motions, the effective variation of
+     the latitude is subject to a systematic alternation in a cycle of
+     seven years' duration, resulting from the commensurability of the two
+     terms. According as they conspire or interfere, the total range
+     varies between two-thirds of a second as a maximum, to but a few
+     hundredths of a second, generally speaking, as a minimum.
+
+     "3. In consequence of the variability of the coefficient of the
+     annual term above mentioned, the apparent average period between 1840
+     and 1855 approximated to 380 or 390 days; widely fluctuated from
+     1855 to 1865; from 1865 to about 1885 was very nearly 427 days, with
+     minor fluctuations; afterwards increased to near 440 days, and very
+     recently fell to somewhat below 400 days. The general course of these
+     fluctuations is quite faithfully represented by the law of eq. (3),
+     (No. 267), and accurately, even down to the minor oscillations of
+     individual periods, by the law of eq. (15), hereafter given, and
+     verbally interpreted above. This law also gives a similarly accurate
+     account of the corresponding oscillations in the amplitude. The
+     closeness of the accordance between observation and the numerical
+     theory, in both particulars, places the reality of the law beyond
+     reasonable doubt."
+
+Those who cannot follow the details of the above statement will
+nevertheless catch the general purport--that the difficulties felt by
+Professor Newcomb have been surmounted; and this is made clearer by a
+later extract:--
+
+     "A very important conclusion necessarily follows from the agreement
+     of the values of the 427-day term, deduced from the intervals between
+     the consecutive values of T in Table XII., namely, that there has
+     been no discontinuity in the revolution, such as Professor Newcomb
+     regarded as so probable that he doubted the possibility of drawing
+     any conclusions from the comparison of observations before and after
+     1860 (_A. J._, 271, p. 50).
+
+     [Sidenote: Theory must go, if it will not fit observation.]
+
+     "The present investigation demonstrates that the way out of the
+     apparently irreconcilable contradiction of theory and observation in
+     this matter does not lie in the direction of discrediting the
+     observations, as he is inclined to do. On the contrary, the result is
+     a beautiful vindication of the trustworthiness of the latter, and, at
+     the same time, of the theory that demands an invariable rate of
+     motion; providing a perfectly fitting key to the riddle by showing
+     that another cause has intervened to produce the variability of the
+     period. I feel confident that Professor Newcomb will agree with the
+     reality of the explanation here set forth, and will reconsider his
+     view that the perturbations in the position of the Pole must be of
+     the nature of chance accumulations of motion, a view which he then
+     considered necessary to the maintenance of the constancy in the
+     period of latitude-variation."
+
+[Sidenote: The final paper.]
+
+The paper from which these words are taken appeared on November 4, 1892.
+The next paper on the main theme did not appear till a year later, though
+much work was being done in the meantime on the constant of aberration and
+other matters arising immediately after the discovery. On November 14,
+1893, Mr. Chandler winds up the series of eight papers "On the Variation
+of Latitude," which he had commenced just two years before. His work was
+by no means done; rather was it only beginning, for the torch he had lit
+illuminated many dark corners. But he rightly regarded his discovery as
+now so firmly established that the series of papers dealing with it as
+still under consideration might be terminated. In this final paper he
+first devotes the most careful attention to one point of detail. He had
+shown earlier in the series that the North Pole must be revolving from
+West to East, and not from East to West; but this was when the motion was
+supposed to be simple and not complex, and it was necessary to re-examine
+the question of direction for each of the components. After establishing
+conclusively that the original direction holds for each of the components,
+he almost apologises for the trouble he has taken, thus:--
+
+     "It is therefore proved beyond reasonable doubt that the directions
+     of the rotations is from West to East in both elements; whence the
+     general form of the equation for the variation of latitude adopted in
+     _A. J._, 284, p. 154, eq. (19). It may be thought that too much pains
+     have been here bestowed upon a point which might be trusted to theory
+     to decide. I cannot think so. One of the most salient results of
+     these articles has been the proof of the fact that theory has been a
+     blind guide with regard to the velocity of the Polar rotation,
+     obscuring truth and misleading investigators for a half a century.
+     And even if we were certain, which we are not, that the fourteen
+     months' term is the Eulerian period in a modified form. It would
+     still be necessary to settle by observation the direction of the
+     annual motion, with regard to which theory is powerless to inform us.
+     To save repetition of argument, I must refer to the statement in _A.
+     J._, 273, pp. 68, 70, of the principles adopted in beginning these
+     inquiries in 1891."
+
+Finally, he answers one of the few objectors of eminence who still
+lingered, the great French physicist Cornu:--
+
+     [Sidenote: Cornu answered.]
+
+     "The ground is now cleared for examination of the only topic
+     remaining to be covered, to establish, upon the foundation of fact,
+     every point in the present theory of these remarkable movements of
+     the earth's axis. This is the question of the possibility that these
+     movements are not real, but merely misinterpretations of the observed
+     phenomena; being in whole or in part an illusory effect of
+     instrumental error due to the influence of temperature. Such a
+     possibility has been a nightmare in practical astronomy from the
+     first, frightening us in every series of unexplained residuals,
+     brought to light continually in nearly all attempts at delicate
+     instrumental research. A source of danger so subtile could not fail
+     to be ever present in the mind of every astronomer and physicist who
+     has given even a superficial attention to the question of the
+     latitude variations, and there is no doubt that some are even now
+     thus deterred from accepting these variations as proved facts.
+     Perhaps the most explicit and forcible statement of the doubts that
+     may arise on this subject has been given very recently by Mr. Cornu.
+     The views of so distinguished a physicist, and of others who are
+     inclined to agree with him, call for careful attention, and cannot be
+     neglected in the present closing argument upon the theory presented
+     in these articles. It is unnecessary, for the purpose of disposing of
+     objections of the sort raised by Cornu, to insist that it is not
+     sufficient to show that the observed variations, attributed to the
+     unsteadiness of the Earth's Pole, are near the limit of precision
+     attainable in linear differential measures, and in the indication of
+     the direction of gravity by means of the air bubble of the level; or
+     to show that there are known variations in divided circles and in
+     levels, dependent on temperature and seasons. Nor need we require of
+     objectors the difficult, although essential, task--which they have
+     not distinctly attempted--of showing that these errors are not
+     eliminated, as they appear to be, by the modes in which astronomers
+     use their instruments. Neither need we even urge the fact that a
+     large portion of the data which have been utilised in the present
+     researches on the latitude were derived by methods which dispense
+     with levels, or with circles, a part of them indeed with both, and
+     yet that the results of all are harmonious. On the contrary, let us
+     admit, although merely for argument's sake, that all the known means
+     of determining the direction of gravity--including the plumb-line,
+     the level, and a fluid at rest, whether used for a reflecting surface
+     or as a support for a floating instrument--are subject to a common
+     law of periodical error which vitiates the result of astronomical
+     observation, obtained by whatever methods, and in precisely the same
+     manner. Now, the observed law of latitude variation includes two
+     terms, with periods of fourteen and twelve months respectively. Since
+     the phases of the first term are repeated at intervals of two months
+     in successive years, and hence in a series of years come into all
+     possible relations to conditions of temperature dependent on season,
+     the argument against the reality of this term, on this ground,
+     absolutely fails, and needs no further notice. As to the second, or
+     annual term, while the phases, as observed in any given longitude,
+     are indeed synchronical with the seasons, they are not so as regards
+     different longitudes. If, therefore, the times of any given phase, as
+     observed in the same latitude, but in successively increasing
+     longitudes, occurred at the same date in all of them, there would be
+     a fatal presumption against the existence of an annual period in the
+     polar motion. If, on the contrary, they occur at times successively
+     corresponding to the differences of longitude, the presumption is
+     equally fatal to the hypothesis that they can possibly be due to
+     temperature variation as affecting instrumental measurement. But the
+     facts given in the foregoing section correspond most distinctly to
+     the latter condition. Therefore, unless additional facts can be
+     brought to disprove successively these observed results, we may
+     dismiss for ever the bugbear which has undoubtedly led many to
+     distrust the reality of the annual component of the
+     latitude-variation, while they admit the existence of the 427-day
+     term."
+
+[Sidenote: Consequences of the discovery.]
+
+[Sidenote: Suspected observers acquitted.]
+
+At this point we must leave the fascinating account of the manner in which
+this great discovery was established, in the teeth of opposition such as
+might have dismayed and dissuaded a less clear-sighted or courageous man.
+It is my purpose to lay more stress upon the method of making the
+discovery than upon its results; but we may afford a brief glance at some
+of the consequences which have already begun to flow from this step in
+advance. Some of them have indeed already come before us, especially that
+large class represented by the explanation of anomalies in series of
+observations which had been put aside as inexplicable. We have seen how
+the observations made in Russia, or in Washington, or at Greenwich, in all
+of which there was some puzzling error, were immediately straightened out
+when Chandler applied his new rule to them. We in England have special
+cause to be grateful to Chandler; not only has he demonstrated more
+clearly than ever the greatness of Bradley, but he has rehabilitated Pond,
+the Astronomer Royal of the beginning of the nineteenth century; showing
+that his observations, which had been condemned as in some way erroneous,
+were really far more accurate than might have been expected; and further
+he has shown that the beautiful instrument designed by Airy, and called
+the Reflex Zenith Tube, which seemed to have unaccountably failed in the
+purpose for which it was designed, was really all the time accumulating
+observations of this new phenomenon, the Variation of Latitude. Instead of
+Airy having failed in his design, he had in Chandler's words "builded
+better than he knew."
+
+[Sidenote: Constant of Aberration improved.]
+
+Secondly, there is the modifying influence of this new phenomenon on other
+phenomena already known, such, for instance, as that of "aberration." We
+saw in the third chapter how Bradley discovered this effect of the
+velocity of light, and how the measure of it is obtained by comparing the
+velocity of light with that of the earth. This comparison can be effected
+in a variety of ways, and we should expect all the results to agree within
+certain limits; but this agreement was not obtained, and Chandler has been
+able to show one reason why, and to remove some of the more troublesome
+differences. It is impossible to give here an idea of the far-reaching
+consequences which such work as this may have; so long as there are
+differences of this kind we cannot trust any part of the chain of
+evidence, and there is in prospect the enormous labour of examining each
+separate link until the error is found. The velocity of light, for
+instance, may be measured by a terrestrial experiment; was there anything
+wrong in the apparatus? The velocity of the earth in its journey round the
+sun depends directly upon the distance of the sun: have we measured this
+distance wrongly, and if so what was the error in the observations made?
+These are some of the questions which may arise so long as the values for
+the _Constant of Aberration_ are still conflicting; but it requires
+considerable knowledge of astronomy to appreciate them fully.
+
+[Sidenote: Latitude Variation Tide.]
+
+[Sidenote: Earthquakes.]
+
+Another example will, perhaps, be of more general interest. If the axis of
+the earth is executing small oscillations of this kind, there should be an
+effect upon the tides; the liquid ocean should feel the wobble of the
+earth's axis in some way; and an examination of tidal registers showed
+that there was in fact a distinct effect. It may cause some amusement when
+I say that the rise and fall are only a few inches in any case; but they
+are unmistakable evidences that the earth is not spinning smoothly, but
+has this kind of unbalanced vibration, which I have compared to the
+vibrations felt by passengers on an imperfectly engineered twin-screw
+steamer. A more sensational effect is that apparently earthquakes are more
+numerous at the time when the vibration is greatest. We remarked that the
+vibration waxes and wanes, much as that of the steamer waxes and wanes if
+the twin-screws are not running quite together. Now the passengers on the
+steamer would be prepared to find that breakages would be more numerous
+during the times of vigorous oscillation; and it seems probable that in a
+similar way the little cracks of the earth's skin which we call great
+earthquakes are more numerous when these unbalanced vibrations are at
+their maximum; that is to say, about once every seven years. This result
+is scarcely yet worthy of complete confidence, for our observations of
+earthquakes have only very recently been reduced to proper order; but if
+it should turn out to be true, it is scarcely necessary to add any words
+of mine to demonstrate the importance of this rather unexpected result of
+the Latitude Variation.
+
+[Sidenote: The Kimura phenomenon.]
+
+Finally I will mention another phenomenon which seems to be at present
+more of a curiosity than anything else, but which may lead to some future
+great discovery. It is the outcome of observations which have been
+recently made to watch these motions of the Pole; for although there seems
+good reason to accept Mr. Chandler's laws of variation as accurate, it is
+necessary to establish their accuracy and complete the details by making
+observations for some time yet to come; and there could be no better proof
+of this necessity than the discovery recently made by Mr. Kimura, one of
+those engaged in this watch of the Pole in Japan. Perhaps I can give the
+best idea of it by mentioning one possible explanation, which, however, I
+must caution you may not be by any means the right one. We are accustomed
+to think of this great earth as being sufficiently constant in shape; if
+asked, for instance, whether its centre of gravity remains constantly in
+the same place inside it, we should almost certainly answer in the
+affirmative, just as only twenty years ago we thought that the North Pole
+remained in the same place. But it seems possible that the centre of
+gravity moves a few feet backwards and forwards each year--this would at
+any rate explain certain curious features in the observations to which Mr.
+Kimura has drawn attention. Whatever the explanation of them may be, or to
+settle whether this explanation is correct, we want more observations,
+especially observations in the Southern Hemisphere; and it is a project
+under consideration by astronomers at the present moment whether three
+stations can be established in the Southern Hemisphere for the further
+observation of this curious phenomenon. The question resolves itself
+chiefly into a question of money; indeed, most astronomical projects do
+ultimately resolve themselves into questions of money; and I fear the
+world looks upon scientific men as insatiable in this respect. One can
+only hope that on the whole the money is expended so as to give a
+satisfactory return. In this instance I have no hesitation in saying that
+an immediate return of value for a comparatively modest expenditure is
+practically certain, if only in some way we can get the means of making
+the observations.
+
+It would be natural, at the conclusion of this brief review of some types
+of astronomical discovery, to summarise the lessons indicated: but there
+is the important difficulty that there appear to be none. It has been
+pointed out as we proceeded that what seemed to be a safe deduction from
+one piece of history has been flatly contradicted by another; no sooner
+have we learnt that important results may be obtained by pursuing steadily
+a line of work in spite of the fact that it seems to have become tedious
+and unprofitable (as in the search for minor planets) than we are
+confronted with the possibility that by such simple devotion to the day's
+work we may be losing a great opportunity, as Challis did. We can scarcely
+go wrong in following up the study of residual phenomena in the wake of
+Bradley; but there is the important difficulty that we may be wholly
+unable to find a clue for the arrangement of our residuals, as is at
+present largely the case in meteorology. And, in general, human
+expectations are likely to be quite misleading, as has been shown in the
+last two chapters; the discoveries we desire may lie in the direction
+precisely opposite to that indicated by the best opinion at present
+available. There is no royal road to discovery, and though this statement
+may meet with such ready acceptance that it seems scarcely worth making,
+it is hoped that there may be sufficient of interest in the illustrations
+of its truth.
+
+The one positive conclusion which we may derive from the examples studied
+is that discoveries are seldom made without both hard work and conspicuous
+ability. A new planet, even as large as Uranus, does not reveal itself to
+a passive observer: thirteen times it may appear to such a one without
+fear of detection, until at last it encounters an alert Herschel, who
+suspects, tests, and verifies, and even then announces a comet--so little
+did he realise the whole truth. Fifteen years of unrequited labour before
+Astræa was found, nineteen years of observation before the discovery of
+nutation could be announced: how seldom do these years of toil present
+themselves to our imaginations when we glibly say that "Bradley discovered
+nutation," or "Hencke discovered Astræa"! That the necessary labour is so
+often forgotten must be my excuse for recalling attention to it somewhat
+persistently in these examples.
+
+But beyond the fact that he must work hard, it would seem as though there
+were little of value to tell the would-be discoverer. The situation has
+been well summarised by Jevons in his chapter on Induction in the
+"Principles of Science;" and his words will form a fitting conclusion to
+these chapters:--
+
+     "It would seem as if the mind of the great discoverer must combine
+     contradictory attributes. He must be fertile in theories and
+     hypotheses, and yet full of facts and precise results of experience.
+     He must entertain the feeblest analogies, and the merest guesses at
+     truth, and yet he must hold them as worthless till they are verified
+     in experiment. When there are any grounds of probability he must hold
+     tenaciously to an old opinion, and yet he must be prepared at any
+     moment to relinquish it when a clearly contradictory fact is
+     encountered."
+
+
+
+
+INDEX
+
+
+  Aberration, 105-109, 111, 112, 117, 118, 185, 188, 192, 214, 215
+
+  Accidental discovery, 15, 73, 121-154
+
+  Adams, 12, 45-85;
+    resolution, 55
+
+  Airy, 32, 40-85, 214
+
+  Algiers, 130
+
+  Alleghenia, 26
+
+  Almucantar, 180, 181
+
+  Alphabet used for planets, 27
+
+  Anderson, Dr. T. C., 8, 142, 143, 144, 146
+
+  Anthelm, 142
+
+  Apollo, 9
+
+  Argon, 109
+
+  Ascension, 34
+
+  Assumption, forgotten, 196
+
+  Astræa, 22, 23, 219
+
+  Astrographic chart, 122, 125, 130
+
+  _Astronomical Journal_, 177-217
+
+  _Astronomische Nachrichten_, 52, 158
+
+  Astrophil, 143
+
+  Auwers, 142
+
+
+  Ball, Sir R., 24
+
+  Balliol College, 87
+
+  Banks, Sir J., 9
+
+  Barnard, E. E., 146, 220
+
+  Berlin, 181, 183, 184, 188, 193
+
+  Berlin star-map, 45, 66, 83, 124
+
+  Bessel, 192
+
+  Bettina, 26, 27
+
+  Birmingham, 142
+
+  "Black Drop" (in transit of Venus), 30
+
+  Bliss, 114
+
+  Board of Visitors of Greenwich Observatory, 63
+
+  Bode, 11, 14, 15, 22
+
+  Bode's Law, 12, 13, 38, 43, 45, 52, 72, 76, 77, 84
+
+  Bourdeaux, 130
+
+  Bouvard, 39, 40, 42, 48, 49, 50, 61
+
+  Bradley, 39, 86-120, 188-192, 213, 214, 218, 219
+
+  Bradley, John, 115
+
+  Bremen, 20
+
+  Bridstow, 87, 88, 94
+
+  Briggs, 119
+
+  Brinkley, 192
+
+  British Association, 63
+
+  Brünnow, 193
+
+
+  California, 26
+
+  Cambridge (Mass.), 180, 184, 188
+
+  Cambridge Observatory, 23, 42, 49, 52, 63, 65, 66, 135, 193
+
+  Cambridge University, 68-71, 114
+
+  Cape Observatory, 123, 124, 130
+
+  Cards, 11
+
+  Cassini II., 156
+
+  Catania, 130
+
+  Ceres, 14-22
+
+  Chacornac, 124
+
+  Challis, 49-54, 63-68, 71, 85, 218
+
+  Chandler, S. C., 118, 177-217
+
+  Chapman's "Homer," 2
+
+  Chicago, 157
+
+  Chromosphere, 170
+
+  Clarke, C. C., 2
+
+  Coelostat, 94
+
+  Columbus, 63
+
+  Comet, 4-8, 88, 108, 117, 123, 125
+
+  Commission, planetary, 27
+
+  Common, A. A., 124, 127
+
+  _Compte Rendu_, 62
+
+  Comstock, 202
+
+  Conference, Astrographic, 125-136
+
+  Copernicus, 79, 95
+
+  Cordoba, 130, 199
+
+  Cornu, 210-213
+
+  Corona, 170-175
+
+  _Cosmos_ (Humboldt's), 160
+
+
+  Delambre, 157
+
+  Deviation of Pole, 187
+
+  Disc of Neptune, 44, 64, 79
+
+  Disc of Uranus, 4-7
+
+  Dorpat, 192
+
+  Doublet (photographic), 127-129
+
+  Draconis, [gamma], 96-104
+
+  Draconis, [beta], 193
+
+  Driessen, 23
+
+  Dry plate, 122
+
+  Dublin, 192
+
+
+  Earthquakes, 215
+
+  Earth's Pole, 177-217
+
+  Eccentricity, 41, 83
+
+  Eclipses, 170-176
+
+  Edinburgh, 143
+
+  Eduarda, 26
+
+  Egeria, 22
+
+  Endymion, 25
+
+  Eriphyla, 26
+
+  Eros, 25, 26, 28, 35, 37, 68
+
+  Eulerian, 200, 209
+
+  Evelyn, 26
+
+  Exposure, times of, 122, 131
+
+
+  Faculæ, 170
+
+  Faraday, 201
+
+  Flamsteed, 39, 53, 115
+
+  Fleming, Mrs., 142
+
+  Flora, 22
+
+  Foulkes, Martin, 94
+
+  French Academy, 43, 51, 62
+
+
+  Galileo, 95, 163
+
+  Galle, 44, 45, 47, 66, 67, 83
+
+  Gasparis, 22
+
+  Gauge (railways), 56
+
+  Gauss, 17-20
+
+  Geminorum, H., 4
+
+  George III., 8, 10
+
+  "Georgian," 11
+
+  _Georgium Sidus_, 8, 10, 11
+
+  Gill, Sir D., 32, 34, 35, 123
+
+  Gilliss, 32
+
+  Gotha, 20
+
+  Gould, 32
+
+  Graham, 22, 23
+
+  Gravitation, law of, 38, 45, 59, 84, 105
+
+  Greaves, 119
+
+  Greenwich Observatory, 48-64, 88, 89, 114-117, 130, 160-169,
+      182, 192, 193, 206, 213
+
+  Gregory, 93, 119
+
+
+  Hale, G. E., 170, 171
+
+  Hall, A., 184, 185
+
+  Halley, 88-92, 108, 112-116, 119
+
+  Hansen, 41, 59
+
+  Harkness, 184
+
+  Hartwig, 142
+
+  Harvard College Observatory, 128, 142, 144, 145
+
+  Hebe, 22
+
+  Hegel, 15
+
+  Heidelberg, 145
+
+  Heliometer, 32, 34
+
+  Helium, 109
+
+  Helsingfors, 130
+
+  Hencke, 22, 23, 64, 153, 219
+
+  Henry brothers, 124-129
+
+  Herschel, Sir John, 63, 75, 83
+
+  Herschel, Sir William, 2-11, 39, 44, 82, 219
+
+  Herschel (Uranus), 11, 12
+
+  Hind, 22, 23, 25, 142
+
+  Hooke, 96, 97
+
+  Hubbard, 184
+
+  Humboldt, 160
+
+  Hussey, Rev. T. J., 40, 42
+
+  Hygeia, 22
+
+
+  Ilmata, 26
+
+  Industria, 26
+
+  Ingeborg, 26
+
+  Instruments at Greenwich, 114-116
+
+  Iris, 22, 23, 32, 35
+
+
+  Janson, 142
+
+  Jevons, 219
+
+  Johnson, M., 156, 160
+
+  Juno, 9, 21, 22
+
+  Jupiter, 9, 28, 43, 49, 50, 61;
+    satellites, 92, 117
+
+
+  Keats, 1-3, 7, 8
+
+  Keill, 94, 112, 119, 156
+
+  Kelvin, Lord, 196, 197
+
+  Kepler, 95, 142
+
+  Kew, 95, 96, 188, 190
+
+  Kiel, 141
+
+  Kimura, 216
+
+  Königsberg, 192
+
+  Küstner, 118, 181, 183
+
+
+  Lalande, 7, 11, 107, 157
+
+  Lameia, 26
+
+  Laplace, 61
+
+  La Plata, 130
+
+  Latitude variation, 99, 100, 117, 118, 177-217
+
+  Lemonnier, 39, 53, 157
+
+  Le Verrier, 12, 43-85
+
+  Libussa, 26
+
+  Lick Observatory, 152
+
+  _Liouville's Journal_, 73
+
+  Lisbon, longitude of, 92
+
+  London, 23, 25, 96
+
+  Long, 157
+
+  Longitude, 92, 117
+
+  Lowth, Bishop, 119
+
+  Lyrae, [alpha], 184, 196
+
+
+  Macclesfield, Earl of, 94, 113
+
+  Mädler, 192
+
+  Magnetic observations, 161, 164, 174
+
+  Magnitude equation, 135
+
+  Markree, 23
+
+  Mars, 9, 28, 32, 34, 35, 91
+
+  Mayer, 39
+
+  Measurement of plates, 132-135
+
+  _Mécanique Céleste_, 61
+
+  Melbourne, 130, 193
+
+  Memorandum (Adams), 55
+
+  Mercury, 9
+
+  Messier, 7
+
+  Meteorites, 59
+
+  Meteors (November), 60
+
+  Metis, 22, 23
+
+  Micrometer, 5, 133
+
+  Milky Way, 125
+
+  Minerva, 9
+
+  Minor planets, 13-28
+
+  Minor planets tables, 22, 24, 26
+
+  Mistakes, 71-83
+
+  Molyneux, Samuel, 94-96, 101, 104
+
+  Monte Video, 130
+
+  Moon, tables of, 117
+
+
+  Names of minor planets, 22-28
+
+  Nasmyth, 162
+
+  "Nautical Almanac," 11
+
+  Nebula, 124, 146-152
+
+  Neptune, 11, 12, 38-85, 124
+
+  New College Lane, 112
+
+  Newcomb, Simon, 81, 183, 184, 195-202, 207, 208
+
+  New stars, 121, 140-154
+
+  Newton, 38, 84, 90-95, 105, 113
+
+  New York, longitude, 92
+
+  Ninina, 26
+
+  Northleach, 87
+
+  Northumberland, 65
+
+  Nova Geminorum, 141, 145, 146
+
+  Nova Persei, 143, 146-152
+
+  Nutation, 99, 100, 110, 115, 117, 118, 188, 219
+
+
+  _Observatory_ (magazine), 26
+
+  Ocllo, 26
+
+  Olbers, 20-22
+
+  Olympic games, 119
+
+  Oriani, 15
+
+  Ornamenta, 26
+
+  Oxford University, 87-89, 94, 105-119
+
+  Oxford University Observatory, 121, 130, 132, 136, 142, 145, 154
+
+
+  Palermo, Observatory of, 18
+
+  Palisa, 26
+
+  Pallas, 9, 21, 22
+
+  Parallax, 34, 91, 95-98, 109, 185
+
+  Paris, 130
+
+  Parkhurst, J. A., 145
+
+  Parthenope, 22
+
+  Peirce, 73, 80-83
+
+  Pendulum, 117
+
+  Perseus, 8, 143
+
+  Personal equation, 31, 134, 135, 185
+
+  Perth, 130
+
+  Perturbations of Uranus, 12, 42, 51, 54, 55, 61, 75
+
+  Peters, 188, 192
+
+  Phaëtusa, 26
+
+  Philosopher, 201, 219
+
+  _Philosophical Transactions_, 3, 4, 9
+
+  Photographica, 26
+
+  Photographic methods, 24, 33, 36, 121-139;
+    lenses, 125, 126
+
+  Photographs of sun, 163, 170-173
+
+  Piazzi, 13-18, 22
+
+  Pickering, E. C., 128, 144
+
+  Pittsburghia, 26
+
+  Plana, 61
+
+  Planetary distances, 13;
+    commission, 27;
+    numbering, 27
+
+  Planets by photography, 24
+
+  Pole Star (_Polaris_), 177, 178, 192, 193
+
+  Pond, 192, 213
+
+  Potsdam, 130, 181
+
+  Pound, Mrs., 104, 110-112
+
+  Pound, Rev. James, 89-94, 104, 115
+
+  Prague, 181
+
+  Precession, 96, 178
+
+  Prymno, 26
+
+  Puiseux, 32
+
+  Pulfrich, 154
+
+  Pulkowa, 181-188, 213
+
+
+  Quadrants at Greenwich, 116
+
+
+  Radium, 175
+
+  Radius vector, 52-58, 60-62, 79, 83
+
+  Rayleigh, Lord, 109
+
+  Records before discovery, 144
+
+  Reflector, 93, 127, 128
+
+  Reflex zenith tube, 192, 214
+
+  Refraction, 96, 101-103, 117
+
+  Refractor, 93, 128
+
+  Réseau, 133
+
+  Residual phenomena, 108-110, 118, 120, 218
+
+  Rigaud, S. P., 87, 115, 119
+
+  Rome, 130
+
+  Rothschild, 27
+
+  Royal Astronomical Society, 40, 47, 68, 74, 124, 155, 157
+
+  Royal Society, 4, 9, 10, 92, 94
+
+
+  Sampson, R. A., 74-76, 84
+
+  San Fernando, 130
+
+  Santiago, 130
+
+  Sappho, 32, 35
+
+  Saturn, 9, 43, 61, 149, 150
+
+  Savile, Sir H., 119
+
+  Savilian professorship, 87-94, 108-119
+
+  Schmidt, Julius, 142, 160
+
+  Schuster, A., 169
+
+  Schwabe, 155-163, 176, 177
+
+  Sheldonian Theatre, 119
+
+  Sherbourn, 87
+
+  Solar eclipse, 26, 170-176
+
+  Spectro-heliograph, 170, 171
+
+  Star-maps, 45, 65, 83, 124
+
+  "Star-trap," 24
+
+  Stereo-comparator, 154
+
+  Stone, E. J., 32
+
+  Struve, 184, 188, 192
+
+  Sun's distance, 28-37
+
+  Sun-spots, 155-176
+
+  Sydney Observatory, 130
+
+
+  Tacubaya Observatory, 130
+
+  Telescopes, 92, 124-129
+
+  Thames River, 105
+
+  Themistocles, 119
+
+  _Theoria Motus_, 17
+
+  Theory and observation, 208
+
+  Thomson, Sir W., 196, 197
+
+  Tides, 215
+
+  Titius, 13
+
+  Toulouse Observatory, 130
+
+  Tycho Brahé, 95, 140, 142
+
+
+  Uranus, 2-14, 25, 38-85, 144, 219
+
+
+  Variable stars, 140
+
+  Variation of latitude, 99, 100, 117, 118, 177-217
+
+  Venus, 9, 79;
+    diameter of, 92;
+    transit of, 28-32, 34
+
+  Vesta, 21, 22
+
+  Victoria, 22, 25, 32, 35
+
+  Von Zach, 20
+
+
+  Wallace, 119
+
+  Wansted, 88-94, 104, 110, 115, 188, 190
+
+  Ward, 119
+
+  Washington Observatory, 184-188, 193, 196, 213
+
+  Weather and sun-spots, 161, 167-169
+
+  Weyer, 193
+
+  Whiteside, 112
+
+  Williams, Mrs. E., 110, 111
+
+  Wind-vane, revolutions, 167-169
+
+  Winnecke, 32
+
+  Wolf, Dr. Max, 145
+
+  Wolf, Rudolf, 163
+
+  Wren, Sir C., 119
+
+
+  Yerkes Observatory, 145, 146, 152, 157, 170, 176
+
+
+  Zeiss, 154
+
+  Zodiac, 64, 124, 137
+
+
+THE END
+
+
+Printed by BALLANTYNE, HANSON & CO.
+
+Edinburgh & London
+
+
+
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+_LONDON: EDWARD ARNOLD, 41 & 43 MADDOX STREET, W._
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+
+
+Footnotes:
+
+[1] The inferior planet Venus comes closer, but is not visible throughout
+the night.
+
+[2] The facts were collected with great care and ability by S. P. Rigaud,
+and published by the Oxford University Press in 1832 as "Miscellaneous
+Works and Correspondence of the Rev. James Bradley."
+
+[3] Since the light must travel from the sun to Saturn _and back again to
+the earth_, the interval would be more nearly 150 minutes.
+
+[4] Monthly Notices of the Royal Astronomical Society, vol. xvii. p. 126.
+
+[5] This should be Cambridge, _Mass._
+
+[6] The distances do not represent the _total_ displacement, but only the
+displacement towards Washington in one case and towards Pulkowa in the
+other.
+
+
+
+
+Transcriber's Notes:
+
+Passages in italics are indicated by _italics_.
+
+Passages in bold are indicated by =bold=.
+
+Subscripted letters are indicated by {subscript}.
+
+The original text includes the Greek a, b, and g. For this text version
+these letters are presented as [alpha], [beta], and [gamma].
+
+All side notes belonging to a single paragraph have been moved to the
+beginning of the paragraph.
+
+Sidenotes split across pages have been joined together.
+
+Punctuation has been corrected without note.
+
+Corrections in the "Errata" have been made in this text version.
+
+The following misprints have been corrected:
+  "Hencke'" corrected to "Hencke's" (page 23 sidenote)
+  "annouced" corrected to "announced" (page 45 sidenote)
+  "are are" corrected to "are" (page 119)
+  "Konigsberg" corrected to "Königsberg" (Index)
+
+Other than the corrections listed above, inconsistencies in spelling and
+hyphenation have been retained from the original.
+
+
+
+
+
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+The Project Gutenberg EBook of Astronomical Discovery, by Herbert Hall Turner
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
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+Title: Astronomical Discovery
+
+Author: Herbert Hall Turner
+
+Release Date: August 3, 2010 [EBook #33337]
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+Language: English
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+Character set encoding: ISO-8859-1
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+*** START OF THIS PROJECT GUTENBERG EBOOK ASTRONOMICAL DISCOVERY ***
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+
+
+Produced by Juliet Sutherland, Joseph Myers and the Online
+Distributed Proofreading Team at http://www.pgdp.net.
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+
+
+
+<h1>ASTRONOMICAL DISCOVERY</h1>
+<p>&nbsp;</p><p><a name="front" id="front"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/i002tmb.jpg" alt="" /><br />
+<a href="images/i002.jpg"><small>Larger Image</small></a></div>
+<p class="center"><span class="smcap">Astronomers Royal.</span></p>
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p>
+
+<h1>ASTRONOMICAL<br />DISCOVERY</h1>
+<p>&nbsp;</p>
+<h4>BY</h4>
+<h3>HERBERT HALL TURNER, D.Sc., F.R.S.</h3>
+<p class="center"><span class="smcaplc">SAVILIAN PROFESSOR OF ASTRONOMY IN THE<br />UNIVERSITY OF OXFORD</span></p>
+<p>&nbsp;</p>
+<p class="center"><i>WITH PLATES</i></p>
+<p>&nbsp;</p>
+<p class="center">LONDON<br />EDWARD ARNOLD<br />41 &amp; 43 MADDOX STREET, W.<br />1904<br />
+<br />(All rights reserved)</p>
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p>
+
+<p class="center"><span class="smcaplc">TO</span><br />EDWARD EMERSON BARNARD<br />ASTRONOMICAL DISCOVERER<br />
+<span class="smcaplc">THESE PAGES ARE INSCRIBED IN MEMORY OF<br />NEVER-TO-BE-FORGOTTEN DAYS SPENT WITH HIM AT THE</span><br />
+YERKES OBSERVATORY<br /><span class="smcaplc">OF</span><br />THE UNIVERSITY OF CHICAGO</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_vii" id="Page_vii">[Pg vii]</a></span></p>
+<h2>PREFACE</h2>
+
+<p>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
+&#8220;chance&#8221; 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 &#8220;luck&#8221; in most discoveries. &#8220;The biggest
+strokes are all luck,&#8221; writes a brother astronomer who had done me the
+honour to glance at a few pages, &#8220;but a man must not drop his catches.
+Have you ever read Montaigne&#8217;s essay &#8216;Of Glory&#8217;? 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.&#8221; Indeed even in cases
+such as those in Chapters V. and VI., where a discovery is made by turning
+over a heap of rubbish&mdash;declared such by experts and abandoned
+accordingly&mdash;we instinctively feel that the finding of something valuable
+was especially &#8220;fortunate.&#8221; We should scarcely recommend such waste
+material as the best hunting ground for gems.</p>
+
+<p><span class="pagenum"><a name="Page_viii" id="Page_viii">[Pg viii]</a></span>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.</p>
+
+<p>In a portion of the first chapter it will be obvious that I am indebted to
+Miss Clerke&#8217;s &#8220;History of Astronomy in the Nineteenth Century&#8221;; in the
+second to Professor R. A. Sampson&#8217;s Memoir on the Adams MSS.; in the third
+to Rigaud&#8217;s &#8220;Life of Bradley.&#8221; 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 <i>The Observatory</i>, the Cambridge
+University Press, the Harvard College Observatory, the Yerkes Observatory,
+and the living representatives of two portraits.</p>
+
+<p class="right">H. H. TURNER.</p>
+
+<p><span class="smcap">University Observatory, Oxford</span>,<br />
+<span style="margin-left: 4em;"><i>November</i> 9, 1904.</span></p>
+
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_ix" id="Page_ix">[Pg ix]</a></span></p>
+<h2>CONTENTS</h2>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="contents">
+<tr><td>&nbsp;</td><td><span class="spacer">&nbsp;</span></td><td align="right"><span class="smcaplc">PAGE</span></td></tr>
+<tr><td><a href="#CHAPTER_I">CHAPTER I</a><br /><span style="margin-left: 2em;"><span class="smcap">Uranus and Eros</span></span></td>
+    <td>&nbsp;</td><td align="right"><a href="#Page_1">1</a></td></tr>
+<tr><td><a href="#CHAPTER_II">CHAPTER II</a><br /><span style="margin-left: 2em;"><span class="smcap">The Discovery of Neptune</span></span></td>
+    <td>&nbsp;</td><td align="right"><a href="#Page_38">38</a></td></tr>
+<tr><td><a href="#CHAPTER_III">CHAPTER III</a><br /><span style="margin-left: 2em;"><span class="smcap">Bradley&#8217;s Discoveries of the Aberration of Light</span></span><br /><span style="margin-left: 2em;"><span class="smcap">and of the Nutation of the Earth&#8217;s Axis</span></span></td>
+    <td>&nbsp;</td><td align="right"><a href="#Page_86">86</a></td></tr>
+<tr><td><a href="#CHAPTER_IV">CHAPTER IV</a><br /><span style="margin-left: 2em;"><span class="smcap">Accidental Discoveries</span></span></td>
+    <td>&nbsp;</td><td align="right"><a href="#Page_121">121</a></td></tr>
+    <tr><td><a href="#CHAPTER_V">CHAPTER V</a><br /><span style="margin-left: 2em;"><span class="smcap">Schwabe and the Sun-Spot Period</span></span></td>
+    <td>&nbsp;</td><td align="right"><a href="#Page_155">155</a></td></tr>
+<tr><td><a href="#CHAPTER_VI">CHAPTER VI</a><br /><span style="margin-left: 2em;"><span class="smcap">The Variation of Latitude</span></span></td>
+    <td>&nbsp;</td><td align="right"><a href="#Page_177">177</a></td></tr>
+<tr><td>INDEX</td><td>&nbsp;</td><td align="right"><a href="#Page_221">221</a></td></tr></table>
+
+<p><span class="pagenum"><a name="Page_x" id="Page_x">[Pg x]</a></span></p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_xi" id="Page_xi">[Pg xi]</a></span></p>
+<h2>LIST OF PLATES</h2>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="plates">
+<tr><td align="right"><span class="smcaplc">PLATE</span></td></tr>
+<tr><td align="right">I.</td><td><span class="smcap">Portrait of J. C. Adams</span></td><td><span class="spacer">&nbsp;</span></td><td><i>To face</i></td><td><i>page</i></td><td align="right"><a href="#Page_23">22</a></td></tr>
+<tr><td align="right">II.</td><td><span class="smcap">Portrait of A. Graham</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_23">22</a></td></tr>
+<tr><td align="right">III.</td><td><span class="smcap">Portrait of U. J. Le Verrier</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_60">60</a></td></tr>
+<tr><td align="right">IV.</td><td><span class="smcap">Portrait of J. G. Galle</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_60">60</a></td></tr>
+<tr><td align="right">V.</td><td><span class="smcap">Corner of the Berlin Map by the use of which Galle found Neptune</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_83">82</a></td></tr>
+<tr><td align="right">VI.</td><td><span class="smcap">Astronomers Royal</span></td><td>&nbsp;</td><td colspan="3" align="right"><a href="#front"><i>Frontispiece</i></a></td></tr>
+<tr><td align="right">VII.</td><td><span class="smcap">Great Comet of Nov. 7, 1882</span></td><td>&nbsp;</td><td><i>To face</i></td><td><i>page</i></td><td align="right"><a href="#Page_123">122</a></td></tr>
+<tr><td align="right">VIII.</td><td><span class="smcap">The Oxford New Star</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_142">142</a></td></tr>
+<tr><td align="right">IX.</td><td><span class="smcap">Nebulosity round Nova Persei</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_147">146</a></td></tr>
+<tr><td align="right">X.</td><td><span class="smcap">Sun-spots at Greenwich, Feb. 18 and 19, 1894</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_160">158</a></td></tr>
+<tr><td align="right">XI.</td><td><span class="smcap">Sun-spots at Greenwich, Feb. 20 and 21, 1894</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_163">162</a></td></tr>
+<tr><td valign="top" align="right">XII.</td><td><span class="smcap">Number of Sun-spots compared with Daily Range of Magnetic<br />Declination and Daily Range of Magnetic Horizontal Force</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_165">164</a></td></tr>
+<tr><td align="right">XIII.</td><td><span class="smcap">Greenwich Magnetic Curves, 1859-60</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_167">166</a></td></tr>
+<tr><td align="right">XIV.</td><td><span class="smcap">Greenwich Magnetic Curves, 1841-1860</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_166">166</a></td></tr>
+<tr><td align="right">XV.</td><td><span class="smcap">Sun-spots and Turns of Vane</span></td><td>&nbsp;</td><td align="center">"</td><td align="center">"</td><td align="right"><a href="#Page_170">170</a></td></tr></table>
+
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_xii" id="Page_xii">[Pg xii]</a></span></p>
+<h2>ERRATA</h2>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="errata">
+<tr><td>Page</td><td>133, line 27, <i>for</i> &#8220;200 stars&#8221; <i>read</i> &#8220;200 stars per hour.&#8221;</td></tr>
+<tr><td align="center">"</td><td>145, See note on page 220.</td></tr>
+<tr><td align="center">"</td><td>146, bottom of page. This nebulosity was first discovered by<br /><span style="margin-left: 4em;">Dr. Max Wolf of Heidelberg. See <i>Astr. Nachr.</i> 3736.</span></td></tr>
+<tr><td align="center">"</td><td>181, line 17, <i>for</i> &#8220;observation&#8221; <i>read</i> &#8220;aberration.&#8221;</td></tr></table>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p>
+<h2>ASTRONOMICAL DISCOVERY</h2>
+<p>&nbsp;</p><p>&nbsp;</p>
+<h2><a name="CHAPTER_I" id="CHAPTER_I"></a>CHAPTER I</h2>
+<h3>URANUS AND EROS</h3>
+
+
+<div class="sidenote">Popular view of discovery.</div>
+
+<p>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.</p>
+
+<div class="sidenote">Keats&#8217; lines.</div>
+
+<p>The popular conception finds expression in the lines of Keats:&mdash;</p>
+
+<p class="poem">Then felt I like some watcher of the skies<br />
+When a new planet swims into his ken.</p>
+
+<p>Keats was born in 1795, published his first volume of poems in 1817, and
+died in 1821. At<span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span> 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&mdash;far larger than any other planet known except
+Jupiter and Saturn, while the others were far smaller&mdash;and that Keats is
+using throughout the poem metaphors drawn from the first glimpses of &#8220;vast
+expanses&#8221; of land or water. Perhaps I may reproduce the whole sonnet. His
+friend C. C. Clarke had put before him Chapman&#8217;s &#8220;paraphrase&#8221; of Homer,
+and they sat up till daylight to read it, &#8220;Keats shouting with delight as
+some passage of especial energy struck his imagination. At ten o&#8217;clock the
+next morning Mr. Clarke found the sonnet on his breakfast-table.&#8221;</p>
+
+<p class="center"><span class="smcap">Sonnet XI</span><br /><i>On first looking into Chapman&#8217;s &#8220;Homer&#8221;</i></p>
+<table border="0" cellpadding="0" cellspacing="5" summary="keats">
+<tr><td>Much have I travell&#8217;d in the realms of gold,<br />
+And many goodly states and kingdoms seen;<br />
+Round many western islands have I been<br />
+Which bards in fealty to Apollo hold.<br />
+<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span>Oft of one wide expanse had I been told<br />
+That deep-brow&#8217;d Homer ruled as his demesne;<br />
+Yet did I never breathe its pure serene<br />
+Till I heard Chapman speak out loud and bold:<br />
+Then felt I like some watcher of the skies<br />
+When a new planet swims into his ken;<br />
+Or like stout Cortez when with eagle eyes<br />
+He star&#8217;d at the Pacific&mdash;and all his men<br />
+Look&#8217;d at each other with a wild surmise&mdash;<br />
+Silent, upon a peak in Darien.</td></tr></table>
+
+<p><span class="sidenote">Comparison with discovery of Uranus.</span>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
+&#8220;watcher of the skies,&#8221; 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 &#8220;swim into his ken&#8221;? Let
+us turn to the original announcement of his discovery as given in the
+Philosophical Transactions for 1781.</p>
+
+<p>&nbsp;</p>
+<div class="blockquot"><p class="center"><span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span>PHILOSOPHICAL TRANSACTIONS, 1781</p>
+<p class="center">XXXII.&mdash;<span class="smcap">Account of a Comet</span><br />
+<span class="smcap">By Mr. Herschel, F.R.S.</span><br />(Communicated by Dr. Watson, jun., of Bath, F.R.S.)<br /><i>Read April 26, 1781</i></p>
+
+<div class="sidenote">Original announcement.</div>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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, &amp;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<span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span> 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.</p>
+
+<p>&#8220;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&#8217;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&#8217;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.&#8221;</p></div>
+
+<div class="sidenote">Called first a comet.</div>
+
+<p>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<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span> 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.<span class="sidenote">Other observers would not have found it at all.</span> 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&#8217;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<span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span>
+Herschel&#8217;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&#8217;s
+words, which Herschel records in the paper already quoted announcing the
+discovery:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;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.&#8221;</p></div>
+
+<div class="sidenote">No &#8220;swimming into ken.&#8221;</div>
+
+<p>We cannot, therefore, fit the facts to Keats&#8217; 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<span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span> 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?</p>
+
+<div class="sidenote">Though this may happen at times.</div>
+
+<p>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
+&#8220;watcher of the skies,&#8221; Dr. Anderson of Edinburgh, suddenly caught sight
+of a brilliant new star in Perseus; though here &#8220;flashed into his ken&#8221;
+would perhaps be a more suitable phrase than &#8220;swam.&#8221; 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.<span class="sidenote">Name of new planet.</span> But before leaving Uranus for them I should like to recall the
+circumstances attending the naming of the planet. Herschel proposed to
+call it <i>Georgium Sidus</i> in honour of his patron, King George III., and<span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span>
+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.</p>
+
+<p>&nbsp;</p>
+<div class="blockquot">
+<p class="center"><i>A Letter from</i> <span class="smcap">William Herschel</span>, Esq., F.R.S.,<br />
+<i>to</i> Sir <span class="smcap">Joseph Banks</span>, Bart., P.R.S.</p>
+
+<p>&#8220;Sir,&mdash;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.</p>
+
+<p>&#8220;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, <i>when</i> this last<span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span> found
+planet was discovered? It would be a very satisfactory answer to say,
+&#8216;In the reign of King George the Third.&#8217; As a philosopher then, the
+name <span class="smcap">Georgium Sidus</span> 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;&mdash;I
+cannot but wish to take this opportunity of expressing my sense of
+gratitude by giving the name<span class="sidenote"><i>Georgium Sidus.</i></span> <i>Georgium Sidus</i>,</p>
+
+<p class="poem"><span style="margin-left: 5em;"><i>Georgium Sidus</i></span><br />
+&mdash;&mdash;<i>jam nunc assuesce vocari,</i><br />
+<span style="margin-left: 12em;"><i>Virg. Georg.</i></span></p>
+
+<p>to a star which (with respect to us) first began to shine under his
+auspicious reign.</p>
+
+<p>&#8220;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.&mdash;I have the honour to be, with the greatest respect, Sir,
+your most humble and most obedient servant,</p>
+
+<p class="right"><span class="smcap">W. Herschel.</span>&#8221;</p></div>
+
+
+<p><span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span>This letter reminds us how long it was since a new name had been required
+for a new planet,&mdash;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.<span class="sidenote">Herschel.</span> 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 &#8220;English Nautical Almanac&#8221; the name &#8220;the Georgian&#8221;
+(apparently preferred to Herschel&#8217;s <i>Georgium Sidus</i>) was being used
+officially after 1791, and did not disappear from that work until 1851
+(published in 1847.)</p>
+
+<div class="sidenote">Uranus finally adopted.</div>
+
+<p>It would appear to have been the discovery of Neptune, with which we shall
+deal in the next<span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span> chapter, which led to this official change; for in the
+volume for 1851 is included Adams&#8217; account of his discovery with the
+title&mdash;</p>
+
+<p class="center">&#8220;<span class="smcap">On the Perturbations of Uranus</span>,&#8221;</p>
+
+<p>and there was thus a definite reason for avoiding two names for the same
+planet in the same work. But Le Verrier&#8217;s paper on the same topic at the
+same date still uses the name &#8220;Herschel&#8221; for the planet.</p>
+
+<p>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.<span class="sidenote">Bode&#8217;s law.</span> Now if we arrange the planetary distances in order, we<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span>
+shall notice a remarkable connection between the terms of the series. Here
+is a table showing this connection.</p>
+
+<p class="center"><span class="smcap">Table of the Distances of the Planets from<br />
+the Sun, showing &#8220;Bode&#8217;s Law.&#8221;</span></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="distances">
+<tr><td valign="top" align="center" class="btl">Name of<br />Planet.</td>
+    <td align="center" class="btl">Distance from<br />Sun, taking<br />that of Earth<br />as 10.</td>
+    <td align="center" class="btrl">&#8220;Bode&#8217;s Law&#8221;<br />(originally formulated<br />by Titius, but brought<br />into notice by Bode).</td></tr>
+<tr><td class="btl">Mercury</td>
+    <td align="center" class="btl">&nbsp;&nbsp;&nbsp;&nbsp;4</td>
+    <td class="btrl"><span style="margin-left: 1.25em;">4 +</span> &nbsp;&nbsp;&nbsp;&nbsp;0= &nbsp;&nbsp;&nbsp;&nbsp;4</td></tr>
+<tr><td class="bl">Venus</td>
+    <td align="center" class="bl">&nbsp;&nbsp;&nbsp;&nbsp;7</td>
+    <td class="blr"><span style="margin-left: 1.25em;">4 +</span> &nbsp;&nbsp;&nbsp;&nbsp;3= &nbsp;&nbsp;&nbsp;&nbsp;7</td></tr>
+<tr><td class="bl">The Earth</td>
+    <td align="center" class="bl">&nbsp;&nbsp;10</td>
+    <td class="blr"><span style="margin-left: 1.25em;">4 +</span> &nbsp;&nbsp;&nbsp;&nbsp;6= &nbsp;&nbsp;10</td></tr>
+<tr><td class="bl">Mars</td>
+    <td align="center" class="bl">&nbsp;&nbsp;15</td>
+    <td class="blr"><span style="margin-left: 1.25em;">4 +</span> &nbsp;&nbsp;12= &nbsp;&nbsp;16</td></tr>
+<tr><td class="bl">(&nbsp; &nbsp; &nbsp; &nbsp;)</td>
+    <td align="center" class="bl">&nbsp;&nbsp;(&nbsp; &nbsp;)</td>
+    <td class="blr"><span style="margin-left: 1.25em;">4 +</span> &nbsp;&nbsp;24= &nbsp;&nbsp;28</td></tr>
+<tr><td class="bl">Jupiter</td>
+    <td align="center" class="bl">&nbsp;&nbsp;52</td>
+    <td class="blr"><span style="margin-left: 1.25em;">4 +</span> &nbsp;&nbsp;48= &nbsp;&nbsp;52</td></tr>
+<tr><td class="bl">Saturn</td>
+    <td align="center" class="bl">&nbsp;&nbsp;95</td>
+    <td class="blr"><span style="margin-left: 1.25em;">4 +</span> &nbsp;&nbsp;96= 100</td></tr>
+<tr><td class="bbl">Uranus</td>
+    <td align="center" class="bbl">192</td>
+    <td align="center" class="bblr">4 + 192= 196</td></tr></table>
+
+<p>If we write down a series of 4&#8217;s, and then add the numbers 3, 6, 12, and
+so on, each formed by doubling the last, we get numbers representing very
+nearly the planetary distances, which are shown approximately in the
+second column. But three points call for notice. Firstly, the number
+before 3 should be 1&#189;, and not zero, to agree with the rest.<span class="sidenote">Gap in the series suggesting unknown planet.</span> 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<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span> the so-called &#8220;law&#8221; 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&#8217;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;<span class="sidenote">Search for it.</span> 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<span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span> dramatically on the first evening of the
+nineteenth century (January 1, 1801).<span class="sidenote">Accidental discovery.</span> 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.</p>
+
+<div class="sidenote">Hegel&#8217;s forecast.</div>
+
+<p>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 <span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span>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.</p>
+
+<div class="sidenote">The planet lost again.</div>
+
+<p>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&#8217;s observations was only three degrees; and<span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span> if any one will kindly
+take out his watch and look at the minute marks round the dial, three
+degrees is just <i>half</i> 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.</p>
+
+<div class="sidenote">Gauss shows how to find it.</div>
+
+<p>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 <i>Theoria Motus</i>, 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):&mdash;</p>
+
+<div class="blockquot">
+<p class="center"><span class="smcap">Extract from the Preface to the</span><br /><i>Theoria Motus</i>.</p>
+
+<div class="sidenote">The <i>Theoria Motus</i>.</div>
+
+<p>&#8220;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
+<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span>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<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span> 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.</p>
+
+<p>&#8220;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<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span> 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.&#8221;</p></div>
+
+<p>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.<span class="sidenote">Rediscovery of Ceres.</span> 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.<span class="sidenote">Another planet found.</span> Olbers had made himself so familiar
+with all the small stars along the track which was being searched for the
+missing body, that he<span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span> 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 <i>one</i>
+planet; but here were <i>two</i>!</p>
+
+<div class="sidenote">Hypothesis of many fragments.</div>
+
+<p>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&#8217; patient<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span> 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.</p>
+
+<p class="center"><span class="smcap">Minor Planets, 1801 to 1850.</span></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="planets">
+<tr><td class="btl">Number</td>
+    <td class="btl" align="center">Name.</td>
+    <td class="btl" align="center">Discoverer.</td>
+    <td class="btrl" align="center">Date.</td></tr>
+<tr><td align="center" class="btl">&nbsp;&nbsp;1</td>
+    <td class="btl" align="center">Ceres</td>
+    <td class="btl" align="center">Piazzi</td>
+    <td class="btrl" align="center">1801</td></tr>
+<tr><td align="center" class="bl">&nbsp;&nbsp;2</td>
+    <td class="bl" align="center">Pallas</td>
+    <td class="bl" align="center">Olbers</td>
+    <td class="blr" align="center">1802</td></tr>
+<tr><td align="center" class="bl">&nbsp;&nbsp;3</td>
+    <td class="bl" align="center">Juno</td>
+    <td class="bl" align="center">Harding</td>
+    <td class="blr" align="center">1804</td></tr>
+<tr><td align="center" class="bl">&nbsp;&nbsp;4</td>
+    <td class="bl" align="center">Vesta</td>
+    <td class="bl" align="center">Olbers</td>
+    <td class="blr" align="center">1807</td></tr>
+<tr><td align="center" class="btl">&nbsp;&nbsp;5</td>
+    <td class="btl" align="center">Astraea</td>
+    <td class="btl" align="center">Hencke</td>
+    <td class="btrl" align="center">1845</td></tr>
+<tr><td align="center" class="bl">&nbsp;&nbsp;6</td>
+    <td class="bl" align="center">Hebe</td>
+    <td class="bl" align="center">Hencke</td>
+    <td class="blr" align="center">1847</td></tr>
+<tr><td align="center" class="bl">&nbsp;&nbsp;7</td>
+    <td class="bl" align="center">Iris</td>
+    <td class="bl" align="center">Hind</td>
+    <td class="blr" align="center">1847</td></tr>
+<tr><td align="center" class="bl">&nbsp;&nbsp;8</td>
+    <td class="bl" align="center">Flora</td>
+    <td class="bl" align="center">Hind</td>
+    <td class="blr" align="center">1847</td></tr>
+<tr><td align="center" class="bl">&nbsp;&nbsp;9</td>
+    <td class="bl" align="center">Metis</td>
+    <td class="bl" align="center">Graham</td>
+    <td class="blr" align="center">1848</td></tr>
+<tr><td align="center" class="bl">10</td>
+    <td class="bl" align="center">Hygeia</td>
+    <td class="bl" align="center">De Gasparis</td>
+    <td class="blr" align="center">1849</td></tr>
+<tr><td align="center" class="bl">11</td>
+    <td class="bl" align="center">Parthenope</td>
+    <td class="bl" align="center">De Gasparis</td>
+    <td class="blr" align="center">1850</td></tr>
+<tr><td align="center" class="bl">12</td>
+    <td class="bl" align="center">Victoria</td>
+    <td class="bl" align="center">Hind</td>
+    <td class="blr" align="center">1850</td></tr>
+<tr><td align="center" class="bbl">13</td>
+    <td class="bbl" align="center">Egeria</td>
+    <td class="bbl" align="center">De Gasparis</td>
+    <td class="bblr" align="center">1850</td></tr></table>
+
+<p>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 <span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span>was at last complete. The
+discoverers of Uranus and of these first four minor planets all died
+before any further addition was made;<span class="sidenote"><ins class="correction" title="original: Henke'">Hencke&#8217;s</ins> long search.</span> 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.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i032top.jpg" alt="" /></div>
+<p class="center"><small><i>By permission of Messrs. Macmillan &amp; Co.</i></small><br />
+I.&mdash;<span class="smcap">J. C. Adams.</span></p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i032bottom.jpg" alt="" /></div>
+<p class="center">II.&mdash;<span class="smcap">A. Graham.</span><br />
+<span class="smcaplc">DISCOVERER OF THE NINTH MINOR PLANET (METIS).</span></p>
+<p>&nbsp;</p>
+
+<p>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&#8217;s fifteen years of
+search before success to recognise<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span> what vast stores of patience and
+diligence were required in carrying out the search.<span class="sidenote">The photographic method.</span> 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
+&#8220;star-trap,&#8221; 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.</p>
+
+<p class="center"><span class="smcap">Table showing the Number of Minor Planets Discovered<br />in each Decade since 1850.</span></p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="planets">
+<tr><td>1801 to 1850&mdash;</td><td>altogether</td><td align="right">13</td><td>discoveries.</td></tr>
+<tr><td>1851 to 1860&mdash;</td><td align="center">"</td><td align="right">49</td><td align="center">"</td></tr>
+<tr><td>1861 to 1870&mdash;</td><td align="center">"</td><td align="right">49</td><td align="center">"</td></tr>
+<tr><td>1871 to 1880&mdash;</td><td align="center">"</td><td align="right">108</td><td align="center">"</td></tr>
+<tr><td>1881 to 1890&mdash;</td><td align="center">"</td><td align="right">83</td><td align="center">"</td></tr>
+<tr><td>1891 to 1900&mdash;</td><td align="center">"</td><td align="right">180</td><td>announcements</td></tr>
+<tr><td><span style="margin-left: 2.25em;">In 1901</span></td><td align="center">"</td><td align="right">36</td><td align="center">"</td></tr>
+<tr><td><span style="margin-left: 2.5em;">"&nbsp; 1902</span></td><td align="center">"</td><td align="right">50</td><td align="center">"</td></tr>
+<tr><td><span style="margin-left: 2.5em;">"&nbsp; 1903</span></td><td align="center">"</td><td class="bbline" align="right">41</td><td align="center">"</td></tr>
+<tr><td>&nbsp;</td><td align="right">Total</td><td align="right">609</td></tr></table>
+
+<p class="center">[<i>N.B.</i>&mdash;Many of the more recent announcements turned out to refer to old discoveries.]</p>
+
+<div class="sidenote">Scarcity of names.</div>
+
+<p><span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span>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 <i>names</i> 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) &#8220;Victoria,&#8221; 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<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span> may
+care to look at some of the names selected for others:&mdash;</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="names">
+<tr><td>No.</td><td><span class="spacer2">&nbsp;</span></td><td class="br">Name.</td><td><span class="spacer">&nbsp;</span></td>
+    <td>No.</td><td><span class="spacer2">&nbsp;</span></td><td>Name.</td></tr>
+<tr><td>248</td><td>&nbsp;</td><td class="br">Lameia</td><td>&nbsp;</td><td>389</td><td>&nbsp;</td><td>Industria</td></tr>
+<tr><td>250</td><td>&nbsp;</td><td class="br">Bettina</td><td>&nbsp;</td><td>391</td><td>&nbsp;</td><td>Ingeborg</td></tr>
+<tr><td>261</td><td>&nbsp;</td><td class="br">Prymno</td><td>&nbsp;</td><td>433</td><td>&nbsp;</td><td>Eros</td></tr>
+<tr><td>264</td><td>&nbsp;</td><td class="br">Libussa</td><td>&nbsp;</td><td>443</td><td>&nbsp;</td><td>Photographica</td></tr>
+<tr><td>296</td><td>&nbsp;</td><td class="br">Pha&euml;tusa</td><td>&nbsp;</td><td>457</td><td>&nbsp;</td><td>Alleghenia</td></tr>
+<tr><td>340</td><td>&nbsp;</td><td class="br">Eduarda</td><td>&nbsp;</td><td>462</td><td>&nbsp;</td><td>Eriphyla</td></tr>
+<tr><td>341</td><td>&nbsp;</td><td class="br">California</td><td>&nbsp;</td><td>475</td><td>&nbsp;</td><td>Ocllo</td></tr>
+<tr><td>350</td><td>&nbsp;</td><td class="br">Ornamenta</td><td>&nbsp;</td><td>484</td><td>&nbsp;</td><td>Pittsburghia</td></tr>
+<tr><td>357</td><td>&nbsp;</td><td class="br">Ninina</td><td>&nbsp;</td><td>503</td><td>&nbsp;</td><td>Evelyn</td></tr>
+<tr><td>385</td><td>&nbsp;</td><td class="br">Ilmatar</td></tr></table>
+
+
+<p><span class="sidenote">Bettina.</span>In connection with No. 250 there is an interesting little history. In the
+<i>Observatory</i> for 1885, page 63, appeared the following
+advertisement:&mdash;&#8220;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 &pound;50.&#8221; 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:&mdash;&#8220;Minor planet No. 250 has been<span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span>
+named &#8216;Bettina&#8217; by Baron Albert de Rothschild.&#8221; 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.
+<span class="sidenote">The provisional letters.</span>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 <i>numbering</i> in
+existence as well as of <i>naming</i>, 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 <i>letter of the
+alphabet</i>, 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, &amp;c.; after
+completing the alphabet<span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span> 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.</p>
+
+<p>Fortunately, however, on running through it for the fifth time, an object
+of particular interest was discovered.<span class="sidenote">Eros.</span> 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&#8217;s distance. To explain this
+importance we must make a small digression.</p>
+
+<div class="sidenote">Transit of Venus.</div>
+
+<p>About the middle of the last century our knowledge of the sun&#8217;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.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i039.jpg" alt="" /></div>
+<p class="center"><span class="smcap">Fig. 1.</span></p>
+<p>&nbsp;</p>
+
+<p>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<span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span> 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 <i>relative</i>
+distance of Venus be known, it can be calculated what this difference in
+path will be. Now the relative distance of Venus <i>is</i> 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&#8217;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&#8217;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&#8217;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,<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>
+it was hoped to determine this very important quantity, the sun&#8217;s
+distance. It was known from previous experience that there were certain
+difficulties in observing very exactly the beginning and end of the
+transit.<span class="sidenote">The &#8220;Black Drop.&#8221;</span> There was an appearance called the &#8220;Black Drop,&#8221; 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&#8217;s disc was reluctant to make the entry and clung to the edge or &#8220;limb&#8221;
+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.</p>
+
+<p>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<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span> 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 &#8220;personal equation&#8221; as it is called,
+could be determined beforehand, and allowed for as a correction when he
+came to observe the actual transit.<span class="sidenote">Failure.</span> 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&#8217;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.</p>
+
+<p>&nbsp;</p>
+<div class="blockquot"><p class="center"><span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span><span class="smcap">Sun&#8217;s Distance, in Millions of Miles, as found by Different Observers</span></p>
+
+<p><b>Before the Transits of Venus</b> estimates varied between <b>96</b> million
+miles (Gilliss and Gould, 1856) and <b>91</b> million (Winneche, 1863), a
+range of 5 million miles.</p>
+
+<p><b>The Transits of 1874 and 1882</b> gave results lying between <b>93&#188;</b>
+million (Airy, from British observations of 1874), <b>92&#189;</b> million
+(Stone, from British observations of 1882), and <b>91&#189;</b> million
+(Puiseux, from French observations), a range of 1&#190; millions.</p>
+
+<p><b>Gill&#8217;s Heliometer results</b> all lie very near <b>93</b> 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 <i>less</i> than
+the 93 millions.</p></div>
+
+<p>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.</p>
+
+<div class="sidenote">Modern method for sun&#8217;s distance.</div>
+
+<p>We have said that the <i>relative</i> 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<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span> 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&#8217;s distance can
+be avoided; for instance, since the sun&#8217;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.<span class="sidenote">Photography.</span> 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&#8217;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<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span> by a known interval. For in that interval the station
+will have been carried by the earth&#8217;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;<span class="sidenote">Dr. Gill&#8217;s expedition to Ascension.</span> and since in 1878,
+when Dr. Gill set out on his enterprise of determining the sun&#8217;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&#8217;s equator, it is carried by
+the earth&#8217;s rotation a longer distance in a given time than places nearer
+the poles, and in these observations for &#8220;parallax,&#8221; 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<small><a name="f1.1" id="f1.1" href="#f1">[1]</a></small> then
+known, was selected for observation with the heliometer.</p>
+
+<p>And now it will be seen why the discovery of<span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span> 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.</p>
+
+
+<p>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.<span class="sidenote">Victoria, Iris, and Sappho.</span> 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&#8217;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.<span class="sidenote">Eros.</span> 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<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span> 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.</p>
+
+<p>To canons for the advantageous prosecution of research, if we care to make
+them, we may therefore add this&mdash;that there is no line of research,
+however apparently unimportant or monotonous, which we can afford to
+neglect. Just when<span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span> 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.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span></p>
+<h2><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II</h2>
+<h3>THE DISCOVERY OF NEPTUNE</h3>
+
+<div class="sidenote">Search for definite objects.</div>
+
+<p>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&#8217;s great law of gravitation&mdash;the discovery of Neptune from its
+observed disturbance of Uranus. I will first briefly recall the main facts
+relating to the actual discovery.</p>
+
+<div class="sidenote">Disturbance of Uranus.</div>
+
+<p><span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span>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&#8217;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.</p>
+
+<p>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<span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span> the old observations with the orbit calculated from the new
+ones.<span class="sidenote">Suspicion of perturbing planet.</span> 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 &#8220;Account of some Circumstances
+historically connected with the Discovery of the Planet exterior to
+Uranus,&#8221; 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.).</p>
+
+<p>&nbsp;</p>
+<div class="blockquot">
+<p class="center"><span class="smcap">No.</span> 1.&mdash;<i>The</i> <span class="smcap">Rev. T. J. Hussey</span> <i>to</i> <span class="smcap">G. B. Airy</span>.<br />
+[<i>Extract.</i>]</p>
+
+<p class="right">&#8220;&#8216;<span class="smcap">Hayes, Kent</span>, 17<i>th November</i> 1834.</p>
+
+<p>&#8220;&#8216;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 <i>Uranus</i>, I was led to examine closely Bouvard&#8217;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 <i>Uranus</i>, not taken into
+account because unknown. My first idea was to ascertain some
+approximate place of this <span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span>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&#8217;s opinion was, that one disturbing body
+would not satisfy the phenomena; but that he conjectured there were
+two planets beyond <i>Uranus</i>. 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 <span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span>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&#8217;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 chim&aelig;ra, which, until my conversation with Bouvard, I was
+afraid it might, I shall be very glad of any sort of hint respecting
+it.&#8217;</p>
+
+<p>&#8220;My answer was in the following terms:&mdash;</p>
+
+
+
+<p class="center"><span class="smcap">No.</span> 2.&mdash;<span class="smcap">G. B. Airy</span> <i>to the</i> <span class="smcap">Rev. T. J. Hussey</span>.<br />
+[<i>Extract.</i>]</p>
+
+<p class="right">&#8220;&#8216;<span class="smcap">Observatory, Cambridge</span>, 1834, <i>Nov.</i> 23.</p>
+
+<div class="sidenote">Airy&#8217;s scepticism.</div>
+<p>&#8220;&#8216;I have often thought of the irregularity of <i>Uranus</i>, 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<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span> the irregularity was
+well determined from several successive revolutions.&#8217;&#8221;</p></div>
+
+<p>Although only a sentence or two have been selected from Airy&#8217;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.<span class="sidenote">Le Verrier&#8217;s papers.</span> 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&#8217;s Law, that the distance of this new planet from the sun would be
+about double that of Uranus (and it<span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span> 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,<span class="sidenote">Planet to be detected by disc.</span> 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&#8217;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.<span class="sidenote">Galle&#8217;s discovery of the planet.</span> 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<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span>
+same night Dr. Galle, by comparing a star map with the heavens, found the
+planet.</p>
+
+<p>To two points to which I have specially called attention in this brief
+summary&mdash;namely, the preliminary assumption that the planet would be,
+according to Bode&#8217;s Law, twice as far away as Uranus; secondly, the
+confident assertion that it would have a visible disc&mdash;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,&mdash;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.<span class="sidenote">Adams&#8217; work publicly <ins class="correction" title="original: annouced">announced</ins>.</span> 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<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span> 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&#8217;s conduct received a large amount of what he called
+&#8220;savage abuse.&#8221; 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.</p>
+
+<div class="sidenote">Facts undoubted.</div>
+
+<p>There is fortunately no doubt whatever about any of the <i>facts</i>. 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,<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span> 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.</p>
+
+<div class="sidenote">Airy&#8217;s &#8220;Account.&#8221;</div>
+
+<p>Airy&#8217;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),<span class="sidenote">&#8220;A movement of the age.&#8221;</span> it might also be regarded
+as to some extent the consequence of a movement of the age. His actual
+words are these: &#8220;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<span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span> or powers best suited to the different parts of
+the researches.&#8221;</p>
+
+<p>I have quoted these words as the first point at which it is difficult to
+understand Airy&#8217;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.<span class="sidenote">Airy under-estimated Adams&#8217; work.</span> It
+seems almost certain that Airy entirely under-estimated the value of
+Adams&#8217; work throughout. But this will become clearer as we proceed. The
+&#8220;account&#8221; 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
+&#8220;account&#8221; are still in the Observatory at Greenwich, pinned together just
+as Airy left them; and in preparing his &#8220;account&#8221; 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.
+&#8220;If it be the effect of any unseen body,&#8221; writes Airy to Bouvard, &#8220;it will
+be nearly impossible ever to find out its place.&#8221; But the first letter
+which need concern<span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span> 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.</p>
+
+<p>&nbsp;</p>
+<div class="blockquot">
+<p class="center">No. 6.&mdash;<span class="smcap">Professor Challis</span> <i>to</i> <span class="smcap">G. B. Airy</span>.<br />
+[<i>Extract.</i>]</p>
+
+<p class="right">&#8220;&#8216;<span class="smcap">Cambridge Observatory</span>, <i>Feb.</i> 13, 1844.</p>
+
+<div class="sidenote">Challis mentions Adams to Airy,</div>
+
+<p>&#8220;&#8216;A young friend of mine, Mr. Adams of St. John&#8217;s College, is working
+at the theory of <i>Uranus</i>, 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&#8217;s <i>Tables of Uranus</i> besides
+that of <i>Jupiter&#8217;s</i> mass.&#8217;</p>
+
+<p>&#8220;My answer to him was as follows:&mdash;</p>
+
+<p class="center">No. 7.&mdash;<span class="smcap">G. B. Airy</span> <i>to</i> <span class="smcap">Professor Challis</span>.<br />
+[<i>Extract.</i>]</p>
+
+<p class="right">&#8220;&#8216;<span class="smcap">Royal Observatory, Greenwich</span>, 1844, <i>Feb.</i> 15.</p>
+
+<p>&#8220;&#8216;I send all the results of the observations of <i>Uranus</i> made with
+both instruments (that is, the<span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span> heliocentric errors of <i>Uranus</i> 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&#8217;s <i>Tables of Uranus</i>
+except in increasing the two equations which depend on <i>Jupiter</i> by
+<span style="font-size: 0.8em;"><sup>1</sup></span>&frasl;<span style="font-size: 0.6em;">50</span> part. As constants have been added (in the printed tables) to
+make the equations positive, and as <span style="font-size: 0.8em;"><sup>1</sup></span>&frasl;<span style="font-size: 0.6em;">50</span> part of the numbers in the
+tables has been added, <span style="font-size: 0.8em;"><sup>1</sup></span>&frasl;<span style="font-size: 0.6em;">50</span> part of the constants has been subtracted
+from the final results.&#8217;</p>
+
+<p>&#8220;Professor Challis in acknowledging the receipt of these, used the
+following expressions:&mdash;</p>
+
+<p class="center">No. 8.&mdash;<span class="smcap">Professor Challis</span> <i>to</i> <span class="smcap">G. B. Airy</span>.<br />
+[<i>Extract.</i>]</p>
+
+<p class="right">&#8220;&#8216;<span class="smcap">Cambridge Observatory</span>, <i>Feb.</i> 16, 1844.</p>
+
+<p>&#8220;&#8216;I am exceedingly obliged by your sending so complete a series of
+tabular errors of <i>Uranus</i>.... 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.&#8217;</p>
+
+<p>&#8220;The next letter shows that Mr. Adams has derived results from these
+errors.</p>
+
+<p class="center">No. 9.&mdash;<span class="smcap">Professor Challis</span> <i>to</i> <span class="smcap">G. B. Airy</span>.</p>
+
+<p class="right">&#8220;&#8216;<span class="smcap">Cambridge Observatory</span>, <i>Sept.</i> 22, 1845.</p>
+
+<p>&#8220;&#8216;My friend Mr. Adams (who will probably deliver this note to you)
+has completed his<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span> calculations respecting the perturbation of the
+orbit of <i>Uranus</i> by a supposed ulterior planet,<span class="sidenote">and suggests Adams&#8217; visit to Greenwich.</span> 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.&#8217;</p>
+
+<p>&#8220;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:&mdash;</p>
+
+<p class="center"><span class="smcap">No. 10.&mdash;G. B. Airy</span> <i>to</i> <span class="smcap">Professor Challis</span>.</p>
+
+<p class="right">&#8220;&#8216;<span class="smcap">Royal Observatory, Greenwich</span>, 1845, <i>Sept.</i> 29.</p>
+
+<p>&#8220;&#8216;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?&#8217;</p>
+
+<p>&#8220;On one of the last days of October 1845, Mr. Adams called at the
+Royal Observatory, <span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span>Greenwich, in my absence and left the following
+important paper:&mdash;</p>
+
+<p class="center">No. 11.&mdash;<span class="smcap">J. C. Adams</span>, Esq., <i>to</i> <span class="smcap">G. B. Airy</span>.</p>
+
+<div class="sidenote">Adams&#8217; announcement of the new planet.</div>
+
+<p>&#8220;&#8216;According to my calculations, the observed irregularities in the
+motion of <i>Uranus</i> may be accounted for by supposing the existence of
+an exterior planet, the mass and orbit of which are as follows:&mdash;</p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="orbit">
+<tr><td>Mean distance (assumed nearly in accordance with Bode&#8217;s Law)</td><td><span class="spacer">&nbsp;</span></td><td>&nbsp;&nbsp;&nbsp;38.4</td></tr>
+<tr><td>Mean sidereal motion in 365.25 days</td><td>&nbsp;</td><td>&nbsp;&nbsp;&nbsp;1&deg; 30&#8242;.9</td></tr>
+<tr><td>Mean longitude, 1st October 1845</td><td>&nbsp;</td><td>323 34</td></tr>
+<tr><td>Longitude of perihelion</td><td>&nbsp;</td><td>315 55</td></tr>
+<tr><td>Eccentricity</td><td>&nbsp;</td><td>0.1610.</td></tr>
+<tr><td>Mass (that of the sun being unity)</td><td>&nbsp;</td><td>0.0001656.</td></tr></table>
+
+<p>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 <i>Astronomische Nachrichten</i>, have been made use of. The
+following are the remaining errors of mean longitude:&mdash;</p>
+
+<p class="center"><i>Observation&mdash;Theory.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="theory">
+<tr><td>&nbsp;</td><td><span class="spacer2">&nbsp;</span></td><td align="center">"</td><td><span class="spacer">&nbsp;</span></td><td><span class="spacer">&nbsp;</span></td><td>&nbsp;</td><td><span class="spacer2">&nbsp;</span></td><td align="center">"</td></tr>
+<tr><td>1780</td><td>&nbsp;</td><td align="right">+0.27</td><td>&nbsp;</td><td>&nbsp;</td><td>1813</td><td>&nbsp;</td><td align="right">-0.94</td></tr>
+<tr><td>1783</td><td>&nbsp;</td><td align="right">-0.23</td><td>&nbsp;</td><td>&nbsp;</td><td>1816</td><td>&nbsp;</td><td align="right">-0.31</td></tr>
+<tr><td>1786</td><td>&nbsp;</td><td align="right">-0.96</td><td>&nbsp;</td><td>&nbsp;</td><td>1819</td><td>&nbsp;</td><td align="right">-2.00</td></tr>
+<tr><td>1789</td><td>&nbsp;</td><td align="right">+1.82</td><td>&nbsp;</td><td>&nbsp;</td><td>1822</td><td>&nbsp;</td><td align="right">+0.30</td></tr>
+<tr><td>1792</td><td>&nbsp;</td><td align="right">-0.91</td><td>&nbsp;</td><td>&nbsp;</td><td>1825</td><td>&nbsp;</td><td align="right">+1.92</td></tr>
+<tr><td>1795</td><td>&nbsp;</td><td align="right">+0.09</td><td>&nbsp;</td><td>&nbsp;</td><td>1828</td><td>&nbsp;</td><td align="right">+2.25</td></tr>
+<tr><td>1798</td><td>&nbsp;</td><td align="right">-0.99</td><td>&nbsp;</td><td>&nbsp;</td><td>1831</td><td>&nbsp;</td><td align="right">-1.06</td></tr>
+<tr><td>1801</td><td>&nbsp;</td><td align="right">-0.04</td><td>&nbsp;</td><td>&nbsp;</td><td>1834</td><td>&nbsp;</td><td align="right">-1.44</td></tr>
+<tr><td>1804</td><td>&nbsp;</td><td align="right">+1.76</td><td>&nbsp;</td><td>&nbsp;</td><td>1837</td><td>&nbsp;</td><td align="right">-1.62</td></tr>
+<tr><td>1807</td><td>&nbsp;</td><td align="right">-0.21</td><td>&nbsp;</td><td>&nbsp;</td><td>1840</td><td>&nbsp;</td><td align="right">+1.73</td></tr>
+<tr><td>1810</td><td>&nbsp;</td><td align="right">+0.56</td></tr></table>
+
+<p><span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>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&#8217;s observations in 1769 and 1771.</p>
+
+<p>&#8220;&#8216;For the ancient observations, the following are the remaining
+errors:&mdash;</p>
+
+<p class="center"><i>Observation&mdash;Theory.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="theory">
+<tr><td>&nbsp;</td><td><span class="spacer2">&nbsp;</span></td><td align="center">"</td><td><span class="spacer">&nbsp;</span></td><td><span class="spacer">&nbsp;</span></td>
+    <td>&nbsp;</td><td><span class="spacer2">&nbsp;</span></td><td align="center">"</td><td><span class="spacer">&nbsp;</span></td><td><span class="spacer">&nbsp;</span></td>
+    <td>&nbsp;</td><td><span class="spacer2">&nbsp;</span></td><td align="center">"</td></tr>
+<tr><td>1690</td><td>&nbsp;</td><td align="right">+44.4</td><td>&nbsp;</td><td>&nbsp;</td>
+   <td>1750</td><td>&nbsp;</td><td align="right">- 1.6</td><td>&nbsp;</td><td>&nbsp;</td>
+   <td>1763</td><td>&nbsp;</td><td align="right">- 5.1</td></tr>
+<tr><td>1712</td><td>&nbsp;</td><td align="right">+ 6.7</td><td>&nbsp;</td><td>&nbsp;</td>
+   <td>1753</td><td>&nbsp;</td><td align="right">+ 5.7</td><td>&nbsp;</td><td>&nbsp;</td>
+   <td>1769</td><td>&nbsp;</td><td align="right">+ 0.6</td></tr>
+<tr><td>1715</td><td>&nbsp;</td><td align="right">- 6.8</td><td>&nbsp;</td><td>&nbsp;</td>
+   <td>1756</td><td>&nbsp;</td><td align="right">- 4.0</td><td>&nbsp;</td><td>&nbsp;</td>
+   <td>1771</td><td>&nbsp;</td><td align="right">+11.8</td></tr></table>
+
+<p>The errors are small, except for Flamsteed&#8217;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.&#8217;</p>
+
+<p>&#8220;I acknowledged the receipt of this paper in the following terms:&mdash;</p>
+
+<p class="center"><span class="smcap">No. 12.&mdash;G. B. Airy</span> <i>to</i> <span class="smcap">J. C. Adams</span>, Esq.</p>
+
+<p class="right">&#8220;&#8216;<span class="smcap">Royal Observatory, Greenwich</span>, 1845, <i>Nov.</i> 5.</p>
+
+<div class="sidenote">Airy&#8217;s inquiry about the &#8220;radius vector.&#8221;</div>
+
+<p>&#8220;&#8216;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 <i>Uranus</i>
+produced by a planet with certain assumed elements. The latter
+numbers are all extremely satisfactory: I am not enough acquainted
+with Flamsteed&#8217;s observations about<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span> 1690 to say whether they bear
+such an error, but I think it extremely probable.</p>
+
+<p>&#8220;&#8216;But I should be very glad to know whether this assumed perturbation
+will explain the error of the radius vector of <i>Uranus</i>. 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 <i>before</i> opposition with the times
+<i>after</i> opposition.&#8217;</p>
+
+<p>&#8220;I have before stated that I considered the establishment of this
+error of the radius vector of <i>Uranus</i> 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 <i>experimentum
+crucis</i>. And I waited with much anxiety for Mr. Adams&#8217; 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&#8217; theory.</p>
+
+<p>&#8220;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.&#8221;</p></div>
+
+<div class="sidenote">Adams&#8217; silence.</div>
+
+<p>Here we may leave Airy&#8217;s &#8220;account&#8221; for a few moments to consider the
+reason why he received no answer. Adams was a very shy and retiring<span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span> 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:</p>
+
+<div class="blockquot"><p>&#8220;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, &amp;c., approximately, which would probably
+lead to its discovery.&#8221;</p></div>
+
+<p>Accordingly, &#8220;as soon as possible after taking his degree&#8221; 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<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span> 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.</p>
+
+<div class="sidenote">His disappointment at Greenwich,</div>
+
+<p>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&#8217;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<span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span> the butler, acting somewhat in the manner of his kind,
+protected his master&#8217;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&#8217; visits until afterwards, and it would scarcely be
+just to blame him for a servant&#8217;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.</p>
+
+<div class="sidenote">and at Airy&#8217;s question.</div>
+
+<p>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&#8217;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 <i>experimentum crucis</i> 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<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span> another solution of
+the problem which had so engrossed his life at that time.</p>
+
+<div class="sidenote">The merits of Airy&#8217;s question.</div>
+
+<p>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 &#8220;error of radius vector&#8221; came before Airy in
+an entirely independent way, and as an entirely independent phenomenon,
+from the &#8220;error of longitude,&#8221; and there was nothing unnatural in
+regarding it as requiring independent explanation. It is true that, <i>as
+the event proved</i>, a mere readjustment of the orbit of Uranus got rid of
+this error of radius vector (this was substantially Le Verrier&#8217;s answer to
+Airy&#8217;s question); but we must not judge of what was possible before the
+event in the light of what we now know.<span class="sidenote">The range of possibilities.</span> 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<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span> 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; <i>and won it</i>; 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&#8217;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.</p>
+
+<p>One such alternative possibility has already been mentioned. &#8220;Hansen&#8217;s
+opinion was, that one disturbing body would not satisfy the phenomena; but
+he conjectured that there were two planets beyond <i>Uranus</i>.&#8221; 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<span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span>
+gives rise to the well-known &#8220;November meteors&#8221; must have passed very
+close to Uranus in <span class="smcaplc">A.D.</span> 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?</p>
+
+<p>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.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i071top.jpg" alt="" /></div>
+<p class="center"><span class="smcap">III&mdash;U. J. Le Verrier.</span><br />
+(<i>From a print in the possession of the Royal Astronomical Society.</i>)</p>
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i071bottom.jpg" alt="" /></div>
+<p class="center"><span class="smcap">IV&mdash;J. G. Galle.</span><br />
+<span class="smcaplc">WHO FIRST SAW THE PLANET NEPTUNE</span></p>
+<p>&nbsp;</p>
+
+<p>We must return, however, to Airy&#8217;s &#8220;account.&#8221; 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 <span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span>he was concerned,<span class="sidenote">Airy receives Le Verrier&#8217;s memoir.</span> until the following June, when Le Verrier&#8217;s
+memoir reached him; and we will let him give his own version of the
+result.</p>
+
+<div class="blockquot"><p>&#8220;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&#8217;
+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&#8217; 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 <i>M&eacute;canique C&eacute;leste</i> of Laplace; in
+the <i>Th&eacute;orie de la Lune</i> of Plana; above all, in Bouvard&#8217;s first
+tables of <i>Jupiter</i> and <i>Saturn</i>; 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<span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span> fully
+explained. I therefore addressed to M. Le Verrier the following
+letter:&mdash;</p>
+
+<p class="center">No. 13.&mdash;<span class="smcap">G. B. Airy</span> <i>to</i> <span class="smcap">M. Le Verrier.</span></p>
+
+<p class="right">&#8220;&#8216;Royal Observatory, Greenwich, 1846, <i>June</i> 26.</p>
+
+<div class="sidenote">He puts the &#8220;radius-vector&#8221; question to Le Verrier,</div>
+
+<p>&#8220;&#8216;I have read, with very great interest, the account of your
+investigations on the probable place of a planet disturbing the
+motions of <i>Uranus</i>, which is contained in the <i>Compte Rendu de
+l&#8217;Acad&eacute;mie</i> of June 1; and I now beg leave to trouble you with the
+following question. It appears, from all the later observations of
+<i>Uranus</i> made at Greenwich (which are most completely reduced in the
+<i>Greenwich Observations</i> 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?&#8217;&#8221;</p></div>
+
+<p>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&#8217;s conduct.<span class="sidenote">but makes no mention of Adams.</span> It seems extraordinary that<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span> 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 &#8220;felt no doubt of the accuracy of both
+calculations.&#8221; 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.</p>
+
+<div class="sidenote">Airy announces the likelihood of a new planet,</div>
+
+<p>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: &#8220;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.&#8221;<span class="sidenote">and suggests a search for it at Cambridge</span> 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<span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span> 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;<span class="sidenote">not having suitable telescope at Greenwich</span> and at that time the
+best telescope possessed by the observatory was not, in Airy&#8217;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&#8217;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,&mdash;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<span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span> 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:&mdash;</p>
+
+<p>&nbsp;</p>
+<div class="blockquot">
+<p class="center">No. 15.&mdash;<span class="smcap">G. B. Airy</span> <i>to</i> <span class="smcap">Professor Challis</span>.</p>
+
+<p class="right">&#8220;<span class="smcap">The Deanery, Ely</span>, 1846, <i>July</i> 9.</p>
+
+<p>&#8220;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 <i>Uranus</i>. 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.</p>
+
+<p>&#8220;Now, I should be glad to ask you, in the first place, whether you
+could make such an examination?</p>
+
+<p>&#8220;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?</p>
+
+<p>&#8220;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<span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span> 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.</p>
+
+<p>&#8220;The time for the said examination is approaching near.&#8221;</p></div>
+
+<div class="sidenote">Challis undertakes the search.</div>
+
+<p>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. &#8220;I get over the ground very slowly,&#8221; he wrote on September 2nd
+to Airy, &#8220;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.&#8221;
+With such a prospect, it is not surprising that one night&#8217;s observations
+were not even compared with the next; there would be a certain economy in
+waiting until a<span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span> large amount of material had been accumulated, and then
+making the comparisons all together, and this was the course adopted. But
+when Le Verrier&#8217;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;<span class="sidenote">He finds too late that he had observed the planet.</span> 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&#8217; observing the planet was in his grasp,
+<i>if</i> only he had examined or mapped the observations, and <i>if</i> he had not
+delayed doing so until he had more observations to reduce, and <i>if</i> he had
+not been very busy with some comet observations. Oh! these terrible <i>ifs</i>
+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,<span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span> 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 <i>better</i> 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.</p>
+
+<p>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.<span class="sidenote">Sensation caused by the discovery.</span> The
+&#8220;Account&#8221; 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&#8217;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.<span class="sidenote">Not all <i>national</i> jealousy.</span> 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<span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span> national jealousy, scientific
+men went almost too far in the opposite direction.</p>
+
+<p>Airy&#8217;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&#8217; 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.<span class="sidenote">The position of Cambridge in the matter.</span> 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<span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span>
+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;<span class="sidenote">Challis the weakest point.</span> 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,
+&#8220;Well! how did you get on? What did the Astronomer Royal say?&#8221; 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&#8217;s question<span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span> 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, &#8220;Oh! but you must answer the Astronomer
+Royal&#8217;s question: you may think it stupid, but you had better answer it
+politely, and show him that you know what you are about.&#8221; It is
+unprofitable to pursue speculation further; this did <i>not</i> 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.</p>
+
+<div class="sidenote">Curious difference between actual and supposed planet.</div>
+
+<p>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
+<span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span>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&#8217;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 <i>infinite</i> 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
+<i>longer</i> than this critical value, some of the mathematical expressions
+would be of contrary sign from those corresponding to a period a little
+<i>shorter</i>.<span class="sidenote">Professor Peirce&#8217;s contention that the discovery was a mere accident.<br /><br />The explanation.</span> 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<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span> 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&mdash;somewhat paradoxical
+though it was&mdash;found considerable support. It was not replied to by Adams
+until some thirty years later, when a short reply was printed in
+<i>Liouville&#8217;s Journal</i>. 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<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span> 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.</p>
+
+<p>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&#8217; work has been published by the
+Royal Astronomical Society; they have reproduced in their Memoirs a
+facsimile of Adams&#8217; MS. containing the &#8220;first solution,&#8221; 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&deg;. 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&#8217;s influence are from those used by Adams, and it is one of the
+curiosities of this remarkable piece of history that<span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span> some of them seem to
+be actually <i>in the wrong direction</i>; 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.</p>
+
+<div class="sidenote">Suggested elementary method for finding Neptune illusory.</div>
+
+<p>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 &#8220;Outlines of Astronomy&#8221; 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&#8217;s words:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;The conclusion is drawn that <i>Uranus</i> 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.&#8221;</p></div>
+
+<p>Professor Sampson goes on to show that a more<span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span> elaborate discussion seems
+quite as unpromising; and he concludes that the refinements employed were
+not superfluous, although it seems <i>now</i> clear that a different mode of
+procedure might have led more certainly to the required conclusion.</p>
+
+<div class="sidenote">The evil influence of Bode&#8217;s Law.</div>
+
+<p>For the third curious point is that both calculators should have adhered
+so closely to Bode&#8217;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&#8217; six solutions gave the true place of the planet and
+the intervals during which the error was within 5&deg; either way.</p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="solutions">
+<tr><td>&nbsp;</td><td>&nbsp;</td><td align="center">I.</td><td><span class="spacer">&nbsp;</span></td><td align="center">II.</td><td><span class="spacer">&nbsp;</span></td><td align="center">III.</td><td><span class="spacer">&nbsp;</span></td><td align="center">IV.</td><td><span class="spacer">&nbsp;</span></td><td align="center">V.</td><td><span class="spacer">&nbsp;</span></td><td align="center">VI.</td></tr>
+<tr><td>Correct</td><td>&nbsp;</td><td>1820</td><td>&nbsp;</td><td>1835</td><td>&nbsp;</td><td>1872</td><td>&nbsp;</td><td>1830</td><td>&nbsp;</td><td>1861</td><td>&nbsp;</td><td>1856</td></tr>
+<tr><td rowspan="2" align="center">Within &plusmn;5&deg;</td><td rowspan="2"><span class="bracket">{</span></td><td>1812</td><td>&nbsp;</td><td>1827</td><td>&nbsp;</td><td>1865</td><td>&nbsp;</td><td>1813</td><td>&nbsp;</td><td>1815</td><td>&nbsp;</td><td>1826</td></tr>
+<tr><td>1827</td><td>&nbsp;</td><td>1842</td><td>&nbsp;</td><td>1877</td><td>&nbsp;</td><td>1866</td><td>&nbsp;</td><td>1871</td><td>&nbsp;</td><td>1868</td></tr></table>
+
+<p>Now the date at which it was most important to obtain the correct place
+was 1845 or thereabouts<span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span> 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&#8217;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.</p>
+
+<div class="sidenote">Le Verrier&#8217;s erroneous limits.</div>
+
+<p>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.</p>
+
+<div class="blockquot"><p>&#8220;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 <span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span>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 <i>locus</i> 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&deg;, and not greater than 335&deg; or 345&deg;,
+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 <i>Uranus</i>.
+<span class="sidenote">The visible disc.</span>From this circumstance, combined with a probable hypothesis as to the
+density, M. Le Verrier concluded that<span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span> the planet would have a
+visible disk, and sufficient light to make it conspicuous in ordinary
+telescopes.</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;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&#8217;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, &#8216;Look in the place which I have indicated, and
+you will see the planet well.&#8217; Since Copernicus declared that, when
+means should be discovered for improving the vision, it would be
+found that <i>Venus</i> 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.&#8221;</p></div>
+
+<div class="sidenote">Peirce&#8217;s views of the limits.</div>
+
+<p><span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span>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.</p>
+
+<div class="blockquot"><p>&#8220;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:&mdash;</p>
+
+<p>&#8220;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.</p>
+
+<p>&#8220;2nd. &#8216;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&deg; and 252&deg;.&#8217;</p>
+
+<p>&#8220;&#8216;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&deg;
+distant from the limits of the second proposition. And again, if the
+planet is assumed to have had in 1800 a<span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span> 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.&#8217;</p>
+
+<p>&#8220;Neptune cannot, then, be the planet of M. Le Verrier&#8217;s theory, and
+cannot account for the observed perturbations of Uranus under the
+form of the inequalities involved in his analysis&#8221;&mdash;(<i>Proc. Amer.
+Acad. I.</i>, 1846-1848, <i>p.</i> 66).</p></div>
+
+<p>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 <i>both wrong</i>. The mean distance of
+Neptune is 30, which does <i>not</i> lie between 35 and 37.9; and the longitude
+in 1800 was 225&deg;, which does <i>not</i> lie between 243&deg; and 252&deg;. The
+ingenious process which Airy admired and which Peirce himself calls
+&#8220;consummately skilful&#8221; was wrong in principle.<span class="sidenote">Newcomb&#8217;s criticism.</span> As Professor Newcomb has
+said, &#8220;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<span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span> make such a blunder. Of course one
+trouble in Le Verrier&#8217;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.&#8221;</p>
+
+<p>The account of Le Verrier&#8217;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&#8217;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.<span class="sidenote">Element of good fortune.</span> 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&mdash;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 <span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span>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.<span class="sidenote">The map used by Galle.</span> 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.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i094tmb.jpg" alt="" /><br />
+<a href="images/i094.jpg"><small>Larger Image</small></a></div>
+<p class="center"><span class="smcap">V.&mdash;Corner of the Berlin Map, by the use of which Galle found Neptune.</span></p>
+<p>&nbsp;</p>
+
+<div class="sidenote">Every one made mistakes.</div>
+
+<p>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.<span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span> Both Adams and Le Verrier gave far
+too much importance to Bode&#8217;s Law.</p>
+
+<p>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, &#8220;who could carry
+through fabulous computations without error,&#8221; for the first time wrote
+down a wrong figure. The mistake was corrected upon the MS., &#8220;probably as
+soon as made,&#8221; 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.</p>
+
+<p>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&#8217;s Law<span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span> 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&#8217;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.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span></p>
+<h2><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III</h2>
+<h3>BRADLEY&#8217;S DISCOVERIES OF THE ABERRATION OF LIGHT AND OF THE NUTATION OF THE EARTH&#8217;S AXIS</h3>
+
+
+<div class="sidenote">Biographical method adopted.</div>
+
+<p>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&#8217;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<span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span> 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,<small><a name="f2.1" id="f2.1" href="#f2">[2]</a></small> 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.</p>
+
+<div class="sidenote">Bradley&#8217;s birth and early life.</div>
+
+<p>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<span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span> astronomer that we may almost disregard
+it, and consider him as an astronomer from the first.<span class="sidenote">Brief clerical career.</span> 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&#8217;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, &#8220;because the duty of
+a pastor was incompatible with his other studies and necessary
+engagements.&#8221;</p>
+
+<div class="sidenote">Learnt astronomy <i>not</i> at Oxford,</div>
+
+<p>But now let us turn to Bradley&#8217;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&mdash;Halley&#8217;s
+Comet&mdash;and returns every seventy-five years, being next expected about
+1910. But there is no record that<span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span> Bradley came under Halley&#8217;s teaching or
+influence as an undergraduate. In later years the two men knew each other
+well, and it was Halley&#8217;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.<span class="sidenote">but from his uncle, James Pound.</span> 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&#8217;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 &#8220;if Dr.
+Pound goes, I and the rest of the Company will not stay behind.&#8221; Soon
+afterwards the settlement was attacked in an<span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span> 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&#8217;s uncle, James Pound;<span class="sidenote">Pound a first-rate observer.</span> but the most important of all remains to be
+told&mdash;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.</p>
+
+<p>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&#8217;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.<span class="sidenote">Bradley worked with him.</span> 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 <span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span>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&#8217;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.</p>
+
+<div class="sidenote">The work done by Pound and Bradley.</div>
+
+<p>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 nebul&aelig;: 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&#8217;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<span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span> 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&#8217;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&#8217;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 <i>skill</i> 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&#8217;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.<span class="sidenote">Use of very long telescopes.</span> And finally, his skill
+in the management of instruments is shown by his measuring the diameter of
+the planet Venus with a telescope actually 212&#188; 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<span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span> all the resources of modern
+engineering, in the shape of rising floors, &amp;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.<span class="sidenote">Reason for great length.</span> 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 <i>single</i> 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&#8217;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&#8217;s; but we shall not use it as he did in any case. It will be laid<span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span>
+comfortably flat on the ground, and the rays of light reflected into it by
+a coelostat.</p>
+
+<div class="sidenote">Bradley appointed at Oxford,</div>
+
+<p>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,<span class="sidenote">but continues to work at Wansted.</span> and after Bradley&#8217;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&#8217;s death in 1724 interrupted the continuity of these
+joint observations, and by an odd accident prepared the way for Bradley&#8217;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.</p>
+
+<div class="sidenote">Samuel Molyneux.</div>
+
+<p>Samuel Molyneux was a gentleman of fortune<span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span> 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 &#8220;parallax,&#8221; as the astronomical term goes, could
+be found for the stars. The observations of Galileo, and the measures of
+Tycho Brah&eacute;, as reduced to systematic laws by Kepler, and finally by the
+great Newton, made it clear that the Copernican theory was <i>true</i>: but no
+one had succeeded in proving its truth in this particular way.<span class="sidenote">Attempts to find stellar parallax.</span> 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<span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span> 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.</p>
+
+<p>I must now briefly explain what these observations were. There is a bright
+star &#947; 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.</p>
+
+<p>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 &#8220;parallax&#8221; (the
+apparent shift due to the earth&#8217;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<span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span> delicate piece of apparatus than Hooke had
+employed.<span class="sidenote">The instrument.</span> 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.<span class="sidenote">Expected results.</span> 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 <i>how much</i> farther south it would
+appear in December than in June&mdash;this was exactly the point to be decided.</p>
+
+<p><a name="fig2" id="fig2"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/i109.jpg" alt="" /></div>
+<p class="center"><span class="smcap">Fig. 2.</span></p>
+<p>&nbsp;</p>
+
+<p><span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span>The reason of this will be clear from <a href="#fig2">Fig. 2</a>. [Remark, however, that this
+figure and the corresponding figure 4 do not represent the case of
+Bradley&#8217;s star, &#947; 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&#8217;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
+&#8220;parallax&#8221; 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.<span class="sidenote">Unexpected results.</span> But when
+Bradley repeated the observation on December 17, he found to his great
+surprise that the star was still moving southwards. Here was <span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span>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&#8243;&mdash;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.</p>
+
+<div class="sidenote">Tentative explanations.</div>
+
+<p>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
+&#947; 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 &#8220;nutation of the axis&#8221;
+and &#8220;variation of latitude&#8221; respectively. In the case<span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span> of nutation the
+North Pole remains in the same geographical position, but points to a
+different part of the heavens. The &#8220;variation of latitude,&#8221; 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.</p>
+
+<div class="sidenote">Nutation?</div>
+
+<p>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 &#947; 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
+&#947; Draconis, the other stars included would make the same circuit,
+preceding or following &#947; Draconis by a constant interval. Most of
+them would be too faint for observation with Bradley&#8217;s telescope; but
+there was one bright enough to be observed, which also came within its
+limited range, and it was promptly put under <i>surveillance</i> when a
+nutation of the earth&#8217;s axis was suspected. Careful watching showed that
+it was not affected in the same way as &#947; Draconis, and hence the
+movement could not be in the plumb-line. Was there, then, after all, some
+effect of the earth&#8217;s atmosphere which had been overlooked? We have
+already remarked that since the star passes<span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span> 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.<span class="sidenote">Anomalous refraction.</span> 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.</p>
+
+<p><a name="fig3" id="fig3"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/i113.jpg" alt="" /></div>
+<p class="center"><span class="smcap">Fig. 3.</span></p>
+<p>&nbsp;</p>
+
+<p>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&#8217;s atmosphere, or &#8220;refracted,&#8221; if they
+enter it obliquely.</p>
+
+<p>If the atmosphere were of the same density throughout, like a piece of
+glass, then a vertical ray of light, A B (see <a href="#fig3">Fig. 3</a>), entering the
+atmosphere at B would suffer no bending or<span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span> 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.</p>
+
+<p><a name="fig4" id="fig4"></a>&nbsp;</p>
+<div class="figcenter"><img src="images/i114.jpg" alt="" /></div>
+<p class="center"><span class="smcap">Fig. 4.</span></p>
+<p>&nbsp;</p>
+
+<p>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,<span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span> 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 &#8220;June,&#8221; the light
+would fall vertically on the nose of the atmosphere at A, and there would
+be no refraction. Similarly in &#8220;December&#8221; 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.</p>
+
+<p>But we have assumed the star to lie in the plane of the earth&#8217;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.</p>
+
+<div class="sidenote">Delay in finding real explanation.</div>
+
+<p>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. <span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span>We have all had experience of
+the <i>kind</i> 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 &#8220;giving it up,&#8221; and the
+simplicity of the answer when once it is declared. But with scientific
+conundrums the expedient of &#8220;giving it up&#8221; 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&#8217;s instrument only allowed of the
+observation of two stars, &#947; Draconis and the small star above
+mentioned.<span class="sidenote">Bradley sets up another instrument at Wansted.</span> 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&#8217;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&#8217;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<span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span> 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 &pound;140 a year, and probably he was glad to accept his aunt&#8217;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.<span class="sidenote">Finds the right clue.</span> 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, &#8220;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.&#8221; 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.<span class="sidenote">A wind-vane on a boat.</span> Dr. Bradley remarked that every time the boat put
+about the vane at the top of the boat&#8217;s mast shifted a little, as if there
+had been a slight change in the direction of the wind. He<span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span> 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.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i118.jpg" alt="" /></div>
+<p class="center"><span class="smcap">Fig. 5.</span></p>
+<p>&nbsp;</p>
+
+<div class="sidenote">Analogy of rain.</div>
+
+<p>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<span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span> days of umbrellas in the following words: &#8220;Je suppose
+que, dans un temps calme, la pluie tombe perpendiculairement, et qu&#8217;on
+soit dans une voiture ouverte sur le devant; si la voiture est en repos,
+on ne re&ccedil;oit pas la moindre goutte de pluie; si la voiture avance avec
+rapidit&eacute;, la pluie entre sensiblement, comme si elle avoit pris une
+direction oblique.&#8221; Lalande&#8217;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.</p>
+
+<div class="sidenote">Aberration.</div>
+
+<p>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 <a href="#fig4">Fig. 4</a> 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&#8217;t! It may comfort us in our struggles<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span> 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.</p>
+
+<div class="sidenote">Results of discovery.</div>
+
+<p>The discovery of aberration made Bradley famous at a bound. Oxford might
+well be proud of her two Savilian Professors at this time, for they had
+both made world-famous discoveries&mdash;Halley that of the periodicity of
+comets, and Bradley of the aberration of light. How different their tastes
+were and how difficult it would have been for either to do the work of the
+other! Bradley was no great mathematician, and though he was quite able to
+calculate the orbit of a comet, and carried on such work when Halley left
+it, it was probably not congenial to him. Halley, on the other hand,
+almost despised accurate observations as finicking. &#8220;Be sure you are
+correct to a minute,&#8221; he was wont to say, &#8220;and the fractions do not so
+much matter.&#8221; With such a precept Bradley would never have made his
+discoveries. No quantity was too small in his eyes, and no sooner was the
+explanation of aberration satisfactorily established than he perceived
+that though it would account for the main facts, it would not explain all.
+There was something left. This is often the case in the<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span> history of
+science. A few years ago it was thought that we knew the constitution of
+our air completely&mdash;oxygen, nitrogen, water vapour, and carbonic acid gas;
+but a great physicist, Lord Rayleigh, found that after extracting all the
+water and carbonic acid gas, all the oxygen and all the nitrogen, there
+was something left&mdash;a very minute residuum, which a careless experimenter
+would have overlooked or neglected, but which a true investigator like
+Lord Rayleigh saw the immense importance of. He kept his eye on that
+something left, and presently discovered a new gas which we now know as
+argon. Had he repeated the process, extracting all the argon after the
+nitrogen, he might have found by a scrutiny much more accurate still yet
+another gas, helium, which we now know to exist in extremely minute
+quantities in the air. But meantime this discovery was made in another
+way.</p>
+
+<div class="sidenote">Still something to be explained.</div>
+
+<p>When Bradley had extracted all the aberration from his observations he
+found that there was something left, another problem to be solved and some
+more thinking to be done to solve it. But he was now able to profit by his
+previous labours, and the second step was made more easily than the first.
+The residuum was not the parallax of which he had originally been in
+search, for it did not complete a cycle within the year; it was rather a
+progressive change from year to year. But there was an important clue of
+another kind. He saw that the apparent movements of<span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span> all stars were in
+this case the same; and he knew that a movement of this kind can be
+referred, not to the stars themselves, but to the plumb-line from which
+their directions are measured.<span class="sidenote">Probably nutation.</span> He had thought out the possible causes of
+such a movement of the plumb-line or of the earth itself, and had realised
+that there might be a <i>nutation</i> which would go through a cycle in about
+nineteen years, the period in which the moon&#8217;s nodes revolve. He was not
+mathematician enough to work out the cause completely, but he saw clearly
+that to trace the whole effect he must continue the observations for
+nineteen years; and accordingly he entered on this long campaign without
+any hesitation. His instrument was still that in his aunt&#8217;s house at
+Wansted, where he continued to live and make the observations for a few
+years, but in 1732 he removed to Oxford, as we shall see, and he must have
+made many journeys between Wansted and Oxford in the course of the
+remaining fifteen years during which he continued to trace out the effects
+of nutation. His aunt too left Wansted to accompany Bradley to Oxford, and
+the house passed into other hands.<span class="sidenote">His nineteen years&#8217; campaign.</span> It is to the lasting credit of the new
+occupant, Mrs. Elizabeth Williams, that the great astronomer was allowed
+to go on and complete the valuable series of observations which he had
+commenced. Bradley was not lodged in her house; he stayed with a friend
+close by on his visits to Wansted, but<span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span> came freely in and out of his
+aunt&#8217;s old home to make his observations. How many of us are there who
+would cheerfully allow an astronomer to enter our house at any hour of the
+night to make observations in the coal-cellar! It says much, not only for
+Bradley&#8217;s fame, but for his personal attractiveness, that he should have
+secured this permission, and that there should be no record of any
+friction during these fifteen years. At the end of the whole series of
+nineteen years his conclusions were abundantly verified, and his second
+great discovery of nutation was established. Honours were showered upon
+him, and no doubt the gentle heart of Mrs. Elizabeth Williams was uplifted
+at the glorious outcome of her long forbearance.</p>
+
+<div class="sidenote">Residence at Oxford.</div>
+
+<p>But we may now turn for a few moments from Bradley&#8217;s scientific work to
+his daily life. We have said that in 1732, after holding his professorship
+for eleven years, he first went definitely to reside in Oxford. He
+actually had not been able to afford it previously. His income was only
+&pound;140 a year, and the statutes prevented him from holding a living: so
+that he was fain to accept Mrs. Pound&#8217;s hospitable shelter. But in 1729 an
+opportunity of adding to his income presented itself, by giving lectures
+in &#8220;experimental philosophy.&#8221; The observations on nutation were not like
+those on aberration: he was not occupied day and night trying to find the
+solution: he had practically made up his mind about the solution,<span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span> and the
+actual observations were to go on in a quiet methodical manner for
+nineteen years, so that he now had leisure to look about him for other
+employment. Dr. Keill, who had been Professor of Astronomy before Bradley,
+had attracted large classes to lectures, not on astronomy, but on
+experimental philosophy: but had sold his apparatus and goodwill to Mr.
+Whiteside, of Christ Church, one of the candidates who were disappointed
+by Bradley&#8217;s election. In 1729 Bradley purchased the apparatus from
+Whiteside, and began to give lectures in experimental philosophy. His
+discovery of aberration had made him famous, so that his classes were
+large from the first, and paid him considerable fees. Suddenly therefore
+he changed his poverty for a comfortable income, and he was able to live
+in Oxford in one of two red brick houses in New College Lane, which were
+in those days assigned to the Savilian Professors (now inhabited by New
+College undergraduates). His aunt, Mrs. Pound, to whom he was devotedly
+attached, came with him, and two of her nephews. In his time of prosperity
+Bradley was thus able to return the hospitality which had been so
+generously afforded him in times of stress.</p>
+
+<div class="sidenote">Astronomer Royal at Greenwich.</div>
+
+<p>Before he completed his observations for nutation another great change in
+his fortunes took place. In 1742 he was elected to succeed Halley as
+Astronomer Royal. It was Halley&#8217;s dying wish that Bradley should succeed
+him, and it is said that he was even willing to resign in his<span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span> favour, for
+his right hand had been attacked by paralysis, and the disease was
+gradually spreading. But he died without any positive assurance that his
+wish would be fulfilled. The chief difficulty in securing the appointment
+of Bradley seems to have been that he was the obvious man for the post in
+universal opinion.<span class="sidenote">Letter from Earl of Macclesfield.</span> &#8220;It is not only my friendship for Mr. Bradley that
+makes me so ardently wish to see him possessed of the position,&#8221; wrote the
+Earl of Macclesfield to the Lord Chancellor; &#8220;it is my real concern for
+the honour of the nation with regard to science. For as our credit and
+reputation have hitherto not been inconsiderable amongst the astronomical
+part of the world, I should be extremely sorry we should forfeit it all at
+once by bestowing upon a man of inferior skill and abilities the most
+honourable, though not the most lucrative, post in the profession (a post
+so well filled by Dr. Halley and his predecessor), when at the same time
+we have amongst us a man known by all the foreign, as well as our own
+astronomers, not to be inferior to either of them, and one whom Sir Isaac
+Newton was pleased to call the best astronomer in Europe.&#8221; And again, &#8220;As
+Mr. Bradley&#8217;s abilities in astronomical learning are allowed and confessed
+by all, so his character in every respect is so well established, and so
+unblemished, that I may defy the worst of his enemies (if so good and
+worthy a man have any) to make even the lowest or most trifling objection
+to it.&#8221;</p>
+
+<p><span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span>&#8220;After all,&#8221; the
+letter goes on, &#8220;it may be said if Mr. Bradley&#8217;s skill is
+so universally acknowledged, and his character so established, there is
+little danger of opposition, since no competitor can entertain the least
+hope of success against him. But, my lord, we live in an age when most men
+how little soever their merit may be, seem to think themselves fit for
+whatever they can get, and often meet with some people, who by their
+recommendations of them appear to entertain the same opinion of them, and
+it is for this reason that I am so pressing with your lordship not to lose
+any time.&#8221;</p>
+
+<p>Such recommendations had, however, their effect: the dreaded possibility
+of a miscarriage of justice was averted, and Bradley became the third
+Astronomer Royal, though he did not resign his professorship at Oxford.
+Halley, Bradley, and Bliss, who were Astronomers Royal in succession, all
+held the appointment along with one of the Savilian professorships at
+Oxford; but since the death of Bliss in 1761, the appointment has always
+gone to a Cambridge man.</p>
+
+<div class="sidenote">Instruments very defective.</div>
+
+<p>When Bradley went to Greenwich, in June 1742, he was at first unable to do
+much from the wretched state in which he found the instruments. Halley was
+not a good observer: his heart was not in the work, and he had not taken
+the trouble to set the instruments right when they went wrong. The
+counterpoises of that instrument which ought to have been the best in the
+world at the time<span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span> rubbed against the roof so that the telescope could
+scarcely be moved in some positions: and some of the screws were broken.
+There was no proper means of illuminating the cross-wires, and so on. With
+care and patience Bradley set all this right, and began observations. He
+had the good fortune to secure the help of his nephew, John Bradley, as
+assistant, and the companionship seems to have been as happy as that
+previous one of James Bradley and his uncle Pound. John Bradley was able
+to carry on the observations when his uncle was absent in Oxford, and the
+work the two got through together in the first year is (in the words of
+Bradley&#8217;s biographer Rigaud) &#8220;scarcely to be credited.&#8221; The transit
+observations occupy 177 folio pages, and no less than 255 observations
+were taken on one night. And at the same time, it must be remembered,
+Bradley was still carrying on his nutation observations at Wansted, still
+lecturing at Oxford, and not content with all this, began a course of
+experiments on the length of the seconds&#8217; pendulum. Truly a giant for hard
+work!</p>
+
+<p>But, in spite of his care in setting them right, the instruments in the
+Observatory were found to be hopelessly defective. The history of the
+instruments at the Royal Observatory is a curious one. When Flamsteed was
+appointed the first Astronomer Royal he was given the magnificent salary
+of &pound;100 a year, and no instruments to observe with. He purchased some
+instruments<span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span> with his own money, and at his death they were claimed by his
+executors. Hence Halley, the second Astronomer Royal, found the
+Observatory totally unprovided in this respect. He managed to persuade the
+nation to furnish the funds for an equipment; but Halley, though a man of
+great ability in other ways, did not know a good instrument from a bad
+one; so that Bradley&#8217;s first few years at the Observatory were wasted
+owing to the imperfection of the equipment.<span class="sidenote">New instruments.</span> When this was fully realised
+he asked for funds to buy new instruments, and such was the confidence
+felt in him that he got what he asked for without much difficulty. More
+than &pound;1000, a large sum for those days, was spent under his direction,
+the principal purchases being two quadrants for observation of the
+position of the stars, one to the north and the other to the south. With
+these quadrants, which represented the perfection of such apparatus at
+that time, Bradley made that long and wonderful series of observations
+which is the starting-point of our knowledge of the movements of the
+stars. The instruments are still in the Royal Observatory, the more
+important of the two in its original position as Bradley mounted it and
+left it.</p>
+
+<div class="sidenote">Work at Greenwich.</div>
+
+<p>It seems needless to mention his work as Astronomer Royal, but I will give
+quite briefly a summary of what he accomplished, and then recall a
+particular incident, which shows how far ahead of his generation his
+genius for observation<span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span> placed him. The summary may be given as follows.
+We owe to Bradley&mdash;</p>
+
+<p>1. A better knowledge of the movements of Jupiter&#8217;s satellites.</p>
+
+<p>2. The orbits of several comets calculated directly from his own
+observations, when such work was new and difficult.</p>
+
+<p>3. Experiments on the length of the pendulum.</p>
+
+<p>4. The foundation of our knowledge of the refraction of our atmosphere.</p>
+
+<p>5. Considerable improvements in the tables of the moon, and the promotion
+of the method for finding the longitude by lunar distances.</p>
+
+<p>6. The proper equipment of our national Observatory with instruments, and
+the use of these to form the basis of our present knowledge of the
+positions and motions of the stars.</p>
+
+<p>Many men would consider any one of these six achievements by itself a
+sufficient title to fame. Bradley accomplished them all in addition to his
+great discoveries of aberration and nutation.</p>
+
+<div class="sidenote">Might have found variation of latitude.</div>
+
+<p>And with a little more opportunity he might have added another great
+discovery which has shed lustre on the work of the last decade. We said
+earlier in this chapter that the axis of the earth may move in one or two
+ways. Either it may point to a different star, remaining fixed relatively
+to the earth, as in the nutation which Bradley discovered; or it may
+actually change its position in the earth. This second kind of movement
+was believed until twenty years ago not to<span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span> exist appreciably; but the
+work of K&uuml;stner and Chandler led to the discovery that it did exist, and
+its complexities have been unravelled, and will be considered in the sixth
+chapter. Now a century and a half ago Bradley was on the track of this
+&#8220;variation of latitude.&#8221; His careful observations actually showed the
+motion of the pole, as Mr. Chandler has recently demonstrated; and,
+moreover, Bradley himself noticed that there was something unexplained.
+Once again there was a <i>residuum</i> after (first) aberration and (next)
+nutation had been extracted from the observations; and with longer life he
+might have explained this residuum, and added a third great discovery to
+the previous two. Or another coming after him might have found it; but
+after the giant came men who could not tread in his footsteps, and the
+world waited 150 years before the discrepancy was explained.</p>
+
+<p>The attitude of our leading universities towards science and scientific
+men is of sufficient importance to justify another glance at the relations
+between Bradley and Oxford.<span class="sidenote">Oxford&#8217;s tardy recognition of Bradley.</span> We have seen that Oxford&#8217;s treatment of
+Bradley was not altogether satisfactory. She left him to learn astronomy
+as he best could, and he owes no teaching to her. She made him Professor
+of Astronomy, but gave him no observatory and a beggarly income which he
+had to supplement by giving lectures on a different subject. But when he
+had disregarded these discouragements and made a name for <span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span>himself, Oxford
+took her share in recognition. He was created D.D. by diploma in 1742; and
+when his discovery of nutation was announced in 1748, and produced
+distinctions and honours of all kinds from over the world, we <ins class="correction" title="original: are are">are</ins> told
+that &#8220;amidst all these distinctions, wide as the range of modern science,
+and permanent as its history, there was one which probably came nearer his
+heart, and was still more gratifying to his feeling than all. Lowth
+(afterwards Bishop of London), a popular man, an elegant scholar, and
+possessed of considerable eloquence, had in 1751 to make his last speech
+in the Sheldonian Theatre at Oxford as Professor of Poetry. In recording
+the benefits for which the University was indebted to its benefactors, he
+mentioned the names of those whom Sir Henry Savile&#8217;s foundation had
+established there: &#8216;What men of learning! what mathematicians! we owe to
+Savile, Briggs, Wallis, Halley; to Savile we owe Greaves, Ward, Wren,
+Gregory, Keill, and one whom I will not name, for posterity will ever have
+his name on its lips.&#8217; Bradley was himself present; there was no one in
+the crowded assembly on whom the allusion was lost, or who did not feel
+the truth and justice of it; all eyes were turned to him, while the walls
+rung with shouts of heartfelt affection and admiration; it was like the
+triumph of Themistocles at the Olympic games.&#8221;</p>
+
+<div class="sidenote">The study of &#8220;residual phenomena.&#8221;</div>
+
+<p>These words of Rigaud indicate the fame deservedly acquired by an earnest
+and <span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span>simple-minded devotion to science: but can we learn anything from the
+study of Bradley&#8217;s work to guide us in further research? The chief lessons
+would seem to be that if we make a series of careful observations, we
+shall probably find some deviation from expectation: that we must follow
+up this clue until we have found some explanation which fits the facts,
+not being discouraged if we cannot hit upon the explanation at once, since
+Bradley himself was puzzled for several years: that after finding one
+<i>vera causa</i>, and allowing for the effect of it, the observations may show
+traces of another which must again be patiently hunted, even though we
+spend nineteen years in the chase: and that again we may have to leave the
+complete rectification of the observations to posterity. But though we may
+admit the general helpfulness of these directions, and that this patient
+dealing with residual phenomena seems to be a method capable of frequent
+application, we cannot deduce any universal principle of procedure from
+them: witness the difficulty of dealing with meteorological observations,
+for instance. It is not always possible to find any orderly arrangement of
+the residuals which will give us a clue to start with. When such an
+arrangement is manifested, we must certainly follow up the clue; it would
+almost seem that no expense should be prohibitive, since it is impossible
+to foresee the importance of the result.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span></p>
+<h2><a name="CHAPTER_IV" id="CHAPTER_IV"></a>CHAPTER IV</h2>
+<h3>ACCIDENTAL DISCOVERIES</h3>
+
+<p>In reviewing various types of astronomical discovery I have laid some
+stress upon the fact that they are, generally speaking, far from being
+accidental in character. A new planet does not &#8220;swim into our ken,&#8221; at any
+rate not usually, but is found only after diligent search, and then only
+by an investigator of acute vision, or other special qualifications. But
+this is, of course, not always the case. Some discoveries are made by the
+merest accident, as we have had occasion to remark incidentally in the
+case of the minor planets; and for the sake of completeness it is
+desirable to include among our types at least one case of such accidental
+discovery. As, however, the selection is a little invidious, I may perhaps
+be pardoned for taking the instance from my own experience, which happens
+to include a case where one of those remarkable objects called &#8220;new stars&#8221;
+walked deliberately into a net spread for totally different objects.<span class="sidenote">The Oxford new star found during work on Astrographic Chart.</span> There
+is the further reason for choosing this instance: that it will afford me
+the opportunity of saying something about the special research in which we
+were actually engaged, the work of mapping out the heavens by
+photography,<span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span> or, as it has been called, the Astrographic Chart&mdash;a great
+scheme of international co-operation by which it is hoped to leave as a
+legacy for future centuries a record of the state of the sky in our age.
+Such a record cannot be complete; for however faint the stars included, we
+know that there are fainter stars which might have been included had we
+given longer exposures to the plates. Nor can it be in other ways final or
+perfect; however large the scale, for instance, on which the map is made,
+we can imagine the scale doubled or increased many-fold. But the map will
+be a great advance on anything that has hitherto been made, and some
+account of it will therefore no doubt be of interest.</p>
+
+<div class="sidenote">Origin of the chart.</div>
+
+<p>We may perhaps begin with a brief historical account of the enterprise.
+Photographs of the stars were taken many years ago, but only by a few
+enthusiasts, and with no serious hope of competing with eye observations
+of the sky. The old wet-plate photography was, in fact, somewhat unsuited
+to astronomical purposes; to photograph faint objects a long exposure is
+necessary, and the wet plate may dry up before the exposure is
+concluded&mdash;nay, even before it is commenced, if the observer has to wait
+for passing clouds&mdash;and therefore it may be said that the successful
+application of photography to astronomy dates from the time when the dry
+plate was invented; when it became possible to expose a plate in the
+telescope for hours, or by accumulation even for days. The dry plate
+remains sensitive for a long period, and if it is desired to extend an
+exposure beyond the<span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span> limits of one night, it is quite easy to close up
+the telescope and return to the operations again on the next fine night;
+and so on, if not perhaps indefinitely, at any rate so long as to
+transcend the limits of human patience up to the present.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i135.jpg" alt="" /></div>
+<p class="center">VII.&mdash;<span class="smcap">Great Comet of Nov. 7th, 1882</span><br />
+(<i>From a photograph taken at the Royal Observatory, Cape of Good Hope.</i>)</p>
+<p>&nbsp;</p>
+
+<div class="sidenote">Comet of 1882.</div>
+
+<p>But to consider our particular project. We may assign, perhaps, the date
+1882 as that in which it first began to take shape. In that year there was
+a magnificent bright comet, the last really large comet which we, in the
+Northern Hemisphere, have had the good fortune to see. Some of us, of
+course, were not born at that time, and perhaps others who were alive may
+nevertheless not have seen that comet; for it kept somewhat uncomfortably
+early morning hours, and I can well remember myself feeling rather more
+resentment than gratitude to the man who waked me up about four o&#8217;clock to
+see it. Many observations were of course made of this interesting visitor,
+and what specially concerns us is that at the Cape of Good Hope some
+enterprising photographers tried to photograph it. They tried in the first
+instance with ordinary cameras, and soon found&mdash;what any astronomer could
+have told them&mdash;that the movement of the earth, causing an apparent
+movement of the comet and the stars in the opposite direction, frustrated
+their efforts. The difficulties of obtaining pictures of moving objects
+are familiar to all photographers. A &#8220;snap-shot&#8221; might have met the
+difficulty, but the comet was scarcely bright enough to affect the plate
+with a short exposure. Ultimately Dr. David Gill, the<span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span> astronomer at the
+Cape Observatory, invited one of the photographers to strap his camera to
+one of the telescopes at the Observatory, a telescope which could be
+carried round by clockwork in the usual way, so as to counteract the
+earth&#8217;s motion, and in effect to keep the comet steadily in view, as
+though it were at rest.<span class="sidenote">Stars shown on the pictures.</span> As a consequence, some very beautiful and
+successful pictures of the comet were obtained, and on them a large number
+of stars were also shown. They were, as I have said, not by any means the
+first pictures of stars obtained by photography, but they represented in
+facility and in success so great an advance upon what had been formerly
+obtained that they attracted considerable attention. They were sent to
+Europe and stimulated various workers to further experiments.</p>
+
+<p>The late Dr. Common in England, an amateur astronomer, began that
+magnificent pioneer work in astronomical photography which soon brought
+him the Gold Medal of the Royal Astronomical Society for his photographs
+of nebul&aelig;. But the most important result for our purpose was produced in
+France. There had been started many years before by the French astronomer
+Chacornac a series of star maps round the Zodiac similar in intention to
+the Berlin maps which figured in the history of the discovery of Neptune.
+Chacornac died before his enterprise was very far advanced, and the work
+was taken up by two brothers, Paul and Prosper Henry, who followed
+Chacornac in adopting for the work the laborious<span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span> method of eye
+observation of each individual star. They proceeded patiently with the
+work on these lines; but when they came to the region where the Zodiac is
+crossed by the Milky Way, and the number of stars in a given area
+increases enormously, they found the labour so great as to be practically
+prohibitive, and were in doubt how to deal with the difficulty.<span class="sidenote">The brothers Henry begin work.</span> It was at
+this critical moment that these comet photographs, showing the stars so
+beautifully, suggested the alternative of mapping the stars
+photographically. They immediately set to work with a trial lens, and
+obtained such encouraging results that they proceeded themselves to make a
+larger lens of the same type; this again was satisfactory, and the idea
+naturally arose of extending to the whole heavens the scheme which they
+had hitherto intended only for the Zodiac, a mere belt of the heavens. But
+this rendered the enterprise too large for a single observatory.<span class="sidenote">Conference of 1887.</span> It became
+necessary to obtain the co-operation of other observatories, and with this
+end in view an International Conference was summoned to meet in Paris in
+1887 to consider the whole project. There were delegates from, if not all
+nations, at any rate a considerable number:&mdash;</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="nations">
+<tr><td class="dent">France</td><td class="br">20</td><td class="dent">U.S. America</td><td class="br">3</td><td class="dent">Spain</td><td class="dent">1</td></tr>
+<tr><td class="dent">British Empire</td><td class="br">8</td><td class="dent">Austria</td><td class="br">2</td><td class="dent">Switzerland</td><td class="dent">1</td></tr>
+<tr><td class="dent">Germany</td><td class="br">6</td><td class="dent">Sweden</td><td class="br">2</td><td class="dent">Portugal</td><td class="dent">1</td></tr>
+<tr><td class="dent">Russia</td><td class="br">3</td><td class="dent">Denmark</td><td class="br">2</td><td class="dent">Brazil</td><td class="dent">1</td></tr>
+<tr><td class="dent">Holland</td><td class="br">3</td><td class="dent">Belgium</td><td class="br">1</td><td class="dent">Argentine Republic</td><td class="dent">1</td></tr>
+<tr><td class="dent">&nbsp;</td><td class="br">&nbsp;</td><td class="dent">Italy</td><td class="br">1</td></tr></table>
+
+
+<p><span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span>The Conference had a number of very important questions to discuss, for
+knowledge of the photographic method and its possibilities was at that
+time in its infancy. There was, for instance, the question whether all the
+instruments need be of the same pattern, and if so what that pattern
+should be. The first of these questions was settled in the affirmative, as
+we might expect; in the interests of uniformity it was desirable that the
+maps should be as nearly similar as possible.<span class="sidenote">Choice of instrument.</span> The second question was not
+so easy; there were at least three different types of instruments which
+might be used. First of all, there was the photographic lens, such as is
+familiar to all who have used an ordinary camera, consisting of two lenses
+with a space between; though since each of these lenses is itself made up
+of two, we should more correctly say four lenses in all. It was with a
+lens of this kind that the comet pictures had been taken at the Cape of
+Good Hope, and it might seem the safest plan to adopt what had been shown
+to be capable of such good work. But there was this difficulty; the
+pictures of the comet were on a very small scale, and taken with a small
+lens; a much larger lens was required for the scheme now under
+contemplation, and when there are four separate lenses to be made, each
+with two surfaces to polish, and each requiring a perfectly sound clear
+piece of glass, it will be obvious that the difficulties of making a large
+compound lens of this kind are much<span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span> greater,<span class="sidenote">Expense of &#8220;doublet.&#8221;</span> and the expense much more
+serious than in the case of a single lens, or even a pair. It was this
+question of expense which had led the brothers Henry to experiment with a
+different kind of instrument, in which only one pair of lenses was used
+instead of two. Their instrument was, in fact, very similar to the
+ordinary telescope, excepting that they were bound to make their lenses
+somewhat different in shape in order to bring to focus the rays of light
+suitable for photography, which are not the same as those suitable for eye
+observation with the ordinary telescope. Dr. Common, again, had used a
+third kind of instrument, mainly with the view of reducing the necessary
+expense still further, or, perhaps, of increasing the size of the
+instrument for the same expense. His telescope had no lens at all, but a
+curved mirror instead, the mirror being made of glass silvered on the face
+(not on the back as in the ordinary looking-glass).<span class="sidenote">Advantages of reflector.</span> In this case there is
+only one surface to polish instead of four, as in the Henrys&#8217; telescope,
+or eight, as in the case of the photographic doublet; and, moreover, since
+the rays of light are reflected from the surface of the glass, and do not
+pass <i>through</i> it at all, the internal structure of the glass is not so
+strictly important as in the other cases. Hence the reflector is a very
+cheap instrument, and it is, moreover, quite free from some difficulties
+attached to the other instruments. No correction for rays of light of
+different colours is<span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span> required, since all rays of whatever colour come to
+the same focus automatically. These advantages of the reflector were so
+considerable as to almost outweigh one well-known disadvantage, which is,
+however, not very easily expressed in words. The reflector might be
+described as an instrument with a temper; sometimes it gives excellent
+results, but at others <i>something</i> seems to be wrong, though the worried
+observer does not exactly know what. Long experience and patience are
+requisite to humour the instrument and get the best results from it, and
+it was felt that this uncertainty was sufficient to disqualify the
+instrument for the serious piece of routine work contemplated in mapping
+the heavens.<span class="sidenote">Refractor chosen.</span> Accordingly the handier and more amiable instrument with
+which the brothers Henry had done such good work was selected as the
+pattern to be adopted.</p>
+
+<p>It is curious that at the Conference of 1887 nothing at all was said about
+the type of instrument first mentioned (the &#8220;doublet lens&#8221;), although a
+letter was written in its favour by Professor Pickering of Harvard College
+Observatory. Since that time we have learnt much of its advantages, and it
+is probable that if the Conference were to meet now they might arrive at a
+different decision; but at that time they were, to put it briefly,
+somewhat afraid of an instrument which seemed to promise, if anything, too
+well, especially in one respect. With the reflector and<span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span> the refractor it
+had been found that the field of good images was strictly limited. The
+Henrys&#8217; telescope would not photograph an area of the sky greater in
+extent than 2&deg; in diameter at any one time, and the reflector was more
+limited still; within this area the images of the stars were good, and it
+had been found that their places were accurately represented.<span class="sidenote">Doublet would have been better.</span> Now the
+&#8220;doublet&#8221; seemed to be able to show much larger areas than this with
+accuracy, but no one had been able to test the accuracy to see whether it
+was sufficient for astronomical purposes; and although no such feeling was
+openly expressed or is on record, I think there is no doubt that a feeling
+existed of general mistrust of an instrument which seemed to offer such
+specious promises. Whatever the reason, its claims were passed over in
+silence at the Conference, and the safer line (as it was then thought) of
+adopting as the type the Henrys&#8217; instrument, was taken.</p>
+
+<p>This was perhaps the most important question settled at the Conference,
+and the answers to many of the others naturally followed. The size of the
+plates, for instance, was settled automatically. The question down to what
+degree of faintness should stars be included, resolved itself into the
+equivalent question, What should be the length of time during which the
+plates were exposed? Then, again, the question, What observatories should
+take part in the work? became simply this: What observatories could
+afford<span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span> to acquire the instruments of this new pattern and get other funds
+for carrying out the work specified?<span class="sidenote">The eighteen observatories.</span> It was ultimately found that eighteen
+observatories were able to obtain the apparatus and funds, though
+unfortunately three of the eighteen have since found it impossible to
+proceed. The following is the original list, and in brackets are added the
+names of three other observatories which in 1900 undertook to fill the
+places of the defaulters.</p>
+
+<p class="center"><span class="smcap">Observatories Co-operating for the Astrographic Chart.</span></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="observatories">
+<tr><td class="btrl" align="center">Observatory.</td>
+    <td class="btr" align="center">Zones of<br />Declination.</td>
+    <td class="btr" align="center">Number<br />of Plates.</td></tr>
+<tr><td class="btrl">Greenwich</td>
+    <td class="btr">+90&deg; to +65&deg;</td>
+    <td class="btr" align="center">1149</td></tr>
+<tr><td class="blr">Rome</td>
+    <td class="br">+64&deg;&nbsp;&nbsp;"&nbsp;&nbsp;+55&deg;</td>
+    <td class="br" align="center">1140</td></tr>
+<tr><td class="blr">Catania</td>
+    <td class="br">+54&deg;&nbsp;&nbsp;"&nbsp;&nbsp;+47&deg;</td>
+    <td class="br" align="center">1008</td></tr>
+<tr><td class="blr">Helsingfors</td>
+    <td class="br">+46&deg;&nbsp;&nbsp;"&nbsp;&nbsp;+40&deg;</td>
+    <td class="br" align="center">1008</td></tr>
+<tr><td class="blr">Potsdam</td>
+    <td class="br">+39&deg;&nbsp;&nbsp;"&nbsp;&nbsp;+32&deg;</td>
+    <td class="br" align="center">1232</td></tr>
+<tr><td class="blr">Oxford</td>
+    <td class="br">+31&deg;&nbsp;&nbsp;"&nbsp;&nbsp;+25&deg;</td>
+    <td class="br" align="center">1180</td></tr>
+<tr><td class="blr">Paris</td>
+    <td class="br">+24&deg;&nbsp;&nbsp;"&nbsp;&nbsp;+18&deg;</td>
+    <td class="br" align="center">1260</td></tr>
+<tr><td class="blr">Bordeaux</td>
+    <td class="br">+17&deg;&nbsp;&nbsp;"&nbsp;&nbsp;+11&deg;</td>
+    <td class="br" align="center">1260</td></tr>
+<tr><td class="blr">Toulouse</td>
+    <td class="br">+10&deg;&nbsp;&nbsp;"&nbsp;&nbsp;+&nbsp;&nbsp;5&deg;</td>
+    <td class="br" align="center">1080</td></tr>
+<tr><td class="blr">Algiers</td>
+    <td class="br">+&nbsp;&nbsp;4&deg;&nbsp;&nbsp;"&nbsp;&nbsp;-&nbsp;&nbsp;2&deg;</td>
+    <td class="br" align="center">1260</td></tr>
+<tr><td class="blr">San Fernando</td>
+    <td class="br">-&nbsp;&nbsp;3&deg;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;-&nbsp;&nbsp;9&deg;</td>
+    <td class="br" align="center">1260</td></tr>
+<tr><td class="blr">Tacubaya</td>
+    <td class="br">-10&deg;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;-16&deg;</td>
+    <td class="br" align="center">1260</td></tr>
+<tr><td class="blr">Santiago (Monte Video)</td>
+    <td class="br">-17&deg;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;-23&deg;</td>
+    <td class="br" align="center">1260</td></tr>
+<tr><td class="blr">La Plata (Cordoba)</td>
+    <td class="br">-24&deg;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;-31&deg;</td>
+    <td class="br" align="center">1360</td></tr>
+<tr><td class="blr">Rio (Perth, Australia)</td>
+    <td class="br">-32&deg;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;-40&deg;</td>
+    <td class="br" align="center">1376</td></tr>
+<tr><td class="blr">Cape of Good Hope</td>
+    <td class="br">-41&deg;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;-51&deg;</td>
+    <td class="br" align="center">1512</td></tr>
+<tr><td class="blr">Sydney</td>
+    <td class="br">-52&deg;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;-64&deg;</td>
+    <td class="br" align="center">1400</td></tr>
+<tr><td class="bblr">Melbourne</td>
+    <td class="bbr">-65&deg;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;-90&deg;</td>
+    <td class="bbr" align="center">1149</td></tr></table>
+
+<div class="sidenote">Sky covered twice.</div>
+
+<p>In the list is also shown the total number of plates that were to be taken
+by each observatory. When once the size of the plates had been settled,<span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span>
+it was a straightforward matter to divide up the sky into the proper
+number of regions necessary to cover it completely, not only without gaps
+between the plates, but with actually a small overlap of contiguous
+plates. And more than this, it was decided that the whole sky should be
+completely covered <i>twice over</i>. It was conceivable that a question might
+arise whether an apparent star image on a plate was, on the one hand, a
+dust speck, or, on the other hand, a planet, or perhaps a variable or new
+star. By taking two different plates at slightly different times,
+questions of this kind could be settled; and to make the check more
+independent it was decided that the plates should not be exactly repeated
+on the same portion of sky, but that in the second series the centre of a
+plate should occupy the point assigned to the corner of a plate in the
+first series.</p>
+
+<div class="sidenote">Times of exposure.</div>
+
+<p>Then there came the important question of time of exposure, which involved
+a long debate between those who desired the most modest programme possible
+consistent with efficiency, and those enthusiasts who were anxious to
+strain the programme to the utmost limits attainable. Ultimately it was
+resolved to take two series of plates; one series of long exposure which
+was set in the first instance at 10 minutes, then became 15, then 30, then
+40, and has by some enterprising observers been extended to 1&#189; hours;
+the other a series of short exposures which have<span class="pagenum"><a name="Page_132" id="Page_132">[Pg 132]</a></span> been generally fixed at
+6 minutes. Thus instead of covering the sky twice, it was decided to cover
+it in all four times, and the number of plates assigned to each
+observatory in the above list must be regarded as doubled by this new
+decision. And further still, on the series of short-exposure plates it was
+decided to add to the exposure of six minutes another one of three
+minutes, having slightly shifted the telescope between the two so that
+they should not be superimposed; and later still, a third exposure of
+twenty seconds was added to these. It would take too long to explain here
+the reasons for these details, but it will be clear that the general
+result of the discussion was to extend the original programme
+considerably, and render the work even more laborious than it had appeared
+at the outset.</p>
+
+<div class="sidenote">Measurement of plates.</div>
+
+<p>When all these plates have been taken, the work is by no means finished;
+indeed, it is only just commencing. There remains the task of measuring
+accurately on each of the short-exposure plates the positions of the stars
+which it represents, numbering on the average some 300 or 400; so that for
+instance at Oxford the total number of stars measured on the twelve
+hundred plates is nearly half a million. These are not all separate stars;
+for the sky is represented twice over, and there is also the slight
+overlap of contiguous plates; but the number of actual separate stars
+measured at this one observatory is not far short of a quarter of a
+million, and it has taken nearly ten years to<span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span> make the measurements, with
+the help of three or four measurers trained for the purpose.<span class="sidenote">The r&eacute;seau.</span> To render the
+measures easy, a network or r&eacute;seau of cross lines is photographed on each
+plate by artificial light after it has been exposed to the stars, so that
+on development these cross lines and the stars both appear. We can see at
+a glance the approximate position of a star by counting the number of the
+space from left to right and from top to bottom in which it occurs; and we
+can also estimate the fraction of a space in addition to the whole number;
+but it is necessary for astronomical purposes to estimate this fraction
+with the greatest exactness. The whole numbers are already given with
+great exactness by the careful ruling of the cross lines, which can be
+spaced with extraordinary perfection.<span class="sidenote">The microscope.</span> To measure the fraction, we place
+the plate under a microscope in the eye-piece of which there is a finally
+divided cross scale; the centre of the cross is placed over a star image,
+and then it is noted where the lines of the r&eacute;seau cut the cross scale. In
+this way the position of the image of a star is read off with accuracy,
+and after a little practice with considerable rapidity. It has been found
+at Oxford that under favourable conditions the places of nearly <ins class="errata" title="Errata: Page 133, line 27, for '200 stars' read '200 stars per hour.'">200 stars per hour</ins>
+can be recorded in this way by a single measurer, if he has some one to
+write down for him the numbers he calls out. This is only one form of
+measuring apparatus; there are others in which, instead of a<span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span> scale in the
+eye-piece, micrometer screws are used to measure the fractions; but the
+general principle in all these instruments is much the same, and the rate
+of work is not very different; while to the minor advantages and
+disadvantages of the different types there seems no need here to refer.
+One particular point, however, is worth noting.<span class="sidenote">Reversal of plates.</span> After a plate has been
+measured, it is turned round completely, so that left is now right, and
+top is now bottom, and the measurements are repeated. This repetition has
+the advantage first of all of checking any mistakes. When a long piece of
+measuring or numerical work of any kind is undertaken there are invariably
+moments when the attention seems to wander, and some small error is the
+result. But there are also certain errors of a systematic character
+similar to those denoted by the term &#8220;personal equation,&#8221; which has found
+its way into other walks of life.<span class="sidenote">Personal equation.</span> In the operation of placing a cross
+exactly over the image of a star, different observers would show slight
+differences of habit; one might place it a little more to the right than
+another. But when the plate is turned round the effect of this habit on
+the measure is exactly reversed, and hence if we take the mean of the two
+measures any personal habit of this kind is eliminated. It has been found
+by experience that such personal habits are much smaller for measures of
+this kind than for those to which we have long been accustomed in
+observations made by eye on the stars<span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span> themselves. The troubles from
+&#8220;personal equation&#8221; have been much diminished by the photographic method,
+and certain peculiarities of the former method have been clearly exhibited
+by the comparison. For instance, it has gradually become clear that with
+eye observations personal equation is not a constant quantity, but is
+different for stars of different brightness. When observing the transit of
+a bright star the observer apparently records an instant definitely
+earlier than in recording the transit of a faint one; and this peculiarity
+seems to be common to the large majority of observers, which is perhaps
+the reason why it was not noticed earlier. But when positions of the stars
+determined in this way are compared with their positions measured on the
+photographic plates, the peculiarity is made clearly manifest. For
+example, at Oxford, our first business after making measurements is to
+compare them with visual observations on a limited number of the brighter
+stars made at Cambridge about twenty years ago. (About 14,000 stars were
+observed at Cambridge, and we are dealing with ten times that number.) The
+comparison shows that the Cambridge observations are affected with the
+following systematic errors:&mdash;</p>
+
+<table border="0" cellpadding="0" cellspacing="5" summary="magnitude">
+<tr><td><span style="margin-left: 1em;">If</span> stars of magnitude 10 are observed correctly,</td></tr>
+<tr><td>then<span style="margin-left: 1em;">"</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2.75em;">9</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2em;">0.10 secs. too early</span></td></tr>
+<tr><td><span style="margin-left: 2.5em;">"</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2.75em;">8</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2em;">0.16</span><span style="margin-left: 3em;">"</span></td></tr>
+<tr><td><span style="margin-left: 2.5em;">"</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2.75em;">7</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2em;">0.19</span><span style="margin-left: 3em;">"</span></td></tr>
+<tr><td><span style="margin-left: 2.5em;">"</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2.75em;">6</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2em;">0.21</span><span style="margin-left: 3em;">"</span></td></tr>
+<tr><td><span style="margin-left: 2.5em;">"</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2.75em;">5</span><span style="margin-left: 3.5em;">"</span><span style="margin-left: 2em;">0.23</span><span style="margin-left: 3em;">"</span></td></tr></table>
+
+<p><span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span>This may serve as an illustration of various incidental results which are
+already flowing from the enormous and laborious piece of work which, as
+far as the University Observatory at Oxford is concerned, we have just
+completed, though some of the other colleagues are not so far advanced.
+<span class="sidenote">Main object of the work.</span>But the main results will not appear just yet. The work must be repeated,
+and the positions of the stars just obtained must be compared with those
+which they will be found to occupy at some future date, in order to see
+what kind of changes are going on in the heavens. Whether this future date
+shall be one hundred years hence, or fifty, or ten, or whether we should
+begin immediately to repeat what has been done, is a matter not yet
+decided, and one which requires some little consideration.</p>
+
+<p>I have said perhaps enough to give you a general idea of the work on which
+we have been engaged at Oxford for the last ten years. Ten years ago it
+seemed to stretch out in front of us rather hopelessly; the pace we were
+able to make seemed so slow in view of the distance to be covered. We felt
+rather like the schoolboy who has just returned to school and sees the
+next holidays as a very remote prospect, and we solaced ourselves much in
+the same way as he does, by making a diagram representing the total number
+of plates to be dealt with and crossing off each one as it was finished,
+just as he sometimes crosses off the days still remaining between him<span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span> and
+the prospective holidays. It was pleasant to watch the growth of the
+number of crosses on this diagram, and by the end of the year 1902 we had
+the satisfaction of seeing very little blank space remaining.<span class="sidenote">The concluding year.</span> Now, up to
+this point it had not much mattered whether any particular plate was
+secured in any particular year, or in a subsequent year, so long as there
+were always sufficient plates to keep us occupied in measuring them. But
+it then became a matter of importance to secure each plate at the proper
+time of year; for the sun, as we know, travels round the Zodiac among the
+stars, obliterating by his radiance a large section of the sky for a
+period of some months, and in this way a particular region of the heavens
+is apt to &#8220;run into daylight,&#8221; as the observatory phrase goes, and ceases
+to be available for photography during several months, until the sun is
+again far enough away to allow of the particular region being seen at
+night.</p>
+
+<p>Roughly speaking then, if a plate which should be taken in February is not
+secured in this month owing to bad weather, the proper time for taking it
+will not occur again until the following February; and when there was a
+fair prospect of finishing our work in 1903, it became important to secure
+each plate at the proper time in that year. Hence we were making special
+efforts to utilise to the full any fine night that Providence sent in our
+way, and on such occasions it is clearly an economy, if not exactly to
+&#8220;make hay while the sun shines,&#8221; at any rate to take plates<span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span> vigorously
+while the sun is <i>not</i> shining and the night is fine; leaving the
+development of them until the daytime. There is, of course, the risk that
+the whole night&#8217;s work may in this way be lost owing to some fault in the
+plates, which might have been detected if some of them were immediately
+developed. Perhaps in the early days of our work it would have been
+reckless or foolish to neglect this little precaution; but we had for
+years been accustomed to rely upon the excellence of the plates without
+finding our trust betrayed; and the sensitiveness of the plates had
+increased rather than diminished as time went on.<span class="sidenote">A disappointment.</span> Hence it will be readily
+understood that when one fatal morning we developed a series of some
+thirty plates, and found that owing to some unexplained lack of
+sensitiveness they were all unsuitable for our purpose, it came as a most
+unwelcome and startling surprise. It was, of course, necessary to make
+certain that there was no oversight, that the developer was not at fault,
+and that the weather had not been treacherous. All such possibilities were
+carefully considered before communication with the makers of the plates,
+but it ultimately became clear that there had been some unfortunate
+failure in sensitiveness, and that it would be necessary to repeat the
+work with opportunities restricted by the intervening lapse of time.
+However, disappointments from this or similar causes are not unknown in
+astronomical work; and we set about this repetition with as little loss of
+time and cheerfulness as was possible. Under the <span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span>circumstances, however,
+it seemed desirable to examine carefully whether anything could be saved
+from the wreck&mdash;whether any of the plates could be admitted as <i>just</i>
+coming up to the minimum requirements. And I devoted a morning to this
+inquiry.<span class="sidenote">A curious plate.</span> In the course of it I came across one plate which certainly
+seemed worth an inclusion among our series from the point of view of the
+number of stars shown upon it. It seemed quite rich in stars, perhaps even
+a little richer than might have been expected. On inquiry I was told that
+this was not one of the originally condemned plates, but one which had
+been taken since the failure in sensitiveness of the plates had been
+detected; was from a new and specially sensitive batch with which the
+courteous makers had supplied us; but though there were certainly a
+sufficient number of stars upon the plate, owing to some unexplained cause
+the telescope had been erroneously pointed, and the region taken did not
+correspond to the region required. To investigate the cause of the
+discrepancy I thereupon took down from our store of plates the other one
+of the same region which had been rejected for insufficiency of stars,<span class="sidenote">A strange object.</span> and
+on comparing the two it was at once evident that there was a strange
+object on the plate taken later of the two, a bright star or other
+heavenly body, which was not on the former plate. I have explained that by
+repeating the exposure more than once, it is easily possible to recognise
+whether a mark upon the plate is really a celestial body or is an
+<span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span>accidental blot or dust speck, and there was no doubt that this was the
+image of some strange celestial body. It might, of course, be a new
+planet, or even an old one which had wandered into the region; but a few
+measures soon showed that it was not in movement. The measures consisted
+in comparing the separation of the three exposures with the separation of
+the corresponding exposures of obvious stars, for the exposures were not,
+of course, simultaneous, and if the body were a planet and had moved in
+the interval between them, this would be made manifest on measuring the
+separations. No such movements could be detected; and the possibilities
+were thus restricted to two. So far as we knew the object was a star, but
+might be either a star of the class known as <i>variable</i> or of that known
+as <i>new</i>. In the former case it would become bright and faint at more or
+less regular intervals, and might possibly have been already catalogued;
+for the number of these bodies already known amounts to some hundreds.
+Search being made in the catalogues, no entry of it was found, though it
+still might be one of this class which had hitherto escaped detection.<span class="sidenote">A new star?</span> Or
+it might be a &#8220;new star,&#8221; one of those curious bodies which blaze up quite
+suddenly to brightness and then die away gradually until they become
+practically invisible. The most famous perhaps of these is the star which
+appeared in 1572, and was so carefully observed by Tycho Brah&eacute;; but such
+apparitions are rare, and altogether we have not records as yet of a score
+altogether; so that in<span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span> this latter case the discovery would be of much
+greater interest than in the former. In either event it was desirable to
+inform other observers as soon as possible of the existence of a strange
+body; already some time had elapsed since the plate had been taken, March
+16th, for the examination of which I have spoken was not made until March
+24th. Accordingly, a telegram was at once despatched to the Central Office
+at Kiel, which undertakes to distribute such information all over the
+world, and a few post-cards were sent to observers close at hand who might
+be able to observe the star the same night. Certain observations with the
+spectroscope soon made it clear that the object was really a &#8220;new star.&#8221;</p>
+
+<p>This, therefore, is the discovery which we made at Oxford: as you will
+see, in an entirely accidental manner, during the course of a piece of
+work in which it was certainly never contemplated.<span class="sidenote">The discovery accidental.</span> Its purely accidental
+nature is sufficiently illustrated by the fact that if the plates
+originally supplied by the makers had been of the proper quality, the
+plate which led to the discovery would never have been taken. If the
+plates exposed in February had been satisfactory, we should have been
+content, and should not have repeated the exposure on March 16th. Again I
+can testify personally how purely accidental it was that the examination
+was made on March 24th to see whether anything could be saved, as I have
+said, from the wreck. The idea came casually into my mind as I was walking
+through the room and saw the neat<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span> pile of rejected plates; and one may
+fairly call it an accidental impulse. This new star is not, however, the
+first of such objects to have been discovered &#8220;accidentally&#8221;; many of the
+others were found just as much by chance, though a notable exception must
+be made of those discovered at the Harvard Observatory, which are the
+result of a deliberate search for such bodies by the careful examination
+of photographic plates.<span class="sidenote">Mrs. Fleming&#8217;s discoveries.</span> Mrs. Fleming, who spends her life in such work,
+has had the good fortune to detect no less than six of these wonderful
+objects as the reward of her laborious scrutiny; and she is the <i>only</i>
+person who has thus found new stars by photography until this accidental
+discovery at Oxford. The following is a complete list of new stars
+discovered to date:&mdash;</p>
+
+<p class="center"><span class="smcap">List of New Stars.</span></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="stars">
+<tr><td class="btrl">Ref. No.</td>
+    <td class="btr" align="center">Constellation.</td>
+    <td class="btr" align="center">Year.</td>
+    <td class="btr" align="center">Discoverer.</td></tr>
+<tr><td class="btrl" align="center">1</td>
+    <td class="btr">Cassiopeia</td>
+    <td class="btr">1572</td>
+    <td class="btr">Tycho Brah&eacute;.</td></tr>
+<tr><td class="blr" align="center">2</td>
+    <td class="br">Cygnus</td>
+    <td class="br">1600</td>
+    <td class="br">Janson.</td></tr>
+<tr><td class="blr" align="center">3</td>
+    <td class="br">Ophiuchus</td>
+    <td class="br">1604</td>
+    <td class="br">Kepler.</td></tr>
+<tr><td class="blr" align="center">4</td>
+    <td class="br">Vulpecula</td>
+    <td class="br">1670</td>
+    <td class="br">Anthelm.</td></tr>
+<tr><td class="blr" align="center">5</td>
+    <td class="br">Ophiuchus</td>
+    <td class="br">1848</td>
+    <td class="br">Hind.</td></tr>
+<tr><td class="blr" align="center">6</td>
+    <td class="br">Scorpio</td>
+    <td class="br">1860</td>
+    <td class="br">Auwers.</td></tr>
+<tr><td class="blr" align="center">7</td>
+    <td class="br">Corona Borealis</td>
+    <td class="br">1866</td>
+    <td class="br">Birmingham.</td></tr>
+<tr><td class="blr" align="center">8</td>
+    <td class="br">Cygnus</td>
+    <td class="br">1876</td>
+    <td class="br">Schmidt.</td></tr>
+<tr><td class="blr" align="center">9</td>
+    <td class="br">Andromeda</td>
+    <td class="br">1885</td>
+    <td class="br">Hartwig.</td></tr>
+<tr><td class="blr" align="center">10</td>
+    <td class="br">Perseus</td>
+    <td class="br">1887</td>
+    <td class="br">Fleming.</td></tr>
+<tr><td class="blr" align="center">11</td>
+    <td class="br">Auriga</td>
+    <td class="br">1891</td>
+    <td class="br">Anderson.</td></tr>
+<tr><td class="blr" align="center">12</td>
+    <td class="br">Norma</td>
+    <td class="br">1893</td>
+    <td class="br">Fleming.</td></tr>
+<tr><td class="blr" align="center">13</td>
+    <td class="br">Carina</td>
+    <td class="br">1895</td>
+    <td class="br">Fleming.</td></tr>
+<tr><td class="blr" align="center">14</td>
+    <td class="br">Centaurus</td>
+    <td class="br">1895</td>
+    <td class="br">Fleming.</td></tr>
+<tr><td class="blr" align="center">15</td>
+    <td class="br">Sagittarius</td>
+    <td class="br">1898</td>
+    <td class="br">Fleming.</td></tr>
+<tr><td class="blr" align="center">16</td>
+    <td class="br">Aquila</td>
+    <td class="br">1899</td>
+    <td class="br">Fleming.</td></tr>
+<tr><td class="blr" align="center">17</td>
+    <td class="br">Perseus</td>
+    <td class="br">1901</td>
+    <td class="br">Anderson.</td></tr>
+<tr><td class="bblr" align="center">18</td>
+    <td class="bbr">Gemini</td>
+    <td class="bbr">1903</td>
+    <td class="bbr">At Oxford.</td></tr></table>
+
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i156tmb.jpg" alt="" /><br />
+<a href="images/i156.jpg"><small>Larger Image</small></a></div>
+
+<p class="center">MARCH 1, 1903<span class="spacer">&nbsp;</span><span class="spacer">&nbsp;</span><span class="spacer">&nbsp;</span><span class="spacer">&nbsp;</span>MARCH 14, 1903</p>
+
+<p class="center">VIII.&mdash;<span class="smcap">The Oxford New Star.</span><br />
+<span class="smcaplc">A PAIR OF PHOTOGRAPHS TAKEN AT THE HARVARD COLLEGE OBSERVATORY BEFORE AND AFTER ITS APPEARANCE</span><br />
+(<i>The arrow indicates the place of the new star. It will be seen that the
+left-hand picture though it shews fainter stars than the other, has not a trace of the new star.</i>)</p>
+<p>&nbsp;</p>
+
+<div class="sidenote">Dr. Anderson.</div>
+
+<p><span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span>Generally these stars have been noted by eye observation, as in the case
+of the two found by Dr. Anderson of Edinburgh. In these cases also we may
+say that deliberate search was rewarded; for Dr. Anderson is probably the
+most assiduous &#8220;watcher of the skies&#8221; living, though he seldom uses a
+telescope; sometimes he uses an opera-glass, but usually the naked eye. He
+describes himself as an &#8220;Astrophil&#8221; rather than as an astronomer. &#8220;I love
+the stars,&#8221; he says; &#8220;and whenever they are shining, I must be looking.&#8221;
+And so on every fine night he stands or sits at his open study window
+gazing at the heavens. I believe he was just about to leave them for his
+bed, near 3 <span class="smcaplc">A.M.</span> on the night of February 21, 1901, when, throwing a last
+glance upward, he suddenly saw a brilliant star in the constellation
+Perseus.<span class="sidenote">Nova Persei.</span> His first feeling was actually one of disappointment, for he felt
+sure that this object must have been there for some time past without his
+knowing of it, and he grudged the time lost when he might have been
+regarding it. More in a spirit of complaint than of inquiry, he made his
+way to the Royal Observatory at Edinburgh next day to hear what they had
+to say about it, though he found it difficult to approach the subject. He
+first talked about the weather, and the crops, and similar topics of
+general interest; and only after some time dared he venture a casual
+reference to the &#8220;new portent in the heavens.&#8221; Seeing his interlocutor
+look somewhat blank, he<span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span> ventured a little farther, and made a direct
+reference to the new star in Perseus; and then found to his astonishment,
+as also to his great delight, that he was the first to bring news of it.
+The news was soon communicated to other observers; all the telescopes of
+the world were soon trained upon it; and this wonderful &#8220;new star of the
+new century&#8221; has taught us more of the nature of these extraordinary
+bodies than all we knew before.</p>
+
+<div class="sidenote">Records previous to discovery.</div>
+
+<p>Perhaps I may add a few remarks on one or two features of these bodies.
+Firstly, let us note that Professor Pickering of Harvard is now able to
+make a most important contribution to the <i>former</i> history of these
+objects&mdash;that is to say, their history preceding their actual detection.
+We remember that, after Uranus had been discovered, it was found that
+several observers had long before recorded its place unknowingly; and
+similarly Professor Pickering and his staff have usually photographed
+other new objects unknowingly. There are on the shelves at Harvard vast
+stores of photographs, so many that they are unable to examine them when
+they have been taken; but once any object of interest has been discovered,
+it is easy to turn over the store and examine the particular plates which
+may possibly show it at an earlier date. In this way it was found that Dr.
+Anderson&#8217;s new star had been visible only for a few days before its
+discovery, there being no trace of it on earlier plates. <span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span>Similarly, in
+the case of the new star found at Oxford, plates taken on March 1st and
+6th, fifteen days and ten days respectively before the discovery-plate of
+March 16th, showed the star. But, in this particular instance, greater
+interest attaches to two still earlier plates taken elsewhere, and with
+exposures much longer than any available at Harvard. One had been obtained
+at Heidelberg by Dr. Max Wolf, and another at the Yerkes Observatory of
+Chicago University, by Mr. Parkhurst; and on both there appeared to be a
+faint star of about the fourteenth or fifteenth magnitude, in the place
+subsequently occupied by the Nova; and the question naturally arose,<span class="sidenote">Was Nova Geminorum previously shining faintly?</span> Was
+this the object which ultimately blazed up and became the new star? To
+settle this point, it was necessary to measure its position, with
+reference to neighbouring stars, with extreme precision; and here it was
+unfortunate that the photographs did not help us as much as they might,
+for they were scarcely capable of being measured with the requisite
+precision. The point was an important one, because if the identity of the
+Nova with this faint star could be established, it would be the second
+instance of the kind; but so far as they went, measurements of the
+photographs were distinctly against the identity. Such was the conclusion
+of Mr. Parkhurst from his photograph alone; and it was confirmed by
+measures made at Oxford on copies of both plates, which<span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span> were kindly sent
+there for the purpose. The conclusion seemed to be that there was a faint
+star <i>very near</i>, but <i>not at</i>, the place of the new star; and it was
+therefore probable that, although this faint star was temporarily
+invisible from the brightness of the adjacent Nova, as the latter became
+fainter (in the way with which we have become familiar in the case of new
+stars), it might be possible to see the two stars alongside each other.
+<span class="sidenote">The suspicion negatived.</span>This critical observation was ultimately made by the sharp eyes of
+Professor Barnard, aided by the giant telescope of the Yerkes Observatory;
+and it seems clear therefore that the object which blazed up to become the
+Nova of 1903 could not have previously been so bright as a faint star of
+the fourteenth magnitude. Although this is merely a negative conclusion,
+it is an important one in the history of these bodies.</p>
+
+<p>The second point to which I will draw your attention is from the history
+of the other Nova just mentioned&mdash;Dr. Anderson&#8217;s New Star of 1901. In this
+instance it is not the history previous to discovery, but what followed
+many months after discovery, that was of engrossing interest; and again
+Yerkes Observatory, with its magnificent equipment, played an important
+part in the drama.<span class="sidenote">Nebula round Nova Persei.<br /><br />Its changes.</span> When, with its giant reflecting telescope, photographs
+were taken of the region of Nova Persei after it had become comparatively
+faint, it was found that there was an extraordinarily faint nebulosity
+surrounding the star. Repeating the <span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span>photographs at intervals, it was
+found that this nebulosity was rapidly changing in shape. &#8220;Rapidly&#8221; is, of
+course, a relative term, and a casual inspection of two of the photographs
+might not convey any impression of rapidity; it is only when we come to
+consider the enormous distance at which the movements, or apparent
+movements, of the nebul&aelig; must be taking place that it becomes clear how
+rapid the changes must be. It was not possible to determine this distance
+with any exactness, but limits to it could be set, and it seemed probable
+that the velocity of the movement was comparable with that of light.<span class="sidenote">Due to travelling illumination.</span> The
+conclusion suggested itself that the velocity might actually be identical
+with that of light, in which case what we saw was not the movement of
+actual matter, but merely that of illumination, travelling from point to
+point of matter already existing.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i161top.jpg" alt="" /></div>
+<p class="center">SEPT. 20, 1901</p>
+<div class="figcenter"><img src="images/i161bottom.jpg" alt="" /></div>
+<p class="center">NOV. 13, 1901</p>
+<p class="center"><span class="smcap">IX&mdash;Nebulosity round Nova Persei</span><br />
+(<i>From photographs taken at the Yerkes Observatory by G. W. Ritchey.</i>)</p>
+<p>&nbsp;</p>
+
+<p>An analogy from the familiar case of sound may make clearer what is meant.
+If a loud noise is made in a large hall, we hear echoes from the walls.
+The sound travels with a velocity of about 1100 feet per second, reaches
+the walls, is reflected back from them, and returns to us with the same
+velocity. From the interval occupied in going and returning we could
+calculate the distance of the walls. The velocity of light is so enormous
+compared with that of sound that we are usually quite unable to observe
+any similar phenomenon in the case of light. If we strike a match in the
+largest hall, all parts of it are<span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span> illuminated so immediately that we
+cannot possibly realise that there was really an interval between the
+striking of the match, the travelling of the light to the walls, and its
+return to our eyes. The scale of our terrestrial phenomenon is far too
+small to render this interval perceptible. But those who accept the theory
+above mentioned regarding the appearances round Nova Persei (although
+there are some who discredit it) believe that we have in this case an
+illustration of just this phenomenon of light echoes, on a scale large
+enough to be easily visible. They think that, surrounding the central star
+which blazed up so brightly in February 1901, there was a vast dark
+nebula, of which we had no previous knowledge, because it was not shining
+with any light of its own. When the star blazed up, the illumination
+travelled from point to point of this dark nebula and lighted it up; but
+the size of the nebula was so vast that, although the light was travelling
+with the enormous velocity of 200,000 miles per second, it was not until
+months afterwards that it reached different portions of this nebula; and
+we accordingly got news of the existence of this nebula some months after
+the news reached us of the central conflagration, whatever it was.<span class="sidenote">When did it all happen?</span> Remark
+that all we can say is that the news of the nebula reached us <i>some months
+later</i> than that of the outburst. The actual date when either of the
+actual things happened, we have as yet no means of knowing; it may have
+been hundreds or even<span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span> thousands of years ago that the conflagration
+actually occurred of which we got news in February 1901, the light having
+taken all that time to reach us from that distant part of space; and the
+light reflected from the nebula was following it on its way to us all
+these years at that same interval of a few months.</p>
+
+<div class="sidenote">An objection.</div>
+
+<p>Now, let me refer before leaving this point to the chief objection which
+has been urged against this theory. It has been maintained that the
+illumination would necessarily appear to travel outwards from the centre
+with an approach to uniformity, whereas the observed rate of travel is not
+uniform, and has been even towards the centre instead of away from it;
+which would seem as though portions of the nebula more distant from the
+centre were lighted up sooner than those closer to it. By a simple
+illustration from our solar system, we shall see that these curious
+anomalies may easily be explained. Let us consider for simplicity two
+planets only, say the Earth and Saturn. We know that Saturn travels round
+the sun in an orbit which is ten times larger than the orbit of the earth.
+Suppose now that the sun were suddenly to be extinguished; light takes
+about eight minutes to travel from the sun to the earth, and consequently
+we should not get news of the extinction for some eight minutes; the sun
+would appear to us to still go on shining for eight minutes after he had
+really been extinguished. Saturn being about ten times as<span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span> far away from
+the sun, the news would take eighty minutes to reach Saturn; and from the
+earth we should see Saturn shining more<small><a name="f3.1" id="f3.1" href="#f3">[3]</a></small> than eighty minutes after the
+sun had been extinguished, although we ourselves should have lost the
+sun&#8217;s light after eight minutes. I think we already begin to see
+possibilities of curious anomalies; but they can be made clearer than
+this. Instead of imagining an observer on the earth, let us suppose him
+removed to a great distance away in the plane of the two orbits; and let
+us suppose that the sun is now lighted up again as suddenly as the new
+star blazed up in February 1901. Then such an observer would first see
+this blaze in the centre; eight minutes afterwards the illumination would
+reach the earth, a little speck of light near the sun would be
+illuminated, just as we saw a portion of the dark nebula round Nova Persei
+illuminated; eighty minutes later another speck, namely, Saturn, would
+begin to shine. But now, would Saturn necessarily appear to the distant
+observer to be farther away from the sun than the earth was? Looking at
+the diagram, we can see that if Saturn were at S<sub>1</sub> then it would present
+this natural appearance of being farther away from the sun than the earth;
+but it might be at S<sub>2</sub> or S<sub>3</sub>, in which case it would seem to be nearer
+the sun, and the illumination would seem to travel inwards towards the
+central body<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span> instead of outwards. Without considering other cases in
+detail, it will be tolerably clear that almost any anomalous appearance
+might be explained by choosing a suitable arrangement of the nebulous
+matter which we suppose lighted up by the explosion of Nova Persei.
+Another objection urged against the theory I have sketched is that the
+light reflected from such a nebula would be so feeble that it would not
+affect our photographic plates. This depends upon various assumptions
+which we have no time to notice here; but I think we may say that there is
+certainly room for the acceptance of the theory.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i166.jpg" alt="" /></div>
+<p class="center"><span class="smcap">Fig. 6.</span></p>
+<p>&nbsp;</p>
+
+<div class="sidenote">Did the nebula cause the outburst?</div>
+
+<p>Now, if this dark nebula was previously existing in this way all round the
+star which blazed up, the question naturally arises whether the nebula had
+anything to do with the conflagration. Was there previously a star, either
+so cold or so distant as not to be shining with appreciable light, which,
+travelling through space, encountered this vast<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span> nebula, and by the
+friction of the encounter was suddenly rendered so luminous as to outshine
+a star of the first magnitude? The case of meteoric stones striking our
+own atmosphere seems to suggest such a possibility. These little stones
+are previously quite cold and invisible, and are travelling in some way
+through space, many of them probably circling round our sun. If they
+happen in their journey to encounter our earth, even the extremely tenuous
+atmosphere, so thin that it will scarcely bend the rays of light
+appreciably, even this is sufficient by its friction to raise the stones
+to a white heat, so that they blaze up into the falling stars with which
+we are familiar. This analogy is suggested, but we must be cautious in
+accepting it; for we know so very little of the nature of nebul&aelig; such as
+that of which we have been speaking. But in any case, a totally new series
+of phenomena have been laid open to our study by those wonderful
+photographs taken at the Yerkes Observatory and the Lick Observatory in
+the few years which the present century has as yet run.</p>
+
+<div class="sidenote">Importance of new stars</div>
+
+<p>One thing is quite certain: we must lose no opportunity of studying such
+stars as may appear, and no diligence spent in discovering them at the
+earliest possible moment is thrown away. We have only known up to the
+present, as already stated, less than a score of them, and of these many
+have told us but little; partly because they were only discovered too late
+(after they had<span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span> become faint), and partly because the earlier ones could
+not be observed with the spectroscope, which had not then been invented.
+It seems clear that in the future we must not allow accident to play so
+large a part in the discovery of these objects; more must be done in the
+way of deliberate search. Although we know beforehand that this will
+involve a vast amount of apparently useless labour, that months and years
+must be spent in comparing photographic plates, or portions of the sky
+itself, with one another without detecting anything remarkable, it will
+not be the first time that years have been cheerfully spent in such
+searches without result. We need only recall Hencke&#8217;s fifteen years of
+fruitless search, before finding a minor planet, to realise this fact.</p>
+
+<p>One thing of importance may be done; we may improve our methods of making
+the search, so as to economise labour, and several successful attempts
+have already been made in this direction.<span class="sidenote">Superposition of plates.</span> The simplest plan is to
+superpose two photographs taken at different dates, so that the stars on
+one lie very close to those on the other; then if an image is seen to be
+unpaired we <i>may</i> have found a new star, though of course the object may
+be merely a planet or a variable. The superposition of the plates may be
+either actual or virtual. A beautiful instrument has been devised on the
+principle of the stereoscope for examining two plates placed side by side,
+one with each eye. We know that in this way two photographs of<span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span> the same
+object from different points of view will appear to coalesce, and at the
+same time to give an appearance of solidity to the object or landscape,
+portions of which will seem to stand out in front of the background.
+<span class="sidenote">The stereo-comparator.</span>Applying this principle to two photographs of stars, what happens is this:
+if the stars have all remained in the same positions exactly, the two
+pictures will seem to us to coalesce, and the images all to lie on a flat
+background; but if in the interval between the exposures of the two plates
+one of the stars has appreciably moved or disappeared, it will seem, when
+looked at with this instrument, to stand out in front of this background,
+and is accordingly detected with comparatively little trouble. This new
+instrument, to which the name Stereo-comparator has been given, promises
+to be of immense value in dredging the sky for strange bodies in the
+future. I am glad to say that a generous friend has kindly presented the
+University Observatory at Oxford with one of these beautiful instruments,
+which have been constructed by Messrs. Zeiss of Jena after the skilful
+designs of Dr. Pulfrich. Whether we shall be able to repeat by deliberate
+search the success which mere accident threw in our way remains to be
+seen.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span></p>
+<h2><a name="CHAPTER_V" id="CHAPTER_V"></a>CHAPTER V</h2>
+<h3>SCHWABE AND THE SUN-SPOT PERIOD</h3>
+
+<div class="sidenote">Discoveries contrary to expectation.</div>
+
+<p>In preceding chapters we have reviewed discoveries, some of which have
+been made as a result of a deliberate search, and others accidentally in
+the course of work directed to a totally different end; but so far we have
+not considered a case in which the discoverer entered upon an enterprise
+from which he was positively dissuaded.</p>
+
+<p>In the next chapter we shall come across a very striking instance of this
+type; but even in the discovery that there was a periodicity in the solar
+spots, with which I propose to deal now, Herr Schwabe began his work in
+the face of deterrent opinions from eminent men. His definite announcement
+was first made in 1843, though he had himself been convinced some years
+earlier. In 1857 the Royal Astronomical Society awarded him their gold
+medal for the discovery; and in the address delivered on the occasion the
+President commenced by drawing attention to this very fact,<span class="sidenote">Nothing expected from spots.</span> that
+astronomers who had expressed any opinions on the subject had been
+uniformly and decidedly against the likelihood of there being anything
+profitable in the study of the solar spots. I will quote the exact words<span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span>
+of the President, Mr. Manuel Johnson, then Radcliffe Observer at Oxford.</p>
+
+<div class="blockquot"><p>&#8220;It was in 1826 that Heinrich Schwabe, a gentleman resident in
+Dessau, entered upon those researches which are now to engage our
+attention. I am not aware of the motive that induced him&mdash;whether any
+particular views had suggested themselves to his own mind&mdash;or whether
+it was a general desire of investigating, more thoroughly than his
+predecessors had done, the laws of a remarkable phenomenon, which it
+had long been the fashion to neglect. He could hardly have
+anticipated the kind of result at which he has arrived; at the same
+time we cannot imagine a course of proceeding better calculated for
+its detection, even if his mind had been prepared for it, than that
+which he has pursued from the very commencement of his career.
+Assuredly if he entertained such an idea, it was not borrowed from
+the authorities of the last century, to whom the solar spots were
+objects of more attention than they have been of late years.</p>
+
+<p>&#8220;&#8216;Nulla constanti temporum lege apparent aut evanescunt,&#8217; says Keill
+in 1739.&mdash;<i>Introduct. ad Physic. Astronom.</i>, p. 253.</p>
+
+<p>&#8220;&#8216;Il est manifest par ce que nous venons de rapporter qu&#8217;il n&#8217;y a
+point de r&egrave;gle certaine de leur formation, ni de leur nombre et de
+leur figure,&#8217; says Cassini II. in 1740.&mdash;<i>El&eacute;m d&#8217;Astron.</i>, vol. i. p.
+82.</p>
+
+<p><span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span>&#8220;&#8216;Il semble qu&#8217;elles ne
+suivent aucune loi dans leur apparitions,&#8217; says Le Monnier in 1746.&mdash;<i>Instit. Astron.</i>, p. 83.</p>
+
+<p>&#8220;&#8216;Solar spots observe no regularity in their shape, magnitude,
+number, or in the time of their appearance or continuance,&#8217; says Long
+in 1764.&mdash;<i>Astron.</i>, vol. ii. p. 472.</p>
+
+<p>&#8220;&#8216;Les apparitions des t&acirc;ches du soleil n&#8217;ont rien de regulier,&#8217; says
+Lalande in 1771.&mdash;<i>Astron.</i>, vol. iii. &sect; 3131, 2nd edit.</p>
+
+<p>&#8220;And Delambre&#8217;s opinion may be inferred from a well-known passage in
+the third volume of his &#8216;Astronomy&#8217; (p. 20), published in 1814, where
+treating of the solar spots he says, &#8216;Il est vrai qu&#8217;elles sont plus
+curieuses que vraiment utiles.&#8217;&#8221;<small><a name="f4.1" id="f4.1" href="#f4">[4]</a></small></p></div>
+
+<p>It will thus be evident that Herr Schwabe had the courage to enter upon a
+line of investigation which others had practically condemned as likely to
+lead nowhere, and that his discovery was quite contrary to expectation. It
+is a lesson to us that not even the most unlikely line of work is to be
+despised; for the outcome of Schwabe&#8217;s work was the first step in the
+whole series of discoveries which have gradually built up the modern
+science of Solar Physics, which occupies so deservedly large a part of the
+energies of, for instance, the great observatory attached to the
+University of Chicago.</p>
+
+<div class="sidenote">Schwabe&#8217;s announcement.</div>
+
+<p>It has been our practice to recall the actual<span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span> words in which the
+discoverer himself stated his discovery, and I will give the original
+modest announcement of Schwabe, though for convenience of those who do not
+read German I will attempt a rough translation. He had communicated year
+by year the results of his daily counting of the solar spots to the
+<i>Astronomische Nachrichten</i>, and after he had given ten years&#8217; results in
+this way he collected them together, but he made no remark on the curious
+sequence which they undoubtedly showed at that time. Waiting patiently six
+years for further material, in 1843 he ventured to make his definite
+announcement as follows:&mdash;&#8220;From my earlier observations, which I have
+communicated annually to this journal, there was manifest already a
+certain periodicity of sun-spots; and the probability of this being really
+the case is confirmed by this year&#8217;s results. Although I gave in volume 15
+the total numbers of groups for the years 1826-1837, nevertheless I will
+repeat here a complete series of all my observations of sun-spots, giving
+not only the number of groups, but also the number of days of observation,
+and further the days when the sun was free from spots. The number of
+groups alone will not in itself give sufficient accuracy for determination
+of a period, since I have convinced myself that when there are a large
+number of sun-spots the number will be reckoned somewhat too small, and
+when few sun-spots, the number somewhat too large; <span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span>in the first case
+several groups are often counted together in one, and in the second it is
+easy to divide a group made up of two component parts into two separate
+groups. This must be my excuse for repeating the early catalogue, as
+follows:&mdash;</p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="groups">
+<tr><td class="btrl" align="center">Year.</td>
+    <td class="btr" align="center">Number of<br />Groups.</td>
+    <td class="btr" align="center">Days free<br />from Spots.</td>
+    <td class="btr" align="center">Days of<br />Observation.</td></tr>
+<tr><td class="btrl" align="center">1826</td>
+    <td class="btr" align="center">118</td>
+    <td class="btr" align="center">&nbsp;&nbsp;22</td>
+    <td class="btr" align="center">277</td></tr>
+<tr><td class="blr" align="center">1827</td>
+    <td class="br" align="center">161</td>
+    <td class="br" align="center">&nbsp;&nbsp;&nbsp;&nbsp;2</td>
+    <td class="br" align="center">273</td></tr>
+<tr><td class="blr" align="center">1828</td>
+    <td class="br" align="center">225</td>
+    <td class="br" align="center">&nbsp;&nbsp;&nbsp;&nbsp;0</td>
+    <td class="br" align="center">282</td></tr>
+<tr><td class="blr" align="center">1829</td>
+    <td class="br" align="center">199</td>
+    <td class="br" align="center">&nbsp;&nbsp;&nbsp;&nbsp;0</td>
+    <td class="br" align="center">244</td></tr>
+<tr><td class="blr" align="center">1830</td>
+    <td class="br" align="center">190</td>
+    <td class="br" align="center">&nbsp;&nbsp;&nbsp;&nbsp;1</td>
+    <td class="br" align="center">217</td></tr>
+<tr><td class="btrl" align="center">1831</td>
+    <td class="btr" align="center">149</td>
+    <td class="btr" align="center">&nbsp;&nbsp;&nbsp;&nbsp;3</td>
+    <td class="btr" align="center">239</td></tr>
+<tr><td class="blr" align="center">1832</td>
+    <td class="br" align="center">&nbsp;&nbsp;84</td>
+    <td class="br" align="center">&nbsp;&nbsp;49</td>
+    <td class="br" align="center">270</td></tr>
+<tr><td class="blr" align="center">1833</td>
+    <td class="br" align="center">&nbsp;&nbsp;33</td>
+    <td class="br" align="center">139</td>
+    <td class="br" align="center">267</td></tr>
+<tr><td class="blr" align="center">1834</td>
+    <td class="br" align="center">&nbsp;&nbsp;51</td>
+    <td class="br" align="center">120</td>
+    <td class="br" align="center">273</td></tr>
+<tr><td class="blr" align="center">1835</td>
+    <td class="br" align="center">173</td>
+    <td class="br" align="center">&nbsp;&nbsp;18</td>
+    <td class="br" align="center">244</td></tr>
+<tr><td class="btrl" align="center">1836</td>
+    <td class="btr" align="center">272</td>
+    <td class="btr" align="center">&nbsp;&nbsp;&nbsp;&nbsp;0</td>
+    <td class="btr" align="center">200</td></tr>
+<tr><td class="blr" align="center">1837</td>
+    <td class="br" align="center">&nbsp;&nbsp;33</td>
+    <td class="br" align="center">&nbsp;&nbsp;&nbsp;&nbsp;0</td>
+    <td class="br" align="center">168</td></tr>
+<tr><td class="blr" align="center">1838</td>
+    <td class="br" align="center">282</td>
+    <td class="br" align="center">&nbsp;&nbsp;&nbsp;&nbsp;0</td>
+    <td class="br" align="center">202</td></tr>
+<tr><td class="blr" align="center">1839</td>
+    <td class="br" align="center">162</td>
+    <td class="br" align="center">&nbsp;&nbsp;&nbsp;&nbsp;0</td>
+    <td class="br" align="center">205</td></tr>
+<tr><td class="blr" align="center">1840</td>
+    <td class="br" align="center">152</td>
+    <td class="br" align="center">&nbsp;&nbsp;&nbsp;&nbsp;3</td>
+    <td class="br" align="center">263</td></tr>
+<tr><td class="btrl" align="center">1841</td>
+    <td class="btr" align="center">102</td>
+    <td class="btr" align="center">&nbsp;&nbsp;15</td>
+    <td class="btr" align="center">283</td></tr>
+<tr><td class="blr" align="center">1842</td>
+    <td class="br" align="center">&nbsp;&nbsp;68</td>
+    <td class="br" align="center">&nbsp;&nbsp;64</td>
+    <td class="br" align="center">307</td></tr>
+<tr><td class="blr" align="center">1843</td>
+    <td class="br" align="center">&nbsp;&nbsp;34</td>
+    <td class="br" align="center">149</td>
+    <td class="br" align="center">324</td></tr>
+<tr><td class="bblr" align="center">(1844)</td>
+    <td class="bbr" align="center">&nbsp;&nbsp;(52)</td>
+    <td class="bbr" align="center">(111)</td>
+    <td class="bbr" align="center">(320)</td></tr></table>
+
+<p>&#8220;If we now compare together the number of groups, and the days free from
+spots, we find that the sun-spots have a period of about ten years, and
+that for about five years they are so numerous that during this period few
+days, if any, are free from spots. The sequel must show whether this
+period is constant, whether the minimum activity<span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span> of the sun in producing
+spots lasts for one or two years, and whether this activity increases more
+quickly than it decreases.&#8221;</p>
+
+<p>&nbsp;<a name="platex" id="platex"></a></p>
+<div class="figcenter"><img src="images/i174top.jpg" alt="" /></div>
+<p class="center">FEB. 18, 1894.</p>
+<div class="figcenter"><img src="images/i174bottom.jpg" alt="" /></div>
+<p class="center">FEB. 19, 1894.</p>
+<p class="center">X.&mdash;<span class="smcap">Photographs of the Sun taken at the Royal Observatory, Greenwich, Shewing Sunspots.</span></p>
+<p>&nbsp;</p>
+
+<div class="sidenote">Attracted little attention,</div>
+
+<p>This brief announcement is all that the discoverer says upon the subject;
+and it is perhaps not remarkable that it attracted very little attention,
+especially when we remember that it related to a matter which the
+astronomical world had agreed to put aside as unprofitable and not worth
+attention. Next year, in giving his usual paper on the spots for 1844 he
+recurs to the subject in the following sentence: &#8220;The periodicity of spots
+of about ten years which was indicated in my summary published last year,
+is confirmed by this year&#8217;s observations.&#8221; I have added in brackets to the
+table above reproduced the numbers for 1844 subsequently given, and it
+will be seen how nearly they might have been predicted.</p>
+
+<p>Still the subject attracted little attention. Turning over the leaves of
+the journal at random, I came across the annual report of the Astronomer
+Royal of England, printed at length. But in it there is no reference to
+this discovery, which opened up a line of work now strongly represented in
+the annual programme of the Royal Observatory at Greenwich. Mr. Johnson
+remarks that the only person who had taken it up was Julius Schmidt, who
+then resided near Hamburg.<span class="sidenote">until eight years later.</span> But Schwabe went on patiently accumulating
+facts; and in 1851 the great Von Humboldt in the third volume of his
+<i>Cosmos</i>, drew attention to<span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span> the discovery, which was accordingly for the
+first time brought into general notice. It will be seen that there are not
+many facts of general interest relating to the actual discovery beyond the
+courage with which the work was commenced in a totally unpromising
+direction, and the scant attention it received after being made for us. We
+may admit that interest centres chiefly in the tremendous consequences
+which flowed from it. We now recognise that many other phenomena are bound
+up with this waxing and waning of the solar spots.<span class="sidenote">Other phenomena sympathetic</span> We might be prepared
+for a sympathy in phenomena obviously connected with the sun itself; but
+it was an unexpected and startling discovery that magnetic phenomena on
+the earth had also a sympathetic relation with the changes in sun-spots,
+and it is perhaps not surprising that when once this connection of solar
+and terrestrial phenomena was realised, various attempts have been made to
+extend it into regions where we cannot as yet allow that it has earned a
+legitimate right of entry. We have heard of the weather and of Indian
+famines occurring in cycles identical with the sun-spot cycle; and it is
+obvious how tremendously important it would be for us if this were found
+to be actually the case. For we might in this way predict years of
+possible famine and guard against them; or if we could even partially
+foretell the kind of weather likely to occur some years hence, we might
+take agricultural measures accordingly. The importance of the connection,<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span>
+if only it could be established, is no doubt the reason which has misled
+investigators into laying undue stress on evidence which will not bear
+close scrutiny.<span class="sidenote">and others not.</span> For the present we must say decidedly that no case has
+been made out for paying serious attention to the influence of sun-spots
+on weather. Nevertheless, putting all this aside, there is quite enough of
+first-rate importance in the sequel to Schwabe&#8217;s discovery.</p>
+
+<p>Let us review the facts in order. Most of us, though we may not have had
+the advantage of seeing an actual sun-spot through a telescope, have seen
+drawings or photographs of spots. There is a famous drawing made by James
+Nasmyth (of steam-hammer fame), in July, 1864, which is of particular
+interest, because at that time Nasmyth was convinced&mdash;and he convinced
+many others with him&mdash;that the solar surface was made up of a
+miscellaneous heap of solid bodies in shape like willow leaves, or grains
+of rice, thrown together almost at random, and the drawing was made by him
+to illustrate this idea. Comparing a modern photograph with it, we see
+that there is something to be said for Nasmyth&#8217;s view, which attracted
+much attention at the time and occasioned a somewhat heated controversy.
+But since the invention of the spectroscope it has become quite obsolete;
+it probably does not correspond in any way to the real facts.<span class="sidenote">Greenwich sun records.</span> But instead
+of looking at pictures which have been enlarged to show the detailed
+structure in and <span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span>near a spot, we will look at a series of pictures of
+the whole sun taken on successive days at Greenwich in which the spots are
+necessarily much smaller, but which show the behaviour of the spots from
+day to day. (See Plates <a href="#platex">X.</a> and <a href="#platexi">XI.</a>) From the date at the foot of each it
+will be seen that they gradually cross the disc of the sun (a fact first
+discovered by Galileo in 1610),<span class="sidenote">The sun&#8217;s rotation.</span> showing that the sun rotates on an axis
+once in about every twenty-five days. There are many interesting facts
+connected with this rotation; especially that the sun does not rotate as a
+solid body, the parts near the (Sun&#8217;s) Equator flowing quicker than those
+nearer the Poles; but for the present we cannot stop to dwell upon them.
+What interests us particularly is the history, not from day to day, but
+from year to year, as Schwabe has already given it for a series of years.</p>
+
+<p>&nbsp;<a name="platexi" id="platexi"></a></p>
+<div class="figcenter"><img src="images/i179top.jpg" alt="" /></div>
+<p class="center">FEB. 20, 1894.</p>
+<div class="figcenter"><img src="images/i179bottom.jpg" alt="" /></div>
+<p class="center">FEB. 21, 1894.</p>
+<p class="center">XI.&mdash;<span class="smcap">Photographs of the Sun taken at the Royal Observatory, Greenwich, shewing Sunspots</span></p>
+<p>&nbsp;</p>
+
+<div class="sidenote">Wolf&#8217;s numbers.</div>
+
+<p>When it became generally established that this periodicity existed, Rudolf
+Wolf of Zurich collected the facts about sun-spots from the earliest
+possible date, and represented this history by a series of numbers which
+are still called Wolf&#8217;s Sun-Spot Numbers. You will see from the diagram
+the obvious rise and fall for eleven years,&mdash;not ten years, as Schwabe
+thought, but just a little over eleven years. The facts are, however,
+given more completely by the work done at the Royal Observatory at
+Greenwich. It is part of the regular daily work of that Observatory to
+photograph the sun at least twice. Many days are of<span class="pagenum"><a name="Page_164" id="Page_164">[Pg 164]</a></span> course cloudy or wet,
+so that photographs cannot be obtained; but there are available
+photographs similarly taken in India or in Mauritius, where the weather is
+more favourable, and from these the gaps are so well filled up that very
+few days, if any, during the whole year are left without some photograph
+of the sun&#8217;s surface.<span class="sidenote">Greenwich areas.</span> On these photographs the positions and the areas of
+the spots are carefully measured under a microscope, and the results when
+submitted to certain necessary calculations are published year by year. It
+is clearly a more accurate estimate of the spottedness of the sun to take
+the total <i>area</i> of all the spots rather than their mere <i>number</i>, for in
+the latter case a large spot and a small one count equally. Hence the
+Greenwich records will perhaps give us an even better idea of the
+periodicity than Wolf&#8217;s numbers. Now, at the same observatory magnetic
+observations are also made continuously. If a magnet be suspended freely
+we are accustomed to say that it will point to the North Pole; but this is
+only very roughly true. In the first place, it is probably well known to
+you that there is a considerable deviation from due north owing to the
+fact that the magnetic North Pole is not the same as the geographical
+North Pole; but this for the present need not concern us.<span class="sidenote">Magnetic fluctuations.</span> What does
+concern us is, that if the needle is hung up and left long enough to come
+to rest, it does not then remain steadily at rest, but executes slow and
+small oscillations backwards and forwards, up and down, <span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span>throughout the
+day; repeating nearly the same oscillations on the following day, but at
+the same time gradually changing its behaviour so as to oscillate
+differently in summer and winter. These changes are very small, and would
+pass unnoticed by the naked eye; but when carefully watched through a
+telescope, or better still, when photographed by some apparatus which will
+at the same time magnify them, they can be rendered easily visible. When
+the history of these changes is traced it is seen at once that there is a
+manifest connection with the cycle of sun-spot changes; for instance, if
+we measure the range of swing backwards and forwards during the day and
+take the average for all the days in the year, and then compare this with
+the average number of sun-spots, we shall see that the averages rise and
+fall together. Similarly we may take the up and down swing, find the
+average amount of it throughout the year, and again we shall find that
+this corresponds very closely with the average number of sun-spots.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i182.jpg" alt="" /></div>
+<p class="center"><span class="smcap">Plate XII.</span></p>
+<p>&nbsp;</p>
+
+<p>But perhaps the most striking way to exhibit the sympathy is to combine
+different variations of the needle into one picture. And first we must
+remark that there is another important variation of the earth&#8217;s magnetic
+action which we have not yet considered. We have mentioned the swing of
+the needle to and fro, and the swing up and down, and these correspond to
+changes in the <i>direction</i> of the force of attraction on the needle. But<span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span>
+there may be also changes in <i>intensity</i> of this action; the pull may be a
+little stronger or a little weaker than before, and these variations are
+not represented by any actual movement of the needle, though they can be
+measured by proper experiments. We can, however, imagine them represented
+by a movement of the end of the needle if we suppose it made of elastic
+material,<span class="sidenote">Daily curves.</span> so that it would lengthen when the force was greater and
+contract slightly when the force was less. If a pencil were attached to
+the end of such an elastic needle so as to make a mark on a sheet of
+paper, and if for a moment we exclude the up and down movements, the
+pencil would describe during the day a curve on the paper, as the end of
+the needle swung backwards and forwards with the change in direction, and
+moved across the direction of swing with the change in intensity. Now when
+curves of this kind are described for a day in each month of the year,
+there is a striking difference between the forms of them.<span class="sidenote">Difference between summer and winter, and between sun-spot maximum and minimum.<br /><br />Cause unknown.</span> During the
+summer months they are, generally speaking, comparatively large and open,
+and during the winter months they are small and close. This change in form
+is seen by a glance at Plate <a href="#platexiii">XIII.</a>, which gives the curves throughout the
+whole of one year. Let us now, instead of forming a curve of this kind for
+each month, form a single average curve for the whole year; and let us
+further do this for a series of years. (Plate <a href="#platexiv">XIV.</a>) We see that the curves
+change from year to year in a <span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span>manner very similar to that in which they
+change from month to month in any particular year, and the law of change
+is such that in years when there are many sun-spots we get a large open
+curve similar to those found in the summer, while for years when there are
+few sun-spots we get small close curves very like those in the winter.
+Hence we have two definite conclusions suggested: firstly, that the
+changes of force are sympathetic with the changes in the sun-spots; and
+secondly, that times of maximum sun-spots correspond to summer, and times
+of minimum to winter. And here I must admit that this is about as far as
+we have got at present in the investigation of this relationship. <i>Why</i>
+the needle behaves in this way we have as yet only the very vaguest ideas;
+suggestions of different kinds have certainly been put forward, but none
+of them as yet can be said to have much evidence in favour of its being
+the true one. For our present purpose, however, it is sufficient to note
+that there is this very real connection, and that consequently Schwabe&#8217;s
+sun-spot period may have a very real importance with regard to changes in
+our earth itself.</p>
+
+<p>&nbsp;<a name="platexiii" id="platexiii"></a></p>
+<div class="figcenter"><img src="images/i185top.png" alt="" /></div>
+<p class="center"><span class="smcap">Plate XIII.</span></p>
+<p>&nbsp;<a name="platexiv" id="platexiv"></a></p>
+<div class="figcenter"><img src="images/i185bottom.png" alt="" /></div>
+<p class="center"><span class="smcap">Plate XIV.</span></p>
+<p>&nbsp;</p>
+
+<p>But I may perhaps repeat the word of caution already uttered against
+extending without sufficient evidence this notion of the influence of
+sun-spots to other phenomena, such as weather. A simple illustration will
+perhaps serve better than a long argument to show both the way in which
+mistakes have been made and the way in<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span> which they can be seen to be
+mistakes. There is at the Royal Observatory at Greenwich an instrument for
+noting the direction of the wind, the essential part being an ordinary
+wind-vane, the movements of which are automatically recorded on a sheet of
+paper.<span class="sidenote">Illustration of spurious connection.</span> As the wind shifts from north to east the pencil moves in one
+direction, and when it shifts back again towards the north the pencil
+moves in the reverse way. But sometimes the wind shifts continuously from
+north to east, south, west, and back to north again, the vane making a
+complete revolution; and this causes the pencil to move continuously in
+one direction, until when the vane has come to north again, the pencil is
+far away from the convenient place of record; on such occasions it is
+often necessary to replace it by hand. Then again, the vane may turn in
+the opposite direction, sending the pencil inconveniently to the other
+side of the record. During the year it is easy to count the number of
+complete changes of wind in either direction, and subtracting one number
+from the other, we get the excess of complete revolutions of the vane in
+one direction over that in the other. Now if these rather arbitrary
+numbers are set down year by year, or plotted in the shape of a diagram,
+we get a curve which may be compared with the sun-spot curve, and during a
+period of no less than sixteen years&mdash;from 1858 to 1874&mdash;there was a
+remarkable similarity between the two diagrams. From this evidence <i>alone</i>
+it might<span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span> fairly be inferred that the sun-spots had some curious effect
+upon the weather at Greenwich, traceable in this extraordinary way in the
+changes of the wind. But the particular way in which these changes are
+recorded is so arbitrary that we should naturally feel surprise if there
+was a real connection between the two phenomena; and fortunately there
+were other records preceding these years and following them which enabled
+us to test the connection further, and it was found, as we might naturally
+expect, that it was not confirmed. On looking at diagrams (Plate <a href="#platexv">XV.</a>) for
+the periods before and after, no similarity can be traced between the
+sun-spot curve and the wind-vane curve, and we infer that the similarity
+during the period first mentioned was entirely accidental. This shows that
+we must be cautious in accepting, from a limited amount of evidence, a
+connection between two phenomena as real and established; for it may be
+purely fortuitous. We may particularly remark that it is desirable to have
+repetitions through several complete periods instead of one alone. It is
+possible to reduce to mathematical laws the rules for caution in this
+matter; and much useful work has already been done in this direction by
+Professor Schuster of Manchester and others, though as yet too little
+attention has been paid to their rules by investigators naturally eager to
+discover some hitherto unthought-of connection between phenomena.</p>
+
+<div class="sidenote">Facul&aelig; follow spots</div>
+
+<p>With this example of the need for caution, we<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span> may return to phenomena of
+which we can certainly say that they vary sympathetically with the
+sun-spots. Roughly speaking, the whole history of the sun seems to be
+bound up with them. Besides these dark patches which we call spots (which,
+by the way, are not really dark but only less bright than the surrounding
+part of the disc), there are patches brighter than the rest which have
+been called facul&aelig;. With ordinary telescopes, either visual or
+photographic, these can generally only be detected near the edge of the
+sun&#8217;s disc; but even with this limitation it can easily be established
+that the facul&aelig; vary in number and size from year to year much in the same
+way as the spots, and this conclusion is amply confirmed by the beautiful
+method of observing the facul&aelig; with the new instrument designed by
+Professor Hale of the Yerkes Observatory. With this instrument, called a
+spectroheliograph, it is possible to photograph the facul&aelig; in all parts of
+the sun&#8217;s disc, and thus to obtain a much more complete history of them,
+and there is no doubt whatever of their variation sympathetically with the
+spots.<span class="sidenote">and the chromosphere.</span> Nor is there any doubt about similar variations in other parts of
+the sun which we cannot see <i>at all</i> with ordinary telescopes, except on
+the occasions when the sun is totally eclipsed. Roughly speaking, these
+outlying portions of the sun consist of two kinds, the chromosphere and
+the corona, the former looking like an irregular close coating of the
+ordinary sun,<span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span> and the latter like a pearly halo of light extending to
+many diameters of the sun&#8217;s disc, but not with any very regular form.</p>
+
+<p>&nbsp;<a name="platexv" id="platexv"></a></p>
+<p class="note"><span class="smcap">Smoothed Sunspot Curve (Wolf) compared with the number of
+turns made in each year by the Osler Anemometer Vane of the Royal
+Observatory, Greenwich (the excess of the direct turns (D) over the
+retrograde turns (R) or <i>vice versa</i>.)</span></p>
+<div class="figcenter"><img src="images/i190tmb.png" alt="" /><br />
+<a href="images/i190.png"><small>Larger Image</small></a></div>
+<p class="center"><span class="smcap">The upper curve is in each case the Sunspot Curve, the lower the Vane
+Curve. The break in 1882 in the Vane Curve is due to the omission of
+evidently accidental turns from that date.</span></p>
+
+<p class="center"><span class="smcap">Plate XV.</span></p>
+<p>&nbsp;</p>
+
+<p>The chromosphere, from which shoot out the prominences or &#8220;red flames,&#8221;
+can now be observed without an eclipse if we employ the beautiful
+instrument above-mentioned, the spectroheliograph; and Professor Hale has
+succeeded in photographing spots, facul&aelig;, and prominences all on the same
+plate. But although many have made the attempt (and Professor Hale,
+perhaps, a more determined attempt than any man living), no one has yet
+succeeded in obtaining any picture or evidence of the existence of the
+corona excepting on the occasion of a total solar eclipse.</p>
+
+<div class="sidenote">Eclipses of sun.</div>
+
+<p>Now these occasions are very rare. There are two or three eclipses of the
+sun every year, but they are generally of the kind known as partial; when
+the moon does indeed come between us and the sun to some extent, but only
+cuts off a portion of his light&mdash;a clean-cut black disc is seen to
+encroach more or less on the surface of the sun. Most of us have had an
+opportunity of seeing a partial eclipse, probably more than once; but few
+have seen a total eclipse. For this the moon must come with great
+exactness centrally between us and the sun; and the spot where this
+condition is fulfilled completely only covers a few hundred miles of the
+earth&#8217;s surface at one moment. As the earth turns round, and as the moon
+revolves in its orbit, this patch from which the sun is totally<span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span> eclipsed
+travels over the earth&#8217;s surface, marking out a track some thousands of
+miles in length possibly, but still not more than 200 miles wide;<span class="sidenote">Total eclipses rare.</span> and in
+order to see the sun totally eclipsed even on the rare occasions when it
+is possible at all (for, as already remarked, in the majority of cases the
+eclipse is only partial), we must occupy some station in this narrow belt
+or track, which often tantalisingly passes over either the ocean or some
+regions not easily accessible to civilised man. Moreover, if we travel to
+such favoured spots the whole time during which the sun is totally
+eclipsed cannot exceed a few minutes, and hence observations are made
+under rather hurried and trying conditions. In these modern days of
+photography it is easier to take advantage of these precious moments than
+it used to be when there was only the eye and memory of an excited
+observer to rely upon. It is perhaps not surprising that some of the
+evidence collected on these earlier occasions was conflicting; but
+nowadays the observers, generally speaking, direct their energies in the
+first place to mounting accurately in position photographic apparatus of
+different kinds, each item of it specially designed to settle some
+particular problem in the most feasible way; secondly, to rehearsing very
+carefully the exact programme of exposures necessary during the critical
+few minutes; and finally, to securing these photographs with as few
+mistakes as possible when the precious moments actually<span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span> arrive. Even then
+the whole of their efforts are quite likely to be rendered unavailing by a
+passing cloud; and bitter is the disappointment when, after travelling
+thousands of miles, and spending months in preparation, the whole
+enterprise ends in nothing owing to some caprice of the weather.</p>
+
+<p>Hence it will easily be imagined that our knowledge of the corona, the
+part of the sun which we can still only study on occasions of a total
+solar eclipse, advances but slowly. During the last twenty years there has
+been altogether scarcely half-an-hour available for this research, though
+it may fairly be said that the very best possible use has been made of
+that half-hour. And, what is of importance for our immediate purpose, it
+has gradually been established by comparing the photographs of one eclipse
+with those of another,<span class="sidenote">Corona follows spots.</span> that the corona itself undergoes distinct changes
+in form in the same period which governs the changes of sun-spots. When
+there are many sun-spots the corona spreads out in all directions from the
+edge of the sun&#8217;s disc; when there are few sun-spots the corona extends
+very much further in the direction of the sun&#8217;s equator, so that at
+sun-spot minimum there is an appearance of two huge wings. Although the
+evidence is necessarily collected in a scrappy manner, by this time there
+is sufficient to remove this relationship out of the region of mere
+suspicion, and to give it a well-established place in our knowledge of the
+sun&#8217;s surroundings.</p>
+
+<p><span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span>Now the corona of the sun may be compared to some rare animal which we
+only see by paying a visit to some distant land, and may consider
+ourselves even then fortunate to get a glimpse of; and it might be thought
+that the habits of such an animal are not likely to be of any great
+importance in our everyday life. But so far from this being the case in
+regard to the corona, it is more than possible that the knowledge of its
+changes may be of vital interest to us. I have already said that, as yet,
+we have no satisfactory account of the reason why changes in sun-spots
+seem to influence changes in our magnets on the earth; but one of the
+theories put forward in explanation, and one by no means the least
+plausible, is that this influence may come, not from the sun-spots
+themselves, but from some other solar phenomenon which varies in sympathy
+with them; and in particular that it may come from the corona.<span class="sidenote">Corona may influence magnets.</span> These wings
+which reach out at sun-spot minimum can be seen to extend a considerable
+distance, and there is no reason to suppose that they actually cease at
+the point where they become too faint for us to detect them further; they
+may extend quite as far as the earth itself and even beyond; and they may
+be of such a nature as to influence our magnets. As the earth revolves
+round the sun it may sometime plunge into them, to emerge later and pass
+above or below them; as again the wings spread themselves at sun-spot
+minimum and seem to<span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span> shrink at maximum, so our magnets may respond by
+sympathetic though very small vibrations. Hence it is quite possible that
+the corona is directly influencing the magnetic changes on the earth.</p>
+
+<div class="sidenote">Possible importance of corona.</div>
+
+<p>But it may be urged that these changes are so slight as to be merely of
+scientific interest. That may be true to-day, but who will be bold enough
+to say that it will be true to-morrow? If we are thinking of practical
+utility alone, we may remember that two great forces of Nature which we
+have chained into the service of man, steam and electricity, put forth
+originally the most feeble manifestations, which might readily have been
+despised as valueless; but by careful attention to proper conditions
+results of overwhelming practical importance have been obtained from these
+forces, which might have been, and for many centuries were, neglected as
+too trivial to be worth attention. Recently the world has been startled by
+the discovery of new elements, such as radium, whose very existence was
+only detected by a triumph of scientific acuteness in investigation, and
+yet which promise to yield influences on our lives which may overwhelm in
+importance all that has gone before. And similarly it may be that these
+magnetic changes, when properly interpreted or developed, may become of an
+importance in the future out of all proportion to the attention which they
+have hitherto attracted. Hence, although perhaps sufficient has already<span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span>
+been established to show the immense consequences which flow from
+Schwabe&#8217;s remarkable discovery of the periodicity in solar spots, we may
+be as yet only on the threshold of its real value.</p>
+
+<p>From what little causes great events spring! How little can Schwabe have
+realised, when he began to point his modest little telescope at the sun,
+and to count the number of spots&mdash;the despised spots which he had been
+assured were of no interest and exhibited no laws, and were generally
+unprofitable&mdash;that he was taking the first step in the invention of the
+great science of Solar Physics!&mdash;a science which is, I am glad to say,
+occupying at the present moment so much of the attention, not only of the
+great Yerkes Observatory, but of many other observatories scattered over
+the globe.</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span></p>
+<h2><a name="CHAPTER_VI" id="CHAPTER_VI"></a>CHAPTER VI</h2>
+<h3>THE VARIATION OF LATITUDE</h3>
+
+<p>If we should desire to classify discoveries in order of merit, we must
+undoubtedly give a high place to those which are made under direct
+discouragements. In the last chapter we saw that Schwabe entered upon his
+work under conditions of this kind, it being the opinion of experienced
+astronomers who had looked at the facts that there was nothing of interest
+to be got by watching sun-spots. In the present chapter I propose to deal
+with a discovery made in the very teeth of the unanimous opinion of the
+astronomical world by an American amateur, Mr. S. C. Chandler of Cambridge
+(Massachusetts). It is my purpose to allow him to himself explain the
+steps of this discovery by giving extracts from the magnificent series of
+papers which he contributed to the <i>Astronomical Journal</i> on the subject
+in the years 1891-94, but it may help in the understanding of these
+extracts if I give a brief summary of the facts. And I will first explain
+what is meant by the &#8220;Variation of Latitude.&#8221;</p>
+
+<div class="sidenote">Latitude.</div>
+
+<p>We are all familiar with the existence of a certain star in the heavens
+called the Pole Star, and we know that at any particular place it is<span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span> seen
+constantly in the north at a definite height above the horizon, which is
+the latitude of the place. When watched carefully with a telescope it is
+found to be not absolutely stationary, but to describe a small circle in
+the heavens day by day, or rather night by night. These simple facts are
+bound up with the phenomenon of the earth&#8217;s rotation in this way: the axis
+about which it is rotating points to the centre of that little circle, and
+any change in the position of the axis can therefore be determined by
+observing these motions of the Pole Star. Such changes may be of two
+kinds: firstly, we might find that the size of the circle increased or
+diminished, and this would mean that the earth&#8217;s axis was pointing farther
+away from the Pole Star or nearer to it&mdash;pointing, that is to say, in a
+different direction in space.<span class="sidenote">Precession.</span> This actually happens (as has been known for
+some thousands of years) owing to the phenomenon called &#8220;precession&#8221;; the
+circle described by our Pole Star is at present getting a little smaller,
+but it will ultimately increase in size, and after thousands of years
+become so large that the Pole Star will entirely lose its character as a
+steady guide to the North.</p>
+
+<div class="sidenote">Change of latitude.</div>
+
+<p>Secondly (and this is what more immediately concerns us), the centre of
+the circle may alter its position and be no longer at the same height
+above the horizon of any given place. This would mean that the earth&#8217;s
+axis was shifting <i>in the earth itself</i>&mdash;that the North Pole which our
+explorers<span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span> go to seek is not remaining in the same place. That it does not
+change appreciably in position we know from familiar experience; our
+climates, for instance, would suffer considerably if there were any large
+changes. But astronomers are concerned with minute changes which would not
+have any appreciable effect on climate, and the question has long been
+before them whether, putting aside large movements, there were any minute
+variations in position of the North Pole.<span class="sidenote">Twenty years ago disbelieved.</span> Twenty years ago the answer to
+this question would have been given decidedly in the negative; it was
+considered as certain that the North Pole did not move at all within the
+limits of our most refined astronomical observations. Accepted theory
+seemed to indicate that any movements must in any case recur after a
+period of ten months, and careful discussion of the observations showed
+that there was no oscillation in such a period. Now we know that the
+theory itself was wrong, or rather was founded upon a mistaken assumption;
+and that the facts when properly examined show clearly a distinct movement
+of the North Pole, not a very large one, for all its movements take place
+within the area occupied by a moderate-sized room, but still a movement
+easily measurable by astronomical observations, and Mr. Chandler was the
+first to point out the law of these movements, and very possibly the first
+to suspect them.</p>
+
+<div class="sidenote">Chandler&#8217;s papers.</div>
+
+<p>With these few words of explanation I will<span class="pagenum"><a name="Page_180" id="Page_180">[Pg 180]</a></span> let Mr. Chandler tell his own
+story. His first paper appeared in the <i>Astronomical Journal</i> in November
+1891, and is courageously headed, &#8220;On the Variation of Latitude&#8221;&mdash;I say
+courageously, because at that time it was believed that the latitude did
+<i>not</i> vary, and Mr. Chandler himself was only in possession of a small
+portion of the facts. They unravelled themselves as he went forward; but
+he felt that he had firm hold of the end of the thread, and he faced the
+world confidently in that belief. He begins thus:&mdash;</p>
+
+<div class="blockquot">
+<div class="sidenote">First signs of change.</div>
+
+<p>&#8220;In the determination of the latitude of Cambridge<small><a name="f5.1" id="f5.1" href="#f5">[5]</a></small> with the
+Almucantar, about six years and a half ago, it was shown that the
+observed values, arranged according to nights of observation,
+exhibited a decided and curious progression throughout the series,
+the earlier values being small, the later ones large, and the range
+from November 1884 to April 1885 being about four-tenths of a second.
+There was no known or imaginable instrumental or personal cause for
+this phenomenon, yet the only alternative seemed to be an inference
+that the latitude had actually changed. This seemed at the time too
+bold an inference to place upon record, and I therefore left the
+results to speak for themselves. The subsequent continuation of the
+series of observations to the end of June 1885 gave a<span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span> maximum about
+May 1, while the discussion of the previous observations from May to
+November 1884 gave a minimum about September 1, indicating a range of
+0&#8243;.7 within a half-period of about seven months.&#8221;</p></div>
+
+<p>Mr. Chandler then gives some figures in support of these statements,
+presenting them with the clearness which is so well marked a feature of
+the whole series of papers, and concludes this introductory paper as
+follows:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;It thus appears that the apparent change in the latitude of
+Cambridge is verified by this discussion of more abundant material.
+The presumption that it is real, on this determination alone, would
+justify further inquiry.</p>
+
+<div class="sidenote">Confirmed in Europe.</div>
+
+<p>&#8220;Curiously enough Dr. K&uuml;stner, in his determination of the
+<ins class="errata" title="Errata: Page 181, line 17, for 'observation' read 'aberration.'">aberration</ins> from a series of observations coincident in time with
+those of the Almucantar, came upon similar anomalies, and his
+results, published in 1888, furnish a counterpart to those which I
+had pointed out in 1885. The verification afforded by the recent
+parallel determinations at Berlin, Prague, Potsdam, and Pulkowa,
+which show a most surprising and satisfactory accordance, as to the
+character of the change, in range and periodicity, with the
+Almucantar results, has led me to make further investigations on the
+subject. They seem to establish the nature of the law of those<span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span>
+changes, and I will proceed to present them in due order.&#8221;</p></div>
+
+<p>The second paper appeared on November 23, and opens with the following
+brief statement of his general results at that time:&mdash;</p>
+
+<div class="blockquot">
+
+<div class="sidenote">427 days&#8217; period.</div>
+
+<p>&#8220;Before entering upon the details of the investigations spoken of in
+the preceding number, it is convenient to say that the general result
+of a preliminary discussion is to show a revolution of the earth&#8217;s
+pole in a period of 427 days, from west to east, with a radius of
+thirty feet, measured at the earth&#8217;s surface. Assuming provisionally,
+for the purpose of statement, that this is a motion of the north pole
+of the principal axis of inertia about that of the axis of rotation,
+the direction of the former from the latter lay towards the Greenwich
+meridian about the beginning of the year 1890. This, with the period
+of 427 days, will serve to fix approximately the relative positions
+of these axes at any other time, for any given meridian. It is not
+possible at this stage of the investigation to be more precise, as
+there are facts which appear to show that the rotation is not a
+perfectly uniform one, but is subject to secular change, and perhaps
+irregularities within brief spaces of time.&#8221;</p></div>
+
+<p>It is almost impossible, now that we have become familiar with the ideas
+conveyed in this<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span> paragraph, to understand, or even fully to remember, the
+impression produced by them at the time; the sensation caused in some
+quarters, and the ridicule excited in others.<span class="sidenote">Contrary to received views.</span> They were in flat
+contradiction to all accepted views; and it was believed that these views
+were not only theoretically sound, but had been matured by a thorough
+examination of observational evidence. The only period in which the
+earth&#8217;s pole could revolve was believed to be ten mouths; and here was Mr.
+Chandler proclaiming, apparently without any idea that he was
+contradicting the laws of dynamics, that it was revolving in fourteen
+months! The radius of its path had been found to be insensible by careful
+discussion of observations, and now he proclaimed a sensible radius o&pound;
+thirty feet. Finally, he had the audacity to announce a <i>variable</i> period,
+to which there was nothing at all corresponding in the mathematical
+possibilities. This was the bitterest pill of all. Even after Professor
+Newcomb had shown us how to swallow the other two, he could not recommend
+any attempt at the third, as we shall presently see; and Mr. Chandler was
+fain ultimately to gild it a little before it could be gulped.</p>
+
+<p>But this is anticipating, and it is our intention to follow patiently the
+evidence adduced in support of the above statements, made with such
+splendid confidence to a totally disbelieving world. Mr. Chandler first
+examines the observations of Dr. K&uuml;stner of Berlin, quoted at the end of
+his last<span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span> paper, and shows how well they are suited by the existence of a
+variation in the latitude of 427 days; and that this new fact is
+added&mdash;when the Cambridge (U.S.A.) latitudes were the smallest those of
+Berlin were the largest, and <i>vice vers&acirc;</i>, as would clearly be the case if
+the phenomenon was due to a motion of the earth&#8217;s pole; for if it moved
+nearer America it must move further from Europe.<span class="sidenote">Pulkowa puzzle solved,</span> He then examines a long
+series of observations made in the years 1864-1873 at Pulkowa, near St.
+Petersburg, and again finds satisfactory confirmation of his law of
+variation. Now it had long been known that there was something curious
+about these observations, but no one could tell what it was. The key
+offered by Mr. Chandler fitted the lock exactly, and the anomalies which
+had been a puzzle were removed. This was in itself a great triumph; but
+there was another to come, which we may let Mr. Chandler describe in his
+own words:&mdash;</p>
+
+<div class="sidenote">also Washington.</div>
+<div class="blockquot"><p>&#8220;In 1862 Professor Hubbard began a series of observations of
+&#945; Lyr&aelig; at the Washington Observatory with the prime vertical transit
+instrument, for the purpose of determining the constants of
+aberration and nutation and the parallax of the star. The methods of
+observation and reduction were conformed to those used with such
+success by W. Struve. After Hubbard&#8217;s death the series was continued
+by Professors Newcomb, Hall, and Harkness until the beginning of
+1867. Professor<span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span> Hall describes these observations as the most
+accurate determinations of declination ever made at the Naval
+Observatory. The probable error of a declination from a single
+transit was &plusmn;0&#8243;.141, and judging from the accidental errors, the
+series ought to give trustworthy results. Upon reducing them,
+however, it was found that some abnormal source of error existed,
+which resulted in anomalous values of the aberration-constant in the
+different years, and a negative parallax in all. A careful
+verification of the processes of reduction failed to discover the
+cause of the trouble, and Professor Hall says that the results must
+stand as printed, and that probably some annual disturbance in the
+observations or the instrument occurred, which will never be
+explained, and which renders all deductions from them uncertain. The
+trouble could not be connected with personal equation, the anomalies
+remaining when the observations of the four observers who took part
+were separately treated. Nor, as Professor Hall points out, will the
+theoretical ten-month period in the latitude furnish the explanation.</p>
+
+<p>&#8220;It is manifest, however, that if the 427-day period exists, its
+effect ought to appear distinctly in declination-measurements of such
+high degree of excellence as these presumably were, and, as I hope
+satisfactorily to show, actually are. When this variation is taken
+into account the observations will unquestionably vindicate the high
+<span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span>expectations entertained with regard to them by the accomplished and
+skilful astronomers who designed and carried them out.&#8221;</p></div>
+
+<p>From this general account I am excluding technical details and figures,
+and unfortunately a great deal is thereby lost. We lose the sense of
+conviction which the long rows of accordant figures force upon us, and we
+lose the opportunities of admiring both the astonishing amount of work
+done and the beautiful way in which the material is handled by a master.
+But I am tempted to give one very small illustration of the numerical
+results from near the end of the paper.<span class="sidenote">Direction of revolution of Pole.</span> After discussing the Washington
+results, and amply fulfilling the promise made in the preceding extract,
+Mr. Chandler compares them with the Pulkowa results, and shows that the
+Earth&#8217;s Pole must be revolving from west to east, and not from east to
+west. And then he writes down a simple formula representing this motion,
+and compares his formula with the observations. He gives the results in
+seconds of arc, but for the benefit of those not familiar with
+astronomical measurements we may readily convert these into feet;<span class="sidenote">Example of results.</span> and in
+the following tables are shown the distances of the Earth&#8217;s Pole <i>in feet</i>
+from its average position,<small><a name="f6.1" id="f6.1" href="#f6">[6]</a></small> as observed at Washington and<span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span> at Pulkowa,
+and the same distances calculated according to the formula which Mr.
+Chandler was able to write down at this early stage. The signs + and - of
+course indicate opposite directions of displacement:&mdash;</p>
+
+<p class="center"><span class="smcap">Washington.</span><br /><i>Deviation of Pole.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="deviation">
+<tr><td class="btrl" align="center">Date.</td>
+    <td class="btr" align="center">Observed.</td>
+    <td class="btr" align="center">Formula.</td></tr>
+<tr><td class="btrl">1864, Dec. 28</td>
+    <td class="btr">-&nbsp;28 feet</td>
+    <td class="btr">-&nbsp;23 feet</td></tr>
+<tr><td class="blr">1865, Mar. 19</td>
+    <td class="br">-&nbsp;&nbsp;&nbsp;1<span style="margin-left: .75em;">"</span></td>
+    <td class="br">-&nbsp;12<span style="margin-left: .75em;">"</span></td></tr>
+<tr><td class="blr"><span style="margin-left: 1em;">"</span><span style="margin-left: 1.25em;">June&nbsp;&nbsp;&nbsp;1</span></td>
+    <td class="br">+15<span style="margin-left: .75em;">"</span></td>
+    <td class="br">+12<span style="margin-left: .75em;">"</span></td></tr>
+<tr><td class="blr"><span style="margin-left: 1em;">"</span><span style="margin-left: 1.25em;">Aug. 11</span></td>
+    <td class="br">+22<span style="margin-left: .75em;">"</span></td>
+    <td class="br">+23<span style="margin-left: .75em;">"</span></td></tr>
+<tr><td class="blr"><span style="margin-left: 1em;">"</span><span style="margin-left: 1.25em;">Oct.&nbsp;&nbsp;&nbsp;9</span></td>
+    <td class="br">+11<span style="margin-left: .75em;">"</span></td>
+    <td class="br">+15<span style="margin-left: .75em;">"</span></td></tr>
+<tr><td class="bblr"><span style="margin-left: 1em;">"</span><span style="margin-left: 1.25em;">Dec. 13</span></td>
+    <td class="bbr">- 17<span style="margin-left: .75em;">"</span></td>
+    <td class="bbr">-&nbsp;&nbsp;&nbsp;6<span style="margin-left: .75em;">"</span></td></tr></table>
+
+<p>&nbsp;</p>
+<p class="center"><span class="smcap">Pulkowa.</span><br /><i>Deviation of Pole.</i></p>
+
+<table border="0" cellpadding="0" cellspacing="0" summary="deviation">
+<tr><td class="btrl" align="center">Date.</td>
+    <td class="btr" align="center">Observed.</td>
+    <td class="btr" align="center">Formula.</td></tr>
+<tr><td class="btrl">1865, July&nbsp;&nbsp;&nbsp;25</td>
+    <td class="btr">-&nbsp;18 feet</td>
+    <td class="btr">-&nbsp;12 feet</td></tr>
+<tr><td class="blr"><span style="margin-left: 1em;">"</span><span style="margin-left: 1.25em;">Sept.&nbsp;&nbsp;9</span></td>
+    <td class="br">+&nbsp;&nbsp;3<span style="margin-left: .75em;">"</span></td>
+    <td class="br">+&nbsp;&nbsp;3<span style="margin-left: .75em;">"</span></td></tr>
+<tr><td class="blr"><span style="margin-left: 1em;">"</span><span style="margin-left: 1.25em;">Nov. 22</span></td>
+    <td class="br">+26<span style="margin-left: .75em;">"</span></td>
+    <td class="br">+22<span style="margin-left: .75em;">"</span></td></tr>
+<tr><td class="blr">1866, Feb.&nbsp;&nbsp;22</td>
+    <td class="br">+18<span style="margin-left: .75em;">"</span></td>
+    <td class="br">+13<span style="margin-left: .75em;">"</span></td></tr>
+<tr><td class="blr"><span style="margin-left: 1em;">"</span><span style="margin-left: 1.25em;">June&nbsp;&nbsp;&nbsp;&nbsp;4</span></td>
+    <td class="br">- 11<span style="margin-left: .75em;">"</span></td>
+    <td class="br">- 18<span style="margin-left: .75em;">"</span></td></tr>
+<tr><td class="bblr"><span style="margin-left: 1em;">"</span><span style="margin-left: 1.25em;">July&nbsp;&nbsp;&nbsp;17</span></td>
+    <td class="bbr">- 16<span style="margin-left: .75em;">"</span></td>
+    <td class="bbr">- 23<span style="margin-left: .75em;">"</span></td></tr></table>
+
+<p>Of course the figures are not exact in every case, but they are never many
+feet wrong; and it may<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span> well be imagined that it is a difficult thing to
+deduce, even from the most refined observations, the position of the
+earth&#8217;s pole to within a foot. The difficulty is exactly the same as that
+of measuring the length of an object 300 miles away to within an inch!</p>
+
+<p>Mr. Chandler winds up his second paper thus:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;We thus find that the comparison of the simultaneous series at
+Pulkowa and Washington, 1863-1867, leads to the same conclusion as
+that already drawn from the simultaneous series at Berlin and
+Cambridge, 1884-1885. The direction of the polar motion may therefore
+be looked upon as established with a large degree of probability.</p>
+
+<p>&#8220;In the next paper I will present the results derived from <span class="smcap">Peters</span>,
+<span class="smcap">Struve</span>, <span class="smcap">Bradley</span>, and various other series of observations, after
+which the results of all will be brought to bear upon the
+determination of the best numerical values of the constants
+involved.&#8221;</p></div>
+
+<div class="sidenote">Bradley&#8217;s observations.</div>
+
+<p>The results were not, however, presented in this order. In the next paper,
+which appeared on December 23, 1891, Mr. Chandler begins, with the work of
+Bradley, the very series of observations at Kew and Wansted which led to
+the discoveries of aberration and nutation, and which we considered in the
+third chapter. He first<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span> shows that, notwithstanding the obvious accuracy
+of the observations, there is some unexplained discordance. The very
+constant of aberration which Bradley discovered from them differs by
+half-a-second of arc from our best modern determinations. Attempts have
+been made to ascribe the discordance to changes in the instrument, but Mr.
+Chandler shows that such changes, setting aside the fact that Bradley
+would almost certainly have discovered them, will not fit in with the
+facts.<span class="sidenote">Latitude varied in twelve months then.</span> The facts, when analysed with the skill to which we have become
+accustomed, are that there is a periodic swing in the results <i>with a
+period of about a year</i>, and not fourteen months, as before, &#8220;a result so
+curious,&#8221; as he admits, that &#8220;if we found no further support, it might
+lead us to distrust the above reasoning, and throw us back to the
+possibility that, after all, <span class="smcap">Bradley&#8217;s</span> observations may have been vitiated
+by some kind of annual instrumental error. But it will abundantly appear,
+when I have had the opportunity to print the deductions from all the other
+series of observations down to the present time, that the inference of an
+increase in the period of polar revolution is firmly established by their
+concurrent testimony.&#8221; We shall presently return to this curious result,
+which might well have dismayed a less determined researcher than Mr.
+Chandler, but which only led him on to renewed exertions.</p>
+
+<p>The results obtained from Bradley&#8217;s <span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span>observations may be put in the form
+of a diagram thus:&mdash;</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i210.png" alt="" /></div>
+<p class="center"><span class="smcap">Fig. 7.</span></p>
+<p>&nbsp;</p>
+
+<p>It will be seen that the maxima and minima fall in the spring and autumn,
+and this fact alone seemed to show that the effect could not be due to
+temperature, for we should expect the greatest effect in that case in
+winter and summer. It could not be due to the parallax of the stars for
+which Bradley began his search, for stars in different quarters of the
+heavens would then be differently affected, and this was not the case.
+&#8220;There remains,&#8221; concluded Mr. Chandler after full discussion, &#8220;the only
+natural conclusion of an actual displacement of the zenith, in other
+words, a change of latitude.&#8221; And he concludes this paper with the
+following fine passage:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;So far, then, as the results of this incomparable series of
+observations at Kew and Wansted,<span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span> considered by themselves alone, can
+now be stated, the period of the polar rotation at that epoch appears
+to have been probably somewhat over a year, and certainly shorter by
+about two months than it is at the present time. The range of the
+variation was apparently in the neighbourhood of a second of arc, or
+considerably larger than that shown by the best modern observations.</p>
+
+<div class="sidenote">Bradley&#8217;s greatness.</div>
+
+<p>&#8220;Before taking leave of these observations for the present I cannot
+forbear to speak of the profound impression which a study of them
+leaves upon the mind, and the satisfaction which all astronomers must
+feel in recognising that, besides its first fruits of the phenomena
+of aberration and nutation, we now owe also our first knowledge of
+the polar motion to this same immortal work of Bradley. Its
+excellence, highly appreciated as it has been, has still been
+hitherto obscured by the presence of this unsuspected phenomenon.
+When divested of its effects, the wonderful accuracy of this work
+must appear in a finer light, and our admiration must be raised to
+higher pitch. Going back to it after one hundred and sixty years
+seems indeed like advancing into an era of practical astronomy more
+refined than that from which we pass. And this leads to a suggestion
+worthy of serious practical consideration&mdash;whether we can do better
+in the future study of the polar rotation, than again to avail
+ourselves of Bradley&#8217;s method,<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span> without endangering its elegant
+simplicity and effectiveness by attempts at improvement, other than
+supplying certain means of instrumental control which would without
+doubt commend themselves to his sagacious mind.</p>
+
+<p>&#8220;In the next article Bradley&#8217;s later observations at Greenwich, the
+results of which are not so distinct, will be discussed; and also
+those of Brinkley at Dublin, 1808-13 and 1818-22. This will bring
+again to the surface one of the most interesting episodes in
+astronomical history,<span class="sidenote">Other puzzles explained.</span> the spirited and almost acrimonious dispute
+between Brinkley and Pond with regard to stellar parallaxes. I hope
+to show that the hitherto unsolved enigma of Brinkley&#8217;s singular
+results finds its easy solution in the fact of the polar motion. The
+period of his epoch appears to have been about a year, and its range
+more than a second. Afterwards will follow various discussions
+already more or less advanced towards completion. These include
+Bessel&#8217;s observations at K&ouml;nigsberg, 1820-24, with the Reichenbach
+circle, and in 1842-44 with the Repsold circle; the latitudes derived
+from the polar-point determinations of Struve and M&auml;dler with the
+Dorpat circle, 1822-38; Struve&#8217;s observations for the determination
+of the aberration; Peters&#8217; observations of <i>Polaris</i>, 1841-43, with
+the vertical-circle; the results obtained from the reflex zenith-tube
+at Greenwich, 1837-75, whose singular anomalies<span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span> can be referred in
+large part to our present phenomenon, complicated with instrumental
+error, to which until now they have been exclusively attributed; the
+Greenwich transit-circle results, 1851-65, in which case, however, a
+similar complication and the large accidental errors of observation
+seem to frustrate efforts to get any pertinent results; the Berlin
+prime-vertical observations of Weyer and Br&uuml;nnow, 1845-46, in which I
+hope to show that the parallax of &#946; <i>Draconis</i> derived
+from them is simply a record of the change of latitude; the
+conflicting latitude determinations at Cambridge, England; the
+Washington observation of <i>Polaris</i> and other close Polars, 1866-87,
+with the transit-circle; also those at Melbourne, 1863-84, a portion
+of which have already been drawn upon in the last number of the
+<i>Journal</i>, and some others. While the list is a considerable one, I
+shall be able to compress the statement of results for many of the
+series into a short space.</p>
+
+<div class="sidenote">Provisional nature of results.</div>
+
+<p>&#8220;In connection with this synopsis of the scope of the investigations,
+one or two particulars may be of interest, which at the present
+writing seem to foreshadow the probable outcome. I beg, however, that
+the statement will be regarded merely as a provisional one. First,
+while the period is manifestly subject to change, as has already once
+or twice been intimated, I have hitherto failed in tracing the
+variations to any regular law, expressible in a numerical formula.
+Indeed, the general<span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span> impression produced by a study of these changes
+in the length of the period is that the cause which produces them
+operates capriciously to a certain degree, although the average
+effect for a century has been to diminish the velocity of the
+revolution of the pole. How far this impression is due to the
+uncertainty of the observations, and to the complication of the
+phenomenon with other periodical changes of a purely instrumental
+kind, I cannot say. Almost all of the series of any extent which have
+been examined, have the peculiarity that they manifest the
+periodicity quite uniformly and distinctly for a number of years,
+then for a while obscurely. In some cases, however, what at first
+appears to be an objective irregularity proves not to be so by
+comparison with overlapping series at other observatories.</p>
+
+<p>&#8220;Another characteristic which has struck my attention, although
+somewhat vaguely, is that the variations in the length of the period
+seem to go hand in hand with simultaneous alterations in the
+amplitude of the rotation; the shorter periods being apparently
+associated with the larger coefficients for the latter. The
+verification of these surmises awaits a closer comparative scrutiny,
+the opportunity for which will come when the computations are in a
+more forward state. If confirmed, these observations will afford a
+valuable touchstone, in seeking for the cause of a phenomenon which
+now seems to be at variance with the accepted laws of terrestrial
+rotation.&#8221;</p></div>
+
+<div class="sidenote">Reception of discovery.</div>
+
+<p><span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span>Let us now for a few moments turn aside from the actual research to see
+how the announcement was received. It would be ungracious to reprint here
+any of the early statements of incredulity which found their way into
+print, especially in Germany. But the first note of welcome came from
+Simon Newcomb, in the same number of the <i>Astronomical Journal</i> as the
+paper just dealt with, and the following extract will indicate both the
+difficulties felt in receiving Mr. Chandler&#8217;s results and the way in which
+Newcomb struck at the root of them.</p>
+
+<div class="blockquot">
+
+<p>&#8220;Mr. Chandler&#8217;s remarkable discovery, that the apparent variations in
+terrestrial latitudes may be accounted for by supposing a revolution
+of the axis of rotation of the earth around that of figure, in a
+period of 427 days, is in such disaccord with the received theory of
+the earth&#8217;s rotation that at first I was disposed to doubt its
+possibility. But I am now able to point out a <i>vera causa</i> which
+affords a complete explanation of this period.<span class="sidenote">Newcomb&#8217;s explanation.</span> Up to the present time
+the treatment of this subject has been this: The ratio of the moment
+of inertia of the earth around its principal axis to the mean of the
+other two principal moments, admits of very accurate determination
+from the amount of precession and nutation. This ratio involves what
+we might call, in a general way, the solid ellipticity of the earth,
+or the ellipticity of a<span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span> homogeneous spheroid having the same moments
+of inertia as the earth.</p>
+
+<p>&#8220;When the differential equations of the earth&#8217;s rotation are
+integrated, there appear two arbitrary constants, representing the
+position of any assigned epoch of the axis of rotation relative to
+that of figure. Theory then shows that the axis of rotation will
+revolve round that of figure, in a period of 306 days, and in a
+direction from west toward east. The attempts to determine the value
+of these constants have seemed to show that both are zero, or that
+the axes of rotation and figure are coincident. Several years since,
+Sir William Thomson published the result of a brief computation from
+the Washington Prime-Vertical observations of &#945; Lyrae
+which I made at his request and which showed a coefficient 0&#8243;.05.
+This coefficient did not exceed the possible error of the result; I
+therefore regarded it as unreal.</p>
+
+<div class="sidenote">The forgotten assumption.</div>
+
+<p>&#8220;The question now arises whether Mr. Chandler&#8217;s result can be
+reconciled with dynamic theory. I answer that it can, because the
+theory which assigns 306 days as the time of revolution is based on
+the hypothesis that the earth is an absolutely rigid body. But, as a
+matter of fact, the fluidity of the ocean plays an important part in
+the phenomenon, as does also the elasticity of the earth. The
+combined effect of this fluidity and elasticity is that if the axis
+of rotation is displaced by a certain amount, the axis of figure
+will, by the<span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span> changed action of the centrifugal force, be moved
+toward coincidence with the new axis of rotation. The result is, that
+the motion of the latter will be diminished in a corresponding ratio,
+and thus the time of revolution will be lengthened. An exact
+computation of the effect is not possible without a knowledge of the
+earth&#8217;s modulus of elasticity. But I think the result of
+investigation will be that the rigidity derived from Mr. Chandler&#8217;s
+period is as great as that claimed by Sir William Thomson from the
+phenomena of the tides.&#8221;</p></div>
+
+<p>This was very satisfactory. Professor Newcomb put his finger on the
+assumption which had been made so long ago that it had been forgotten: and
+the lesson is well worth taking to heart, for it is not the first time
+that mistaken confidence in a supposed fact has been traced to some
+forgotten preliminary assumption: and we must be ever ready to cast our
+eyes backward over all our assumptions, when some new fact seems to
+challenge our conclusions. It might further be expected that this
+discovery of the way in which theory had been defective would as a
+secondary consequence<span class="sidenote">But Chandler&#8217;s work still mistrusted.</span> inspire confidence in the other conclusions which
+Mr. Chandler had arrived at in apparent contradiction to theory; or at
+least suggest the suspension of judgment. But Professor Newcomb did not
+feel that this was possible in respect of the <i>change</i> of period,<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span> from
+about twelve months in Bradley&#8217;s time to fourteen months in ours. We have
+seen that Mr. Chandler himself regarded this as a &#8220;curious result&#8221;
+requiring confirmation: but since the confirmation was forthcoming, he
+stated it with full confidence, and drew the following remarks from
+Professor Newcomb in July 22, 1892:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;The fact of a periodic variation of terrestrial latitudes, and the
+general law of that variation, have been established beyond
+reasonable doubt by the observations collected by Mr. Chandler. But
+two of his minor conclusions, as enumerated in No. 3 of this volume,
+do not seem to me well founded. They are&mdash;</p>
+
+<p>&#8220;1. That the period of the inequality is a variable quantity.</p>
+
+<p>&#8220;2. That the amplitude of the inequality has remained constant for
+the last half century.&#8221;</p></div>
+
+<p>Professor Newcomb proceeds to give his reasons for scepticism, which are
+too technical in character to reproduce here. But I will quote the
+following further sentence from his paper:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;The question now arises how far we are entitled to assume that the
+period must be invariable. I reply that, perturbations aside, any
+variation of the period is in such direct conflict with the laws of
+dynamics that we are entitled to pronounce it impossible. But we know
+that there are perturbations, and I do not see how one can<span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span> doubt
+that they have so acted as to increase the amplitude of the variation
+since 1840.&#8221;</p></div>
+
+<p>In other words, while recognising that there may be a way of reconciling
+one of the &#8220;minor&#8221; conclusions with theory, Professor Newcomb considers
+that in this case the other must go.<span class="sidenote">Chandler&#8217;s reply.</span> Mr. Chandler&#8217;s answer will speak for
+itself. It was delayed a little in order that he might present an immense
+mass of evidence in support of his conclusions, and was ultimately printed
+on August 23, 1892.</p>
+
+<div class="blockquot"><p>&#8220;The material utilised in the foregoing forty-five series aggregates
+more than thirty-three thousand observations. Of these more than
+one-third were made in the southern hemisphere, a fact which we owe
+principally to Cordoba. It comprises the work of seventeen
+observatories (four of them in the southern hemisphere) with
+twenty-one different instruments, and by nine distinct methods of
+observation. Only three of the series (XXI., XXV., and XXXV.), and
+these among the least precise intrinsically, give results
+contradictory of the general law developed in No. 267. This degree of
+general harmony is indeed surprising when the evanescent character of
+the phenomenon under investigation is considered.</p>
+
+<p>&#8220;The reader has now before him the means for independent scrutiny of
+the material on which the conclusions already drawn, and those which
+are<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span> to follow, are based. The space taken in the printing may seem
+unconscionable, but I hope this will be charged to the extent of the
+evidence collected, and not to diffuseness or the presentation of
+needless detail; for I have studiously sought to compress the form of
+statement without omitting anything essential for searching
+criticism. That it was important to do this is manifest, since the
+conclusions, if established, overthrow the existing theory of the
+earth&#8217;s rotation, as I have pointed out on p. 21. I am neither
+surprised nor disconcerted, therefore, that Professor Newcomb should
+hesitate to accept some of these conclusions on the ground (<i>A. J.</i>,
+No. 271) that they are in such conflict with the laws of dynamics
+that we are entitled to pronounce them impossible. He has been so
+considerate and courteous in his treatment of my work thus far, that
+I am sure he will not deem presumptuous the following argument in
+rebuttal.</p>
+
+<div class="sidenote">He &#8220;put aside all teachings of theory,&#8221;</div>
+
+<p>&#8220;It should be said, first, that in beginning these investigations
+last year, I deliberately put aside all teachings of theory, because
+it seemed to me high time that the facts should be examined by a
+purely inductive process; that the nugatory results of all attempts
+to detect the existence of the Eulerian period probably arose from a
+defect of the theory itself; and that the entangled condition of the
+whole subject required that it should be examined afresh by processes
+unfettered by<span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span> any preconceived notions whatever. The problem which I
+therefore proposed to myself was to see whether it would not be
+possible to lay the numerous ghosts&mdash;in the shape of numerous
+discordant residual phenomena pertaining to determinations of
+aberration, parallaxes, latitudes, and the like&mdash;which had heretofore
+flitted elusively about the astronomy of precision during the
+century; or to reduce them to tangible form by some simple consistent
+hypothesis. It was thought that if this could be done, a study of the
+nature of the forces, as thus indicated, by which the earth&#8217;s
+rotation is influenced, might lead to a physical explanation of them.</p>
+
+<div class="sidenote">and &#8220;is not dismayed.&#8221;</div>
+
+<p>&#8220;Naturally, then, I am not much dismayed by the argument of conflict
+with dynamic laws, since all that such a phrase means must refer
+merely to the existent state of the theory at any given time. When
+the 427-day period was propounded, it was as inconsistent with known
+dynamic law as the variation of it now appears to be. Professor
+Newcomb&#8217;s own happy explanation has already set aside the first
+difficulty, as it would appear, and advanced the theory by an
+important step. Are we so sure yet of a complete knowledge of all the
+forces at work as to exclude the chance of a <i>vera causa</i> for the
+second?&#8221;</p></div>
+
+<div class="sidenote">Faraday&#8217;s words.</div>
+
+<p>There is a splendid ring of resolution about these words. Let us compare
+them with a notable utterance of Faraday:&mdash;</p>
+
+<div class="blockquot"><p><span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span>&#8220;The philosopher should be a man willing to listen to every
+suggestion, but determined to judge for himself. He should not be
+biassed by appearances; have no favourite hypothesis; be of no
+school; and in doctrine have no master. He should not be a respecter
+of persons, but of things. Truth should be his primary object. If to
+these qualities be added industry, he may indeed hope to walk within
+the veil of the temple of Nature.&#8221;</p></div>
+
+<p>Tested by this severe standard, Mr. Chandler fails in no particular, least
+of all in that of industry.<span class="sidenote">Chandler&#8217;s other work at this time.</span> The amount of work he got through about this
+time was enormous, for besides the main line of investigation, of which we
+have only had after all a mere glimpse, he had been able to turn aside to
+discuss a subsidiary question with Professor Comstock; he had examined
+with great care some puzzling characteristics in the variability of stars;
+he computed some comet ephemerides; and he was preparing a new catalogue
+of variable stars&mdash;a piece of work involving the collection and
+arrangement of great masses of miscellaneous material. Yet within a few
+months after replying as above to Professor Newcomb&#8217;s criticism,<span class="sidenote">His ultimate satisfactory solution.</span> he was
+able to announce that he had found the key to the new puzzle, and that
+&#8220;theory and observation were again brought into complete accord.&#8221; We will
+as before listen to the account of this new step in his own words,<span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span> but a
+slight preliminary explanation may help those unaccustomed to the
+terminology. The polar motion was found to be compounded of <i>two</i>
+independent motions, both periodic, but having different periods. Now, the
+general results of such a composition are well known in several different
+branches of physics, especially in the theory of sound.<span class="sidenote">Interference of two waves.</span> If two notes of
+nearly the same pitch be struck at the same time, we hear the resultant
+sound alternately swell and die away, because the vibrations caused by the
+two notes are sometimes going in the same direction, and after an interval
+are going exactly in opposite directions. Diagrammatically we should
+represent the vibrations by two waves, as below; the upper wave goes
+through its period seven and a half times between A and D, the lower only
+six times; and it is easily seen that at A and C the waves are
+sympathetic, at B and D antipathetic. At A and C the compound vibration
+would be doubled; at B and D reduced to insensibility. The point is so
+important that perhaps a numerical illustration of it will not be
+superfluous. The waves are now represented by rows<span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span> of figures as below.
+The first series recurs after every 6, the second after every 7.</p>
+
+<p>&nbsp;</p>
+<div class="figcenter"><img src="images/i223.png" alt="" /></div>
+<p class="center"><span class="smcap">Fig. 8.</span></p>
+<p>&nbsp;</p>
+
+
+<table border="0" cellpadding="0" cellspacing="0" summary="waves">
+<tr><td>First Wave</td><td class="dent">1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1</td></tr>
+<tr><td>Second Wave</td><td class="bb">1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3</td></tr>
+<tr><td>Combined Effect</td><td class="dent">2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5 5 5 5 5 5 6 6 6 4 4 4</td></tr>
+<tr><td>&nbsp;</td><td class="dent">Great disturbance.<span class="spacer">&nbsp;</span><span class="spacer">&nbsp;</span><span class="spacer">&nbsp;</span><span class="spacer">&nbsp;</span>Calm.</td></tr>
+<tr><td class="bb">&nbsp;</td><td class="bb">&nbsp;</td></tr>
+<tr><td>&nbsp;</td></tr>
+<tr><td>First Wave</td><td class="dent">2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2</td></tr>
+<tr><td>Second Wave</td><td class="bb">4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3</td></tr>
+<tr><td>Combined Effect</td><td class="dent">6 7 7 5 3 3 5 7 8 6 4 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5</td></tr>
+<tr><td>&nbsp;</td><td class="dent"><span class="spacer">&nbsp; &nbsp;</span><span class="spacer">&nbsp; &nbsp;</span><span class="spacer">&nbsp;</span>Great disturbance.</td></tr></table>
+
+<p>&nbsp;</p>
+<p>Adding the two rows together, the oscillations at first reinforce one
+another and we get numbers ranging from 2 to 8 instead of from 1 to 4; but
+one wave gains on the other, until it is rising when the other is falling,
+and the numbers add up to a steady series of 5&#8217;s. It will be seen that
+there are no less than seven consecutive 5&#8217;s, and all the variation seems
+to have disappeared. But presently the waves separate again, and the
+period of great disturbance recurs; it will be seen that in the &#8220;combined
+effect&#8221; the numbers repeat exactly after the 42nd term. Now those
+unfamiliar with the subject may not be prepared for the addition of one
+physical wave to another, as though they were numbers, but the analogy is
+perfect.<span class="sidenote">Illustration from ocean travel.</span> Travellers by some of the fast twin-screw steamers have had
+unpleasant occasion to notice this phenomenon, when the engineer does not
+run the two screws precisely at the same speed; there come times when the
+ship vibrates violently, separated by<span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span> periods of comparative stillness.
+Instances from other walks of life may recur to the memory when once
+attention is called to the general facts; but enough has been said to
+explain the point numbered (2) in the subjoined statement. To understand
+the rest, we must remember that if the two waves are not equal in
+&#8220;amplitude,&#8221; <i>i.e.</i> if the backward and forward motion is not the same in
+both, they cannot annul one another, but the greater will always
+predominate. Those interested in following the matter further should have
+no difficulty in constructing simple examples to illustrate such points.
+We will proceed to give Mr. Chandler&#8217;s statements:&mdash;</p>
+
+<div class="sidenote">Chandler&#8217;s final formul&aelig;.</div>
+
+<div class="blockquot"><p>&#8220;We now come upon a new line of investigation. Heretofore, as has
+been seen, the method has been to condense the results of each series
+of observations into the interval comprised by a single period, then
+to determine the mean epoch of minimum and the mean range for each
+series, and, finally, by a discussion of these quantities, to
+establish the general character of the law of the rotation of the
+pole. It is now requisite to analyse the observations in a different
+way, and discover whether the deviations from the general provisional
+law, in the last column of Table II., are real, and also in what
+manner the variation of the period is brought about. The outcome of
+this discussion, which is to be presented in the present paper, is
+extremely satisfactory. The<span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span> real nature of the phenomenon is most
+distinctly revealed, and may be described as follows:&mdash;</p>
+
+<p>&#8220;1. The observed variation of the latitude is the resultant curve
+arising from two periodic fluctuations superposed upon each other.
+The first of these, and in general the more considerable, has a
+period of about 427 days, and a semi-amplitude of about 0&#8243;.12. The
+second has an annual period with a range variable between 0&#8243;.04 and
+0&#8243;.20 during the last half-century. During the middle portion of this
+interval, roughly characterised as between 1860 and 1880, the value
+represented by the lower limit has prevailed, but before and after
+those dates, the higher one. The minimum and maximum of this annual
+component of the variation occur at the meridian of Greenwich, about
+ten days before the vernal and autumnal equinoxes respectively, and
+it becomes zero just before the solstices.</p>
+
+<p>&#8220;2. As the resultant of these two motions, the effective variation of
+the latitude is subject to a systematic alternation in a cycle of
+seven years&#8217; duration, resulting from the commensurability of the two
+terms. According as they conspire or interfere, the total range
+varies between two-thirds of a second as a maximum, to but a few
+hundredths of a second, generally speaking, as a minimum.</p>
+
+<p>&#8220;3. In consequence of the variability of the coefficient of the
+annual term above mentioned, the apparent average period between 1840
+and 1855<span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span> approximated to 380 or 390 days; widely fluctuated from
+1855 to 1865; from 1865 to about 1885 was very nearly 427 days, with
+minor fluctuations; afterwards increased to near 440 days, and very
+recently fell to somewhat below 400 days. The general course of these
+fluctuations is quite faithfully represented by the law of eq. (3),
+(No. 267), and accurately, even down to the minor oscillations of
+individual periods, by the law of eq. (15), hereafter given, and
+verbally interpreted above. This law also gives a similarly accurate
+account of the corresponding oscillations in the amplitude. The
+closeness of the accordance between observation and the numerical
+theory, in both particulars, places the reality of the law beyond
+reasonable doubt.&#8221;</p></div>
+
+<p>Those who cannot follow the details of the above statement will
+nevertheless catch the general purport&mdash;that the difficulties felt by
+Professor Newcomb have been surmounted; and this is made clearer by a
+later extract:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;A very important conclusion necessarily follows from the agreement
+of the values of the 427-day term, deduced from the intervals between
+the consecutive values of T in Table XII., namely, that there has
+been no discontinuity in the revolution, such as Professor Newcomb
+regarded as so probable that he doubted the possibility of drawing
+any conclusions from the comparison of observations before and after
+1860 (<i>A. J.</i>, 271, p. 50).</p>
+
+<div class="sidenote">Theory must go, if it will not fit observation.</div>
+
+<p><span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span>&#8220;The present investigation demonstrates that the way out of the
+apparently irreconcilable contradiction of theory and observation in
+this matter does not lie in the direction of discrediting the
+observations, as he is inclined to do. On the contrary, the result is
+a beautiful vindication of the trustworthiness of the latter, and, at
+the same time, of the theory that demands an invariable rate of
+motion; providing a perfectly fitting key to the riddle by showing
+that another cause has intervened to produce the variability of the
+period. I feel confident that Professor Newcomb will agree with the
+reality of the explanation here set forth, and will reconsider his
+view that the perturbations in the position of the Pole must be of
+the nature of chance accumulations of motion, a view which he then
+considered necessary to the maintenance of the constancy in the
+period of latitude-variation.&#8221;</p></div>
+
+<p>The paper from which these words are taken appeared on November 4, 1892.
+The next paper on the main theme did not appear till a year later, though
+much work was being done in the meantime on the constant of aberration and
+other matters arising immediately after the discovery.<span class="sidenote">The final paper.</span> On November 14,
+1893, Mr. Chandler winds up the series of eight papers &#8220;On the Variation
+of Latitude,&#8221; which he had commenced just two years before. His work was
+by no means done; rather was it only beginning, for the torch he had<span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span> lit
+illuminated many dark corners. But he rightly regarded his discovery as
+now so firmly established that the series of papers dealing with it as
+still under consideration might be terminated. In this final paper he
+first devotes the most careful attention to one point of detail. He had
+shown earlier in the series that the North Pole must be revolving from
+West to East, and not from East to West; but this was when the motion was
+supposed to be simple and not complex, and it was necessary to re-examine
+the question of direction for each of the components. After establishing
+conclusively that the original direction holds for each of the components,
+he almost apologises for the trouble he has taken, thus:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;It is therefore proved beyond reasonable doubt that the directions
+of the rotations is from West to East in both elements; whence the
+general form of the equation for the variation of latitude adopted in
+<i>A. J.</i>, 284, p. 154, eq. (19). It may be thought that too much pains
+have been here bestowed upon a point which might be trusted to theory
+to decide. I cannot think so. One of the most salient results of
+these articles has been the proof of the fact that theory has been a
+blind guide with regard to the velocity of the Polar rotation,
+obscuring truth and misleading investigators for a half a century.
+And even if we were certain, which we are not, that the fourteen
+months&#8217; term is the Eulerian period in a <span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span>modified form. It would
+still be necessary to settle by observation the direction of the
+annual motion, with regard to which theory is powerless to inform us.
+To save repetition of argument, I must refer to the statement in <i>A.
+J.</i>, 273, pp. 68, 70, of the principles adopted in beginning these
+inquiries in 1891.&#8221;</p></div>
+
+<p>Finally, he answers one of the few objectors of eminence who still
+lingered, the great French physicist Cornu:&mdash;</p>
+
+<div class="blockquot"><div class="sidenote">Cornu answered.</div>
+
+<p>&#8220;The ground is now cleared for examination of the only topic
+remaining to be covered, to establish, upon the foundation of fact,
+every point in the present theory of these remarkable movements of
+the earth&#8217;s axis. This is the question of the possibility that these
+movements are not real, but merely misinterpretations of the observed
+phenomena; being in whole or in part an illusory effect of
+instrumental error due to the influence of temperature. Such a
+possibility has been a nightmare in practical astronomy from the
+first, frightening us in every series of unexplained residuals,
+brought to light continually in nearly all attempts at delicate
+instrumental research. A source of danger so subtile could not fail
+to be ever present in the mind of every astronomer and physicist who
+has given even a superficial attention to the question of the
+latitude variations, and there is no doubt that some are even now
+thus deterred from accepting these variations as<span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span> proved facts.
+Perhaps the most explicit and forcible statement of the doubts that
+may arise on this subject has been given very recently by Mr. Cornu.
+The views of so distinguished a physicist, and of others who are
+inclined to agree with him, call for careful attention, and cannot be
+neglected in the present closing argument upon the theory presented
+in these articles. It is unnecessary, for the purpose of disposing of
+objections of the sort raised by Cornu, to insist that it is not
+sufficient to show that the observed variations, attributed to the
+unsteadiness of the Earth&#8217;s Pole, are near the limit of precision
+attainable in linear differential measures, and in the indication of
+the direction of gravity by means of the air bubble of the level; or
+to show that there are known variations in divided circles and in
+levels, dependent on temperature and seasons. Nor need we require of
+objectors the difficult, although essential, task&mdash;which they have
+not distinctly attempted&mdash;of showing that these errors are not
+eliminated, as they appear to be, by the modes in which astronomers
+use their instruments. Neither need we even urge the fact that a
+large portion of the data which have been utilised in the present
+researches on the latitude were derived by methods which dispense
+with levels, or with circles, a part of them indeed with both, and
+yet that the results of all are harmonious. On the contrary, let us
+admit, although merely for argument&#8217;s sake, that all the known means
+of determining the direction<span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span> of gravity&mdash;including the plumb-line,
+the level, and a fluid at rest, whether used for a reflecting surface
+or as a support for a floating instrument&mdash;are subject to a common
+law of periodical error which vitiates the result of astronomical
+observation, obtained by whatever methods, and in precisely the same
+manner. Now, the observed law of latitude variation includes two
+terms, with periods of fourteen and twelve months respectively. Since
+the phases of the first term are repeated at intervals of two months
+in successive years, and hence in a series of years come into all
+possible relations to conditions of temperature dependent on season,
+the argument against the reality of this term, on this ground,
+absolutely fails, and needs no further notice. As to the second, or
+annual term, while the phases, as observed in any given longitude,
+are indeed synchronical with the seasons, they are not so as regards
+different longitudes. If, therefore, the times of any given phase, as
+observed in the same latitude, but in successively increasing
+longitudes, occurred at the same date in all of them, there would be
+a fatal presumption against the existence of an annual period in the
+polar motion. If, on the contrary, they occur at times successively
+corresponding to the differences of longitude, the presumption is
+equally fatal to the hypothesis that they can possibly be due to
+temperature variation as affecting instrumental measurement. But the
+facts given in the foregoing section <span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span>correspond most distinctly to
+the latter condition. Therefore, unless additional facts can be
+brought to disprove successively these observed results, we may
+dismiss for ever the bugbear which has undoubtedly led many to
+distrust the reality of the annual component of the
+latitude-variation, while they admit the existence of the 427-day
+term.&#8221;</p></div>
+
+<p>At this point we must leave the fascinating account of the manner in which
+this great discovery was established, in the teeth of opposition such as
+might have dismayed and dissuaded a less clear-sighted or courageous man.
+It is my purpose to lay more stress upon the method of making the
+discovery than upon its results;<span class="sidenote">Consequences of the discovery.</span> but we may afford a brief glance at some
+of the consequences which have already begun to flow from this step in
+advance. Some of them have indeed already come before us, especially that
+large class represented by the explanation of anomalies in series of
+observations which had been put aside as inexplicable. We have seen how
+the observations made in Russia, or in Washington, or at Greenwich, in all
+of which there was some puzzling error, were immediately straightened out
+when Chandler applied his new rule to them.<span class="sidenote">Suspected observers acquitted.</span> We in England have special
+cause to be grateful to Chandler; not only has he demonstrated more
+clearly than ever the greatness of Bradley, but he has rehabilitated Pond,
+the Astronomer Royal of the beginning of the nineteenth century; showing
+that his <span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a></span>observations, which had been condemned as in some way erroneous,
+were really far more accurate than might have been expected; and further
+he has shown that the beautiful instrument designed by Airy, and called
+the Reflex Zenith Tube, which seemed to have unaccountably failed in the
+purpose for which it was designed, was really all the time accumulating
+observations of this new phenomenon, the Variation of Latitude. Instead of
+Airy having failed in his design, he had in Chandler&#8217;s words &#8220;builded
+better than he knew.&#8221;</p>
+
+<div class="sidenote">Constant of Aberration improved.</div>
+
+<p>Secondly, there is the modifying influence of this new phenomenon on other
+phenomena already known, such, for instance, as that of &#8220;aberration.&#8221; We
+saw in the third chapter how Bradley discovered this effect of the
+velocity of light, and how the measure of it is obtained by comparing the
+velocity of light with that of the earth. This comparison can be effected
+in a variety of ways, and we should expect all the results to agree within
+certain limits; but this agreement was not obtained, and Chandler has been
+able to show one reason why, and to remove some of the more troublesome
+differences. It is impossible to give here an idea of the far-reaching
+consequences which such work as this may have; so long as there are
+differences of this kind we cannot trust any part of the chain of
+evidence, and there is in prospect the enormous labour of examining each
+separate link until the error is found. The velocity of light, for
+instance, may be<span class="pagenum"><a name="Page_215" id="Page_215">[Pg 215]</a></span> measured by a terrestrial experiment; was there anything
+wrong in the apparatus? The velocity of the earth in its journey round the
+sun depends directly upon the distance of the sun: have we measured this
+distance wrongly, and if so what was the error in the observations made?
+These are some of the questions which may arise so long as the values for
+the <i>Constant of Aberration</i> are still conflicting; but it requires
+considerable knowledge of astronomy to appreciate them fully.</p>
+
+<div class="sidenote">Latitude Variation Tide.</div>
+
+<p>Another example will, perhaps, be of more general interest. If the axis of
+the earth is executing small oscillations of this kind, there should be an
+effect upon the tides; the liquid ocean should feel the wobble of the
+earth&#8217;s axis in some way; and an examination of tidal registers showed
+that there was in fact a distinct effect. It may cause some amusement when
+I say that the rise and fall are only a few inches in any case; but they
+are unmistakable evidences that the earth is not spinning smoothly, but
+has this kind of unbalanced vibration, which I have compared to the
+vibrations felt by passengers on an imperfectly engineered twin-screw
+steamer. A more sensational effect is that apparently earthquakes are more
+numerous at the time when the vibration is greatest.<span class="sidenote">Earthquakes.</span> We remarked that the
+vibration waxes and wanes, much as that of the steamer waxes and wanes if
+the twin-screws are not running quite together. Now the passengers on the
+steamer would be prepared to find that breakages<span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span> would be more numerous
+during the times of vigorous oscillation; and it seems probable that in a
+similar way the little cracks of the earth&#8217;s skin which we call great
+earthquakes are more numerous when these unbalanced vibrations are at
+their maximum; that is to say, about once every seven years. This result
+is scarcely yet worthy of complete confidence, for our observations of
+earthquakes have only very recently been reduced to proper order; but if
+it should turn out to be true, it is scarcely necessary to add any words
+of mine to demonstrate the importance of this rather unexpected result of
+the Latitude Variation.</p>
+
+<p>Finally I will mention another phenomenon which seems to be at present
+more of a curiosity than anything else, but which may lead to some future
+great discovery. It is the outcome of observations which have been
+recently made to watch these motions of the Pole; for although there seems
+good reason to accept Mr. Chandler&#8217;s laws of variation as accurate, it is
+necessary to establish their accuracy and complete the details by making
+observations for some time yet to come;<span class="sidenote">The Kimura phenomenon.</span> and there could be no better proof
+of this necessity than the discovery recently made by Mr. Kimura, one of
+those engaged in this watch of the Pole in Japan. Perhaps I can give the
+best idea of it by mentioning one possible explanation, which, however, I
+must caution you may not be by any means the right one. We are accustomed
+to think of this great earth as being sufficiently constant in shape;<span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span> if
+asked, for instance, whether its centre of gravity remains constantly in
+the same place inside it, we should almost certainly answer in the
+affirmative, just as only twenty years ago we thought that the North Pole
+remained in the same place. But it seems possible that the centre of
+gravity moves a few feet backwards and forwards each year&mdash;this would at
+any rate explain certain curious features in the observations to which Mr.
+Kimura has drawn attention. Whatever the explanation of them may be, or to
+settle whether this explanation is correct, we want more observations,
+especially observations in the Southern Hemisphere; and it is a project
+under consideration by astronomers at the present moment whether three
+stations can be established in the Southern Hemisphere for the further
+observation of this curious phenomenon. The question resolves itself
+chiefly into a question of money; indeed, most astronomical projects do
+ultimately resolve themselves into questions of money; and I fear the
+world looks upon scientific men as insatiable in this respect. One can
+only hope that on the whole the money is expended so as to give a
+satisfactory return. In this instance I have no hesitation in saying that
+an immediate return of value for a comparatively modest expenditure is
+practically certain, if only in some way we can get the means of making
+the observations.</p>
+
+<p><span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span>It would be natural, at the conclusion of this brief review of some types
+of astronomical discovery, to summarise the lessons indicated: but there
+is the important difficulty that there appear to be none. It has been
+pointed out as we proceeded that what seemed to be a safe deduction from
+one piece of history has been flatly contradicted by another; no sooner
+have we learnt that important results may be obtained by pursuing steadily
+a line of work in spite of the fact that it seems to have become tedious
+and unprofitable (as in the search for minor planets) than we are
+confronted with the possibility that by such simple devotion to the day&#8217;s
+work we may be losing a great opportunity, as Challis did. We can scarcely
+go wrong in following up the study of residual phenomena in the wake of
+Bradley; but there is the important difficulty that we may be wholly
+unable to find a clue for the arrangement of our residuals, as is at
+present largely the case in meteorology. And, in general, human
+expectations are likely to be quite misleading, as has been shown in the
+last two chapters; the discoveries we desire may lie in the direction
+precisely opposite to that indicated by the best opinion at present
+available. There is no royal road to discovery, and though this statement
+may meet with such ready acceptance that it seems scarcely worth making,
+it is hoped that there may be sufficient of interest in the illustrations
+of its truth.</p>
+
+<p><span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span>The one positive conclusion which we may derive from the examples studied
+is that discoveries are seldom made without both hard work and conspicuous
+ability. A new planet, even as large as Uranus, does not reveal itself to
+a passive observer: thirteen times it may appear to such a one without
+fear of detection, until at last it encounters an alert Herschel, who
+suspects, tests, and verifies, and even then announces a comet&mdash;so little
+did he realise the whole truth. Fifteen years of unrequited labour before
+Astr&aelig;a was found, nineteen years of observation before the discovery of
+nutation could be announced: how seldom do these years of toil present
+themselves to our imaginations when we glibly say that &#8220;Bradley discovered
+nutation,&#8221; or &#8220;Hencke discovered Astr&aelig;a&#8221;! That the necessary labour is so
+often forgotten must be my excuse for recalling attention to it somewhat
+persistently in these examples.</p>
+
+<p>But beyond the fact that he must work hard, it would seem as though there
+were little of value to tell the would-be discoverer. The situation has
+been well summarised by Jevons in his chapter on Induction in the
+&#8220;Principles of Science;&#8221; and his words will form a fitting conclusion to
+these chapters:&mdash;</p>
+
+<div class="blockquot"><p>&#8220;It would seem as if the mind of the great discoverer must combine
+contradictory attributes. He must be fertile in theories and
+hypotheses,<span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span> and yet full of facts and precise results of experience.
+He must entertain the feeblest analogies, and the merest guesses at
+truth, and yet he must hold them as worthless till they are verified
+in experiment. When there are any grounds of probability he must hold
+tenaciously to an old opinion, and yet he must be prepared at any
+moment to relinquish it when a clearly contradictory fact is
+encountered.&#8221;</p></div>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span></p>
+<h2>INDEX</h2>
+
+<div class="note">
+<p>
+Aberration, <a href="#Page_105">105-109</a>, <a href="#Page_111">111</a>, <a href="#Page_112">112</a>, <a href="#Page_117">117</a>, <a href="#Page_118">118</a>, <a href="#Page_185">185</a>, <a href="#Page_188">188</a>, <a href="#Page_192">192</a>, <a href="#Page_214">214</a>, <a href="#Page_215">215</a><br />
+<br />
+Accidental discovery, <a href="#Page_15">15</a>, <a href="#Page_73">73</a>, <a href="#Page_121">121-154</a><br />
+<br />
+Adams, <a href="#Page_12">12</a>, <a href="#Page_45">45-85</a>;<br />
+<span style="margin-left: 1em;">resolution, <a href="#Page_55">55</a></span><br />
+<br />
+Airy, <a href="#Page_32">32</a>, <a href="#Page_40">40-85</a>, <a href="#Page_214">214</a><br />
+<br />
+Algiers, <a href="#Page_130">130</a><br />
+<br />
+Alleghenia, <a href="#Page_26">26</a><br />
+<br />
+Almucantar, <a href="#Page_180">180</a>, <a href="#Page_181">181</a><br />
+<br />
+Alphabet used for planets, <a href="#Page_27">27</a><br />
+<br />
+Anderson, Dr. T. C., <a href="#Page_8">8</a>, <a href="#Page_142">142</a>, <a href="#Page_143">143</a>, <a href="#Page_144">144</a>, <a href="#Page_146">146</a><br />
+<br />
+Anthelm, <a href="#Page_142">142</a><br />
+<br />
+Apollo, <a href="#Page_9">9</a><br />
+<br />
+Argon, <a href="#Page_109">109</a><br />
+<br />
+Ascension, <a href="#Page_34">34</a><br />
+<br />
+Assumption, forgotten, <a href="#Page_196">196</a><br />
+<br />
+Astr&aelig;a, <a href="#Page_22">22</a>, <a href="#Page_23">23</a>, <a href="#Page_219">219</a><br />
+<br />
+Astrographic chart, <a href="#Page_122">122</a>, <a href="#Page_125">125</a>, <a href="#Page_130">130</a><br />
+<br />
+<i>Astronomical Journal</i>, <a href="#Page_177">177-217</a><br />
+<br />
+<i>Astronomische Nachrichten</i>, <a href="#Page_52">52</a>, <a href="#Page_158">158</a><br />
+<br />
+Astrophil, <a href="#Page_143">143</a><br />
+<br />
+Auwers, <a href="#Page_142">142</a><br />
+<br />
+<br />
+Ball, Sir R., <a href="#Page_24">24</a><br />
+<br />
+Balliol College, <a href="#Page_87">87</a><br />
+<br />
+Banks, Sir J., <a href="#Page_9">9</a><br />
+<br />
+Barnard, E. E., <a href="#Page_146">146</a>, <a href="#Page_220">220</a><br />
+<br />
+Berlin, <a href="#Page_181">181</a>, <a href="#Page_183">183</a>, <a href="#Page_184">184</a>, <a href="#Page_188">188</a>, <a href="#Page_193">193</a><br />
+<br />
+Berlin star-map, <a href="#Page_45">45</a>, <a href="#Page_66">66</a>, <a href="#Page_83">83</a>, <a href="#Page_124">124</a><br />
+<br />
+Bessel, <a href="#Page_192">192</a><br />
+<br />
+Bettina, <a href="#Page_26">26</a>, <a href="#Page_27">27</a><br />
+<br />
+Birmingham, <a href="#Page_142">142</a><br />
+<br />
+&#8220;Black Drop&#8221; (in transit of Venus), <a href="#Page_30">30</a><br />
+<br />
+Bliss, <a href="#Page_114">114</a><br />
+<br />
+Board of Visitors of Greenwich Observatory, <a href="#Page_63">63</a><br />
+<br />
+Bode, <a href="#Page_11">11</a>, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_22">22</a><br />
+<br />
+Bode&#8217;s Law, <a href="#Page_12">12</a>, <a href="#Page_13">13</a>, <a href="#Page_38">38</a>, <a href="#Page_43">43</a>, <a href="#Page_45">45</a>, <a href="#Page_52">52</a>, <a href="#Page_72">72</a>, <a href="#Page_76">76</a>, <a href="#Page_77">77</a>, <a href="#Page_84">84</a><br />
+<br />
+Bourdeaux, <a href="#Page_130">130</a><br />
+<br />
+Bouvard, <a href="#Page_39">39</a>, <a href="#Page_40">40</a>, <a href="#Page_42">42</a>, <a href="#Page_48">48</a>, <a href="#Page_49">49</a>, <a href="#Page_50">50</a>, <a href="#Page_61">61</a><br />
+<br />
+Bradley, <a href="#Page_39">39</a>, <a href="#Page_86">86-120</a>, <a href="#Page_188">188-192</a>, <a href="#Page_213">213</a>, <a href="#Page_214">214</a>, <a href="#Page_218">218</a>, <a href="#Page_219">219</a><br />
+<br />
+Bradley, John, <a href="#Page_115">115</a><br />
+<br />
+Bremen, <a href="#Page_20">20</a><br />
+<br />
+Bridstow, <a href="#Page_87">87</a>, <a href="#Page_88">88</a>, <a href="#Page_94">94</a><br />
+<br />
+Briggs, <a href="#Page_119">119</a><br />
+<br />
+Brinkley, <a href="#Page_192">192</a><br />
+<br />
+British Association, <a href="#Page_63">63</a><br />
+<br />
+Br&uuml;nnow, <a href="#Page_193">193</a><br />
+<br />
+<br />
+California, <a href="#Page_26">26</a><br />
+<br />
+Cambridge (Mass.), <a href="#Page_180">180</a>, <a href="#Page_184">184</a>, <a href="#Page_188">188</a><br />
+<br />
+Cambridge Observatory, <a href="#Page_23">23</a>, <a href="#Page_42">42</a>, <a href="#Page_49">49</a>, <a href="#Page_52">52</a>, <a href="#Page_63">63</a>, <a href="#Page_65">65</a>, <a href="#Page_66">66</a>, <a href="#Page_135">135</a>, <a href="#Page_193">193</a><br />
+<br />
+Cambridge University, <a href="#Page_68">68-71</a>, <a href="#Page_114">114</a><br />
+<br />
+Cape Observatory, <a href="#Page_123">123</a>, <a href="#Page_124">124</a>, <a href="#Page_130">130</a><br />
+<br />
+Cards, <a href="#Page_11">11</a><br />
+<br />
+Cassini II., <a href="#Page_157">156</a><br />
+<br />
+Catania, <a href="#Page_130">130</a><br />
+<br />
+Ceres, <a href="#Page_14">14-22</a><br />
+<br />
+Chacornac, <a href="#Page_124">124</a><br />
+<br />
+Challis, <a href="#Page_49">49-54</a>, <a href="#Page_63">63-68</a>, <a href="#Page_71">71</a>, <a href="#Page_85">85</a>, <a href="#Page_218">218</a><br />
+<span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span><br />
+Chandler, S. C., <a href="#Page_118">118</a>, <a href="#Page_177">177-217</a><br />
+<br />
+Chapman&#8217;s &#8220;Homer,&#8221; <a href="#Page_2">2</a><br />
+<br />
+Chicago, <a href="#Page_157">157</a><br />
+<br />
+Chromosphere, <a href="#Page_170">170</a><br />
+<br />
+Clarke, C. C., <a href="#Page_2">2</a><br />
+<br />
+Coelostat, <a href="#Page_94">94</a><br />
+<br />
+Columbus, <a href="#Page_63">63</a><br />
+<br />
+Comet, <a href="#Page_4">4-8</a>, <a href="#Page_88">88</a>, <a href="#Page_108">108</a>, <a href="#Page_117">117</a>, <a href="#Page_123">123</a>, <a href="#Page_125">125</a><br />
+<br />
+Commission, planetary, <a href="#Page_27">27</a><br />
+<br />
+Common, A. A., <a href="#Page_124">124</a>, <a href="#Page_127">127</a><br />
+<br />
+<i>Compte Rendu</i>, <a href="#Page_62">62</a><br />
+<br />
+Comstock, <a href="#Page_202">202</a><br />
+<br />
+Conference, Astrographic, <a href="#Page_125">125-136</a><br />
+<br />
+Copernicus, <a href="#Page_79">79</a>, <a href="#Page_95">95</a><br />
+<br />
+Cordoba, <a href="#Page_130">130</a>, <a href="#Page_199">199</a><br />
+<br />
+Cornu, <a href="#Page_210">210-213</a><br />
+<br />
+Corona, <a href="#Page_170">170-175</a><br />
+<br />
+<i>Cosmos</i> (Humboldt&#8217;s), <a href="#Page_160">160</a><br />
+<br />
+<br />
+Delambre, <a href="#Page_157">157</a><br />
+<br />
+Deviation of Pole, <a href="#Page_187">187</a><br />
+<br />
+Disc of Neptune, <a href="#Page_44">44</a>, <a href="#Page_64">64</a>, <a href="#Page_79">79</a><br />
+<br />
+Disc of Uranus, <a href="#Page_4">4-7</a><br />
+<br />
+Dorpat, <a href="#Page_192">192</a><br />
+<br />
+Doublet (photographic), <a href="#Page_127">127-129</a><br />
+<br />
+Draconis, &#947;, <a href="#Page_96">96-104</a><br />
+<br />
+Draconis, &#946;, <a href="#Page_193">193</a><br />
+<br />
+Driessen, <a href="#Page_23">23</a><br />
+<br />
+Dry plate, <a href="#Page_122">122</a><br />
+<br />
+Dublin, <a href="#Page_192">192</a><br />
+<br />
+<br />
+Earthquakes, <a href="#Page_215">215</a><br />
+<br />
+Earth&#8217;s Pole, <a href="#Page_177">177-217</a><br />
+<br />
+Eccentricity, <a href="#Page_41">41</a>, <a href="#Page_83">83</a><br />
+<br />
+Eclipses, <a href="#Page_170">170-176</a><br />
+<br />
+Edinburgh, <a href="#Page_143">143</a><br />
+<br />
+Eduarda, <a href="#Page_26">26</a><br />
+<br />
+Egeria, <a href="#Page_22">22</a><br />
+<br />
+Endymion, <a href="#Page_25">25</a><br />
+<br />
+Eriphyla, <a href="#Page_26">26</a><br />
+<br />
+Eros, <a href="#Page_25">25</a>, <a href="#Page_26">26</a>, <a href="#Page_28">28</a>, <a href="#Page_35">35</a>, <a href="#Page_37">37</a>, <a href="#Page_68">68</a><br />
+<br />
+Eulerian, <a href="#Page_200">200</a>, <a href="#Page_209">209</a><br />
+<br />
+Evelyn, <a href="#Page_26">26</a><br />
+<br />
+Exposure, times of, <a href="#Page_122">122</a>, <a href="#Page_131">131</a><br />
+<br />
+<br />
+Facul&aelig;, <a href="#Page_170">170</a><br />
+<br />
+Faraday, <a href="#Page_201">201</a><br />
+<br />
+Flamsteed, <a href="#Page_39">39</a>, <a href="#Page_53">53</a>, <a href="#Page_115">115</a><br />
+<br />
+Fleming, Mrs., <a href="#Page_142">142</a><br />
+<br />
+Flora, <a href="#Page_22">22</a><br />
+<br />
+Foulkes, Martin, <a href="#Page_94">94</a><br />
+<br />
+French Academy, <a href="#Page_43">43</a>, <a href="#Page_51">51</a>, <a href="#Page_62">62</a><br />
+<br />
+<br />
+Galileo, <a href="#Page_95">95</a>, <a href="#Page_163">163</a><br />
+<br />
+Galle, <a href="#Page_44">44</a>, <a href="#Page_45">45</a>, <a href="#Page_47">47</a>, <a href="#Page_66">66</a>, <a href="#Page_67">67</a>, <a href="#Page_83">83</a><br />
+<br />
+Gasparis, <a href="#Page_22">22</a><br />
+<br />
+Gauge (railways), <a href="#Page_56">56</a><br />
+<br />
+Gauss, <a href="#Page_17">17-20</a><br />
+<br />
+Geminorum, H., <a href="#Page_4">4</a><br />
+<br />
+George III., <a href="#Page_8">8</a>, <a href="#Page_10">10</a><br />
+<br />
+&#8220;Georgian,&#8221; <a href="#Page_11">11</a><br />
+<br />
+<i>Georgium Sidus</i>, <a href="#Page_8">8</a>, <a href="#Page_10">10</a>, <a href="#Page_11">11</a><br />
+<br />
+Gill, Sir D., <a href="#Page_32">32</a>, <a href="#Page_34">34</a>, <a href="#Page_35">35</a>, <a href="#Page_123">123</a><br />
+<br />
+Gilliss, <a href="#Page_32">32</a><br />
+<br />
+Gotha, <a href="#Page_20">20</a><br />
+<br />
+Gould, <a href="#Page_32">32</a><br />
+<br />
+Graham, <a href="#Page_22">22</a>, <a href="#Page_23">23</a><br />
+<br />
+Gravitation, law of, <a href="#Page_38">38</a>, <a href="#Page_45">45</a>, <a href="#Page_59">59</a>, <a href="#Page_84">84</a>, <a href="#Page_105">105</a><br />
+<br />
+Greaves, <a href="#Page_119">119</a><br />
+<br />
+Greenwich Observatory, <a href="#Page_48">48-64</a>, <a href="#Page_88">88</a>, <a href="#Page_89">89</a>, <a href="#Page_114">114-117</a>, <a href="#Page_130">130</a>, <a href="#Page_160">160-169</a>, <a href="#Page_182">182</a>, <a href="#Page_192">192</a>, <a href="#Page_193">193</a>, <a href="#Page_206">206</a>, <a href="#Page_213">213</a><br />
+<br />
+Gregory, <a href="#Page_93">93</a>, <a href="#Page_119">119</a><br />
+<br />
+<br />
+Hale, G. E., <a href="#Page_170">170</a>, <a href="#Page_171">171</a><br />
+<br />
+Hall, A., <a href="#Page_184">184</a>, <a href="#Page_185">185</a><br />
+<br />
+Halley, <a href="#Page_88">88-92</a>, <a href="#Page_108">108</a>, <a href="#Page_112">112-116</a>, <a href="#Page_119">119</a><br />
+<br />
+Hansen, <a href="#Page_41">41</a>, <a href="#Page_59">59</a><br />
+<br />
+Harkness, <a href="#Page_184">184</a><br />
+<br />
+Hartwig, <a href="#Page_142">142</a><br />
+<br />
+Harvard College Observatory, <a href="#Page_128">128</a>, <a href="#Page_142">142</a>, <a href="#Page_144">144</a>, <a href="#Page_145">145</a><br />
+<br />
+Hebe, <a href="#Page_22">22</a><br />
+<br />
+Hegel, <a href="#Page_15">15</a><br />
+<br />
+Heidelberg, <a href="#Page_145">145</a><br />
+<br />
+Heliometer, <a href="#Page_32">32</a>, <a href="#Page_34">34</a><br />
+<span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span><br />
+Helium, <a href="#Page_109">109</a><br />
+<br />
+Helsingfors, <a href="#Page_130">130</a><br />
+<br />
+Hencke, <a href="#Page_22">22</a>, <a href="#Page_23">23</a>, <a href="#Page_64">64</a>, <a href="#Page_153">153</a>, <a href="#Page_219">219</a><br />
+<br />
+Henry brothers, <a href="#Page_124">124-129</a><br />
+<br />
+Herschel, Sir John, <a href="#Page_63">63</a>, <a href="#Page_75">75</a>, <a href="#Page_83">83</a><br />
+<br />
+Herschel, Sir William, <a href="#Page_2">2-11</a>, <a href="#Page_39">39</a>, <a href="#Page_44">44</a>, <a href="#Page_82">82</a>, <a href="#Page_219">219</a><br />
+<br />
+Herschel (Uranus), <a href="#Page_11">11</a>, <a href="#Page_12">12</a><br />
+<br />
+Hind, <a href="#Page_22">22</a>, <a href="#Page_23">23</a>, <a href="#Page_25">25</a>, <a href="#Page_142">142</a><br />
+<br />
+Hooke, <a href="#Page_96">96</a>, <a href="#Page_97">97</a><br />
+<br />
+Hubbard, <a href="#Page_184">184</a><br />
+<br />
+Humboldt, <a href="#Page_160">160</a><br />
+<br />
+Hussey, Rev. T. J., <a href="#Page_40">40</a>, <a href="#Page_42">42</a><br />
+<br />
+Hygeia, <a href="#Page_22">22</a><br />
+<br />
+<br />
+Ilmata, <a href="#Page_26">26</a><br />
+<br />
+Industria, <a href="#Page_26">26</a><br />
+<br />
+Ingeborg, <a href="#Page_26">26</a><br />
+<br />
+Instruments at Greenwich, <a href="#Page_114">114-116</a><br />
+<br />
+Iris, <a href="#Page_22">22</a>, <a href="#Page_23">23</a>, <a href="#Page_32">32</a>, <a href="#Page_35">35</a><br />
+<br />
+<br />
+Janson, <a href="#Page_142">142</a><br />
+<br />
+Jevons, <a href="#Page_219">219</a><br />
+<br />
+Johnson, M., <a href="#Page_156">156</a>, <a href="#Page_160">160</a><br />
+<br />
+Juno, <a href="#Page_9">9</a>, <a href="#Page_21">21</a>, <a href="#Page_22">22</a><br />
+<br />
+Jupiter, <a href="#Page_9">9</a>, <a href="#Page_28">28</a>, <a href="#Page_43">43</a>, <a href="#Page_49">49</a>, <a href="#Page_50">50</a>, <a href="#Page_61">61</a>;<br />
+<span style="margin-left: 1em;">satellites, <a href="#Page_92">92</a>, <a href="#Page_117">117</a></span><br />
+<br />
+<br />
+Keats, <a href="#Page_1">1-3</a>, <a href="#Page_7">7</a>, <a href="#Page_8">8</a><br />
+<br />
+Keill, <a href="#Page_94">94</a>, <a href="#Page_112">112</a>, <a href="#Page_119">119</a>, <a href="#Page_156">156</a><br />
+<br />
+Kelvin, Lord, <a href="#Page_196">196</a>, <a href="#Page_197">197</a><br />
+<br />
+Kepler, <a href="#Page_95">95</a>, <a href="#Page_142">142</a><br />
+<br />
+Kew, <a href="#Page_95">95</a>, <a href="#Page_96">96</a>, <a href="#Page_188">188</a>, <a href="#Page_190">190</a><br />
+<br />
+Kiel, <a href="#Page_141">141</a><br />
+<br />
+Kimura, <a href="#Page_216">216</a><br />
+<br />
+<ins class="correction" title="original: Konigsberg">K&ouml;nigsberg</ins>, <a href="#Page_192">192</a><br />
+<br />
+K&uuml;stner, <a href="#Page_118">118</a>, <a href="#Page_181">181</a>, <a href="#Page_183">183</a><br />
+<br />
+<br />
+Lalande, <a href="#Page_7">7</a>, <a href="#Page_11">11</a>, <a href="#Page_107">107</a>, <a href="#Page_157">157</a><br />
+<br />
+Lameia, <a href="#Page_26">26</a><br />
+<br />
+Laplace, <a href="#Page_61">61</a><br />
+<br />
+La Plata, <a href="#Page_130">130</a><br />
+<br />
+Latitude variation, <a href="#Page_99">99</a>, <a href="#Page_100">100</a>, <a href="#Page_117">117</a>, <a href="#Page_118">118</a>, <a href="#Page_177">177-217</a><br />
+<br />
+Lemonnier, <a href="#Page_39">39</a>, <a href="#Page_53">53</a>, <a href="#Page_157">157</a><br />
+<br />
+Le Verrier, <a href="#Page_12">12</a>, <a href="#Page_43">43-85</a><br />
+<br />
+Libussa, <a href="#Page_26">26</a><br />
+<br />
+Lick Observatory, <a href="#Page_152">152</a><br />
+<br />
+<i>Liouville&#8217;s Journal</i>, <a href="#Page_73">73</a><br />
+<br />
+Lisbon, longitude of, <a href="#Page_92">92</a><br />
+<br />
+London, <a href="#Page_23">23</a>, <a href="#Page_25">25</a>, <a href="#Page_96">96</a><br />
+<br />
+Long, <a href="#Page_157">157</a><br />
+<br />
+Longitude, <a href="#Page_92">92</a>, <a href="#Page_117">117</a><br />
+<br />
+Lowth, Bishop, <a href="#Page_119">119</a><br />
+<br />
+Lyrae, &#945;, <a href="#Page_184">184</a>, <a href="#Page_196">196</a><br />
+<br />
+<br />
+Macclesfield, Earl of, <a href="#Page_94">94</a>, <a href="#Page_113">113</a><br />
+<br />
+M&auml;dler, <a href="#Page_192">192</a><br />
+<br />
+Magnetic observations, <a href="#Page_161">161</a>, <a href="#Page_164">164</a>, <a href="#Page_174">174</a><br />
+<br />
+Magnitude equation, <a href="#Page_135">135</a><br />
+<br />
+Markree, <a href="#Page_23">23</a><br />
+<br />
+Mars, <a href="#Page_9">9</a>, <a href="#Page_28">28</a>, <a href="#Page_32">32</a>, <a href="#Page_34">34</a>, <a href="#Page_35">35</a>, <a href="#Page_91">91</a><br />
+<br />
+Mayer, <a href="#Page_39">39</a><br />
+<br />
+Measurement of plates, <a href="#Page_132">132-135</a><br />
+<br />
+<i>M&eacute;canique C&eacute;leste</i>, <a href="#Page_61">61</a><br />
+<br />
+Melbourne, <a href="#Page_130">130</a>, <a href="#Page_193">193</a><br />
+<br />
+Memorandum (Adams), <a href="#Page_55">55</a><br />
+<br />
+Mercury, <a href="#Page_9">9</a><br />
+<br />
+Messier, <a href="#Page_7">7</a><br />
+<br />
+Meteorites, <a href="#Page_59">59</a><br />
+<br />
+Meteors (November), <a href="#Page_60">60</a><br />
+<br />
+Metis, <a href="#Page_22">22</a>, <a href="#Page_23">23</a><br />
+<br />
+Micrometer, <a href="#Page_5">5</a>, <a href="#Page_133">133</a><br />
+<br />
+Milky Way, <a href="#Page_125">125</a><br />
+<br />
+Minerva, <a href="#Page_9">9</a><br />
+<br />
+Minor planets, <a href="#Page_13">13-28</a><br />
+<br />
+Minor planets tables, <a href="#Page_22">22</a>, <a href="#Page_24">24</a>, <a href="#Page_26">26</a><br />
+<br />
+Mistakes, <a href="#Page_71">71-83</a><br />
+<br />
+Molyneux, Samuel, <a href="#Page_94">94-96</a>, <a href="#Page_101">101</a>, <a href="#Page_104">104</a><br />
+<br />
+Monte Video, <a href="#Page_130">130</a><br />
+<br />
+Moon, tables of, <a href="#Page_117">117</a><br />
+<br />
+<br />
+Names of minor planets, <a href="#Page_22">22-28</a><br />
+<br />
+Nasmyth, <a href="#Page_162">162</a><br />
+<br />
+&#8220;Nautical Almanac,&#8221; <a href="#Page_11">11</a><br />
+<br />
+Nebula, <a href="#Page_124">124</a>, <a href="#Page_146">146-152</a><br />
+<span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span><br />
+Neptune, <a href="#Page_11">11</a>, <a href="#Page_12">12</a>, <a href="#Page_38">38-85</a>, <a href="#Page_124">124</a><br />
+<br />
+New College Lane, <a href="#Page_112">112</a><br />
+<br />
+Newcomb, Simon, <a href="#Page_81">81</a>, <a href="#Page_183">183</a>, <a href="#Page_184">184</a>, <a href="#Page_195">195-202</a>, <a href="#Page_207">207</a>, <a href="#Page_208">208</a><br />
+<br />
+New stars, <a href="#Page_121">121</a>, <a href="#Page_140">140-154</a><br />
+<br />
+Newton, <a href="#Page_38">38</a>, <a href="#Page_84">84</a>, <a href="#Page_90">90-95</a>, <a href="#Page_105">105</a>, <a href="#Page_113">113</a><br />
+<br />
+New York, longitude, <a href="#Page_92">92</a><br />
+<br />
+Ninina, <a href="#Page_26">26</a><br />
+<br />
+Northleach, <a href="#Page_87">87</a><br />
+<br />
+Northumberland, <a href="#Page_65">65</a><br />
+<br />
+Nova Geminorum, <a href="#Page_141">141</a>, <a href="#Page_145">145</a>, <a href="#Page_146">146</a><br />
+<br />
+Nova Persei, <a href="#Page_143">143</a>, <a href="#Page_146">146-152</a><br />
+<br />
+Nutation, <a href="#Page_99">99</a>, <a href="#Page_100">100</a>, <a href="#Page_110">110</a>, <a href="#Page_115">115</a>, <a href="#Page_117">117</a>, <a href="#Page_118">118</a>, <a href="#Page_188">188</a>, <a href="#Page_219">219</a><br />
+<br />
+<br />
+<i>Observatory</i> (magazine), <a href="#Page_26">26</a><br />
+<br />
+Ocllo, <a href="#Page_26">26</a><br />
+<br />
+Olbers, <a href="#Page_20">20-22</a><br />
+<br />
+Olympic games, <a href="#Page_119">119</a><br />
+<br />
+Oriani, <a href="#Page_15">15</a><br />
+<br />
+Ornamenta, <a href="#Page_26">26</a><br />
+<br />
+Oxford University, <a href="#Page_87">87-89</a>, <a href="#Page_94">94</a>, <a href="#Page_105">105-119</a><br />
+<br />
+Oxford University Observatory, <a href="#Page_121">121</a>, <a href="#Page_130">130</a>, <a href="#Page_132">132</a>, <a href="#Page_136">136</a>, <a href="#Page_142">142</a>, <a href="#Page_145">145</a>, <a href="#Page_154">154</a><br />
+<br />
+<br />
+Palermo, Observatory of, <a href="#Page_18">18</a><br />
+<br />
+Palisa, <a href="#Page_26">26</a><br />
+<br />
+Pallas, <a href="#Page_9">9</a>, <a href="#Page_21">21</a>, <a href="#Page_22">22</a><br />
+<br />
+Parallax, <a href="#Page_34">34</a>, <a href="#Page_91">91</a>, <a href="#Page_95">95-98</a>, <a href="#Page_109">109</a>, <a href="#Page_185">185</a><br />
+<br />
+Paris, <a href="#Page_130">130</a><br />
+<br />
+Parkhurst, J. A., <a href="#Page_145">145</a><br />
+<br />
+Parthenope, <a href="#Page_22">22</a><br />
+<br />
+Peirce, <a href="#Page_73">73</a>, <a href="#Page_80">80-83</a><br />
+<br />
+Pendulum, <a href="#Page_117">117</a><br />
+<br />
+Perseus, <a href="#Page_8">8</a>, <a href="#Page_143">143</a><br />
+<br />
+Personal equation, <a href="#Page_31">31</a>, <a href="#Page_134">134</a>, <a href="#Page_135">135</a>, <a href="#Page_185">185</a><br />
+<br />
+Perth, <a href="#Page_130">130</a><br />
+<br />
+Perturbations of Uranus, <a href="#Page_12">12</a>, <a href="#Page_42">42</a>, <a href="#Page_51">51</a>, <a href="#Page_54">54</a>, <a href="#Page_55">55</a>, <a href="#Page_61">61</a>, <a href="#Page_75">75</a><br />
+<br />
+Peters, <a href="#Page_188">188</a>, <a href="#Page_192">192</a><br />
+<br />
+Pha&euml;tusa, <a href="#Page_26">26</a><br />
+<br />
+Philosopher, <a href="#Page_201">201</a>, <a href="#Page_219">219</a><br />
+<br />
+<i>Philosophical Transactions</i>, <a href="#Page_3">3</a>, <a href="#Page_4">4</a>, <a href="#Page_9">9</a><br />
+<br />
+Photographica, <a href="#Page_26">26</a><br />
+<br />
+Photographic methods, <a href="#Page_24">24</a>, <a href="#Page_33">33</a>, <a href="#Page_36">36</a>, <a href="#Page_121">121-139</a>;<br />
+<span style="margin-left: 1em;">lenses, <a href="#Page_125">125</a>, <a href="#Page_126">126</a></span><br />
+<br />
+Photographs of sun, <a href="#Page_163">163</a>, <a href="#Page_170">170-173</a><br />
+<br />
+Piazzi, <a href="#Page_13">13-18</a>, <a href="#Page_22">22</a><br />
+<br />
+Pickering, E. C., <a href="#Page_128">128</a>, <a href="#Page_144">144</a><br />
+<br />
+Pittsburghia, <a href="#Page_26">26</a><br />
+<br />
+Plana, <a href="#Page_61">61</a><br />
+<br />
+Planetary distances, <a href="#Page_13">13</a>;<br />
+<span style="margin-left: 1em;">commission, <a href="#Page_27">27</a>;</span><br />
+<span style="margin-left: 1em;">numbering, <a href="#Page_27">27</a></span><br />
+<br />
+Planets by photography, <a href="#Page_24">24</a><br />
+<br />
+Pole Star (<i>Polaris</i>), <a href="#Page_177">177</a>, <a href="#Page_178">178</a>, <a href="#Page_192">192</a>, <a href="#Page_193">193</a><br />
+<br />
+Pond, <a href="#Page_192">192</a>, <a href="#Page_213">213</a><br />
+<br />
+Potsdam, <a href="#Page_130">130</a>, <a href="#Page_181">181</a><br />
+<br />
+Pound, Mrs., <a href="#Page_104">104</a>, <a href="#Page_110">110-112</a><br />
+<br />
+Pound, Rev. James, <a href="#Page_89">89-94</a>, <a href="#Page_104">104</a>, <a href="#Page_115">115</a><br />
+<br />
+Prague, <a href="#Page_181">181</a><br />
+<br />
+Precession, <a href="#Page_96">96</a>, <a href="#Page_178">178</a><br />
+<br />
+Prymno, <a href="#Page_26">26</a><br />
+<br />
+Puiseux, <a href="#Page_32">32</a><br />
+<br />
+Pulfrich, <a href="#Page_154">154</a><br />
+<br />
+Pulkowa, <a href="#Page_181">181-188</a>, <a href="#Page_213">213</a><br />
+<br />
+<br />
+Quadrants at Greenwich, <a href="#Page_116">116</a><br />
+<br />
+<br />
+Radium, <a href="#Page_175">175</a><br />
+<br />
+Radius vector, <a href="#Page_52">52-58</a>, <a href="#Page_60">60-62</a>, <a href="#Page_79">79</a>, <a href="#Page_83">83</a><br />
+<br />
+Rayleigh, Lord, <a href="#Page_109">109</a><br />
+<br />
+Records before discovery, <a href="#Page_144">144</a><br />
+<br />
+Reflector, <a href="#Page_93">93</a>, <a href="#Page_127">127</a>, <a href="#Page_128">128</a><br />
+<br />
+Reflex zenith tube, <a href="#Page_192">192</a>, <a href="#Page_214">214</a><br />
+<br />
+Refraction, <a href="#Page_96">96</a>, <a href="#Page_101">101-103</a>, <a href="#Page_117">117</a><br />
+<br />
+Refractor, <a href="#Page_93">93</a>, <a href="#Page_128">128</a><br />
+<br />
+R&eacute;seau, <a href="#Page_133">133</a><br />
+<br />
+Residual phenomena, <a href="#Page_108">108-110</a>, <a href="#Page_118">118</a>, <a href="#Page_120">120</a>, <a href="#Page_218">218</a><br />
+<br />
+Rigaud, S. P., <a href="#Page_87">87</a>, <a href="#Page_115">115</a>, <a href="#Page_119">119</a><br />
+<br />
+Rome, <a href="#Page_130">130</a><br />
+<br />
+Rothschild, <a href="#Page_27">27</a><br />
+<span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span><br />
+Royal Astronomical Society, <a href="#Page_40">40</a>, <a href="#Page_47">47</a>, <a href="#Page_68">68</a>, <a href="#Page_74">74</a>, <a href="#Page_124">124</a>, <a href="#Page_155">155</a>, <a href="#Page_157">157</a><br />
+<br />
+Royal Society, <a href="#Page_4">4</a>, <a href="#Page_9">9</a>, <a href="#Page_10">10</a>, <a href="#Page_92">92</a>, <a href="#Page_94">94</a><br />
+<br />
+<br />
+Sampson, R. A., <a href="#Page_74">74-76</a>, <a href="#Page_84">84</a><br />
+<br />
+San Fernando, <a href="#Page_130">130</a><br />
+<br />
+Santiago, <a href="#Page_130">130</a><br />
+<br />
+Sappho, <a href="#Page_32">32</a>, <a href="#Page_35">35</a><br />
+<br />
+Saturn, <a href="#Page_9">9</a>, <a href="#Page_43">43</a>, <a href="#Page_61">61</a>, <a href="#Page_149">149</a>, <a href="#Page_150">150</a><br />
+<br />
+Savile, Sir H., <a href="#Page_119">119</a><br />
+<br />
+Savilian professorship, <a href="#Page_87">87-94</a>, <a href="#Page_108">108-119</a><br />
+<br />
+Schmidt, Julius, <a href="#Page_142">142</a>, <a href="#Page_160">160</a><br />
+<br />
+Schuster, A., <a href="#Page_169">169</a><br />
+<br />
+Schwabe, <a href="#Page_155">155-163</a>, <a href="#Page_176">176</a>, <a href="#Page_177">177</a><br />
+<br />
+Sheldonian Theatre, <a href="#Page_119">119</a><br />
+<br />
+Sherbourn, <a href="#Page_87">87</a><br />
+<br />
+Solar eclipse, <a href="#Page_26">26</a>, <a href="#Page_170">170-176</a><br />
+<br />
+Spectro-heliograph, <a href="#Page_170">170</a>, <a href="#Page_171">171</a><br />
+<br />
+Star-maps, <a href="#Page_45">45</a>, <a href="#Page_65">65</a>, <a href="#Page_83">83</a>, <a href="#Page_124">124</a><br />
+<br />
+&#8220;Star-trap,&#8221; <a href="#Page_24">24</a><br />
+<br />
+Stereo-comparator, <a href="#Page_154">154</a><br />
+<br />
+Stone, E. J., <a href="#Page_32">32</a><br />
+<br />
+Struve, <a href="#Page_184">184</a>, <a href="#Page_188">188</a>, <a href="#Page_192">192</a><br />
+<br />
+Sun&#8217;s distance, <a href="#Page_28">28-37</a><br />
+<br />
+Sun-spots, <a href="#Page_155">155-176</a><br />
+<br />
+Sydney Observatory, <a href="#Page_130">130</a><br />
+<br />
+<br />
+Tacubaya Observatory, <a href="#Page_130">130</a><br />
+<br />
+Telescopes, <a href="#Page_92">92</a>, <a href="#Page_124">124-129</a><br />
+<br />
+Thames River, <a href="#Page_105">105</a><br />
+<br />
+Themistocles, <a href="#Page_119">119</a><br />
+<br />
+<i>Theoria Motus</i>, <a href="#Page_17">17</a><br />
+<br />
+Theory and observation, <a href="#Page_208">208</a><br />
+<br />
+Thomson, Sir W., <a href="#Page_196">196</a>, <a href="#Page_197">197</a><br />
+<br />
+Tides, <a href="#Page_215">215</a><br />
+<br />
+Titius, <a href="#Page_13">13</a><br />
+<br />
+Toulouse Observatory, <a href="#Page_130">130</a><br />
+<br />
+Tycho Brah&eacute;, <a href="#Page_95">95</a>, <a href="#Page_140">140</a>, <a href="#Page_142">142</a><br />
+<br />
+<br />
+Uranus, <a href="#Page_2">2-14</a>, <a href="#Page_25">25</a>, <a href="#Page_38">38-85</a>, <a href="#Page_144">144</a>, <a href="#Page_219">219</a><br />
+<br />
+<br />
+Variable stars, <a href="#Page_140">140</a><br />
+<br />
+Variation of latitude, <a href="#Page_99">99</a>, <a href="#Page_100">100</a>, <a href="#Page_117">117</a>, <a href="#Page_118">118</a>, <a href="#Page_177">177-217</a><br />
+<br />
+Venus, <a href="#Page_9">9</a>, <a href="#Page_79">79</a>;<br />
+<span style="margin-left: 1em;">diameter of, <a href="#Page_92">92</a>;</span><br />
+<span style="margin-left: 1em;">transit of, <a href="#Page_28">28-32</a>, <a href="#Page_34">34</a></span><br />
+<br />
+Vesta, <a href="#Page_21">21</a>, <a href="#Page_22">22</a><br />
+<br />
+Victoria, <a href="#Page_22">22</a>, <a href="#Page_25">25</a>, <a href="#Page_32">32</a>, <a href="#Page_35">35</a><br />
+<br />
+Von Zach, <a href="#Page_20">20</a><br />
+<br />
+<br />
+Wallace, <a href="#Page_119">119</a><br />
+<br />
+Wansted, <a href="#Page_88">88-94</a>, <a href="#Page_104">104</a>, <a href="#Page_110">110</a>, <a href="#Page_115">115</a>, <a href="#Page_188">188</a>, <a href="#Page_190">190</a><br />
+<br />
+Ward, <a href="#Page_119">119</a><br />
+<br />
+Washington Observatory, <a href="#Page_184">184-188</a>, <a href="#Page_193">193</a>, <a href="#Page_196">196</a>, <a href="#Page_213">213</a><br />
+<br />
+Weather and sun-spots, <a href="#Page_161">161</a>, <a href="#Page_167">167-169</a><br />
+<br />
+Weyer, <a href="#Page_193">193</a><br />
+<br />
+Whiteside, <a href="#Page_112">112</a><br />
+<br />
+Williams, Mrs. E., <a href="#Page_110">110</a>, <a href="#Page_111">111</a><br />
+<br />
+Wind-vane, revolutions, <a href="#Page_167">167-169</a><br />
+<br />
+Winnecke, <a href="#Page_32">32</a><br />
+<br />
+Wolf, Dr. Max, <a href="#Page_145">145</a><br />
+<br />
+Wolf, Rudolf, <a href="#Page_163">163</a><br />
+<br />
+Wren, Sir C., <a href="#Page_119">119</a><br />
+<br />
+<br />
+Yerkes Observatory, <a href="#Page_145">145</a>, <a href="#Page_146">146</a>, <a href="#Page_152">152</a>, <a href="#Page_157">157</a>, <a href="#Page_170">170</a>, <a href="#Page_176">176</a><br />
+<br />
+<br />
+Zeiss, <a href="#Page_154">154</a><br />
+<br />
+Zodiac, <a href="#Page_64">64</a>, <a href="#Page_124">124</a>, <a href="#Page_137">137</a></p></div>
+
+
+<p>&nbsp;</p>
+<p class="center">THE END</p>
+
+<p>&nbsp;</p>
+<p class="center">Printed by <span class="smcap">Ballantyne, Hanson &amp; Co.</span><br />Edinburgh &amp; London</p>
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<div class="adverts">
+<p><span class="pagenum">[Pg 1]</span></p>
+<p class="center"><big>MR. EDWARD ARNOLD&#8217;S</big><br /><strong>LIST OF</strong><br /><big>Scientific and Technical Books.</big></p>
+
+<p>&nbsp;</p>
+<p class="hang"><b>LECTURES ON DISEASES OF CHILDREN.</b> By <span class="smcap">Robert Hutchison</span>, M.D. (Edin.),
+F.R.C.P., Assistant Physician to the London Hospital and to the Hospital
+for Sick Children, Great Ormond Street, London. With numerous
+Illustrations. Crown 8vo., 8s. 6d. net.</p>
+
+<p class="hang"><b>PRACTICAL PHYSIOLOGY.</b> By <span class="smcap">A. P. Beddard</span>, M.A., M.D., Demonstrator of
+Physiology, Guy&#8217;s Hospital; <span class="smcap">J. S. Edkins</span>, M.A., M.B., Lecturer in
+Physiology and Demonstrator of Physiology, St. Bartholomew&#8217;s Hospital;
+<span class="smcap">Leonard Hill</span>, M.B., F.R.S., Lecturer on Physiology, London Hospital
+Medical School; <span class="smcap">J. J. R. Macleod</span>, M.B.; and <span class="smcap">M. S. Pembrey</span>, M.A., M.D.,
+Lecturer on Physiology in Guy&#8217;s Hospital Medical School. Copiously
+Illustrated. Demy 8vo., 15s. net.</p>
+
+<p class="hang"><b>HUMAN EMBRYOLOGY AND MORPHOLOGY.</b> By <span class="smcap">A. Keith</span>, M.D., F.R.C.S. Eng.,
+Lecturer on Anatomy at the London Hospital Medical College. With 300
+Illustrations. New, Revised, and Enlarged Edition. Demy 8vo., 12s. 6d.
+net.</p>
+
+<p class="hang"><b>FOOD AND THE PRINCIPLES OF DIETETICS.</b> By <span class="smcap">Robert Hutchison</span>, M.D. Edin.,
+F.R.C.P., Assistant Physician to the London Hospital. Fifth Impression.
+Illustrated. Demy 8vo., 16s. net.</p>
+
+<p class="hang"><b>THE PHYSIOLOGICAL ACTION OF DRUGS.</b> An Introduction to Practical
+Pharmacology. By <span class="smcap">M. S. Pembrey</span>, M.A., M.D., Lecturer on Physiology in
+Guy&#8217;s Hospital Medical School; and <span class="smcap">C. D. F. Phillips</span>, M.D., LL.D. Fully
+Illustrated. Demy 8vo., 4s. 6d. net.</p>
+
+<p class="hang"><b>PHOTOTHERAPY.</b> By <span class="smcap">N. R. Finsen</span>. Translated by <span class="smcap">J. H. Sequeira</span>, M.D. With
+Illustrations. Demy 8vo., 4s. 6d. net.<br />
+<span class="smcap">Contents.</span>&mdash;I. The Chemical Rays of Light and Small-pox&mdash;II. Light as
+an Irritant&mdash;III. Treatment of Lupus Vulgaris by concentrated
+Chemical Rays.</p>
+
+<p class="hang"><b>A MANUAL OF HUMAN PHYSIOLOGY.</b> By <span class="smcap">Leonard Hill</span>, M.B., F.R.S. With 173
+Illustrations, xii + 484 pages. Crown 8vo., cloth, 6s.</p>
+
+<p class="hang"><b>A PRIMER OF PHYSIOLOGY.</b> By <span class="smcap">Leonard Hill</span>, M.B. 1s.</p>
+
+<p class="hang"><b>LECTURES ON THEORETICAL AND PHYSICAL CHEMISTRY.</b> By Dr. <span class="smcap">J. H. Van &#8217;T Hoff</span>,
+Professor of Chemistry at the University of Berlin. Translated by Dr. <span class="smcap">R.
+A. Lehfeldt</span>. In three volumes. Illustrated. Demy 8vo., 28s. net; or
+obtainable separately, as follows: Vol. I.&mdash;<b>Chemical Dynamics.</b> 12s. net.
+Vol. II.&mdash;<b>Chemical Statics.</b> 8s. 6d. net. Vol. III.&mdash;<b>Relations between
+Properties and Composition.</b> 7s. 6d. net.</p>
+
+<p class="hang"><b>THE ELEMENTS OF INORGANIC CHEMISTRY.</b> For use in Schools and Colleges. By
+<span class="smcap">W. A. Shenstone</span>, Lecturer in Chemistry at Clifton College, xii + 506
+pages. With nearly 150 Illustrations. 4s. 6d.</p>
+
+<p class="hang"><b>A COURSE OF PRACTICAL CHEMISTRY.</b> Being a Revised Edition of &#8216;A Laboratory
+Companion for Use with Shenstone&#8217;s Inorganic Chemistry.&#8217; By <span class="smcap">W. A.
+Shenstone</span>. 144 pages. Crown 8vo., 1s. 6d.</p>
+
+<p><span class="pagenum">[Pg 2]</span></p>
+<p class="hang"><b>A TEXT-BOOK OF PHYSICAL CHEMISTRY.</b> By Dr. <span class="smcap">R. A. Lehfeldt</span>, Professor of
+Physics at the East London Technical College. With 40 Illustrations. Crown
+8vo., cloth, 7s. 6d.</p>
+
+<p class="hang"><b>THE CHEMICAL SYNTHESIS OF VITAL PRODUCTS AND THE INTER-RELATIONS BETWEEN
+ORGANIC COMPOUNDS.</b> By Professor <span class="smcap">Raphael Meldola</span>, F.R.S., of the City and
+Guilds of London Technical College, Finsbury. Two vols. Vol. I. now ready.
+Super Royal 8vo., 21s. net.</p>
+
+<p class="hang"><b>A TEXT-BOOK OF PHYSICS.</b> With Sections on the Applications of Physics to
+Physiology and Medicine. By Dr. <span class="smcap">R. A. Lehfeldt</span>. Fully Illustrated. Crown
+8vo., cloth, 6s.</p>
+
+<p class="hang"><b>PHYSICAL CHEMISTRY FOR BEGINNERS.</b> By Dr. Ch. <span class="smcap">M. Van Deventer</span>. With a
+Preface by <span class="smcap">J. H. Van &#8217;T Hoff</span>. Translated by Dr. <span class="smcap">R. A. Lehfeldt</span>, Professor
+of Physics at the East London Technical College, 2s. 6d.</p>
+
+<p class="hang"><b>A FIRST YEAR&#8217;S COURSE OF EXPERIMENTAL WORK IN CHEMISTRY.</b> By <span class="smcap">Ernest H.
+Cook</span>, D.Sc., F.I.C., Principal of the Clifton Laboratory, Bristol. With 26
+Illustrations. Crown 8vo., cloth, 1s. 6d.</p>
+
+<p class="hang"><b>AN EXPERIMENTAL COURSE OF CHEMISTRY FOR AGRICULTURAL STUDENTS.</b> By <span class="smcap">T. S.
+Dymond</span>, F.I.C., Lecturer on Agricultural Chemistry in the County Technical
+Laboratories, Chelmsford. With 50 Illustrations. 192 pages. Crown 8vo.,
+cloth, 2s. 6d.</p>
+
+<p class="hang"><b>THE STANDARD COURSE OF ELEMENTARY CHEMISTRY.</b> By <span class="smcap">E. J. Cox</span>, F.C.S. With 90
+Illustrations. 350 pages. Crown 8vo., cloth, 3s. Also obtainable in five
+parts, limp cloth. Parts I.-IV., 7d. each; Part V., 1s.</p>
+
+<p class="hang"><b>A PRELIMINARY COURSE OF PRACTICAL PHYSICS.</b> By <span class="smcap">C. E. Ashford</span>, M.A.,
+Headmaster of the Royal Naval College, Osborne. Fcap. 4to., 1s. 6d.</p>
+
+<p class="hang"><b>PHYSICAL DETERMINATIONS.</b> A Manual of Laboratory Instructions for the
+Determination of Physical Quantities. By <span class="smcap">W. R. Kelsey</span>, B.Sc., A.I.E.E.,
+Lecturer in Physics to the Bradford Municipal Technical College. 4s. 6d.</p>
+
+<p class="hang"><b>ELECTROLYTIC PREPARATIONS.</b> Exercises for use in the laboratory by chemists
+and electro-chemists. By Dr. <span class="smcap">Karl Elbs</span>, Professor of Chemistry at the
+University of Giessen. Translated by <span class="smcap">R. S. Hutton</span>, M.Sc. Demy 8vo., 4s.
+6d. net.</p>
+
+<p class="hang"><b>THE ELECTRIC FURNACE.</b> By <span class="smcap">Henri Moissan</span>, Professor of Chemistry at the
+Sorbonne. Authorized English Edition. Translated by <span class="smcap">A. T. de Mouilpied</span>,
+M.Sc., Ph.D. With Illustrations. Demy 8vo., 10s. 6d. net.</p>
+
+<p class="hang"><b>ELECTRICAL TRACTION.</b> By <span class="smcap">Ernest Wilson</span>, Wh.Sc., M.I.E.E., Professor of
+Electrical Engineering in the Siemens Laboratory, King&#8217;s College, London.
+Crown 8vo., 5s.</p>
+
+<p class="hang"><b>ELECTRICITY AND MAGNETISM.</b> By <span class="smcap">C. E. Ashford</span>, M.A., Headmaster of the
+Osborne Royal Naval College, late Senior Science Master at Harrow School.
+With over 200 Diagrams. Crown 8vo., 3s. 6d.</p>
+
+<p class="hang"><b>MAGNETISM AND ELECTRICITY.</b> An Elementary Treatise for Junior Students,
+Descriptive and Experimental. By <span class="smcap">J. Paley Yorke</span>, of the Northern
+Polytechnic Institute, London. With nearly 150 Illustrations. 3s. 6d.</p>
+
+<p><span class="pagenum">[Pg 3]</span></p>
+<p class="hang"><b>THE BALANCING OF ENGINES.</b> By <span class="smcap">W. E. Daley</span>, M.A., B.Sc., M.Inst.C.E.,
+M.I.M.E., Professor of Mechanical Engineering and Applied Mathematics in
+the City and Guilds of London Technical College, Finsbury. With 173
+Illustrations. Demy 8vo., 10s. 6d. net.</p>
+
+<p class="hang"><b>THE STRENGTH AND ELASTICITY OF STRUCTURAL MEMBERS.</b> By <span class="smcap">R. J. Woods</span>, Master
+of Engineering, Royal University of Ireland, Fellow of the Royal Indian
+Engineering College, and Assistant Professor of Engineering Cooper&#8217;s Hill
+College. Demy 8vo. 10s. 6d. net.</p>
+
+<p class="hang"><b>TRAVERSE TABLES.</b> With an Introductory Chapter on Coordinate Surveying. By
+<span class="smcap">Henry Louis</span>, M.A., A.R.S.M., F.I.C., F.G.S., etc., Professor of Mining and
+Lecturer on Surveying, Durham College of Science, Newcastle-on-Tyne; and
+<span class="smcap">G. W. Caunt</span>, M.A. Demy 8vo., 4s. 6d. net.</p>
+
+<p class="hang"><b>THE CALCULUS FOR ENGINEERS.</b> By <span class="smcap">John Perry</span>, M.E., D.Sc., F.R.S., Professor
+of Mechanics and Mathematics in the Royal College of Science, etc. Crown
+8vo., cloth, 7s. 6d.</p>
+
+<p class="hang"><b>ELECTRIC AND MAGNETIC CIRCUITS.</b> By <span class="smcap">Ellis H. Crapper</span>, M.I.E.E., Head of the
+Electrical Engineering Department in the University College, Sheffield,
+viii + 380 pages. Demy 8vo., 10s. 6d. net.</p>
+
+<p class="hang"><b>AN INTRODUCTION TO THE THEORY OF OPTICS.</b> By Professor <span class="smcap">Arthur Schuster</span>,
+Ph.D., F.R.S., Professor of Physics at the University of Manchester. With
+numerous Diagrams. Demy 8vo., 15s. net.</p>
+
+<p class="hang"><b>ASTRONOMICAL DISCOVERY.</b> By <span class="smcap">H. H. Turner</span>, Savilian Professor of Astronomy
+in the University of Oxford. With Diagrams. Demy 8vo., 10s. 6d. net.</p>
+
+<p class="hang"><b>VECTORS AND ROTORS.</b> With Applications. Being Lectures delivered at the
+Central Technical College By Professor <span class="smcap">O. Henrici</span>, F.R.S. Edited by <span class="smcap">G. C.
+Turner</span>, Goldsmith Institute. Crown 8vo., cloth. 4s. 6d.</p>
+
+<p class="hang"><b>THE PRINCIPLES OF MECHANISM.</b> By <span class="smcap">H. A. Garratt</span>, A.M.I.C.E., Head of the
+Engineering Department of the Northern Polytechnic Institute, Holloway.
+Crown 8vo., cloth, 3s. 6d.</p>
+
+<p class="hang"><b>ELEMENTARY PLANE AND SOLID MENSURATION.</b> By <span class="smcap">R. W. K. Edwards</span>, M.A.,
+Lecturer on Mathematics at King&#8217;s College, London. For use in Schools,
+Colleges, and Technical Classes. 304 pages, Crown 8vo., 3s. 6d.</p>
+
+<p class="hang"><b>FIVE-FIGURE TABLES OF MATHEMATICAL FUNCTIONS.</b> By <span class="smcap">J. B. Dale</span>, M.A. Camb.,
+B.A. Lond., late Scholar St. John&#8217;s College, Cambridge, Lecturer on Pure
+and Applied Mathematics, King&#8217;s College, University of London. Demy 8vo.,
+3s. 6d. net.</p>
+
+<p class="hang"><b>AN ELEMENTARY TREATISE ON PRACTICAL MATHEMATICS.</b> By <span class="smcap">John Graham</span>, B.A.,
+Demonstrator of Mechanical Engineering and Applied Mathematics in the
+Technical College, Finsbury. Crown 8vo., cloth, 3s. 6d.</p>
+
+<p class="hang"><b>PRELIMINARY PRACTICAL MATHEMATICS.</b> BY <span class="smcap">S. G. Starling</span>, A.R.C.Sc., B.Sc.,
+Head of the Mathematics and Physics Department of the West Ham Municipal
+Technical Institute; and <span class="smcap">F. C. Clarke</span>, A.R.C.Sc., B.Sc.</p>
+
+<p><span class="pagenum">[Pg 4]</span></p>
+<p class="hang"><b>THE EVOLUTION THEORY.</b> By <span class="smcap">August Weismann</span>, Professor of Zoology in the
+University of Freiburg-im-Breisgau. Translated by Professor <span class="smcap">J. Arthur
+Thomson</span>. With numerous Illustrations and Coloured Plates. Two Vols. Royal
+8vo., 32s. net.<br /><br />
+The importance of this work is twofold. In the first place, it sums
+up the teaching of one of Darwin&#8217;s greatest successors, who has been
+for many years a leader in biological progress. As Professor Weismann
+has from time to time during the last quarter of a century frankly
+altered some of his positions, this deliberate summing up of his
+mature conclusions is very valuable. In the second place, as the
+volumes discuss all the chief problems of organic evolution, they
+form a reliable guide to the whole subject, and may be regarded as
+furnishing&mdash;what is much needed&mdash;a Text-book of Evolution Theory.</p>
+
+<p class="hang"><b>ANIMAL BEHAVIOUR.</b> By <span class="smcap">C. Lloyd Morgan</span>, LL.D., F.R.S., Principal of
+University College Bristol, author of &#8216;Animal Life and Intelligence,&#8217; etc.
+With numerous Illustrations. Large crown 8vo., 10s. 6d.</p>
+
+<p class="hang"><b>HABIT AND INSTINCT.</b> By <span class="smcap">C. Lloyd Morgan</span>, LL.D., F.R.S. With Photogravure
+Frontispiece. viii + 352 pages. Demy 8vo., cloth, 16s.</p>
+
+<p class="hang"><b>A TEXT-BOOK OF ZOOLOGY.</b> By <span class="smcap">G. P. Mudge</span>, A.R.C.Sc. Lond., Lecturer on
+Biology at the London School of Medicine for Women, and the Polytechnic
+Institute, Regent Street. With about 200 original Illustrations. Crown
+8vo., cloth, 7s. 6d.</p>
+
+<p class="hang"><b>ELEMENTARY NATURAL PHILOSOPHY.</b> By <span class="smcap">Alfred Earl</span>, M.A., Assistant Master at
+Tonbridge School. With numerous Illustrations and Diagrams. Crown 8vo.,
+cloth, 4s. 6d.</p>
+
+<p class="hang"><b>A CLASS-BOOK OF BOTANY.</b> By <span class="smcap">G. P. Mudge</span>, A.R.C.Sc. Lond., F.Z.S., and <span class="smcap">A. J.
+Maslen</span>, F.L.S., Lecturer on Botany at the Woolwich Polytechnic. With over
+200 Illustrations. Crown 8vo., 7s. 6d.</p>
+
+<p class="hang"><b>THE BECQUEREL RAYS AND THE PROPERTIES OF RADIUM.</b> By the Hon. <span class="smcap">R. J. Strutt</span>,
+Fellow of Trinity College, Cambridge. With Diagrams. Demy 8vo. 8s. 6d.
+net.</p>
+
+<p class="hang"><b>A MANUAL OF ALCOHOLIC FERMENTATION AND THE ALLIED INDUSTRIES.</b> By <span class="smcap">Charles
+G. Matthews</span>, F.I.C., F.C.S., etc. Fully Illustrated. Crown 8vo., cloth,
+7s. 6d. net.</p>
+
+<p class="hang"><b>WOOD.</b> A Manual of the Natural History and Industrial Applications of the
+Timbers of Commerce. By <span class="smcap">G. S. Boulger</span>, F.L.S., F.G.S. Fully Illustrated.
+Crown 8vo., 7s. 6d. net.</p>
+
+<p class="hang"><b>PSYCHOLOGY FOR TEACHERS.</b> By <span class="smcap">C. Lloyd Morgan</span>, LL.D., F.R.S. xii + 251
+pages. Crown 8vo., 3s. 6d.</p>
+
+<p class="hang"><b>ANIMAL SKETCHES.</b> By <span class="smcap">C. Lloyd Morgan</span>, LL.D., F.R.S. viii + 312 pages, with
+52 Illustrations (many of them full-page). Crown 8vo., cloth, 3s. 6d.</p>
+
+
+<p>&nbsp;</p>
+<p class="center"><i>LONDON: EDWARD ARNOLD, 41 &amp; 43 MADDOX STREET, W.</i></p></div>
+
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><b>Footnotes:</b></p>
+
+<p><a name="f1" id="f1" href="#f1.1">[1]</a> The inferior planet Venus comes closer, but is not visible throughout
+the night.</p>
+
+<p><a name="f2" id="f2" href="#f2.1">[2]</a> The facts were collected with great care and ability by S. P. Rigaud,
+and published by the Oxford University Press in 1832 as &#8220;Miscellaneous
+Works and Correspondence of the Rev. James Bradley.&#8221;</p>
+
+<p><a name="f3" id="f3" href="#f3.1">[3]</a> Since the light must travel from the sun to Saturn <i>and back again to
+the earth</i>, the interval would be more nearly 150 minutes.</p>
+
+<p><a name="f4" id="f4" href="#f4.1">[4]</a> Monthly Notices of the Royal Astronomical Society, vol. xvii. p. 126.</p>
+
+<p><a name="f5" id="f5" href="#f5.1">[5]</a> This should be Cambridge, <i>Mass.</i></p>
+
+<p><a name="f6" id="f6" href="#f6.1">[6]</a> The distances do not represent the <i>total</i> displacement, but only the
+displacement towards Washington in one case and towards Pulkowa in the other.</p>
+
+
+
+<p>&nbsp;</p><p>&nbsp;</p>
+<hr style="width: 50%;" />
+<p><b>Transcriber&#8217;s Notes:</b></p>
+
+<p>Images have been moved from the middle of a paragraph to a nearby paragraph break.</p>
+
+<p>The text in the list of illustrations is presented as in the original text, but the links
+navigate to the page number closest to the illustration&#8217;s loaction in this document.</p>
+
+<p>Punctuation has been corrected without note.</p>
+
+<p>Other than the corrections noted by hover information, inconsistencies in
+spelling and hyphenation have been retained from the original.</p>
+
+<p>Errata corrections have been made in this text by the transcriber. They are noted by red underline.</p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of Project Gutenberg's Astronomical Discovery, by Herbert Hall Turner
+
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+The Project Gutenberg EBook of Astronomical Discovery, by Herbert Hall Turner
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Astronomical Discovery
+
+Author: Herbert Hall Turner
+
+Release Date: August 3, 2010 [EBook #33337]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK ASTRONOMICAL DISCOVERY ***
+
+
+
+
+Produced by Juliet Sutherland, Joseph Myers and the Online
+Distributed Proofreading Team at http://www.pgdp.net.
+
+
+
+
+
+
+
+
+
+ASTRONOMICAL DISCOVERY
+
+
+
+
+[Illustration: 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
+
+
+                                                                    PAGE
+  CHAPTER I
+      URANUS AND EROS                                                  1
+
+  CHAPTER II
+      THE DISCOVERY OF NEPTUNE                                        38
+
+  CHAPTER III
+      BRADLEY'S DISCOVERIES OF THE ABERRATION OF LIGHT AND OF THE
+      NUTATION OF THE EARTH'S AXIS                                    86
+
+  CHAPTER IV
+      ACCIDENTAL DISCOVERIES                                         121
+
+  CHAPTER V
+      SCHWABE AND THE SUN-SPOT PERIOD                                155
+
+  CHAPTER VI
+      THE VARIATION OF LATITUDE                                      177
+
+  INDEX                                                              221
+
+
+
+
+LIST OF PLATES
+
+
+  PLATE
+
+     I. PORTRAIT OF J. C. ADAMS                        _To face page_ 22
+
+    II. PORTRAIT OF A. GRAHAM                               "    "    22
+
+   III. PORTRAIT OF U. J. LE VERRIER                        "    "    60
+
+    IV. PORTRAIT OF J. G. GALLE                             "    "    60
+
+     V. CORNER OF THE BERLIN MAP BY THE USE OF WHICH
+        GALLE FOUND NEPTUNE                                 "    "    82
+
+    VI. ASTRONOMERS ROYAL                                 _Frontispiece_
+
+   VII. GREAT COMET OF NOV. 7, 1882                   _To face page_ 122
+
+  VIII. THE OXFORD NEW STAR                                "    "    142
+
+    IX. NEBULOSITY ROUND NOVA PERSEI                       "    "    146
+
+     X. SUN-SPOTS AT GREENWICH, FEB. 18 AND 19, 1894       "    "    158
+
+    XI. SUN-SPOTS AT GREENWICH, FEB. 20 AND 21, 1894       "    "    162
+
+   XII. NUMBER OF SUN-SPOTS COMPARED WITH DAILY RANGE
+        OF MAGNETIC DECLINATION AND DAILY RANGE OF
+        MAGNETIC HORIZONTAL FORCE                          "    "    164
+
+  XIII. GREENWICH MAGNETIC CURVES, 1859-60                 "    "    166
+
+   XIV. GREENWICH MAGNETIC CURVES, 1841-1860               "    "    166
+
+    XV. SUN-SPOTS AND TURNS OF VANE                        "    "    170
+
+
+
+
+ERRATA
+
+
+  Page 133, line 27, _for_ "200 stars" _read_ "200 stars per hour."
+
+   "   145, See note on page 220.
+
+   "   146, bottom of page. This nebulosity was first discovered by Dr.
+            Max Wolf of Heidelberg. See _Astr. Nachr._ 3736.
+
+   "   181, line 17, _for_ "observation" _read_ "aberration."
+
+
+
+
+ASTRONOMICAL DISCOVERY
+
+
+
+
+CHAPTER I
+
+URANUS AND EROS
+
+
+[Sidenote: 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.
+
+[Sidenote: 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"_
+
+  Much have I travell'd in the realms of gold,
+  And many goodly states and kingdoms seen;
+  Round many western islands have I been
+  Which bards in fealty to Apollo hold.
+  Oft of one wide expanse had I been told
+  That deep-brow'd Homer ruled as his demesne;
+  Yet did I never breathe its pure serene
+  Till I heard Chapman speak out loud and bold:
+  Then felt I like some watcher of the skies
+  When a new planet swims into his ken;
+  Or like stout Cortez when with eagle eyes
+  He star'd at the Pacific--and all his men
+  Look'd at each other with a wild surmise--
+  Silent, upon a peak in Darien.
+
+[Sidenote: 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_
+
+     [Sidenote: 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."
+
+[Sidenote: Called first a comet.]
+
+[Sidenote: Other observers would not have found it at all.]
+
+At first sight this seems to be the wrong reference, for it speaks of a
+new comet, not a new planet. But it is indeed of Uranus that Herschel is
+speaking; and so little did he realise the full magnitude of his
+discovery at once, that he announced it as that of a comet; and a comet
+the object was called for some months. Attempts were made to calculate its
+orbit as a comet, and broke down; and it was only after much work of this
+kind had been done that the real nature of the object began to be
+suspected. But far more striking than this misconception is the display of
+skill necessary to detect any peculiarity in the object at all. Among a
+number of stars one seemed somewhat exceptional in size, but the
+difference was only just sufficient to awaken suspicion in a keen-eyed
+Herschel. Would any other observer have noticed the difference at all?
+Certainly several good observers had looked at the object before, and
+looked at it with the care necessary to record its position, without
+noting any peculiarity. Their observations were recovered subsequently and
+used to fix the orbit of the new planet more accurately. I shall remind
+you in the next chapter that Uranus had been observed in this way no less
+than seventeen times by first-rate observers without exciting their
+attention to anything remarkable. The first occasion was in 1690, nearly a
+century before Herschel's grand discovery, and these chance observations,
+which lay so long unnoticed as in some way erroneous, subsequently proved
+to be of the utmost value in fixing the orbit of the new planet. But there
+is even more striking testimony than this to the exceptional nature of
+Herschel's achievement. It is a common experience in astronomy that an
+observer may fail to notice in a general scrutiny some phenomenon which he
+can see perfectly well when his attention is directed to it: when a man
+has made a discovery and others are told what to look for, they often see
+it so easily that they are filled with amazement and chagrin that they
+never saw it before. Not so in the case of Uranus. At least two great
+astronomers, Lalande and Messier, have left on record their astonishment
+that Herschel could differentiate it from an ordinary star at all; for
+even when instructed where to look and what to look for, they had the
+greatest difficulty in finding it. I give a translation of Messier's
+words, which Herschel records in the paper already quoted announcing the
+discovery:--
+
+     "Nothing was more difficult than to recognise it; and I cannot
+     conceive how you have been able to return several times to this star
+     or comet; for absolutely it has been necessary to observe it for
+     several consecutive days to perceive that it was in motion."
+
+[Sidenote: 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?
+
+[Sidenote: Though this may happen at times.]
+
+[Sidenote: Name of new planet.]
+
+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. 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.
+
+     [Sidenote: _Georgium Sidus._]
+
+     "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 name _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."
+
+[Sidenote: Herschel.]
+
+This letter reminds us how long it was since a new name had been required
+for a new planet,--to find a similar occasion Herschel had to go to the
+almost prehistoric past, when the names of heroes and divinities were
+given to the planets. It is, perhaps, not unnatural that he should have
+considered an entirely new departure appropriate for a discovery separated
+by so great a length of time from the others; but his views were not
+generally accepted, especially on the Continent. Lalande courteously
+proposed the name of Herschel for the new planet, in honour of the
+discoverer, and this name was used in France; but Bode, on the other hand,
+was in favour of retaining the old practice simply, and calling the new
+planet Uranus. All three names seem to have been used for many years. Only
+the other day I was interested to see an old pack of cards, used for
+playing a parlour game of Astronomy, in which the name Herschel is used.
+The owner told me that they had belonged to his grandfather; and the date
+of publication was 1829, and the place London, so that this name was in
+common use in England nearly half a century after the actual discovery;
+though in the "English Nautical Almanac" the name "the Georgian"
+(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.)
+
+[Sidenote: 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.
+
+[Sidenote: Bode's law.]
+
+The discovery of Neptune, as we shall see, was totally different in
+character from that of Uranus. The latter may be described as the finding
+of something by an observer who was looking for anything; Neptune was the
+finding of something definitely sought for, and definitely pointed out by
+a most successful and brilliant piece of methodical work. But before that
+time several planets had been found, as the practical result of a definite
+search, although the guiding principle was such as cannot command our
+admiration to quite the same extent as in the case of Neptune. To explain
+it I must say something of the relative sizes of the orbits in which
+planets move round the sun. These orbits are, as we know, ellipses; but
+they are very nearly circles, and, excluding refinements, we may consider
+them as circles, with the sun at the centre of each, so that we may talk
+of the distance of any planet from the sun as a constant quantity without
+serious error. Now if we arrange the planetary distances in order, we
+shall notice a remarkable connection between the terms of the series. Here
+is a table showing this connection.
+
+  TABLE OF THE DISTANCES OF THE PLANETS FROM THE SUN, SHOWING "BODE'S LAW."
+
+  +----------------------------------------------------+
+  | Name of   | Distance from |     "Bode's Law"       |
+  | Planet.   | Sun, taking   | (originally formulated |
+  |           | that of Earth | by Titius, but brought |
+  |           | as 10.        | into notice by Bode).  |
+  |----------------------------------------------------|
+  | Mercury   |        4      |     4 +   0=   4       |
+  | Venus     |        7      |     4 +   3=   7       |
+  | The Earth |       10      |     4 +   6=  10       |
+  | Mars      |       15      |     4 +  12=  16       |
+  | (     )   |      ( )      |     4 +  24=  28       |
+  | Jupiter   |       52      |     4 +  48=  52       |
+  | Saturn    |       95      |     4 +  96= 100       |
+  | Uranus    |      192      |     4 + 192= 196       |
+  +----------------------------------------------------+
+
+[Sidenote: Gap in the series suggesting unknown planet.]
+
+[Sidenote: Search for it.]
+
+[Sidenote: Accidental discovery.]
+
+If we write down a series of 4's, and then add the numbers 3, 6, 12, and
+so on, each formed by doubling the last, we get numbers representing very
+nearly the planetary distances, which are shown approximately in the
+second column. But three points call for notice. Firstly, the number
+before 3 should be 1-1/2, and not zero, to agree with the rest. Secondly,
+there is a gap, or rather was a gap, after the discovery of Uranus,
+between Mars and Jupiter; and thirdly, we see that when Uranus was
+discovered, and its distance from the sun determined, this distance was
+found to fall in satisfactorily with this law, which was first stated by
+Titius of Wittenberg. This third fact naturally attracted attention. No
+explanation of the so-called "law" was known at the time; nor is any
+known even yet, though we may be said to have some glimmerings of a
+possible cause; and in the absence of such explanation it must be regarded
+as merely a curious coincidence. But the chances that we are in the
+presence of a mere coincidence diminish very quickly with each new term
+added to the series, and when it was found that Herschel's new planet
+fitted in so well at the end of the arrangement, the question arose
+whether the gap above noticed was real, or whether there was perhaps
+another planet which had hitherto escaped notice, revolving in an orbit
+represented by this blank term. This question had indeed been asked even
+before the discovery of Uranus, by Bode, a young astronomer of Berlin; and
+for fifteen years he kept steadily in view this idea of finding a planet
+to fill the vacant interval. The search would be a very arduous one,
+involving a careful scrutiny, not perhaps of the whole heavens, but of a
+considerable portion of it along the Zodiac; too great for one would-be
+discoverer single-handed; but in September 1800 Bode succeeded in
+organising a band of six German astronomers (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). 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.
+
+[Sidenote: 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.
+
+[Sidenote: 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.
+
+[Sidenote: 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_.
+
+     [Sidenote: 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."
+
+[Sidenote: Rediscovery of Ceres.]
+
+[Sidenote: Another planet found.]
+
+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. 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. 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_!
+
+[Sidenote: 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.
+
+  +---------------------------------------+
+  |Number|   Name.   | Discoverer. | Date.|
+  |---------------------------------------|
+  |   1  | Ceres     | Piazzi      | 1801 |
+  |   2  | Pallas    | Olbers      | 1802 |
+  |   3  | Juno      | Harding     | 1804 |
+  |   4  | Vesta     | Olbers      | 1807 |
+  |------|-----------|-------------|------|
+  |   5  | Astraea   | Hencke      | 1845 |
+  |   6  | Hebe      | Hencke      | 1847 |
+  |   7  | Iris      | Hind        | 1847 |
+  |   8  | Flora     | Hind        | 1847 |
+  |   9  | Metis     | Graham      | 1848 |
+  |  10  | Hygeia    | De Gasparis | 1849 |
+  |  11  | Parthenope| De Gasparis | 1850 |
+  |  12  | Victoria  | Hind        | 1850 |
+  |  13  | Egeria    | De Gasparis | 1850 |
+  +---------------------------------------+
+
+[Sidenote: Hencke's long search.]
+
+Here now is a table showing how other bodies were gradually added to this
+first list of four, but you will see that no addition was made for a long
+time. Not that the search was immediately abandoned; but being rewarded by
+no success for some years, it was gradually dropped, and the belief gained
+ground that the number of the planets was at last complete. The
+discoverers of Uranus and of these first four minor planets all died
+before any further addition was made; and it was not until the end of 1845
+that Astraea was found by an ex-postmaster of the Prussian town of
+Driessen, by name Hencke, who, in spite of the general disbelief in the
+existence of any more planets, set himself diligently to search for them,
+and toiled for fifteen long years before at length reaping his reward.
+Others then resumed the search; Hind, the observer of an English amateur
+astronomer near London, found Iris a few weeks after Hencke had been
+rewarded by a second discovery in 1847, and in the following year Mr.
+Graham at Markree in Ireland (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.
+
+[Illustration:
+
+  _By permission of Messrs. Macmillan & Co._
+  I.--J. C. ADAMS.]
+
+[Illustration:
+
+  II.--A. GRAHAM.
+  DISCOVERER OF THE NINTH MINOR PLANET (METIS).]
+
+[Sidenote: The photographic method.]
+
+You will see the great variety characterising these discoveries; some of
+them are the result of deliberate search, others have come accidentally,
+and some even contrary to expectation. Of the great majority of the
+earlier ones it may be said that enormous diligence was required for each
+discovery; to identify a planet it is necessary to have either a good map
+of the stars or to know them thoroughly, so that the map practically
+exists in the brain. We need only remember Hencke's fifteen years of
+search before success to recognise what vast stores of patience and
+diligence were required in carrying out the search. But of late years
+photography has effected a great revolution in this respect. It is no
+longer necessary to do more than set what Sir Robert Ball has called a
+"star-trap," or rather planet-trap. If a photograph be taken of a region
+of the heavens, by the methods familiar to astronomers, so that each star
+makes a round dot on the photographic plate, any sufficiently bright
+object moving relatively to the stars will make a small line or trail, and
+thus betray its planetary character. In this way most of the recent
+discoveries have been made, and although diligence is still required in
+taking the photographs, and again in identifying the objects thus found
+(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.
+
+  1801 to 1850--altogether 13 discoveries.
+  1851 to 1860--     "     49      "
+  1861 to 1870--     "     49      "
+  1871 to 1880--     "    108      "
+  1881 to 1890--     "     83      "
+  1891 to 1900--     "    180 announcements
+       In 1901       "     36      "
+        " 1902       "     50      "
+        " 1903       "     41      "
+                          ---
+                   Total  609
+
+  [_N.B._--Many of the more recent announcements turned out to refer to
+  old discoveries.]
+
+[Sidenote: 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:--
+
+  No.   Name.
+  248   Lameia
+  250   Bettina
+  261   Prymno
+  264   Libussa
+  296   Phaetusa
+  340   Eduarda
+  341   California
+  350   Ornamenta
+  357   Ninina
+  385   Ilmatar
+  389   Industria
+  391   Ingeborg
+  433   Eros
+  443   Photographica
+  457   Alleghenia
+  462   Eriphyla
+  475   Ocllo
+  484   Pittsburghia
+  503   Evelyn
+
+[Sidenote: Bettina.]
+
+[Sidenote: The provisional letters.]
+
+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 L50." 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.
+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.
+
+[Sidenote: Eros.]
+
+Fortunately, however, on running through it for the fifth time, an object
+of particular interest was discovered. Most of these bodies revolve at a
+distance from the sun intermediate between that of Mars and that of
+Jupiter, but the little planet which took the symbol DQ, and afterwards
+the name of Eros, was found to have a mean distance actually less than
+that of Mars, and this gave it an extraordinary importance with respect to
+the great problem of determining the sun's distance. To explain this
+importance we must make a small digression.
+
+[Sidenote: 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.
+
+[Illustration: FIG. 1.]
+
+[Sidenote: The "Black Drop."]
+
+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. 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.
+
+[Sidenote: Failure.]
+
+These difficulties, as already stated, were known to exist; but there is a
+long interval between transits of Venus, or rather between every pair of
+such transits. After those of 1874 and 1882 there will be no more until
+2004 and 2012, so that we shall never see another; similarly, before that
+pair of the last century, there had not been any such occasion since 1761
+and 1769, and no one was alive who remembered at first hand the trouble
+which was known to exist. It was proposed to obviate the anticipated
+difficulties by careful practice beforehand; models were prepared to
+resemble as nearly as possible the expected appearances, and the times
+recorded by different observers were compared with the true time, which
+could, in this case of a model, be determined. In this way it was hoped
+that the habit of each observer, his "personal equation" as it is called,
+could be determined beforehand, and allowed for as a correction when he
+came to observe the actual transit. The result, however, was a great
+disappointment. The actual appearances were found to be totally different
+in character from those shown by the model; chiefly, perhaps, because it
+had been impossible to imitate with a model the effect of the atmosphere
+which surrounds the planet Venus. Observers trained beforehand, using
+similar instruments, and standing within a few feet of each other, were
+expected, after making due allowance for personal equation, to give the
+same instant for contact; but their observations when made were found to
+differ by nearly a minute of time, and after an exhaustive review of the
+whole material it was felt that all hope of determining accurately the
+sun's distance by this method must be given up. The following table will
+show how much was learned from the transits of Venus, and how much
+remained to be settled. They left the result in doubt over a range of
+about two million miles.
+
+     SUN'S DISTANCE, IN MILLIONS OF MILES, AS FOUND BY DIFFERENT OBSERVERS
+
+     =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 =93-1/4=
+     million (Airy, from British observations of 1874), =92-1/2= million
+     (Stone, from British observations of 1882), and =91-1/2= million
+     (Puiseux, from French observations), a range of 1-3/4 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.
+
+[Sidenote: Modern method for sun's distance.]
+
+[Sidenote: Photography.]
+
+[Sidenote: Dr. Gill's expedition to Ascension.]
+
+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. 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; 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.
+
+[Sidenote: Victoria, Iris, and Sappho.]
+
+[Sidenote: Eros.]
+
+Further, a small planet which is in appearance just like an ordinary star
+has, irrespective of this great proximity, some distinct advantages over a
+planet like Mars, which appears as a round disc, and is, moreover, of a
+somewhat reddish colour. When the distance of an object of this kind from
+a point of line such as a star is measured with the heliometer it is found
+that a certain bias, somewhat difficult to allow for with certainty, is
+introduced into the measures; and our confidence in the final results
+suffers accordingly. After his observations of Mars in 1878, Dr. David
+Gill was sufficiently impressed with this source of error to make three
+new determinations of the sun's distance, using three of the minor planets
+instead of Mars, in spite of the fact that they were sensibly farther
+away; and his choice was justified by finding that the results from these
+three different sets of observations agreed well among themselves, and
+differed slightly from that given by the observations of Mars. Hence it
+seems conclusively proved that one of these bodies is a better selection
+than Mars in any case, and the discovery of Eros, which offered the
+advantage of greater proximity in addition, was hailed as a new
+opportunity of a most welcome kind. It was seen by a little calculation
+that in the winter of 1900-1901 the planet would come very near the
+earth; not the nearest possible (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
+
+
+[Sidenote: 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.
+
+[Sidenote: 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.
+
+[Sidenote: Suspicion of perturbing planet.]
+
+It is difficult to mention an exact date for the conversion into certainty
+of the suspicion that no single orbit could be found to satisfy all the
+observations; but we may certainly regard this fact as established in
+1821, when Alexis Bouvard published some tables of the planet, and showed
+fully in the introduction that when every correction for the disturbing
+action of other planets had been applied, it was still impossible to
+reconcile the old observations with the orbit calculated from the new
+ones. The idea accordingly grew up that there might be some other body or
+bodies attracting the planet and causing these discrepancies. Here again
+it is not easy to say exactly when this notion arose, but it was certainly
+existent in 1834, as the following letter to the Astronomer Royal will
+show. I take it from his well-known "Account of some Circumstances
+historically connected with the Discovery of the Planet exterior to
+Uranus," which he gave to the Royal Astronomical Society at its first
+meeting after that famous discovery (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 chimaera, 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:--
+
+     [Sidenote: Airy's scepticism.]
+
+
+     NO. 2.--G. B. AIRY _to the_ REV. T. J. HUSSEY.
+     [_Extract._]
+
+     "'OBSERVATORY, CAMBRIDGE, _1834, Nov. 23_.
+
+     "'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.'"
+
+[Sidenote: Le Verrier's papers.]
+
+[Sidenote: Planet to be detected by disc.]
+
+[Sidenote: Galle's discovery of the planet.]
+
+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. 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, 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. 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.
+
+[Sidenote: Adams' work publicly announced.]
+
+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. 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.
+
+[Sidenote: 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.
+
+[Sidenote: Airy's "Account."]
+
+[Sidenote: "A movement of the age."]
+
+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), 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."
+
+[Sidenote: Airy under-estimated Adams' work.]
+
+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. 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_.
+
+     [Sidenote: Challis mentions Adams to Airy, and suggests Adams' visit
+     to Greenwich.]
+
+     "'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 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.
+
+     [Sidenote: 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:--
+
+        Mean distance (assumed nearly in accordance
+            with Bode's Law)                           38.4
+        Mean sidereal motion in 365.25 days             1 deg.30'.9
+        Mean longitude, 1st October 1845              323 34
+        Longitude of perihelion                       315 55
+        Eccentricity                                  0.1610.
+        Mass (that of the sun being unity)            0.0001656.
+
+     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._
+
+                "
+        1780  +0.27
+        1783  -0.23
+        1786  -0.96
+        1789  +1.82
+        1792  -0.91
+        1795  +0.09
+        1798  -0.99
+        1801  -0.04
+        1804  +1.76
+        1807  -0.21
+        1810  +0.56
+        1813  -0.94
+        1816  -0.31
+        1819  -2.00
+        1822  +0.30
+        1825  +1.92
+        1828  +2.25
+        1831  -1.06
+        1834  -1.44
+        1837  -1.62
+        1840  +1.73
+
+     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._
+
+               "
+        1690  +44.4
+        1712  + 6.7
+        1715  - 6.8
+        1750  - 1.6
+        1753  + 5.7
+        1756  - 4.0
+        1763  - 5.1
+        1769  + 0.6
+        1771  +11.8
+
+     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_.
+
+     [Sidenote: 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."
+
+[Sidenote: 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.
+
+[Sidenote: His disappointment at Greenwich, and at Airy's question.]
+
+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.
+
+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.
+
+[Sidenote: The merits of Airy's question.]
+
+[Sidenote: The range of possibilities.]
+
+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 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.
+
+[Illustration:
+
+  III--U. J. LE VERRIER.
+  (_From a print in the possession of the Royal Astronomical Society._)]
+
+[Illustration:
+
+  IV--J. G. GALLE.
+  WHO FIRST SAW THE PLANET NEPTUNE]
+
+[Sidenote: Airy receives Le Verrier's memoir.]
+
+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, 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 _Mecanique Celeste_ of Laplace; in
+     the _Theorie 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_.
+
+     [Sidenote: He puts the "radius-vector" question to Le Verrier, but
+     makes no mention of Adams.]
+
+     "'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'Academie_ 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. 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.
+
+[Sidenote: Airy announces the likelihood of a new planet, and suggests a
+search for it at Cambridge not having suitable telescope at Greenwich]
+
+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." 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; 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."
+
+[Sidenote: Challis undertakes the search.]
+
+[Sidenote: He finds too late that he had observed the planet.]
+
+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 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.
+
+[Sidenote: Sensation caused by the discovery.]
+
+[Sidenote: Not all _national_ jealousy.]
+
+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. 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. 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.
+
+[Sidenote: The position of Cambridge in the matter.]
+
+[Sidenote: Challis the weakest point.]
+
+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. 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; 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.
+
+[Sidenote: Curious difference between actual and supposed planet.]
+
+[Sidenote: Professor Peirce's contention that the discovery was a mere
+accident.]
+
+[Sidenote: The explanation.]
+
+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_. 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 deg.. 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.
+
+[Sidenote: 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.
+
+[Sidenote: 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 deg. either way.
+
+                 I.    II.   III.    IV.    V.     VI.
+
+  Correct      1820   1835   1872   1830   1861   1856
+
+  Within +-5 deg.  {1812   1827   1865   1813   1815   1826
+              {1827   1842   1877   1866   1871   1868
+
+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.
+
+[Sidenote: 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.
+
+     [Sidenote: The visible disc.]
+
+     "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 deg., and not greater than 335 deg. or 345 deg.,
+     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_.
+     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."
+
+[Sidenote: 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 deg. and 252 deg..'
+
+     "'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 deg.
+     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).
+
+[Sidenote: Newcomb's criticism.]
+
+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 deg., which does _not_ lie between 243 deg. and 252 deg.. The
+ingenious process which Airy admired and which Peirce himself calls
+"consummately skilful" was wrong in principle. 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."
+
+[Sidenote: Element of good fortune.]
+
+[Sidenote: The map used by Galle.]
+
+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. 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. 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.
+
+[Illustration: V.--CORNER OF THE BERLIN MAP, BY THE USE OF WHICH GALLE
+FOUND NEPTUNE.]
+
+[Sidenote: 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
+
+
+[Sidenote: 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.
+
+[Sidenote: Bradley's birth and early life.]
+
+[Sidenote: Brief clerical career.]
+
+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. 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."
+
+[Sidenote: Learnt astronomy _not_ at Oxford, but from his uncle, James
+Pound.]
+
+[Sidenote: Pound a first-rate observer.]
+
+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. 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; 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.
+
+[Sidenote: Bradley worked with him.]
+
+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. 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.
+
+[Sidenote: The work done by Pound and Bradley.]
+
+[Sidenote: Use of very long telescopes.]
+
+[Sidenote: Reason for great length.]
+
+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 nebulae: 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. And finally, his skill
+in the management of instruments is shown by his measuring the diameter of
+the planet Venus with a telescope actually 212-1/4 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. 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.
+
+[Sidenote: Bradley appointed at Oxford, but continues to work at Wansted.]
+
+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, 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.
+
+[Sidenote: Samuel Molyneux.]
+
+[Sidenote: Attempts to find stellar parallax.]
+
+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 Brahe, 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. 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 [gamma] 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.
+
+[Sidenote: The instrument.]
+
+[Sidenote: Expected results.]
+
+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. 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. 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.
+
+[Illustration: FIG. 2.]
+
+[Sidenote: Unexpected results.]
+
+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, [gamma] 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. 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.
+
+[Sidenote: 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
+[gamma] 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.
+
+[Sidenote: Nutation?]
+
+[Sidenote: Anomalous refraction.]
+
+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 [gamma] 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
+[gamma] Draconis, the other stars included would make the same circuit,
+preceding or following [gamma] 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 [gamma] 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. 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.
+
+[Illustration: 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.
+
+[Illustration: 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.
+
+[Sidenote: Delay in finding real explanation.]
+
+[Sidenote: Bradley sets up another instrument at Wansted.]
+
+[Sidenote: Finds the right clue.]
+
+[Sidenote: A wind-vane on a boat.]
+
+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, [gamma] Draconis and the small star above
+mentioned. 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 L140 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. 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. 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.
+
+[Illustration: FIG. 5.]
+
+[Sidenote: 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 recoit pas la moindre goutte de pluie; si la voiture avance avec
+rapidite, 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.
+
+[Sidenote: 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.
+
+[Sidenote: Results of discovery.]
+
+The discovery of aberration made Bradley famous at a bound. Oxford might
+well be proud of her two Savilian Professors at this time, for they had
+both made world-famous discoveries--Halley that of the periodicity of
+comets, and Bradley of the aberration of light. How different their tastes
+were and how difficult it would have been for either to do the work of the
+other! Bradley was no great mathematician, and though he was quite able to
+calculate the orbit of a comet, and carried on such work when Halley left
+it, it was probably not congenial to him. Halley, on the other hand,
+almost despised accurate observations as finicking. "Be sure you are
+correct to a minute," he was wont to say, "and the fractions do not so
+much matter." With such a precept Bradley would never have made his
+discoveries. No quantity was too small in his eyes, and no sooner was the
+explanation of aberration satisfactorily established than he perceived
+that though it would account for the main facts, it would not explain all.
+There was something left. This is often the case in the history of
+science. A few years ago it was thought that we knew the constitution of
+our air completely--oxygen, nitrogen, water vapour, and carbonic acid gas;
+but a great physicist, Lord Rayleigh, found that after extracting all the
+water and carbonic acid gas, all the oxygen and all the nitrogen, there
+was something left--a very minute residuum, which a careless experimenter
+would have overlooked or neglected, but which a true investigator like
+Lord Rayleigh saw the immense importance of. He kept his eye on that
+something left, and presently discovered a new gas which we now know as
+argon. Had he repeated the process, extracting all the argon after the
+nitrogen, he might have found by a scrutiny much more accurate still yet
+another gas, helium, which we now know to exist in extremely minute
+quantities in the air. But meantime this discovery was made in another
+way.
+
+[Sidenote: Still something to be explained.]
+
+[Sidenote: Probably nutation.]
+
+[Sidenote: His nineteen years' campaign.]
+
+When Bradley had extracted all the aberration from his observations he
+found that there was something left, another problem to be solved and some
+more thinking to be done to solve it. But he was now able to profit by his
+previous labours, and the second step was made more easily than the first.
+The residuum was not the parallax of which he had originally been in
+search, for it did not complete a cycle within the year; it was rather a
+progressive change from year to year. But there was an important clue of
+another kind. He saw that the apparent movements of all stars were in
+this case the same; and he knew that a movement of this kind can be
+referred, not to the stars themselves, but to the plumb-line from which
+their directions are measured. He had thought out the possible causes of
+such a movement of the plumb-line or of the earth itself, and had realised
+that there might be a _nutation_ which would go through a cycle in about
+nineteen years, the period in which the moon's nodes revolve. He was not
+mathematician enough to work out the cause completely, but he saw clearly
+that to trace the whole effect he must continue the observations for
+nineteen years; and accordingly he entered on this long campaign without
+any hesitation. His instrument was still that in his aunt's house at
+Wansted, where he continued to live and make the observations for a few
+years, but in 1732 he removed to Oxford, as we shall see, and he must have
+made many journeys between Wansted and Oxford in the course of the
+remaining fifteen years during which he continued to trace out the effects
+of nutation. His aunt too left Wansted to accompany Bradley to Oxford, and
+the house passed into other hands. It is to the lasting credit of the new
+occupant, Mrs. Elizabeth Williams, that the great astronomer was allowed
+to go on and complete the valuable series of observations which he had
+commenced. Bradley was not lodged in her house; he stayed with a friend
+close by on his visits to Wansted, but came freely in and out of his
+aunt's old home to make his observations. How many of us are there who
+would cheerfully allow an astronomer to enter our house at any hour of the
+night to make observations in the coal-cellar! It says much, not only for
+Bradley's fame, but for his personal attractiveness, that he should have
+secured this permission, and that there should be no record of any
+friction during these fifteen years. At the end of the whole series of
+nineteen years his conclusions were abundantly verified, and his second
+great discovery of nutation was established. Honours were showered upon
+him, and no doubt the gentle heart of Mrs. Elizabeth Williams was uplifted
+at the glorious outcome of her long forbearance.
+
+[Sidenote: Residence at Oxford.]
+
+But we may now turn for a few moments from Bradley's scientific work to
+his daily life. We have said that in 1732, after holding his professorship
+for eleven years, he first went definitely to reside in Oxford. He
+actually had not been able to afford it previously. His income was only
+L140 a year, and the statutes prevented him from holding a living: so
+that he was fain to accept Mrs. Pound's hospitable shelter. But in 1729 an
+opportunity of adding to his income presented itself, by giving lectures
+in "experimental philosophy." The observations on nutation were not like
+those on aberration: he was not occupied day and night trying to find the
+solution: he had practically made up his mind about the solution, and the
+actual observations were to go on in a quiet methodical manner for
+nineteen years, so that he now had leisure to look about him for other
+employment. Dr. Keill, who had been Professor of Astronomy before Bradley,
+had attracted large classes to lectures, not on astronomy, but on
+experimental philosophy: but had sold his apparatus and goodwill to Mr.
+Whiteside, of Christ Church, one of the candidates who were disappointed
+by Bradley's election. In 1729 Bradley purchased the apparatus from
+Whiteside, and began to give lectures in experimental philosophy. His
+discovery of aberration had made him famous, so that his classes were
+large from the first, and paid him considerable fees. Suddenly therefore
+he changed his poverty for a comfortable income, and he was able to live
+in Oxford in one of two red brick houses in New College Lane, which were
+in those days assigned to the Savilian Professors (now inhabited by New
+College undergraduates). His aunt, Mrs. Pound, to whom he was devotedly
+attached, came with him, and two of her nephews. In his time of prosperity
+Bradley was thus able to return the hospitality which had been so
+generously afforded him in times of stress.
+
+[Sidenote: Astronomer Royal at Greenwich.]
+
+[Sidenote: Letter from Earl of Macclesfield.]
+
+Before he completed his observations for nutation another great change in
+his fortunes took place. In 1742 he was elected to succeed Halley as
+Astronomer Royal. It was Halley's dying wish that Bradley should succeed
+him, and it is said that he was even willing to resign in his favour, for
+his right hand had been attacked by paralysis, and the disease was
+gradually spreading. But he died without any positive assurance that his
+wish would be fulfilled. The chief difficulty in securing the appointment
+of Bradley seems to have been that he was the obvious man for the post in
+universal opinion. "It is not only my friendship for Mr. Bradley that
+makes me so ardently wish to see him possessed of the position," wrote the
+Earl of Macclesfield to the Lord Chancellor; "it is my real concern for
+the honour of the nation with regard to science. For as our credit and
+reputation have hitherto not been inconsiderable amongst the astronomical
+part of the world, I should be extremely sorry we should forfeit it all at
+once by bestowing upon a man of inferior skill and abilities the most
+honourable, though not the most lucrative, post in the profession (a post
+so well filled by Dr. Halley and his predecessor), when at the same time
+we have amongst us a man known by all the foreign, as well as our own
+astronomers, not to be inferior to either of them, and one whom Sir Isaac
+Newton was pleased to call the best astronomer in Europe." And again, "As
+Mr. Bradley's abilities in astronomical learning are allowed and confessed
+by all, so his character in every respect is so well established, and so
+unblemished, that I may defy the worst of his enemies (if so good and
+worthy a man have any) to make even the lowest or most trifling objection
+to it."
+
+"After all," the letter goes on, "it may be said if Mr. Bradley's skill is
+so universally acknowledged, and his character so established, there is
+little danger of opposition, since no competitor can entertain the least
+hope of success against him. But, my lord, we live in an age when most men
+how little soever their merit may be, seem to think themselves fit for
+whatever they can get, and often meet with some people, who by their
+recommendations of them appear to entertain the same opinion of them, and
+it is for this reason that I am so pressing with your lordship not to lose
+any time."
+
+Such recommendations had, however, their effect: the dreaded possibility
+of a miscarriage of justice was averted, and Bradley became the third
+Astronomer Royal, though he did not resign his professorship at Oxford.
+Halley, Bradley, and Bliss, who were Astronomers Royal in succession, all
+held the appointment along with one of the Savilian professorships at
+Oxford; but since the death of Bliss in 1761, the appointment has always
+gone to a Cambridge man.
+
+[Sidenote: Instruments very defective.]
+
+When Bradley went to Greenwich, in June 1742, he was at first unable to do
+much from the wretched state in which he found the instruments. Halley was
+not a good observer: his heart was not in the work, and he had not taken
+the trouble to set the instruments right when they went wrong. The
+counterpoises of that instrument which ought to have been the best in the
+world at the time rubbed against the roof so that the telescope could
+scarcely be moved in some positions: and some of the screws were broken.
+There was no proper means of illuminating the cross-wires, and so on. With
+care and patience Bradley set all this right, and began observations. He
+had the good fortune to secure the help of his nephew, John Bradley, as
+assistant, and the companionship seems to have been as happy as that
+previous one of James Bradley and his uncle Pound. John Bradley was able
+to carry on the observations when his uncle was absent in Oxford, and the
+work the two got through together in the first year is (in the words of
+Bradley's biographer Rigaud) "scarcely to be credited." The transit
+observations occupy 177 folio pages, and no less than 255 observations
+were taken on one night. And at the same time, it must be remembered,
+Bradley was still carrying on his nutation observations at Wansted, still
+lecturing at Oxford, and not content with all this, began a course of
+experiments on the length of the seconds' pendulum. Truly a giant for hard
+work!
+
+[Sidenote: New instruments.]
+
+But, in spite of his care in setting them right, the instruments in the
+Observatory were found to be hopelessly defective. The history of the
+instruments at the Royal Observatory is a curious one. When Flamsteed was
+appointed the first Astronomer Royal he was given the magnificent salary
+of L100 a year, and no instruments to observe with. He purchased some
+instruments with his own money, and at his death they were claimed by his
+executors. Hence Halley, the second Astronomer Royal, found the
+Observatory totally unprovided in this respect. He managed to persuade the
+nation to furnish the funds for an equipment; but Halley, though a man of
+great ability in other ways, did not know a good instrument from a bad
+one; so that Bradley's first few years at the Observatory were wasted
+owing to the imperfection of the equipment. When this was fully realised
+he asked for funds to buy new instruments, and such was the confidence
+felt in him that he got what he asked for without much difficulty. More
+than L1000, a large sum for those days, was spent under his direction,
+the principal purchases being two quadrants for observation of the
+position of the stars, one to the north and the other to the south. With
+these quadrants, which represented the perfection of such apparatus at
+that time, Bradley made that long and wonderful series of observations
+which is the starting-point of our knowledge of the movements of the
+stars. The instruments are still in the Royal Observatory, the more
+important of the two in its original position as Bradley mounted it and
+left it.
+
+[Sidenote: Work at Greenwich.]
+
+It seems needless to mention his work as Astronomer Royal, but I will give
+quite briefly a summary of what he accomplished, and then recall a
+particular incident, which shows how far ahead of his generation his
+genius for observation placed him. The summary may be given as follows.
+We owe to Bradley--
+
+1. A better knowledge of the movements of Jupiter's satellites.
+
+2. The orbits of several comets calculated directly from his own
+observations, when such work was new and difficult.
+
+3. Experiments on the length of the pendulum.
+
+4. The foundation of our knowledge of the refraction of our atmosphere.
+
+5. Considerable improvements in the tables of the moon, and the promotion
+of the method for finding the longitude by lunar distances.
+
+6. The proper equipment of our national Observatory with instruments, and
+the use of these to form the basis of our present knowledge of the
+positions and motions of the stars.
+
+Many men would consider any one of these six achievements by itself a
+sufficient title to fame. Bradley accomplished them all in addition to his
+great discoveries of aberration and nutation.
+
+[Sidenote: Might have found variation of latitude.]
+
+And with a little more opportunity he might have added another great
+discovery which has shed lustre on the work of the last decade. We said
+earlier in this chapter that the axis of the earth may move in one or two
+ways. Either it may point to a different star, remaining fixed relatively
+to the earth, as in the nutation which Bradley discovered; or it may
+actually change its position in the earth. This second kind of movement
+was believed until twenty years ago not to exist appreciably; but the
+work of Kuestner and Chandler led to the discovery that it did exist, and
+its complexities have been unravelled, and will be considered in the sixth
+chapter. Now a century and a half ago Bradley was on the track of this
+"variation of latitude." His careful observations actually showed the
+motion of the pole, as Mr. Chandler has recently demonstrated; and,
+moreover, Bradley himself noticed that there was something unexplained.
+Once again there was a _residuum_ after (first) aberration and (next)
+nutation had been extracted from the observations; and with longer life he
+might have explained this residuum, and added a third great discovery to
+the previous two. Or another coming after him might have found it; but
+after the giant came men who could not tread in his footsteps, and the
+world waited 150 years before the discrepancy was explained.
+
+[Sidenote: Oxford's tardy recognition of Bradley.]
+
+The attitude of our leading universities towards science and scientific
+men is of sufficient importance to justify another glance at the relations
+between Bradley and Oxford. We have seen that Oxford's treatment of
+Bradley was not altogether satisfactory. She left him to learn astronomy
+as he best could, and he owes no teaching to her. She made him Professor
+of Astronomy, but gave him no observatory and a beggarly income which he
+had to supplement by giving lectures on a different subject. But when he
+had disregarded these discouragements and made a name for himself, Oxford
+took her share in recognition. He was created D.D. by diploma in 1742; and
+when his discovery of nutation was announced in 1748, and produced
+distinctions and honours of all kinds from over the world, we are told
+that "amidst all these distinctions, wide as the range of modern science,
+and permanent as its history, there was one which probably came nearer his
+heart, and was still more gratifying to his feeling than all. Lowth
+(afterwards Bishop of London), a popular man, an elegant scholar, and
+possessed of considerable eloquence, had in 1751 to make his last speech
+in the Sheldonian Theatre at Oxford as Professor of Poetry. In recording
+the benefits for which the University was indebted to its benefactors, he
+mentioned the names of those whom Sir Henry Savile's foundation had
+established there: 'What men of learning! what mathematicians! we owe to
+Savile, Briggs, Wallis, Halley; to Savile we owe Greaves, Ward, Wren,
+Gregory, Keill, and one whom I will not name, for posterity will ever have
+his name on its lips.' Bradley was himself present; there was no one in
+the crowded assembly on whom the allusion was lost, or who did not feel
+the truth and justice of it; all eyes were turned to him, while the walls
+rung with shouts of heartfelt affection and admiration; it was like the
+triumph of Themistocles at the Olympic games."
+
+[Sidenote: The study of "residual phenomena."]
+
+These words of Rigaud indicate the fame deservedly acquired by an earnest
+and simple-minded devotion to science: but can we learn anything from the
+study of Bradley's work to guide us in further research? The chief lessons
+would seem to be that if we make a series of careful observations, we
+shall probably find some deviation from expectation: that we must follow
+up this clue until we have found some explanation which fits the facts,
+not being discouraged if we cannot hit upon the explanation at once, since
+Bradley himself was puzzled for several years: that after finding one
+_vera causa_, and allowing for the effect of it, the observations may show
+traces of another which must again be patiently hunted, even though we
+spend nineteen years in the chase: and that again we may have to leave the
+complete rectification of the observations to posterity. But though we may
+admit the general helpfulness of these directions, and that this patient
+dealing with residual phenomena seems to be a method capable of frequent
+application, we cannot deduce any universal principle of procedure from
+them: witness the difficulty of dealing with meteorological observations,
+for instance. It is not always possible to find any orderly arrangement of
+the residuals which will give us a clue to start with. When such an
+arrangement is manifested, we must certainly follow up the clue; it would
+almost seem that no expense should be prohibitive, since it is impossible
+to foresee the importance of the result.
+
+
+
+
+CHAPTER IV
+
+ACCIDENTAL DISCOVERIES
+
+
+[Sidenote: The Oxford new star found during work on Astrographic Chart.]
+
+In reviewing various types of astronomical discovery I have laid some
+stress upon the fact that they are, generally speaking, far from being
+accidental in character. A new planet does not "swim into our ken," at any
+rate not usually, but is found only after diligent search, and then only
+by an investigator of acute vision, or other special qualifications. But
+this is, of course, not always the case. Some discoveries are made by the
+merest accident, as we have had occasion to remark incidentally in the
+case of the minor planets; and for the sake of completeness it is
+desirable to include among our types at least one case of such accidental
+discovery. As, however, the selection is a little invidious, I may perhaps
+be pardoned for taking the instance from my own experience, which happens
+to include a case where one of those remarkable objects called "new stars"
+walked deliberately into a net spread for totally different objects. There
+is the further reason for choosing this instance: that it will afford me
+the opportunity of saying something about the special research in which we
+were actually engaged, the work of mapping out the heavens by
+photography, or, as it has been called, the Astrographic Chart--a great
+scheme of international co-operation by which it is hoped to leave as a
+legacy for future centuries a record of the state of the sky in our age.
+Such a record cannot be complete; for however faint the stars included, we
+know that there are fainter stars which might have been included had we
+given longer exposures to the plates. Nor can it be in other ways final or
+perfect; however large the scale, for instance, on which the map is made,
+we can imagine the scale doubled or increased many-fold. But the map will
+be a great advance on anything that has hitherto been made, and some
+account of it will therefore no doubt be of interest.
+
+[Sidenote: Origin of the chart.]
+
+We may perhaps begin with a brief historical account of the enterprise.
+Photographs of the stars were taken many years ago, but only by a few
+enthusiasts, and with no serious hope of competing with eye observations
+of the sky. The old wet-plate photography was, in fact, somewhat unsuited
+to astronomical purposes; to photograph faint objects a long exposure is
+necessary, and the wet plate may dry up before the exposure is
+concluded--nay, even before it is commenced, if the observer has to wait
+for passing clouds--and therefore it may be said that the successful
+application of photography to astronomy dates from the time when the dry
+plate was invented; when it became possible to expose a plate in the
+telescope for hours, or by accumulation even for days. The dry plate
+remains sensitive for a long period, and if it is desired to extend an
+exposure beyond the limits of one night, it is quite easy to close up
+the telescope and return to the operations again on the next fine night;
+and so on, if not perhaps indefinitely, at any rate so long as to
+transcend the limits of human patience up to the present.
+
+[Illustration:
+
+  VII.--GREAT COMET OF NOV. 7TH, 1882
+  (_From a photograph taken at the Royal Observatory, Cape of Good Hope._)]
+
+[Sidenote: Comet of 1882.]
+
+[Sidenote: Stars shown on the pictures.]
+
+But to consider our particular project. We may assign, perhaps, the date
+1882 as that in which it first began to take shape. In that year there was
+a magnificent bright comet, the last really large comet which we, in the
+Northern Hemisphere, have had the good fortune to see. Some of us, of
+course, were not born at that time, and perhaps others who were alive may
+nevertheless not have seen that comet; for it kept somewhat uncomfortably
+early morning hours, and I can well remember myself feeling rather more
+resentment than gratitude to the man who waked me up about four o'clock to
+see it. Many observations were of course made of this interesting visitor,
+and what specially concerns us is that at the Cape of Good Hope some
+enterprising photographers tried to photograph it. They tried in the first
+instance with ordinary cameras, and soon found--what any astronomer could
+have told them--that the movement of the earth, causing an apparent
+movement of the comet and the stars in the opposite direction, frustrated
+their efforts. The difficulties of obtaining pictures of moving objects
+are familiar to all photographers. A "snap-shot" might have met the
+difficulty, but the comet was scarcely bright enough to affect the plate
+with a short exposure. Ultimately Dr. David Gill, the astronomer at the
+Cape Observatory, invited one of the photographers to strap his camera to
+one of the telescopes at the Observatory, a telescope which could be
+carried round by clockwork in the usual way, so as to counteract the
+earth's motion, and in effect to keep the comet steadily in view, as
+though it were at rest. As a consequence, some very beautiful and
+successful pictures of the comet were obtained, and on them a large number
+of stars were also shown. They were, as I have said, not by any means the
+first pictures of stars obtained by photography, but they represented in
+facility and in success so great an advance upon what had been formerly
+obtained that they attracted considerable attention. They were sent to
+Europe and stimulated various workers to further experiments.
+
+[Sidenote: The brothers Henry begin work.]
+
+[Sidenote: Conference of 1887.]
+
+The late Dr. Common in England, an amateur astronomer, began that
+magnificent pioneer work in astronomical photography which soon brought
+him the Gold Medal of the Royal Astronomical Society for his photographs
+of nebulae. But the most important result for our purpose was produced in
+France. There had been started many years before by the French astronomer
+Chacornac a series of star maps round the Zodiac similar in intention to
+the Berlin maps which figured in the history of the discovery of Neptune.
+Chacornac died before his enterprise was very far advanced, and the work
+was taken up by two brothers, Paul and Prosper Henry, who followed
+Chacornac in adopting for the work the laborious method of eye
+observation of each individual star. They proceeded patiently with the
+work on these lines; but when they came to the region where the Zodiac is
+crossed by the Milky Way, and the number of stars in a given area
+increases enormously, they found the labour so great as to be practically
+prohibitive, and were in doubt how to deal with the difficulty. It was at
+this critical moment that these comet photographs, showing the stars so
+beautifully, suggested the alternative of mapping the stars
+photographically. They immediately set to work with a trial lens, and
+obtained such encouraging results that they proceeded themselves to make a
+larger lens of the same type; this again was satisfactory, and the idea
+naturally arose of extending to the whole heavens the scheme which they
+had hitherto intended only for the Zodiac, a mere belt of the heavens. But
+this rendered the enterprise too large for a single observatory. It became
+necessary to obtain the co-operation of other observatories, and with this
+end in view an International Conference was summoned to meet in Paris in
+1887 to consider the whole project. There were delegates from, if not all
+nations, at any rate a considerable number:--
+
+  France            20
+  British Empire     8
+  Germany            6
+  Russia             3
+  Holland            3
+  U.S. America       3
+  Austria            2
+  Sweden             2
+  Denmark            2
+  Belgium            1
+  Italy              1
+  Spain              1
+  Switzerland        1
+  Portugal           1
+  Brazil             1
+  Argentine Republic 1
+
+[Sidenote: Choice of instrument.]
+
+[Sidenote: Expense of "doublet."]
+
+[Sidenote: Advantages of reflector.]
+
+[Sidenote: Refractor chosen.]
+
+The Conference had a number of very important questions to discuss, for
+knowledge of the photographic method and its possibilities was at that
+time in its infancy. There was, for instance, the question whether all the
+instruments need be of the same pattern, and if so what that pattern
+should be. The first of these questions was settled in the affirmative, as
+we might expect; in the interests of uniformity it was desirable that the
+maps should be as nearly similar as possible. The second question was not
+so easy; there were at least three different types of instruments which
+might be used. First of all, there was the photographic lens, such as is
+familiar to all who have used an ordinary camera, consisting of two lenses
+with a space between; though since each of these lenses is itself made up
+of two, we should more correctly say four lenses in all. It was with a
+lens of this kind that the comet pictures had been taken at the Cape of
+Good Hope, and it might seem the safest plan to adopt what had been shown
+to be capable of such good work. But there was this difficulty; the
+pictures of the comet were on a very small scale, and taken with a small
+lens; a much larger lens was required for the scheme now under
+contemplation, and when there are four separate lenses to be made, each
+with two surfaces to polish, and each requiring a perfectly sound clear
+piece of glass, it will be obvious that the difficulties of making a large
+compound lens of this kind are much greater, and the expense much more
+serious than in the case of a single lens, or even a pair. It was this
+question of expense which had led the brothers Henry to experiment with a
+different kind of instrument, in which only one pair of lenses was used
+instead of two. Their instrument was, in fact, very similar to the
+ordinary telescope, excepting that they were bound to make their lenses
+somewhat different in shape in order to bring to focus the rays of light
+suitable for photography, which are not the same as those suitable for eye
+observation with the ordinary telescope. Dr. Common, again, had used a
+third kind of instrument, mainly with the view of reducing the necessary
+expense still further, or, perhaps, of increasing the size of the
+instrument for the same expense. His telescope had no lens at all, but a
+curved mirror instead, the mirror being made of glass silvered on the face
+(not on the back as in the ordinary looking-glass). In this case there is
+only one surface to polish instead of four, as in the Henrys' telescope,
+or eight, as in the case of the photographic doublet; and, moreover, since
+the rays of light are reflected from the surface of the glass, and do not
+pass _through_ it at all, the internal structure of the glass is not so
+strictly important as in the other cases. Hence the reflector is a very
+cheap instrument, and it is, moreover, quite free from some difficulties
+attached to the other instruments. No correction for rays of light of
+different colours is required, since all rays of whatever colour come to
+the same focus automatically. These advantages of the reflector were so
+considerable as to almost outweigh one well-known disadvantage, which is,
+however, not very easily expressed in words. The reflector might be
+described as an instrument with a temper; sometimes it gives excellent
+results, but at others _something_ seems to be wrong, though the worried
+observer does not exactly know what. Long experience and patience are
+requisite to humour the instrument and get the best results from it, and
+it was felt that this uncertainty was sufficient to disqualify the
+instrument for the serious piece of routine work contemplated in mapping
+the heavens. Accordingly the handier and more amiable instrument with
+which the brothers Henry had done such good work was selected as the
+pattern to be adopted.
+
+[Sidenote: Doublet would have been better.]
+
+It is curious that at the Conference of 1887 nothing at all was said about
+the type of instrument first mentioned (the "doublet lens"), although a
+letter was written in its favour by Professor Pickering of Harvard College
+Observatory. Since that time we have learnt much of its advantages, and it
+is probable that if the Conference were to meet now they might arrive at a
+different decision; but at that time they were, to put it briefly,
+somewhat afraid of an instrument which seemed to promise, if anything, too
+well, especially in one respect. With the reflector and the refractor it
+had been found that the field of good images was strictly limited. The
+Henrys' telescope would not photograph an area of the sky greater in
+extent than 2 deg. in diameter at any one time, and the reflector was more
+limited still; within this area the images of the stars were good, and it
+had been found that their places were accurately represented. Now the
+"doublet" seemed to be able to show much larger areas than this with
+accuracy, but no one had been able to test the accuracy to see whether it
+was sufficient for astronomical purposes; and although no such feeling was
+openly expressed or is on record, I think there is no doubt that a feeling
+existed of general mistrust of an instrument which seemed to offer such
+specious promises. Whatever the reason, its claims were passed over in
+silence at the Conference, and the safer line (as it was then thought) of
+adopting as the type the Henrys' instrument, was taken.
+
+[Sidenote: The eighteen observatories.]
+
+This was perhaps the most important question settled at the Conference,
+and the answers to many of the others naturally followed. The size of the
+plates, for instance, was settled automatically. The question down to what
+degree of faintness should stars be included, resolved itself into the
+equivalent question, What should be the length of time during which the
+plates were exposed? Then, again, the question, What observatories should
+take part in the work? became simply this: What observatories could
+afford to acquire the instruments of this new pattern and get other funds
+for carrying out the work specified? It was ultimately found that eighteen
+observatories were able to obtain the apparatus and funds, though
+unfortunately three of the eighteen have since found it impossible to
+proceed. The following is the original list, and in brackets are added the
+names of three other observatories which in 1900 undertook to fill the
+places of the defaulters.
+
+  OBSERVATORIES CO-OPERATING FOR THE ASTROGRAPHIC CHART.
+
+  +----------------------+------------+----------+
+  |    Observatory.      |  Zones of  |  Number  |
+  |                      |Declination.|of Plates.|
+  +----------------------+------------+----------+
+  |Greenwich             |+90 deg. to +65 deg.|   1149   |
+  |Rome                  |+64 deg.  " +55 deg.|   1140   |
+  |Catania               |+54 deg.  " +47 deg.|   1008   |
+  |Helsingfors           |+46 deg.  " +40 deg.|   1008   |
+  |Potsdam               |+39 deg.  " +32 deg.|   1232   |
+  |Oxford                |+31 deg.  " +25 deg.|   1180   |
+  |Paris                 |+24 deg.  " +18 deg.|   1260   |
+  |Bordeaux              |+17 deg.  " +11 deg.|   1260   |
+  |Toulouse              |+10 deg.  " + 5 deg.|   1080   |
+  |Algiers               |+ 4 deg.  " - 2 deg.|   1260   |
+  |San Fernando          |- 3 deg.  " - 9 deg.|   1260   |
+  |Tacubaya              |-10 deg.  " -16 deg.|   1260   |
+  |Santiago (Monte Video)|-17 deg.  " -23 deg.|   1260   |
+  |La Plata (Cordoba)    |-24 deg.  " -31 deg.|   1360   |
+  |Rio (Perth, Australia)|-32 deg.  " -40 deg.|   1376   |
+  |Cape of Good Hope     |-41 deg.  " -51 deg.|   1512   |
+  |Sydney                |-52 deg.  " -64 deg.|   1400   |
+  |Melbourne             |-65 deg.  " -90 deg.|   1149   |
+  +----------------------+------------+----------+
+
+[Sidenote: Sky covered twice.]
+
+In the list is also shown the total number of plates that were to be taken
+by each observatory. When once the size of the plates had been settled,
+it was a straightforward matter to divide up the sky into the proper
+number of regions necessary to cover it completely, not only without gaps
+between the plates, but with actually a small overlap of contiguous
+plates. And more than this, it was decided that the whole sky should be
+completely covered _twice over_. It was conceivable that a question might
+arise whether an apparent star image on a plate was, on the one hand, a
+dust speck, or, on the other hand, a planet, or perhaps a variable or new
+star. By taking two different plates at slightly different times,
+questions of this kind could be settled; and to make the check more
+independent it was decided that the plates should not be exactly repeated
+on the same portion of sky, but that in the second series the centre of a
+plate should occupy the point assigned to the corner of a plate in the
+first series.
+
+[Sidenote: Times of exposure.]
+
+Then there came the important question of time of exposure, which involved
+a long debate between those who desired the most modest programme possible
+consistent with efficiency, and those enthusiasts who were anxious to
+strain the programme to the utmost limits attainable. Ultimately it was
+resolved to take two series of plates; one series of long exposure which
+was set in the first instance at 10 minutes, then became 15, then 30, then
+40, and has by some enterprising observers been extended to 1-1/2 hours;
+the other a series of short exposures which have been generally fixed at
+6 minutes. Thus instead of covering the sky twice, it was decided to cover
+it in all four times, and the number of plates assigned to each
+observatory in the above list must be regarded as doubled by this new
+decision. And further still, on the series of short-exposure plates it was
+decided to add to the exposure of six minutes another one of three
+minutes, having slightly shifted the telescope between the two so that
+they should not be superimposed; and later still, a third exposure of
+twenty seconds was added to these. It would take too long to explain here
+the reasons for these details, but it will be clear that the general
+result of the discussion was to extend the original programme
+considerably, and render the work even more laborious than it had appeared
+at the outset.
+
+[Sidenote: Measurement of plates.]
+
+[Sidenote: The reseau.]
+
+[Sidenote: The microscope.]
+
+[Sidenote: Reversal of plates.]
+
+[Sidenote: Personal equation.]
+
+When all these plates have been taken, the work is by no means finished;
+indeed, it is only just commencing. There remains the task of measuring
+accurately on each of the short-exposure plates the positions of the stars
+which it represents, numbering on the average some 300 or 400; so that for
+instance at Oxford the total number of stars measured on the twelve
+hundred plates is nearly half a million. These are not all separate stars;
+for the sky is represented twice over, and there is also the slight
+overlap of contiguous plates; but the number of actual separate stars
+measured at this one observatory is not far short of a quarter of a
+million, and it has taken nearly ten years to make the measurements, with
+the help of three or four measurers trained for the purpose. To render the
+measures easy, a network or reseau of cross lines is photographed on each
+plate by artificial light after it has been exposed to the stars, so that
+on development these cross lines and the stars both appear. We can see at
+a glance the approximate position of a star by counting the number of the
+space from left to right and from top to bottom in which it occurs; and we
+can also estimate the fraction of a space in addition to the whole number;
+but it is necessary for astronomical purposes to estimate this fraction
+with the greatest exactness. The whole numbers are already given with
+great exactness by the careful ruling of the cross lines, which can be
+spaced with extraordinary perfection. To measure the fraction, we place
+the plate under a microscope in the eye-piece of which there is a finally
+divided cross scale; the centre of the cross is placed over a star image,
+and then it is noted where the lines of the reseau cut the cross scale. In
+this way the position of the image of a star is read off with accuracy,
+and after a little practice with considerable rapidity. It has been found
+at Oxford that under favourable conditions the places of nearly 200 stars
+per hour can be recorded in this way by a single measurer, if he has some
+one to write down for him the numbers he calls out. This is only one form
+of measuring apparatus; there are others in which, instead of a scale in
+the eye-piece, micrometer screws are used to measure the fractions; but
+the general principle in all these instruments is much the same, and the
+rate of work is not very different; while to the minor advantages and
+disadvantages of the different types there seems no need here to refer.
+One particular point, however, is worth noting. After a plate has been
+measured, it is turned round completely, so that left is now right, and
+top is now bottom, and the measurements are repeated. This repetition has
+the advantage first of all of checking any mistakes. When a long piece of
+measuring or numerical work of any kind is undertaken there are invariably
+moments when the attention seems to wander, and some small error is the
+result. But there are also certain errors of a systematic character
+similar to those denoted by the term "personal equation," which has found
+its way into other walks of life. In the operation of placing a cross
+exactly over the image of a star, different observers would show slight
+differences of habit; one might place it a little more to the right than
+another. But when the plate is turned round the effect of this habit on
+the measure is exactly reversed, and hence if we take the mean of the two
+measures any personal habit of this kind is eliminated. It has been found
+by experience that such personal habits are much smaller for measures of
+this kind than for those to which we have long been accustomed in
+observations made by eye on the stars themselves. The troubles from
+"personal equation" have been much diminished by the photographic method,
+and certain peculiarities of the former method have been clearly exhibited
+by the comparison. For instance, it has gradually become clear that with
+eye observations personal equation is not a constant quantity, but is
+different for stars of different brightness. When observing the transit of
+a bright star the observer apparently records an instant definitely
+earlier than in recording the transit of a faint one; and this peculiarity
+seems to be common to the large majority of observers, which is perhaps
+the reason why it was not noticed earlier. But when positions of the stars
+determined in this way are compared with their positions measured on the
+photographic plates, the peculiarity is made clearly manifest. For
+example, at Oxford, our first business after making measurements is to
+compare them with visual observations on a limited number of the brighter
+stars made at Cambridge about twenty years ago. (About 14,000 stars were
+observed at Cambridge, and we are dealing with ten times that number.) The
+comparison shows that the Cambridge observations are affected with the
+following systematic errors:--
+
+    If stars of magnitude 10 are observed correctly,
+  then   "        "        9        "     0.10 secs. too early
+         "        "        8        "     0.16        "
+         "        "        7        "     0.19        "
+         "        "        6        "     0.21        "
+         "        "        5        "     0.23        "
+
+[Sidenote: Main object of the work.]
+
+This may serve as an illustration of various incidental results which are
+already flowing from the enormous and laborious piece of work which, as
+far as the University Observatory at Oxford is concerned, we have just
+completed, though some of the other colleagues are not so far advanced.
+But the main results will not appear just yet. The work must be repeated,
+and the positions of the stars just obtained must be compared with those
+which they will be found to occupy at some future date, in order to see
+what kind of changes are going on in the heavens. Whether this future date
+shall be one hundred years hence, or fifty, or ten, or whether we should
+begin immediately to repeat what has been done, is a matter not yet
+decided, and one which requires some little consideration.
+
+[Sidenote: The concluding year.]
+
+I have said perhaps enough to give you a general idea of the work on which
+we have been engaged at Oxford for the last ten years. Ten years ago it
+seemed to stretch out in front of us rather hopelessly; the pace we were
+able to make seemed so slow in view of the distance to be covered. We felt
+rather like the schoolboy who has just returned to school and sees the
+next holidays as a very remote prospect, and we solaced ourselves much in
+the same way as he does, by making a diagram representing the total number
+of plates to be dealt with and crossing off each one as it was finished,
+just as he sometimes crosses off the days still remaining between him and
+the prospective holidays. It was pleasant to watch the growth of the
+number of crosses on this diagram, and by the end of the year 1902 we had
+the satisfaction of seeing very little blank space remaining. Now, up to
+this point it had not much mattered whether any particular plate was
+secured in any particular year, or in a subsequent year, so long as there
+were always sufficient plates to keep us occupied in measuring them. But
+it then became a matter of importance to secure each plate at the proper
+time of year; for the sun, as we know, travels round the Zodiac among the
+stars, obliterating by his radiance a large section of the sky for a
+period of some months, and in this way a particular region of the heavens
+is apt to "run into daylight," as the observatory phrase goes, and ceases
+to be available for photography during several months, until the sun is
+again far enough away to allow of the particular region being seen at
+night.
+
+[Sidenote: A disappointment.]
+
+[Sidenote: A curious plate.]
+
+[Sidenote: A strange object.]
+
+[Sidenote: A new star?]
+
+Roughly speaking then, if a plate which should be taken in February is not
+secured in this month owing to bad weather, the proper time for taking it
+will not occur again until the following February; and when there was a
+fair prospect of finishing our work in 1903, it became important to secure
+each plate at the proper time in that year. Hence we were making special
+efforts to utilise to the full any fine night that Providence sent in our
+way, and on such occasions it is clearly an economy, if not exactly to
+"make hay while the sun shines," at any rate to take plates vigorously
+while the sun is _not_ shining and the night is fine; leaving the
+development of them until the daytime. There is, of course, the risk that
+the whole night's work may in this way be lost owing to some fault in the
+plates, which might have been detected if some of them were immediately
+developed. Perhaps in the early days of our work it would have been
+reckless or foolish to neglect this little precaution; but we had for
+years been accustomed to rely upon the excellence of the plates without
+finding our trust betrayed; and the sensitiveness of the plates had
+increased rather than diminished as time went on. Hence it will be readily
+understood that when one fatal morning we developed a series of some
+thirty plates, and found that owing to some unexplained lack of
+sensitiveness they were all unsuitable for our purpose, it came as a most
+unwelcome and startling surprise. It was, of course, necessary to make
+certain that there was no oversight, that the developer was not at fault,
+and that the weather had not been treacherous. All such possibilities were
+carefully considered before communication with the makers of the plates,
+but it ultimately became clear that there had been some unfortunate
+failure in sensitiveness, and that it would be necessary to repeat the
+work with opportunities restricted by the intervening lapse of time.
+However, disappointments from this or similar causes are not unknown in
+astronomical work; and we set about this repetition with as little loss of
+time and cheerfulness as was possible. Under the circumstances, however,
+it seemed desirable to examine carefully whether anything could be saved
+from the wreck--whether any of the plates could be admitted as _just_
+coming up to the minimum requirements. And I devoted a morning to this
+inquiry. In the course of it I came across one plate which certainly
+seemed worth an inclusion among our series from the point of view of the
+number of stars shown upon it. It seemed quite rich in stars, perhaps even
+a little richer than might have been expected. On inquiry I was told that
+this was not one of the originally condemned plates, but one which had
+been taken since the failure in sensitiveness of the plates had been
+detected; was from a new and specially sensitive batch with which the
+courteous makers had supplied us; but though there were certainly a
+sufficient number of stars upon the plate, owing to some unexplained cause
+the telescope had been erroneously pointed, and the region taken did not
+correspond to the region required. To investigate the cause of the
+discrepancy I thereupon took down from our store of plates the other one
+of the same region which had been rejected for insufficiency of stars, and
+on comparing the two it was at once evident that there was a strange
+object on the plate taken later of the two, a bright star or other
+heavenly body, which was not on the former plate. I have explained that by
+repeating the exposure more than once, it is easily possible to recognise
+whether a mark upon the plate is really a celestial body or is an
+accidental blot or dust speck, and there was no doubt that this was the
+image of some strange celestial body. It might, of course, be a new
+planet, or even an old one which had wandered into the region; but a few
+measures soon showed that it was not in movement. The measures consisted
+in comparing the separation of the three exposures with the separation of
+the corresponding exposures of obvious stars, for the exposures were not,
+of course, simultaneous, and if the body were a planet and had moved in
+the interval between them, this would be made manifest on measuring the
+separations. No such movements could be detected; and the possibilities
+were thus restricted to two. So far as we knew the object was a star, but
+might be either a star of the class known as _variable_ or of that known
+as _new_. In the former case it would become bright and faint at more or
+less regular intervals, and might possibly have been already catalogued;
+for the number of these bodies already known amounts to some hundreds.
+Search being made in the catalogues, no entry of it was found, though it
+still might be one of this class which had hitherto escaped detection. Or
+it might be a "new star," one of those curious bodies which blaze up quite
+suddenly to brightness and then die away gradually until they become
+practically invisible. The most famous perhaps of these is the star which
+appeared in 1572, and was so carefully observed by Tycho Brahe; but such
+apparitions are rare, and altogether we have not records as yet of a score
+altogether; so that in this latter case the discovery would be of much
+greater interest than in the former. In either event it was desirable to
+inform other observers as soon as possible of the existence of a strange
+body; already some time had elapsed since the plate had been taken, March
+16th, for the examination of which I have spoken was not made until March
+24th. Accordingly, a telegram was at once despatched to the Central Office
+at Kiel, which undertakes to distribute such information all over the
+world, and a few post-cards were sent to observers close at hand who might
+be able to observe the star the same night. Certain observations with the
+spectroscope soon made it clear that the object was really a "new star."
+
+[Sidenote: The discovery accidental.]
+
+[Sidenote: Mrs. Fleming's discoveries.]
+
+This, therefore, is the discovery which we made at Oxford: as you will
+see, in an entirely accidental manner, during the course of a piece of
+work in which it was certainly never contemplated. Its purely accidental
+nature is sufficiently illustrated by the fact that if the plates
+originally supplied by the makers had been of the proper quality, the
+plate which led to the discovery would never have been taken. If the
+plates exposed in February had been satisfactory, we should have been
+content, and should not have repeated the exposure on March 16th. Again I
+can testify personally how purely accidental it was that the examination
+was made on March 24th to see whether anything could be saved, as I have
+said, from the wreck. The idea came casually into my mind as I was walking
+through the room and saw the neat pile of rejected plates; and one may
+fairly call it an accidental impulse. This new star is not, however, the
+first of such objects to have been discovered "accidentally"; many of the
+others were found just as much by chance, though a notable exception must
+be made of those discovered at the Harvard Observatory, which are the
+result of a deliberate search for such bodies by the careful examination
+of photographic plates. Mrs. Fleming, who spends her life in such work,
+has had the good fortune to detect no less than six of these wonderful
+objects as the reward of her laborious scrutiny; and she is the _only_
+person who has thus found new stars by photography until this accidental
+discovery at Oxford. The following is a complete list of new stars
+discovered to date:--
+
+  LIST OF NEW STARS.
+
+  +----------------------------------------------+
+  |Ref. No.| Constellation. | Year.| Discoverer. |
+  +----------------------------------------------+
+  |   1    | Cassiopeia     | 1572 | Tycho Brahe.|
+  |   2    | Cygnus         | 1600 | Janson.     |
+  |   3    | Ophiuchus      | 1604 | Kepler.     |
+  |   4    | Vulpecula      | 1670 | Anthelm.    |
+  |   5    | Ophiuchus      | 1848 | Hind.       |
+  |   6    | Scorpio        | 1860 | Auwers.     |
+  |   7    | Corona Borealis| 1866 | Birmingham. |
+  |   8    | Cygnus         | 1876 | Schmidt.    |
+  |   9    | Andromeda      | 1885 | Hartwig.    |
+  |  10    | Perseus        | 1887 | Fleming.    |
+  |  11    | Auriga         | 1891 | Anderson.   |
+  |  12    | Norma          | 1893 | Fleming.    |
+  |  13    | Carina         | 1895 | Fleming.    |
+  |  14    | Centaurus      | 1895 | Fleming.    |
+  |  15    | Sagittarius    | 1898 | Fleming.    |
+  |  16    | Aquila         | 1899 | Fleming.    |
+  |  17    | Perseus        | 1901 | Anderson.   |
+  |  18    | Gemini         | 1903 | At Oxford.  |
+  +----------------------------------------------+
+
+[Illustration:
+
+  MARCH 1, 1903      MARCH 14, 1903
+  VIII.--THE OXFORD NEW STAR.
+
+  A PAIR OF PHOTOGRAPHS TAKEN AT THE HARVARD COLLEGE OBSERVATORY BEFORE
+  AND AFTER ITS APPEARANCE
+
+  (_The arrow indicates the place of the new star. It will be seen that
+  the left-hand picture though it shews fainter stars than the other, has
+  not a trace of the new star._)]
+
+[Sidenote: Dr. Anderson.]
+
+[Sidenote: Nova Persei.]
+
+Generally these stars have been noted by eye observation, as in the case
+of the two found by Dr. Anderson of Edinburgh. In these cases also we may
+say that deliberate search was rewarded; for Dr. Anderson is probably the
+most assiduous "watcher of the skies" living, though he seldom uses a
+telescope; sometimes he uses an opera-glass, but usually the naked eye. He
+describes himself as an "Astrophil" rather than as an astronomer. "I love
+the stars," he says; "and whenever they are shining, I must be looking."
+And so on every fine night he stands or sits at his open study window
+gazing at the heavens. I believe he was just about to leave them for his
+bed, near 3 A.M. on the night of February 21, 1901, when, throwing a last
+glance upward, he suddenly saw a brilliant star in the constellation
+Perseus. His first feeling was actually one of disappointment, for he felt
+sure that this object must have been there for some time past without his
+knowing of it, and he grudged the time lost when he might have been
+regarding it. More in a spirit of complaint than of inquiry, he made his
+way to the Royal Observatory at Edinburgh next day to hear what they had
+to say about it, though he found it difficult to approach the subject. He
+first talked about the weather, and the crops, and similar topics of
+general interest; and only after some time dared he venture a casual
+reference to the "new portent in the heavens." Seeing his interlocutor
+look somewhat blank, he ventured a little farther, and made a direct
+reference to the new star in Perseus; and then found to his astonishment,
+as also to his great delight, that he was the first to bring news of it.
+The news was soon communicated to other observers; all the telescopes of
+the world were soon trained upon it; and this wonderful "new star of the
+new century" has taught us more of the nature of these extraordinary
+bodies than all we knew before.
+
+[Sidenote: Records previous to discovery.]
+
+[Sidenote: Was Nova Geminorum previously shining faintly?]
+
+[Sidenote: The suspicion negatived.]
+
+Perhaps I may add a few remarks on one or two features of these bodies.
+Firstly, let us note that Professor Pickering of Harvard is now able to
+make a most important contribution to the _former_ history of these
+objects--that is to say, their history preceding their actual detection.
+We remember that, after Uranus had been discovered, it was found that
+several observers had long before recorded its place unknowingly; and
+similarly Professor Pickering and his staff have usually photographed
+other new objects unknowingly. There are on the shelves at Harvard vast
+stores of photographs, so many that they are unable to examine them when
+they have been taken; but once any object of interest has been discovered,
+it is easy to turn over the store and examine the particular plates which
+may possibly show it at an earlier date. In this way it was found that Dr.
+Anderson's new star had been visible only for a few days before its
+discovery, there being no trace of it on earlier plates. Similarly, in
+the case of the new star found at Oxford, plates taken on March 1st and
+6th, fifteen days and ten days respectively before the discovery-plate of
+March 16th, showed the star. But, in this particular instance, greater
+interest attaches to two still earlier plates taken elsewhere, and with
+exposures much longer than any available at Harvard. One had been obtained
+at Heidelberg by Dr. Max Wolf, and another at the Yerkes Observatory of
+Chicago University, by Mr. Parkhurst; and on both there appeared to be a
+faint star of about the fourteenth or fifteenth magnitude, in the place
+subsequently occupied by the Nova; and the question naturally arose, Was
+this the object which ultimately blazed up and became the new star? To
+settle this point, it was necessary to measure its position, with
+reference to neighbouring stars, with extreme precision; and here it was
+unfortunate that the photographs did not help us as much as they might,
+for they were scarcely capable of being measured with the requisite
+precision. The point was an important one, because if the identity of the
+Nova with this faint star could be established, it would be the second
+instance of the kind; but so far as they went, measurements of the
+photographs were distinctly against the identity. Such was the conclusion
+of Mr. Parkhurst from his photograph alone; and it was confirmed by
+measures made at Oxford on copies of both plates, which were kindly sent
+there for the purpose. The conclusion seemed to be that there was a faint
+star _very near_, but _not at_, the place of the new star; and it was
+therefore probable that, although this faint star was temporarily
+invisible from the brightness of the adjacent Nova, as the latter became
+fainter (in the way with which we have become familiar in the case of new
+stars), it might be possible to see the two stars alongside each other.
+This critical observation was ultimately made by the sharp eyes of
+Professor Barnard, aided by the giant telescope of the Yerkes Observatory;
+and it seems clear therefore that the object which blazed up to become the
+Nova of 1903 could not have previously been so bright as a faint star of
+the fourteenth magnitude. Although this is merely a negative conclusion,
+it is an important one in the history of these bodies.
+
+[Sidenote: Nebula round Nova Persei.]
+
+[Sidenote: Its changes.]
+
+[Sidenote: Due to travelling illumination.]
+
+The second point to which I will draw your attention is from the history
+of the other Nova just mentioned--Dr. Anderson's New Star of 1901. In this
+instance it is not the history previous to discovery, but what followed
+many months after discovery, that was of engrossing interest; and again
+Yerkes Observatory, with its magnificent equipment, played an important
+part in the drama. When, with its giant reflecting telescope, photographs
+were taken of the region of Nova Persei after it had become comparatively
+faint, it was found that there was an extraordinarily faint nebulosity
+surrounding the star. Repeating the photographs at intervals, it was
+found that this nebulosity was rapidly changing in shape. "Rapidly" is, of
+course, a relative term, and a casual inspection of two of the photographs
+might not convey any impression of rapidity; it is only when we come to
+consider the enormous distance at which the movements, or apparent
+movements, of the nebulae must be taking place that it becomes clear how
+rapid the changes must be. It was not possible to determine this distance
+with any exactness, but limits to it could be set, and it seemed probable
+that the velocity of the movement was comparable with that of light. The
+conclusion suggested itself that the velocity might actually be identical
+with that of light, in which case what we saw was not the movement of
+actual matter, but merely that of illumination, travelling from point to
+point of matter already existing.
+
+[Illustration:
+
+  SEPT. 20, 1901   NOV. 13, 1901
+  IX--NEBULOSITY ROUND NOVA PERSEI
+  (_From photographs taken at the Yerkes Observatory by G. W. Ritchey._)]
+
+
+[Sidenote: When did it all happen?]
+
+An analogy from the familiar case of sound may make clearer what is meant.
+If a loud noise is made in a large hall, we hear echoes from the walls.
+The sound travels with a velocity of about 1100 feet per second, reaches
+the walls, is reflected back from them, and returns to us with the same
+velocity. From the interval occupied in going and returning we could
+calculate the distance of the walls. The velocity of light is so enormous
+compared with that of sound that we are usually quite unable to observe
+any similar phenomenon in the case of light. If we strike a match in the
+largest hall, all parts of it are illuminated so immediately that we
+cannot possibly realise that there was really an interval between the
+striking of the match, the travelling of the light to the walls, and its
+return to our eyes. The scale of our terrestrial phenomenon is far too
+small to render this interval perceptible. But those who accept the theory
+above mentioned regarding the appearances round Nova Persei (although
+there are some who discredit it) believe that we have in this case an
+illustration of just this phenomenon of light echoes, on a scale large
+enough to be easily visible. They think that, surrounding the central star
+which blazed up so brightly in February 1901, there was a vast dark
+nebula, of which we had no previous knowledge, because it was not shining
+with any light of its own. When the star blazed up, the illumination
+travelled from point to point of this dark nebula and lighted it up; but
+the size of the nebula was so vast that, although the light was travelling
+with the enormous velocity of 200,000 miles per second, it was not until
+months afterwards that it reached different portions of this nebula; and
+we accordingly got news of the existence of this nebula some months after
+the news reached us of the central conflagration, whatever it was. Remark
+that all we can say is that the news of the nebula reached us _some months
+later_ than that of the outburst. The actual date when either of the
+actual things happened, we have as yet no means of knowing; it may have
+been hundreds or even thousands of years ago that the conflagration
+actually occurred of which we got news in February 1901, the light having
+taken all that time to reach us from that distant part of space; and the
+light reflected from the nebula was following it on its way to us all
+these years at that same interval of a few months.
+
+[Sidenote: An objection.]
+
+Now, let me refer before leaving this point to the chief objection which
+has been urged against this theory. It has been maintained that the
+illumination would necessarily appear to travel outwards from the centre
+with an approach to uniformity, whereas the observed rate of travel is not
+uniform, and has been even towards the centre instead of away from it;
+which would seem as though portions of the nebula more distant from the
+centre were lighted up sooner than those closer to it. By a simple
+illustration from our solar system, we shall see that these curious
+anomalies may easily be explained. Let us consider for simplicity two
+planets only, say the Earth and Saturn. We know that Saturn travels round
+the sun in an orbit which is ten times larger than the orbit of the earth.
+Suppose now that the sun were suddenly to be extinguished; light takes
+about eight minutes to travel from the sun to the earth, and consequently
+we should not get news of the extinction for some eight minutes; the sun
+would appear to us to still go on shining for eight minutes after he had
+really been extinguished. Saturn being about ten times as far away from
+the sun, the news would take eighty minutes to reach Saturn; and from the
+earth we should see Saturn shining more[3] than eighty minutes after the
+sun had been extinguished, although we ourselves should have lost the
+sun's light after eight minutes. I think we already begin to see
+possibilities of curious anomalies; but they can be made clearer than
+this. Instead of imagining an observer on the earth, let us suppose him
+removed to a great distance away in the plane of the two orbits; and let
+us suppose that the sun is now lighted up again as suddenly as the new
+star blazed up in February 1901. Then such an observer would first see
+this blaze in the centre; eight minutes afterwards the illumination would
+reach the earth, a little speck of light near the sun would be
+illuminated, just as we saw a portion of the dark nebula round Nova Persei
+illuminated; eighty minutes later another speck, namely, Saturn, would
+begin to shine. But now, would Saturn necessarily appear to the distant
+observer to be farther away from the sun than the earth was? Looking at
+the diagram, we can see that if Saturn were at S{1} then it would present
+this natural appearance of being farther away from the sun than the earth;
+but it might be at S{2} or S{3}, in which case it would seem to be nearer
+the sun, and the illumination would seem to travel inwards towards the
+central body instead of outwards. Without considering other cases in
+detail, it will be tolerably clear that almost any anomalous appearance
+might be explained by choosing a suitable arrangement of the nebulous
+matter which we suppose lighted up by the explosion of Nova Persei.
+Another objection urged against the theory I have sketched is that the
+light reflected from such a nebula would be so feeble that it would not
+affect our photographic plates. This depends upon various assumptions
+which we have no time to notice here; but I think we may say that there is
+certainly room for the acceptance of the theory.
+
+[Illustration: FIG. 6.]
+
+[Sidenote: Did the nebula cause the outburst?]
+
+Now, if this dark nebula was previously existing in this way all round the
+star which blazed up, the question naturally arises whether the nebula had
+anything to do with the conflagration. Was there previously a star, either
+so cold or so distant as not to be shining with appreciable light, which,
+travelling through space, encountered this vast nebula, and by the
+friction of the encounter was suddenly rendered so luminous as to outshine
+a star of the first magnitude? The case of meteoric stones striking our
+own atmosphere seems to suggest such a possibility. These little stones
+are previously quite cold and invisible, and are travelling in some way
+through space, many of them probably circling round our sun. If they
+happen in their journey to encounter our earth, even the extremely tenuous
+atmosphere, so thin that it will scarcely bend the rays of light
+appreciably, even this is sufficient by its friction to raise the stones
+to a white heat, so that they blaze up into the falling stars with which
+we are familiar. This analogy is suggested, but we must be cautious in
+accepting it; for we know so very little of the nature of nebulae such as
+that of which we have been speaking. But in any case, a totally new series
+of phenomena have been laid open to our study by those wonderful
+photographs taken at the Yerkes Observatory and the Lick Observatory in
+the few years which the present century has as yet run.
+
+[Sidenote: Importance of new stars]
+
+One thing is quite certain: we must lose no opportunity of studying such
+stars as may appear, and no diligence spent in discovering them at the
+earliest possible moment is thrown away. We have only known up to the
+present, as already stated, less than a score of them, and of these many
+have told us but little; partly because they were only discovered too late
+(after they had become faint), and partly because the earlier ones could
+not be observed with the spectroscope, which had not then been invented.
+It seems clear that in the future we must not allow accident to play so
+large a part in the discovery of these objects; more must be done in the
+way of deliberate search. Although we know beforehand that this will
+involve a vast amount of apparently useless labour, that months and years
+must be spent in comparing photographic plates, or portions of the sky
+itself, with one another without detecting anything remarkable, it will
+not be the first time that years have been cheerfully spent in such
+searches without result. We need only recall Hencke's fifteen years of
+fruitless search, before finding a minor planet, to realise this fact.
+
+[Sidenote: Superposition of plates.]
+
+[Sidenote: The stereo-comparator.]
+
+One thing of importance may be done; we may improve our methods of making
+the search, so as to economise labour, and several successful attempts
+have already been made in this direction. The simplest plan is to
+superpose two photographs taken at different dates, so that the stars on
+one lie very close to those on the other; then if an image is seen to be
+unpaired we _may_ have found a new star, though of course the object may
+be merely a planet or a variable. The superposition of the plates may be
+either actual or virtual. A beautiful instrument has been devised on the
+principle of the stereoscope for examining two plates placed side by side,
+one with each eye. We know that in this way two photographs of the same
+object from different points of view will appear to coalesce, and at the
+same time to give an appearance of solidity to the object or landscape,
+portions of which will seem to stand out in front of the background.
+Applying this principle to two photographs of stars, what happens is this:
+if the stars have all remained in the same positions exactly, the two
+pictures will seem to us to coalesce, and the images all to lie on a flat
+background; but if in the interval between the exposures of the two plates
+one of the stars has appreciably moved or disappeared, it will seem, when
+looked at with this instrument, to stand out in front of this background,
+and is accordingly detected with comparatively little trouble. This new
+instrument, to which the name Stereo-comparator has been given, promises
+to be of immense value in dredging the sky for strange bodies in the
+future. I am glad to say that a generous friend has kindly presented the
+University Observatory at Oxford with one of these beautiful instruments,
+which have been constructed by Messrs. Zeiss of Jena after the skilful
+designs of Dr. Pulfrich. Whether we shall be able to repeat by deliberate
+search the success which mere accident threw in our way remains to be
+seen.
+
+
+
+
+CHAPTER V
+
+SCHWABE AND THE SUN-SPOT PERIOD
+
+
+[Sidenote: Discoveries contrary to expectation.]
+
+In preceding chapters we have reviewed discoveries, some of which have
+been made as a result of a deliberate search, and others accidentally in
+the course of work directed to a totally different end; but so far we have
+not considered a case in which the discoverer entered upon an enterprise
+from which he was positively dissuaded.
+
+[Sidenote: Nothing expected from spots.]
+
+In the next chapter we shall come across a very striking instance of this
+type; but even in the discovery that there was a periodicity in the solar
+spots, with which I propose to deal now, Herr Schwabe began his work in
+the face of deterrent opinions from eminent men. His definite announcement
+was first made in 1843, though he had himself been convinced some years
+earlier. In 1857 the Royal Astronomical Society awarded him their gold
+medal for the discovery; and in the address delivered on the occasion the
+President commenced by drawing attention to this very fact, that
+astronomers who had expressed any opinions on the subject had been
+uniformly and decidedly against the likelihood of there being anything
+profitable in the study of the solar spots. I will quote the exact words
+of the President, Mr. Manuel Johnson, then Radcliffe Observer at Oxford.
+
+     "It was in 1826 that Heinrich Schwabe, a gentleman resident in
+     Dessau, entered upon those researches which are now to engage our
+     attention. I am not aware of the motive that induced him--whether any
+     particular views had suggested themselves to his own mind--or whether
+     it was a general desire of investigating, more thoroughly than his
+     predecessors had done, the laws of a remarkable phenomenon, which it
+     had long been the fashion to neglect. He could hardly have
+     anticipated the kind of result at which he has arrived; at the same
+     time we cannot imagine a course of proceeding better calculated for
+     its detection, even if his mind had been prepared for it, than that
+     which he has pursued from the very commencement of his career.
+     Assuredly if he entertained such an idea, it was not borrowed from
+     the authorities of the last century, to whom the solar spots were
+     objects of more attention than they have been of late years.
+
+     "'Nulla constanti temporum lege apparent aut evanescunt,' says Keill
+     in 1739.--_Introduct. ad Physic. Astronom._, p. 253.
+
+     "'Il est manifest par ce que nous venons de rapporter qu'il n'y a
+     point de regle certaine de leur formation, ni de leur nombre et de
+     leur figure,' says Cassini II. in 1740.--_Elem d'Astron._, vol. i. p.
+     82.
+
+     "'Il semble qu'elles ne suivent aucune loi dans leur apparitions,'
+     says Le Monnier in 1746.--_Instit. Astron._, p. 83.
+
+     "'Solar spots observe no regularity in their shape, magnitude,
+     number, or in the time of their appearance or continuance,' says Long
+     in 1764.--_Astron._, vol. ii. p. 472.
+
+     "'Les apparitions des taches du soleil n'ont rien de regulier,' says
+     Lalande in 1771.--_Astron._, vol. iii. Sec. 3131, 2nd edit.
+
+     "And Delambre's opinion may be inferred from a well-known passage in
+     the third volume of his 'Astronomy' (p. 20), published in 1814, where
+     treating of the solar spots he says, 'Il est vrai qu'elles sont plus
+     curieuses que vraiment utiles.'"[4]
+
+It will thus be evident that Herr Schwabe had the courage to enter upon a
+line of investigation which others had practically condemned as likely to
+lead nowhere, and that his discovery was quite contrary to expectation. It
+is a lesson to us that not even the most unlikely line of work is to be
+despised; for the outcome of Schwabe's work was the first step in the
+whole series of discoveries which have gradually built up the modern
+science of Solar Physics, which occupies so deservedly large a part of the
+energies of, for instance, the great observatory attached to the
+University of Chicago.
+
+[Sidenote: Schwabe's announcement.]
+
+It has been our practice to recall the actual words in which the
+discoverer himself stated his discovery, and I will give the original
+modest announcement of Schwabe, though for convenience of those who do not
+read German I will attempt a rough translation. He had communicated year
+by year the results of his daily counting of the solar spots to the
+_Astronomische Nachrichten_, and after he had given ten years' results in
+this way he collected them together, but he made no remark on the curious
+sequence which they undoubtedly showed at that time. Waiting patiently six
+years for further material, in 1843 he ventured to make his definite
+announcement as follows:--"From my earlier observations, which I have
+communicated annually to this journal, there was manifest already a
+certain periodicity of sun-spots; and the probability of this being really
+the case is confirmed by this year's results. Although I gave in volume 15
+the total numbers of groups for the years 1826-1837, nevertheless I will
+repeat here a complete series of all my observations of sun-spots, giving
+not only the number of groups, but also the number of days of observation,
+and further the days when the sun was free from spots. The number of
+groups alone will not in itself give sufficient accuracy for determination
+of a period, since I have convinced myself that when there are a large
+number of sun-spots the number will be reckoned somewhat too small, and
+when few sun-spots, the number somewhat too large; in the first case
+several groups are often counted together in one, and in the second it is
+easy to divide a group made up of two component parts into two separate
+groups. This must be my excuse for repeating the early catalogue, as
+follows:--
+
+  +---------------------------------------------+
+  | Year.| Number of |  Days free |   Days of   |
+  |      |  Groups.  | from Spots.| Observation.|
+  |---------------------------------------------|
+  | 1826 |    118    |     22     |     277     |
+  | 1827 |    161    |      2     |     273     |
+  | 1828 |    225    |      0     |     282     |
+  | 1829 |    199    |      0     |     244     |
+  | 1830 |    190    |      1     |     217     |
+  |---------------------------------------------|
+  | 1831 |    149    |      3     |     239     |
+  | 1832 |     84    |     49     |     270     |
+  | 1833 |     33    |    139     |     267     |
+  | 1834 |     51    |    120     |     273     |
+  | 1835 |    173    |     18     |     244     |
+  |---------------------------------------------|
+  | 1836 |    272    |      0     |     200     |
+  | 1837 |    333    |      0     |     168     |
+  | 1838 |    282    |      0     |     202     |
+  | 1839 |    162    |      0     |     205     |
+  | 1840 |    152    |      3     |     263     |
+  |---------------------------------------------|
+  | 1841 |    102    |     15     |     283     |
+  | 1842 |     68    |     64     |     307     |
+  | 1843 |     34    |    149     |     324     |
+  |(1844)|    (52)   |  (111)     |    (320)    |
+  +---------------------------------------------+
+
+"If we now compare together the number of groups, and the days free from
+spots, we find that the sun-spots have a period of about ten years, and
+that for about five years they are so numerous that during this period few
+days, if any, are free from spots. The sequel must show whether this
+period is constant, whether the minimum activity of the sun in producing
+spots lasts for one or two years, and whether this activity increases more
+quickly than it decreases."
+
+[Illustration:
+
+  FEB. 18, 1894.   FEB. 19, 1894.
+
+  X.--PHOTOGRAPHS OF THE SUN TAKEN AT THE ROYAL OBSERVATORY, GREENWICH,
+  SHEWING SUNSPOTS.]
+
+[Sidenote: Attracted little attention, until eight years later.]
+
+This brief announcement is all that the discoverer says upon the subject;
+and it is perhaps not remarkable that it attracted very little attention,
+especially when we remember that it related to a matter which the
+astronomical world had agreed to put aside as unprofitable and not worth
+attention. Next year, in giving his usual paper on the spots for 1844 he
+recurs to the subject in the following sentence: "The periodicity of spots
+of about ten years which was indicated in my summary published last year,
+is confirmed by this year's observations." I have added in brackets to the
+table above reproduced the numbers for 1844 subsequently given, and it
+will be seen how nearly they might have been predicted.
+
+[Sidenote: Other phenomena sympathetic and others not.]
+
+Still the subject attracted little attention. Turning over the leaves of
+the journal at random, I came across the annual report of the Astronomer
+Royal of England, printed at length. But in it there is no reference to
+this discovery, which opened up a line of work now strongly represented in
+the annual programme of the Royal Observatory at Greenwich. Mr. Johnson
+remarks that the only person who had taken it up was Julius Schmidt, who
+then resided near Hamburg. But Schwabe went on patiently accumulating
+facts; and in 1851 the great Von Humboldt in the third volume of his
+_Cosmos_, drew attention to the discovery, which was accordingly for the
+first time brought into general notice. It will be seen that there are not
+many facts of general interest relating to the actual discovery beyond the
+courage with which the work was commenced in a totally unpromising
+direction, and the scant attention it received after being made for us. We
+may admit that interest centres chiefly in the tremendous consequences
+which flowed from it. We now recognise that many other phenomena are bound
+up with this waxing and waning of the solar spots. We might be prepared
+for a sympathy in phenomena obviously connected with the sun itself; but
+it was an unexpected and startling discovery that magnetic phenomena on
+the earth had also a sympathetic relation with the changes in sun-spots,
+and it is perhaps not surprising that when once this connection of solar
+and terrestrial phenomena was realised, various attempts have been made to
+extend it into regions where we cannot as yet allow that it has earned a
+legitimate right of entry. We have heard of the weather and of Indian
+famines occurring in cycles identical with the sun-spot cycle; and it is
+obvious how tremendously important it would be for us if this were found
+to be actually the case. For we might in this way predict years of
+possible famine and guard against them; or if we could even partially
+foretell the kind of weather likely to occur some years hence, we might
+take agricultural measures accordingly. The importance of the connection,
+if only it could be established, is no doubt the reason which has misled
+investigators into laying undue stress on evidence which will not bear
+close scrutiny. For the present we must say decidedly that no case has
+been made out for paying serious attention to the influence of sun-spots
+on weather. Nevertheless, putting all this aside, there is quite enough of
+first-rate importance in the sequel to Schwabe's discovery.
+
+[Sidenote: Greenwich sun records.]
+
+[Sidenote: The sun's rotation.]
+
+Let us review the facts in order. Most of us, though we may not have had
+the advantage of seeing an actual sun-spot through a telescope, have seen
+drawings or photographs of spots. There is a famous drawing made by James
+Nasmyth (of steam-hammer fame), in July, 1864, which is of particular
+interest, because at that time Nasmyth was convinced--and he convinced
+many others with him--that the solar surface was made up of a
+miscellaneous heap of solid bodies in shape like willow leaves, or grains
+of rice, thrown together almost at random, and the drawing was made by him
+to illustrate this idea. Comparing a modern photograph with it, we see
+that there is something to be said for Nasmyth's view, which attracted
+much attention at the time and occasioned a somewhat heated controversy.
+But since the invention of the spectroscope it has become quite obsolete;
+it probably does not correspond in any way to the real facts. But instead
+of looking at pictures which have been enlarged to show the detailed
+structure in and near a spot, we will look at a series of pictures of
+the whole sun taken on successive days at Greenwich in which the spots are
+necessarily much smaller, but which show the behaviour of the spots from
+day to day. (See Plates X. and XI.) From the date at the foot of each it
+will be seen that they gradually cross the disc of the sun (a fact first
+discovered by Galileo in 1610), showing that the sun rotates on an axis
+once in about every twenty-five days. There are many interesting facts
+connected with this rotation; especially that the sun does not rotate as a
+solid body, the parts near the (Sun's) Equator flowing quicker than those
+nearer the Poles; but for the present we cannot stop to dwell upon them.
+What interests us particularly is the history, not from day to day, but
+from year to year, as Schwabe has already given it for a series of years.
+
+[Illustration:
+
+  FEB. 20, 1894.   FEB. 21, 1894.
+
+  XI.--PHOTOGRAPHS OF THE SUN TAKEN AT THE ROYAL OBSERVATORY, GREENWICH,
+  SHEWING SUNSPOTS]
+
+[Sidenote: Wolf's numbers.]
+
+[Sidenote: Greenwich areas.]
+
+[Sidenote: Magnetic fluctuations.]
+
+When it became generally established that this periodicity existed, Rudolf
+Wolf of Zurich collected the facts about sun-spots from the earliest
+possible date, and represented this history by a series of numbers which
+are still called Wolf's Sun-Spot Numbers. You will see from the diagram
+the obvious rise and fall for eleven years,--not ten years, as Schwabe
+thought, but just a little over eleven years. The facts are, however,
+given more completely by the work done at the Royal Observatory at
+Greenwich. It is part of the regular daily work of that Observatory to
+photograph the sun at least twice. Many days are of course cloudy or wet,
+so that photographs cannot be obtained; but there are available
+photographs similarly taken in India or in Mauritius, where the weather is
+more favourable, and from these the gaps are so well filled up that very
+few days, if any, during the whole year are left without some photograph
+of the sun's surface. On these photographs the positions and the areas of
+the spots are carefully measured under a microscope, and the results when
+submitted to certain necessary calculations are published year by year. It
+is clearly a more accurate estimate of the spottedness of the sun to take
+the total _area_ of all the spots rather than their mere _number_, for in
+the latter case a large spot and a small one count equally. Hence the
+Greenwich records will perhaps give us an even better idea of the
+periodicity than Wolf's numbers. Now, at the same observatory magnetic
+observations are also made continuously. If a magnet be suspended freely
+we are accustomed to say that it will point to the North Pole; but this is
+only very roughly true. In the first place, it is probably well known to
+you that there is a considerable deviation from due north owing to the
+fact that the magnetic North Pole is not the same as the geographical
+North Pole; but this for the present need not concern us. What does
+concern us is, that if the needle is hung up and left long enough to come
+to rest, it does not then remain steadily at rest, but executes slow and
+small oscillations backwards and forwards, up and down, throughout the
+day; repeating nearly the same oscillations on the following day, but at
+the same time gradually changing its behaviour so as to oscillate
+differently in summer and winter. These changes are very small, and would
+pass unnoticed by the naked eye; but when carefully watched through a
+telescope, or better still, when photographed by some apparatus which will
+at the same time magnify them, they can be rendered easily visible. When
+the history of these changes is traced it is seen at once that there is a
+manifest connection with the cycle of sun-spot changes; for instance, if
+we measure the range of swing backwards and forwards during the day and
+take the average for all the days in the year, and then compare this with
+the average number of sun-spots, we shall see that the averages rise and
+fall together. Similarly we may take the up and down swing, find the
+average amount of it throughout the year, and again we shall find that
+this corresponds very closely with the average number of sun-spots.
+
+[Illustration: PLATE XII. NUMBER OF SUNSPOTS (Wolf) Compared with DAILY
+RANGE of MAGNETIC DECLINATION & DAILY RANGE of MAGNETIC HORZL. FORCE
+(as observed at Greenwich.)]
+
+[Sidenote: Daily curves.]
+
+[Sidenote: Difference between summer and winter, and between sun-spot
+maximum and minimum.]
+
+[Sidenote: Cause unknown.]
+
+But perhaps the most striking way to exhibit the sympathy is to combine
+different variations of the needle into one picture. And first we must
+remark that there is another important variation of the earth's magnetic
+action which we have not yet considered. We have mentioned the swing of
+the needle to and fro, and the swing up and down, and these correspond to
+changes in the _direction_ of the force of attraction on the needle. But
+there may be also changes in _intensity_ of this action; the pull may be a
+little stronger or a little weaker than before, and these variations are
+not represented by any actual movement of the needle, though they can be
+measured by proper experiments. We can, however, imagine them represented
+by a movement of the end of the needle if we suppose it made of elastic
+material, so that it would lengthen when the force was greater and
+contract slightly when the force was less. If a pencil were attached to
+the end of such an elastic needle so as to make a mark on a sheet of
+paper, and if for a moment we exclude the up and down movements, the
+pencil would describe during the day a curve on the paper, as the end of
+the needle swung backwards and forwards with the change in direction, and
+moved across the direction of swing with the change in intensity. Now when
+curves of this kind are described for a day in each month of the year,
+there is a striking difference between the forms of them. During the
+summer months they are, generally speaking, comparatively large and open,
+and during the winter months they are small and close. This change in form
+is seen by a glance at Plate XIII., which gives the curves throughout the
+whole of one year. Let us now, instead of forming a curve of this kind for
+each month, form a single average curve for the whole year; and let us
+further do this for a series of years. (Plate XIV.) We see that the curves
+change from year to year in a manner very similar to that in which they
+change from month to month in any particular year, and the law of change
+is such that in years when there are many sun-spots we get a large open
+curve similar to those found in the summer, while for years when there are
+few sun-spots we get small close curves very like those in the winter.
+Hence we have two definite conclusions suggested: firstly, that the
+changes of force are sympathetic with the changes in the sun-spots; and
+secondly, that times of maximum sun-spots correspond to summer, and times
+of minimum to winter. And here I must admit that this is about as far as
+we have got at present in the investigation of this relationship. _Why_
+the needle behaves in this way we have as yet only the very vaguest ideas;
+suggestions of different kinds have certainly been put forward, but none
+of them as yet can be said to have much evidence in favour of its being
+the true one. For our present purpose, however, it is sufficient to note
+that there is this very real connection, and that consequently Schwabe's
+sun-spot period may have a very real importance with regard to changes in
+our earth itself.
+
+[Illustration:
+
+  GREENWICH MAGNETIC CURVES
+  1859-60
+  PLATE XIII.
+  GREENWICH MAGNETIC CURVES FOR APRIL 1841-1860]
+
+[Sidenote: Illustration of spurious connection.]
+
+But I may perhaps repeat the word of caution already uttered against
+extending without sufficient evidence this notion of the influence of
+sun-spots to other phenomena, such as weather. A simple illustration will
+perhaps serve better than a long argument to show both the way in which
+mistakes have been made and the way in which they can be seen to be
+mistakes. There is at the Royal Observatory at Greenwich an instrument for
+noting the direction of the wind, the essential part being an ordinary
+wind-vane, the movements of which are automatically recorded on a sheet of
+paper. As the wind shifts from north to east the pencil moves in one
+direction, and when it shifts back again towards the north the pencil
+moves in the reverse way. But sometimes the wind shifts continuously from
+north to east, south, west, and back to north again, the vane making a
+complete revolution; and this causes the pencil to move continuously in
+one direction, until when the vane has come to north again, the pencil is
+far away from the convenient place of record; on such occasions it is
+often necessary to replace it by hand. Then again, the vane may turn in
+the opposite direction, sending the pencil inconveniently to the other
+side of the record. During the year it is easy to count the number of
+complete changes of wind in either direction, and subtracting one number
+from the other, we get the excess of complete revolutions of the vane in
+one direction over that in the other. Now if these rather arbitrary
+numbers are set down year by year, or plotted in the shape of a diagram,
+we get a curve which may be compared with the sun-spot curve, and during a
+period of no less than sixteen years--from 1858 to 1874--there was a
+remarkable similarity between the two diagrams. From this evidence _alone_
+it might fairly be inferred that the sun-spots had some curious effect
+upon the weather at Greenwich, traceable in this extraordinary way in the
+changes of the wind. But the particular way in which these changes are
+recorded is so arbitrary that we should naturally feel surprise if there
+was a real connection between the two phenomena; and fortunately there
+were other records preceding these years and following them which enabled
+us to test the connection further, and it was found, as we might naturally
+expect, that it was not confirmed. On looking at diagrams (Plate XV.) for
+the periods before and after, no similarity can be traced between the
+sun-spot curve and the wind-vane curve, and we infer that the similarity
+during the period first mentioned was entirely accidental. This shows that
+we must be cautious in accepting, from a limited amount of evidence, a
+connection between two phenomena as real and established; for it may be
+purely fortuitous. We may particularly remark that it is desirable to have
+repetitions through several complete periods instead of one alone. It is
+possible to reduce to mathematical laws the rules for caution in this
+matter; and much useful work has already been done in this direction by
+Professor Schuster of Manchester and others, though as yet too little
+attention has been paid to their rules by investigators naturally eager to
+discover some hitherto unthought-of connection between phenomena.
+
+[Sidenote: Faculae follow spots and the chromosphere.]
+
+With this example of the need for caution, we may return to phenomena of
+which we can certainly say that they vary sympathetically with the
+sun-spots. Roughly speaking, the whole history of the sun seems to be
+bound up with them. Besides these dark patches which we call spots (which,
+by the way, are not really dark but only less bright than the surrounding
+part of the disc), there are patches brighter than the rest which have
+been called faculae. With ordinary telescopes, either visual or
+photographic, these can generally only be detected near the edge of the
+sun's disc; but even with this limitation it can easily be established
+that the faculae vary in number and size from year to year much in the same
+way as the spots, and this conclusion is amply confirmed by the beautiful
+method of observing the faculae with the new instrument designed by
+Professor Hale of the Yerkes Observatory. With this instrument, called a
+spectroheliograph, it is possible to photograph the faculae in all parts of
+the sun's disc, and thus to obtain a much more complete history of them,
+and there is no doubt whatever of their variation sympathetically with the
+spots. Nor is there any doubt about similar variations in other parts of
+the sun which we cannot see _at all_ with ordinary telescopes, except on
+the occasions when the sun is totally eclipsed. Roughly speaking, these
+outlying portions of the sun consist of two kinds, the chromosphere and
+the corona, the former looking like an irregular close coating of the
+ordinary sun, and the latter like a pearly halo of light extending to
+many diameters of the sun's disc, but not with any very regular form.
+
+[Illustration: PLATE XV. SMOOTHED SUNSPOT CURVE (WOLF) COMPARED WITH THE
+NUMBER OF TURNS MADE IN EACH YEAR BY THE OSLER ANEMOMETER VANE OF THE
+ROYAL OBSERVATORY, GREENWICH (THE EXCESS OF THE DIRECT TURNS (D) OVER THE
+RETROGRADE TURNS (R) OR _VICE VERSA_.)
+
+THE UPPER CURVE IS IN EACH CASE THE SUNSPOT CURVE, THE LOWER THE VANE
+CURVE. THE BREAK IN 1882 IN THE VANE CURVE IS DUE TO THE OMISSION OF
+EVIDENTLY ACCIDENTAL TURNS FROM THAT DATE.]
+
+The chromosphere, from which shoot out the prominences or "red flames,"
+can now be observed without an eclipse if we employ the beautiful
+instrument above-mentioned, the spectroheliograph; and Professor Hale has
+succeeded in photographing spots, faculae, and prominences all on the same
+plate. But although many have made the attempt (and Professor Hale,
+perhaps, a more determined attempt than any man living), no one has yet
+succeeded in obtaining any picture or evidence of the existence of the
+corona excepting on the occasion of a total solar eclipse.
+
+[Sidenote: Eclipses of sun.]
+
+[Sidenote: Total eclipses rare.]
+
+Now these occasions are very rare. There are two or three eclipses of the
+sun every year, but they are generally of the kind known as partial; when
+the moon does indeed come between us and the sun to some extent, but only
+cuts off a portion of his light--a clean-cut black disc is seen to
+encroach more or less on the surface of the sun. Most of us have had an
+opportunity of seeing a partial eclipse, probably more than once; but few
+have seen a total eclipse. For this the moon must come with great
+exactness centrally between us and the sun; and the spot where this
+condition is fulfilled completely only covers a few hundred miles of the
+earth's surface at one moment. As the earth turns round, and as the moon
+revolves in its orbit, this patch from which the sun is totally eclipsed
+travels over the earth's surface, marking out a track some thousands of
+miles in length possibly, but still not more than 200 miles wide; and in
+order to see the sun totally eclipsed even on the rare occasions when it
+is possible at all (for, as already remarked, in the majority of cases the
+eclipse is only partial), we must occupy some station in this narrow belt
+or track, which often tantalisingly passes over either the ocean or some
+regions not easily accessible to civilised man. Moreover, if we travel to
+such favoured spots the whole time during which the sun is totally
+eclipsed cannot exceed a few minutes, and hence observations are made
+under rather hurried and trying conditions. In these modern days of
+photography it is easier to take advantage of these precious moments than
+it used to be when there was only the eye and memory of an excited
+observer to rely upon. It is perhaps not surprising that some of the
+evidence collected on these earlier occasions was conflicting; but
+nowadays the observers, generally speaking, direct their energies in the
+first place to mounting accurately in position photographic apparatus of
+different kinds, each item of it specially designed to settle some
+particular problem in the most feasible way; secondly, to rehearsing very
+carefully the exact programme of exposures necessary during the critical
+few minutes; and finally, to securing these photographs with as few
+mistakes as possible when the precious moments actually arrive. Even then
+the whole of their efforts are quite likely to be rendered unavailing by a
+passing cloud; and bitter is the disappointment when, after travelling
+thousands of miles, and spending months in preparation, the whole
+enterprise ends in nothing owing to some caprice of the weather.
+
+[Sidenote: Corona follows spots.]
+
+Hence it will easily be imagined that our knowledge of the corona, the
+part of the sun which we can still only study on occasions of a total
+solar eclipse, advances but slowly. During the last twenty years there has
+been altogether scarcely half-an-hour available for this research, though
+it may fairly be said that the very best possible use has been made of
+that half-hour. And, what is of importance for our immediate purpose, it
+has gradually been established by comparing the photographs of one eclipse
+with those of another, that the corona itself undergoes distinct changes
+in form in the same period which governs the changes of sun-spots. When
+there are many sun-spots the corona spreads out in all directions from the
+edge of the sun's disc; when there are few sun-spots the corona extends
+very much further in the direction of the sun's equator, so that at
+sun-spot minimum there is an appearance of two huge wings. Although the
+evidence is necessarily collected in a scrappy manner, by this time there
+is sufficient to remove this relationship out of the region of mere
+suspicion, and to give it a well-established place in our knowledge of the
+sun's surroundings.
+
+[Sidenote: Corona may influence magnets.]
+
+Now the corona of the sun may be compared to some rare animal which we
+only see by paying a visit to some distant land, and may consider
+ourselves even then fortunate to get a glimpse of; and it might be thought
+that the habits of such an animal are not likely to be of any great
+importance in our everyday life. But so far from this being the case in
+regard to the corona, it is more than possible that the knowledge of its
+changes may be of vital interest to us. I have already said that, as yet,
+we have no satisfactory account of the reason why changes in sun-spots
+seem to influence changes in our magnets on the earth; but one of the
+theories put forward in explanation, and one by no means the least
+plausible, is that this influence may come, not from the sun-spots
+themselves, but from some other solar phenomenon which varies in sympathy
+with them; and in particular that it may come from the corona. These wings
+which reach out at sun-spot minimum can be seen to extend a considerable
+distance, and there is no reason to suppose that they actually cease at
+the point where they become too faint for us to detect them further; they
+may extend quite as far as the earth itself and even beyond; and they may
+be of such a nature as to influence our magnets. As the earth revolves
+round the sun it may sometime plunge into them, to emerge later and pass
+above or below them; as again the wings spread themselves at sun-spot
+minimum and seem to shrink at maximum, so our magnets may respond by
+sympathetic though very small vibrations. Hence it is quite possible that
+the corona is directly influencing the magnetic changes on the earth.
+
+[Sidenote: Possible importance of corona.]
+
+But it may be urged that these changes are so slight as to be merely of
+scientific interest. That may be true to-day, but who will be bold enough
+to say that it will be true to-morrow? If we are thinking of practical
+utility alone, we may remember that two great forces of Nature which we
+have chained into the service of man, steam and electricity, put forth
+originally the most feeble manifestations, which might readily have been
+despised as valueless; but by careful attention to proper conditions
+results of overwhelming practical importance have been obtained from these
+forces, which might have been, and for many centuries were, neglected as
+too trivial to be worth attention. Recently the world has been startled by
+the discovery of new elements, such as radium, whose very existence was
+only detected by a triumph of scientific acuteness in investigation, and
+yet which promise to yield influences on our lives which may overwhelm in
+importance all that has gone before. And similarly it may be that these
+magnetic changes, when properly interpreted or developed, may become of an
+importance in the future out of all proportion to the attention which they
+have hitherto attracted. Hence, although perhaps sufficient has already
+been established to show the immense consequences which flow from
+Schwabe's remarkable discovery of the periodicity in solar spots, we may
+be as yet only on the threshold of its real value.
+
+From what little causes great events spring! How little can Schwabe have
+realised, when he began to point his modest little telescope at the sun,
+and to count the number of spots--the despised spots which he had been
+assured were of no interest and exhibited no laws, and were generally
+unprofitable--that he was taking the first step in the invention of the
+great science of Solar Physics!--a science which is, I am glad to say,
+occupying at the present moment so much of the attention, not only of the
+great Yerkes Observatory, but of many other observatories scattered over
+the globe.
+
+
+
+
+CHAPTER VI
+
+THE VARIATION OF LATITUDE
+
+
+If we should desire to classify discoveries in order of merit, we must
+undoubtedly give a high place to those which are made under direct
+discouragements. In the last chapter we saw that Schwabe entered upon his
+work under conditions of this kind, it being the opinion of experienced
+astronomers who had looked at the facts that there was nothing of interest
+to be got by watching sun-spots. In the present chapter I propose to deal
+with a discovery made in the very teeth of the unanimous opinion of the
+astronomical world by an American amateur, Mr. S. C. Chandler of Cambridge
+(Massachusetts). It is my purpose to allow him to himself explain the
+steps of this discovery by giving extracts from the magnificent series of
+papers which he contributed to the _Astronomical Journal_ on the subject
+in the years 1891-94, but it may help in the understanding of these
+extracts if I give a brief summary of the facts. And I will first explain
+what is meant by the "Variation of Latitude."
+
+[Sidenote: Latitude.]
+
+[Sidenote: Precession.]
+
+We are all familiar with the existence of a certain star in the heavens
+called the Pole Star, and we know that at any particular place it is seen
+constantly in the north at a definite height above the horizon, which is
+the latitude of the place. When watched carefully with a telescope it is
+found to be not absolutely stationary, but to describe a small circle in
+the heavens day by day, or rather night by night. These simple facts are
+bound up with the phenomenon of the earth's rotation in this way: the axis
+about which it is rotating points to the centre of that little circle, and
+any change in the position of the axis can therefore be determined by
+observing these motions of the Pole Star. Such changes may be of two
+kinds: firstly, we might find that the size of the circle increased or
+diminished, and this would mean that the earth's axis was pointing farther
+away from the Pole Star or nearer to it--pointing, that is to say, in a
+different direction in space. This actually happens (as has been known for
+some thousands of years) owing to the phenomenon called "precession"; the
+circle described by our Pole Star is at present getting a little smaller,
+but it will ultimately increase in size, and after thousands of years
+become so large that the Pole Star will entirely lose its character as a
+steady guide to the North.
+
+[Sidenote: Change of latitude.]
+
+[Sidenote: Twenty years ago disbelieved.]
+
+Secondly (and this is what more immediately concerns us), the centre of
+the circle may alter its position and be no longer at the same height
+above the horizon of any given place. This would mean that the earth's
+axis was shifting _in the earth itself_--that the North Pole which our
+explorers go to seek is not remaining in the same place. That it does not
+change appreciably in position we know from familiar experience; our
+climates, for instance, would suffer considerably if there were any large
+changes. But astronomers are concerned with minute changes which would not
+have any appreciable effect on climate, and the question has long been
+before them whether, putting aside large movements, there were any minute
+variations in position of the North Pole. Twenty years ago the answer to
+this question would have been given decidedly in the negative; it was
+considered as certain that the North Pole did not move at all within the
+limits of our most refined astronomical observations. Accepted theory
+seemed to indicate that any movements must in any case recur after a
+period of ten months, and careful discussion of the observations showed
+that there was no oscillation in such a period. Now we know that the
+theory itself was wrong, or rather was founded upon a mistaken assumption;
+and that the facts when properly examined show clearly a distinct movement
+of the North Pole, not a very large one, for all its movements take place
+within the area occupied by a moderate-sized room, but still a movement
+easily measurable by astronomical observations, and Mr. Chandler was the
+first to point out the law of these movements, and very possibly the first
+to suspect them.
+
+[Sidenote: Chandler's papers.]
+
+With these few words of explanation I will let Mr. Chandler tell his own
+story. His first paper appeared in the _Astronomical Journal_ in November
+1891, and is courageously headed, "On the Variation of Latitude"--I say
+courageously, because at that time it was believed that the latitude did
+_not_ vary, and Mr. Chandler himself was only in possession of a small
+portion of the facts. They unravelled themselves as he went forward; but
+he felt that he had firm hold of the end of the thread, and he faced the
+world confidently in that belief. He begins thus:--
+
+     [Sidenote: First signs of change.]
+
+     "In the determination of the latitude of Cambridge[5] with the
+     Almucantar, about six years and a half ago, it was shown that the
+     observed values, arranged according to nights of observation,
+     exhibited a decided and curious progression throughout the series,
+     the earlier values being small, the later ones large, and the range
+     from November 1884 to April 1885 being about four-tenths of a second.
+     There was no known or imaginable instrumental or personal cause for
+     this phenomenon, yet the only alternative seemed to be an inference
+     that the latitude had actually changed. This seemed at the time too
+     bold an inference to place upon record, and I therefore left the
+     results to speak for themselves. The subsequent continuation of the
+     series of observations to the end of June 1885 gave a maximum about
+     May 1, while the discussion of the previous observations from May to
+     November 1884 gave a minimum about September 1, indicating a range of
+     0".7 within a half-period of about seven months."
+
+Mr. Chandler then gives some figures in support of these statements,
+presenting them with the clearness which is so well marked a feature of
+the whole series of papers, and concludes this introductory paper as
+follows:--
+
+     "It thus appears that the apparent change in the latitude of
+     Cambridge is verified by this discussion of more abundant material.
+     The presumption that it is real, on this determination alone, would
+     justify further inquiry.
+
+     [Sidenote: Confirmed in Europe.]
+
+     "Curiously enough Dr. Kuestner, in his determination of the
+     aberration from a series of observations coincident in time with
+     those of the Almucantar, came upon similar anomalies, and his
+     results, published in 1888, furnish a counterpart to those which I
+     had pointed out in 1885. The verification afforded by the recent
+     parallel determinations at Berlin, Prague, Potsdam, and Pulkowa,
+     which show a most surprising and satisfactory accordance, as to the
+     character of the change, in range and periodicity, with the
+     Almucantar results, has led me to make further investigations on the
+     subject. They seem to establish the nature of the law of those
+     changes, and I will proceed to present them in due order."
+
+The second paper appeared on November 23, and opens with the following
+brief statement of his general results at that time:--
+
+     [Sidenote: 427 days' period.]
+
+     "Before entering upon the details of the investigations spoken of in
+     the preceding number, it is convenient to say that the general result
+     of a preliminary discussion is to show a revolution of the earth's
+     pole in a period of 427 days, from west to east, with a radius of
+     thirty feet, measured at the earth's surface. Assuming provisionally,
+     for the purpose of statement, that this is a motion of the north pole
+     of the principal axis of inertia about that of the axis of rotation,
+     the direction of the former from the latter lay towards the Greenwich
+     meridian about the beginning of the year 1890. This, with the period
+     of 427 days, will serve to fix approximately the relative positions
+     of these axes at any other time, for any given meridian. It is not
+     possible at this stage of the investigation to be more precise, as
+     there are facts which appear to show that the rotation is not a
+     perfectly uniform one, but is subject to secular change, and perhaps
+     irregularities within brief spaces of time."
+
+[Sidenote: Contrary to received views.]
+
+It is almost impossible, now that we have become familiar with the ideas
+conveyed in this paragraph, to understand, or even fully to remember, the
+impression produced by them at the time; the sensation caused in some
+quarters, and the ridicule excited in others. They were in flat
+contradiction to all accepted views; and it was believed that these views
+were not only theoretically sound, but had been matured by a thorough
+examination of observational evidence. The only period in which the
+earth's pole could revolve was believed to be ten mouths; and here was Mr.
+Chandler proclaiming, apparently without any idea that he was
+contradicting the laws of dynamics, that it was revolving in fourteen
+months! The radius of its path had been found to be insensible by careful
+discussion of observations, and now he proclaimed a sensible radius oL
+thirty feet. Finally, he had the audacity to announce a _variable_ period,
+to which there was nothing at all corresponding in the mathematical
+possibilities. This was the bitterest pill of all. Even after Professor
+Newcomb had shown us how to swallow the other two, he could not recommend
+any attempt at the third, as we shall presently see; and Mr. Chandler was
+fain ultimately to gild it a little before it could be gulped.
+
+[Sidenote: Pulkowa puzzle solved, also Washington.]
+
+But this is anticipating, and it is our intention to follow patiently the
+evidence adduced in support of the above statements, made with such
+splendid confidence to a totally disbelieving world. Mr. Chandler first
+examines the observations of Dr. Kuestner of Berlin, quoted at the end of
+his last paper, and shows how well they are suited by the existence of a
+variation in the latitude of 427 days; and that this new fact is
+added--when the Cambridge (U.S.A.) latitudes were the smallest those of
+Berlin were the largest, and _vice versa_, as would clearly be the case if
+the phenomenon was due to a motion of the earth's pole; for if it moved
+nearer America it must move further from Europe. He then examines a long
+series of observations made in the years 1864-1873 at Pulkowa, near St.
+Petersburg, and again finds satisfactory confirmation of his law of
+variation. Now it had long been known that there was something curious
+about these observations, but no one could tell what it was. The key
+offered by Mr. Chandler fitted the lock exactly, and the anomalies which
+had been a puzzle were removed. This was in itself a great triumph; but
+there was another to come, which we may let Mr. Chandler describe in his
+own words:--
+
+     "In 1862 Professor Hubbard began a series of observations of [a]
+     Lyrae at the Washington Observatory with the prime vertical transit
+     instrument, for the purpose of determining the constants of
+     aberration and nutation and the parallax of the star. The methods of
+     observation and reduction were conformed to those used with such
+     success by W. Struve. After Hubbard's death the series was continued
+     by Professors Newcomb, Hall, and Harkness until the beginning of
+     1867. Professor Hall describes these observations as the most
+     accurate determinations of declination ever made at the Naval
+     Observatory. The probable error of a declination from a single
+     transit was +-0".141, and judging from the accidental errors, the
+     series ought to give trustworthy results. Upon reducing them,
+     however, it was found that some abnormal source of error existed,
+     which resulted in anomalous values of the aberration-constant in the
+     different years, and a negative parallax in all. A careful
+     verification of the processes of reduction failed to discover the
+     cause of the trouble, and Professor Hall says that the results must
+     stand as printed, and that probably some annual disturbance in the
+     observations or the instrument occurred, which will never be
+     explained, and which renders all deductions from them uncertain. The
+     trouble could not be connected with personal equation, the anomalies
+     remaining when the observations of the four observers who took part
+     were separately treated. Nor, as Professor Hall points out, will the
+     theoretical ten-month period in the latitude furnish the explanation.
+
+     "It is manifest, however, that if the 427-day period exists, its
+     effect ought to appear distinctly in declination-measurements of such
+     high degree of excellence as these presumably were, and, as I hope
+     satisfactorily to show, actually are. When this variation is taken
+     into account the observations will unquestionably vindicate the high
+     expectations entertained with regard to them by the accomplished and
+     skilful astronomers who designed and carried them out."
+
+[Sidenote: Direction of revolution of Pole.]
+
+[Sidenote: Example of results.]
+
+From this general account I am excluding technical details and figures,
+and unfortunately a great deal is thereby lost. We lose the sense of
+conviction which the long rows of accordant figures force upon us, and we
+lose the opportunities of admiring both the astonishing amount of work
+done and the beautiful way in which the material is handled by a master.
+But I am tempted to give one very small illustration of the numerical
+results from near the end of the paper. After discussing the Washington
+results, and amply fulfilling the promise made in the preceding extract,
+Mr. Chandler compares them with the Pulkowa results, and shows that the
+Earth's Pole must be revolving from west to east, and not from east to
+west. And then he writes down a simple formula representing this motion,
+and compares his formula with the observations. He gives the results in
+seconds of arc, but for the benefit of those not familiar with
+astronomical measurements we may readily convert these into feet; and in
+the following tables are shown the distances of the Earth's Pole _in feet_
+from its average position,[6] as observed at Washington and at Pulkowa,
+and the same distances calculated according to the formula which Mr.
+Chandler was able to write down at this early stage. The signs + and - of
+course indicate opposite directions of displacement:--
+
+  WASHINGTON.
+
+  _Deviation of Pole._
+
+  +-------------------------------------+
+  |     Date.     | Observed.| Formula. |
+  |-------------------------------------|
+  | 1864, Dec. 28 | -28 feet | -23 feet |
+  | 1865, Mar. 19 | - 1  "   | -12  "   |
+  |  "    June  1 | +15  "   | +12  "   |
+  |  "    Aug. 11 | +22  "   | +23  "   |
+  |  "    Oct.  9 | +11  "   | +15  "   |
+  |  "    Dec. 13 | -17  "   | - 6  "   |
+  +-------------------------------------+
+
+
+  PULKOWA.
+
+  _Deviation of Pole._
+
+  +-------------------------------------+
+  |     Date.     | Observed.| Formula. |
+  |-------------------------------------|
+  | 1865, July 25 | -18 feet | -12 feet |
+  |   "   Sept. 9 | + 3  "   | + 3  "   |
+  |   "   Nov. 22 | +26  "   | +22  "   |
+  | 1866, Feb. 22 | +18  "   | +13  "   |
+  |   "   June  4 | -11  "   | -18  "   |
+  |   "   July 17 | -16  "   | -23  "   |
+  +-------------------------------------+
+
+Of course the figures are not exact in every case, but they are never many
+feet wrong; and it may well be imagined that it is a difficult thing to
+deduce, even from the most refined observations, the position of the
+earth's pole to within a foot. The difficulty is exactly the same as that
+of measuring the length of an object 300 miles away to within an inch!
+
+Mr. Chandler winds up his second paper thus:--
+
+     "We thus find that the comparison of the simultaneous series at
+     Pulkowa and Washington, 1863-1867, leads to the same conclusion as
+     that already drawn from the simultaneous series at Berlin and
+     Cambridge, 1884-1885. The direction of the polar motion may therefore
+     be looked upon as established with a large degree of probability.
+
+     "In the next paper I will present the results derived from PETERS,
+     STRUVE, BRADLEY, and various other series of observations, after
+     which the results of all will be brought to bear upon the
+     determination of the best numerical values of the constants
+     involved."
+
+[Sidenote: Bradley's observations.]
+
+[Sidenote: Latitude varied in twelve months then.]
+
+The results were not, however, presented in this order. In the next paper,
+which appeared on December 23, 1891, Mr. Chandler begins, with the work of
+Bradley, the very series of observations at Kew and Wansted which led to
+the discoveries of aberration and nutation, and which we considered in the
+third chapter. He first shows that, notwithstanding the obvious accuracy
+of the observations, there is some unexplained discordance. The very
+constant of aberration which Bradley discovered from them differs by
+half-a-second of arc from our best modern determinations. Attempts have
+been made to ascribe the discordance to changes in the instrument, but Mr.
+Chandler shows that such changes, setting aside the fact that Bradley
+would almost certainly have discovered them, will not fit in with the
+facts. The facts, when analysed with the skill to which we have become
+accustomed, are that there is a periodic swing in the results _with a
+period of about a year_, and not fourteen months, as before, "a result so
+curious," as he admits, that "if we found no further support, it might
+lead us to distrust the above reasoning, and throw us back to the
+possibility that, after all, BRADLEY'S observations may have been vitiated
+by some kind of annual instrumental error. But it will abundantly appear,
+when I have had the opportunity to print the deductions from all the other
+series of observations down to the present time, that the inference of an
+increase in the period of polar revolution is firmly established by their
+concurrent testimony." We shall presently return to this curious result,
+which might well have dismayed a less determined researcher than Mr.
+Chandler, but which only led him on to renewed exertions.
+
+The results obtained from Bradley's observations may be put in the form
+of a diagram thus:--
+
+[Illustration: FIG. 7.]
+
+It will be seen that the maxima and minima fall in the spring and autumn,
+and this fact alone seemed to show that the effect could not be due to
+temperature, for we should expect the greatest effect in that case in
+winter and summer. It could not be due to the parallax of the stars for
+which Bradley began his search, for stars in different quarters of the
+heavens would then be differently affected, and this was not the case.
+"There remains," concluded Mr. Chandler after full discussion, "the only
+natural conclusion of an actual displacement of the zenith, in other
+words, a change of latitude." And he concludes this paper with the
+following fine passage:--
+
+     "So far, then, as the results of this incomparable series of
+     observations at Kew and Wansted, considered by themselves alone, can
+     now be stated, the period of the polar rotation at that epoch appears
+     to have been probably somewhat over a year, and certainly shorter by
+     about two months than it is at the present time. The range of the
+     variation was apparently in the neighbourhood of a second of arc, or
+     considerably larger than that shown by the best modern observations.
+
+     [Sidenote: Bradley's greatness.]
+
+     "Before taking leave of these observations for the present I cannot
+     forbear to speak of the profound impression which a study of them
+     leaves upon the mind, and the satisfaction which all astronomers must
+     feel in recognising that, besides its first fruits of the phenomena
+     of aberration and nutation, we now owe also our first knowledge of
+     the polar motion to this same immortal work of Bradley. Its
+     excellence, highly appreciated as it has been, has still been
+     hitherto obscured by the presence of this unsuspected phenomenon.
+     When divested of its effects, the wonderful accuracy of this work
+     must appear in a finer light, and our admiration must be raised to
+     higher pitch. Going back to it after one hundred and sixty years
+     seems indeed like advancing into an era of practical astronomy more
+     refined than that from which we pass. And this leads to a suggestion
+     worthy of serious practical consideration--whether we can do better
+     in the future study of the polar rotation, than again to avail
+     ourselves of Bradley's method, without endangering its elegant
+     simplicity and effectiveness by attempts at improvement, other than
+     supplying certain means of instrumental control which would without
+     doubt commend themselves to his sagacious mind.
+
+     [Sidenote: Other puzzles explained.]
+
+     "In the next article Bradley's later observations at Greenwich, the
+     results of which are not so distinct, will be discussed; and also
+     those of Brinkley at Dublin, 1808-13 and 1818-22. This will bring
+     again to the surface one of the most interesting episodes in
+     astronomical history, the spirited and almost acrimonious dispute
+     between Brinkley and Pond with regard to stellar parallaxes. I hope
+     to show that the hitherto unsolved enigma of Brinkley's singular
+     results finds its easy solution in the fact of the polar motion. The
+     period of his epoch appears to have been about a year, and its range
+     more than a second. Afterwards will follow various discussions
+     already more or less advanced towards completion. These include
+     Bessel's observations at Koenigsberg, 1820-24, with the Reichenbach
+     circle, and in 1842-44 with the Repsold circle; the latitudes derived
+     from the polar-point determinations of Struve and Maedler with the
+     Dorpat circle, 1822-38; Struve's observations for the determination
+     of the aberration; Peters' observations of _Polaris_, 1841-43, with
+     the vertical-circle; the results obtained from the reflex zenith-tube
+     at Greenwich, 1837-75, whose singular anomalies can be referred in
+     large part to our present phenomenon, complicated with instrumental
+     error, to which until now they have been exclusively attributed; the
+     Greenwich transit-circle results, 1851-65, in which case, however, a
+     similar complication and the large accidental errors of observation
+     seem to frustrate efforts to get any pertinent results; the Berlin
+     prime-vertical observations of Weyer and Bruennow, 1845-46, in which I
+     hope to show that the parallax of [beta] _Draconis_ derived from them
+     is simply a record of the change of latitude; the conflicting
+     latitude determinations at Cambridge, England; the Washington
+     observation of _Polaris_ and other close Polars, 1866-87, with the
+     transit-circle; also those at Melbourne, 1863-84, a portion of which
+     have already been drawn upon in the last number of the _Journal_,
+     and some others. While the list is a considerable one, I shall be
+     able to compress the statement of results for many of the series into
+     a short space.
+
+     [Sidenote: Provisional nature of results.]
+
+     "In connection with this synopsis of the scope of the investigations,
+     one or two particulars may be of interest, which at the present
+     writing seem to foreshadow the probable outcome. I beg, however, that
+     the statement will be regarded merely as a provisional one. First,
+     while the period is manifestly subject to change, as has already once
+     or twice been intimated, I have hitherto failed in tracing the
+     variations to any regular law, expressible in a numerical formula.
+     Indeed, the general impression produced by a study of these changes
+     in the length of the period is that the cause which produces them
+     operates capriciously to a certain degree, although the average
+     effect for a century has been to diminish the velocity of the
+     revolution of the pole. How far this impression is due to the
+     uncertainty of the observations, and to the complication of the
+     phenomenon with other periodical changes of a purely instrumental
+     kind, I cannot say. Almost all of the series of any extent which have
+     been examined, have the peculiarity that they manifest the
+     periodicity quite uniformly and distinctly for a number of years,
+     then for a while obscurely. In some cases, however, what at first
+     appears to be an objective irregularity proves not to be so by
+     comparison with overlapping series at other observatories.
+
+     "Another characteristic which has struck my attention, although
+     somewhat vaguely, is that the variations in the length of the period
+     seem to go hand in hand with simultaneous alterations in the
+     amplitude of the rotation; the shorter periods being apparently
+     associated with the larger coefficients for the latter. The
+     verification of these surmises awaits a closer comparative scrutiny,
+     the opportunity for which will come when the computations are in a
+     more forward state. If confirmed, these observations will afford a
+     valuable touchstone, in seeking for the cause of a phenomenon which
+     now seems to be at variance with the accepted laws of terrestrial
+     rotation."
+
+[Sidenote: Reception of discovery.]
+
+Let us now for a few moments turn aside from the actual research to see
+how the announcement was received. It would be ungracious to reprint here
+any of the early statements of incredulity which found their way into
+print, especially in Germany. But the first note of welcome came from
+Simon Newcomb, in the same number of the _Astronomical Journal_ as the
+paper just dealt with, and the following extract will indicate both the
+difficulties felt in receiving Mr. Chandler's results and the way in which
+Newcomb struck at the root of them.
+
+     [Sidenote: Newcomb's explanation.]
+
+     "Mr. Chandler's remarkable discovery, that the apparent variations in
+     terrestrial latitudes may be accounted for by supposing a revolution
+     of the axis of rotation of the earth around that of figure, in a
+     period of 427 days, is in such disaccord with the received theory of
+     the earth's rotation that at first I was disposed to doubt its
+     possibility. But I am now able to point out a _vera causa_ which
+     affords a complete explanation of this period. Up to the present time
+     the treatment of this subject has been this: The ratio of the moment
+     of inertia of the earth around its principal axis to the mean of the
+     other two principal moments, admits of very accurate determination
+     from the amount of precession and nutation. This ratio involves what
+     we might call, in a general way, the solid ellipticity of the earth,
+     or the ellipticity of a homogeneous spheroid having the same moments
+     of inertia as the earth.
+
+     "When the differential equations of the earth's rotation are
+     integrated, there appear two arbitrary constants, representing the
+     position of any assigned epoch of the axis of rotation relative to
+     that of figure. Theory then shows that the axis of rotation will
+     revolve round that of figure, in a period of 306 days, and in a
+     direction from west toward east. The attempts to determine the value
+     of these constants have seemed to show that both are zero, or that
+     the axes of rotation and figure are coincident. Several years since,
+     Sir William Thomson published the result of a brief computation from
+     the Washington Prime-Vertical observations of [alpha] Lyrae which I
+     made at his request and which showed a coefficient 0".05. This
+     coefficient did not exceed the possible error of the result; I
+     therefore regarded it as unreal.
+
+     [Sidenote: The forgotten assumption.]
+
+     "The question now arises whether Mr. Chandler's result can be
+     reconciled with dynamic theory. I answer that it can, because the
+     theory which assigns 306 days as the time of revolution is based on
+     the hypothesis that the earth is an absolutely rigid body. But, as a
+     matter of fact, the fluidity of the ocean plays an important part in
+     the phenomenon, as does also the elasticity of the earth. The
+     combined effect of this fluidity and elasticity is that if the axis
+     of rotation is displaced by a certain amount, the axis of figure
+     will, by the changed action of the centrifugal force, be moved
+     toward coincidence with the new axis of rotation. The result is, that
+     the motion of the latter will be diminished in a corresponding ratio,
+     and thus the time of revolution will be lengthened. An exact
+     computation of the effect is not possible without a knowledge of the
+     earth's modulus of elasticity. But I think the result of
+     investigation will be that the rigidity derived from Mr. Chandler's
+     period is as great as that claimed by Sir William Thomson from the
+     phenomena of the tides."
+
+[Sidenote: But Chandler's work still mistrusted.]
+
+This was very satisfactory. Professor Newcomb put his finger on the
+assumption which had been made so long ago that it had been forgotten: and
+the lesson is well worth taking to heart, for it is not the first time
+that mistaken confidence in a supposed fact has been traced to some
+forgotten preliminary assumption: and we must be ever ready to cast our
+eyes backward over all our assumptions, when some new fact seems to
+challenge our conclusions. It might further be expected that this
+discovery of the way in which theory had been defective would as a
+secondary consequence inspire confidence in the other conclusions which
+Mr. Chandler had arrived at in apparent contradiction to theory; or at
+least suggest the suspension of judgment. But Professor Newcomb did not
+feel that this was possible in respect of the _change_ of period, from
+about twelve months in Bradley's time to fourteen months in ours. We have
+seen that Mr. Chandler himself regarded this as a "curious result"
+requiring confirmation: but since the confirmation was forthcoming, he
+stated it with full confidence, and drew the following remarks from
+Professor Newcomb in July 22, 1892:--
+
+     "The fact of a periodic variation of terrestrial latitudes, and the
+     general law of that variation, have been established beyond
+     reasonable doubt by the observations collected by Mr. Chandler. But
+     two of his minor conclusions, as enumerated in No. 3 of this volume,
+     do not seem to me well founded. They are--
+
+     "1. That the period of the inequality is a variable quantity.
+
+     "2. That the amplitude of the inequality has remained constant for
+     the last half century."
+
+Professor Newcomb proceeds to give his reasons for scepticism, which are
+too technical in character to reproduce here. But I will quote the
+following further sentence from his paper:--
+
+     "The question now arises how far we are entitled to assume that the
+     period must be invariable. I reply that, perturbations aside, any
+     variation of the period is in such direct conflict with the laws of
+     dynamics that we are entitled to pronounce it impossible. But we know
+     that there are perturbations, and I do not see how one can doubt
+     that they have so acted as to increase the amplitude of the variation
+     since 1840."
+
+[Sidenote: Chandler's reply.]
+
+In other words, while recognising that there may be a way of reconciling
+one of the "minor" conclusions with theory, Professor Newcomb considers
+that in this case the other must go. Mr. Chandler's answer will speak for
+itself. It was delayed a little in order that he might present an immense
+mass of evidence in support of his conclusions, and was ultimately printed
+on August 23, 1892.
+
+     "The material utilised in the foregoing forty-five series aggregates
+     more than thirty-three thousand observations. Of these more than
+     one-third were made in the southern hemisphere, a fact which we owe
+     principally to Cordoba. It comprises the work of seventeen
+     observatories (four of them in the southern hemisphere) with
+     twenty-one different instruments, and by nine distinct methods of
+     observation. Only three of the series (XXI., XXV., and XXXV.), and
+     these among the least precise intrinsically, give results
+     contradictory of the general law developed in No. 267. This degree of
+     general harmony is indeed surprising when the evanescent character of
+     the phenomenon under investigation is considered.
+
+     "The reader has now before him the means for independent scrutiny of
+     the material on which the conclusions already drawn, and those which
+     are to follow, are based. The space taken in the printing may seem
+     unconscionable, but I hope this will be charged to the extent of the
+     evidence collected, and not to diffuseness or the presentation of
+     needless detail; for I have studiously sought to compress the form of
+     statement without omitting anything essential for searching
+     criticism. That it was important to do this is manifest, since the
+     conclusions, if established, overthrow the existing theory of the
+     earth's rotation, as I have pointed out on p. 21. I am neither
+     surprised nor disconcerted, therefore, that Professor Newcomb should
+     hesitate to accept some of these conclusions on the ground (_A. J._,
+     No. 271) that they are in such conflict with the laws of dynamics
+     that we are entitled to pronounce them impossible. He has been so
+     considerate and courteous in his treatment of my work thus far, that
+     I am sure he will not deem presumptuous the following argument in
+     rebuttal.
+
+     [Sidenote: He "put aside all teachings of theory," and "is not
+     dismayed."]
+
+     "It should be said, first, that in beginning these investigations
+     last year, I deliberately put aside all teachings of theory, because
+     it seemed to me high time that the facts should be examined by a
+     purely inductive process; that the nugatory results of all attempts
+     to detect the existence of the Eulerian period probably arose from a
+     defect of the theory itself; and that the entangled condition of the
+     whole subject required that it should be examined afresh by processes
+     unfettered by any preconceived notions whatever. The problem which I
+     therefore proposed to myself was to see whether it would not be
+     possible to lay the numerous ghosts--in the shape of numerous
+     discordant residual phenomena pertaining to determinations of
+     aberration, parallaxes, latitudes, and the like--which had heretofore
+     flitted elusively about the astronomy of precision during the
+     century; or to reduce them to tangible form by some simple consistent
+     hypothesis. It was thought that if this could be done, a study of the
+     nature of the forces, as thus indicated, by which the earth's
+     rotation is influenced, might lead to a physical explanation of them.
+
+     "Naturally, then, I am not much dismayed by the argument of conflict
+     with dynamic laws, since all that such a phrase means must refer
+     merely to the existent state of the theory at any given time. When
+     the 427-day period was propounded, it was as inconsistent with known
+     dynamic law as the variation of it now appears to be. Professor
+     Newcomb's own happy explanation has already set aside the first
+     difficulty, as it would appear, and advanced the theory by an
+     important step. Are we so sure yet of a complete knowledge of all the
+     forces at work as to exclude the chance of a _vera causa_ for the
+     second?"
+
+[Sidenote: Faraday's words.]
+
+There is a splendid ring of resolution about these words. Let us compare
+them with a notable utterance of Faraday:--
+
+     "The philosopher should be a man willing to listen to every
+     suggestion, but determined to judge for himself. He should not be
+     biassed by appearances; have no favourite hypothesis; be of no
+     school; and in doctrine have no master. He should not be a respecter
+     of persons, but of things. Truth should be his primary object. If to
+     these qualities be added industry, he may indeed hope to walk within
+     the veil of the temple of Nature."
+
+[Sidenote: Chandler's other work at this time.]
+
+[Sidenote: His ultimate satisfactory solution.]
+
+[Sidenote: Interference of two waves.]
+
+Tested by this severe standard, Mr. Chandler fails in no particular, least
+of all in that of industry. The amount of work he got through about this
+time was enormous, for besides the main line of investigation, of which we
+have only had after all a mere glimpse, he had been able to turn aside to
+discuss a subsidiary question with Professor Comstock; he had examined
+with great care some puzzling characteristics in the variability of stars;
+he computed some comet ephemerides; and he was preparing a new catalogue
+of variable stars--a piece of work involving the collection and
+arrangement of great masses of miscellaneous material. Yet within a few
+months after replying as above to Professor Newcomb's criticism, he was
+able to announce that he had found the key to the new puzzle, and that
+"theory and observation were again brought into complete accord." We will
+as before listen to the account of this new step in his own words, but a
+slight preliminary explanation may help those unaccustomed to the
+terminology. The polar motion was found to be compounded of _two_
+independent motions, both periodic, but having different periods. Now, the
+general results of such a composition are well known in several different
+branches of physics, especially in the theory of sound. If two notes of
+nearly the same pitch be struck at the same time, we hear the resultant
+sound alternately swell and die away, because the vibrations caused by the
+two notes are sometimes going in the same direction, and after an interval
+are going exactly in opposite directions. Diagrammatically we should
+represent the vibrations by two waves, as below; the upper wave goes
+through its period seven and a half times between A and D, the lower only
+six times; and it is easily seen that at A and C the waves are
+sympathetic, at B and D antipathetic. At A and C the compound vibration
+would be doubled; at B and D reduced to insensibility. The point is so
+important that perhaps a numerical illustration of it will not be
+superfluous. The waves are now represented by rows of figures as below.
+The first series recurs after every 6, the second after every 7.
+
+[Illustration: FIG. 8.]
+
+  First Wave      1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1
+  Second Wave     1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3
+                  -------------------------------------------------------------
+  Combined Effect 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5 5 5 5 5 5 6 6 6 4 4 4
+                  Great disturbance.                      Calm.
+  -----------------------------------------------------------------------------
+
+  First Wave      2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4 3 2 1 2
+  Second Wave     4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3 2 1 2 3 4 4 3
+                  -------------------------------------------------------------
+
+  Combined Effect 6 7 7 5 3 3 5 7 8 6 4 2 4 6 8 7 5 3 3 5 7 7 6 4 4 4 6 6 6 5 5
+                                    Great disturbance.
+
+[Sidenote: Illustration from ocean travel.]
+
+Adding the two rows together, the oscillations at first reinforce one
+another and we get numbers ranging from 2 to 8 instead of from 1 to 4; but
+one wave gains on the other, until it is rising when the other is falling,
+and the numbers add up to a steady series of 5's. It will be seen that
+there are no less than seven consecutive 5's, and all the variation seems
+to have disappeared. But presently the waves separate again, and the
+period of great disturbance recurs; it will be seen that in the "combined
+effect" the numbers repeat exactly after the 42nd term. Now those
+unfamiliar with the subject may not be prepared for the addition of one
+physical wave to another, as though they were numbers, but the analogy is
+perfect. Travellers by some of the fast twin-screw steamers have had
+unpleasant occasion to notice this phenomenon, when the engineer does not
+run the two screws precisely at the same speed; there come times when the
+ship vibrates violently, separated by periods of comparative stillness.
+Instances from other walks of life may recur to the memory when once
+attention is called to the general facts; but enough has been said to
+explain the point numbered (2) in the subjoined statement. To understand
+the rest, we must remember that if the two waves are not equal in
+"amplitude," _i.e._ if the backward and forward motion is not the same in
+both, they cannot annul one another, but the greater will always
+predominate. Those interested in following the matter further should have
+no difficulty in constructing simple examples to illustrate such points.
+We will proceed to give Mr. Chandler's statements:--
+
+     [Sidenote: Chandler's final formulae.]
+
+     "We now come upon a new line of investigation. Heretofore, as has
+     been seen, the method has been to condense the results of each series
+     of observations into the interval comprised by a single period, then
+     to determine the mean epoch of minimum and the mean range for each
+     series, and, finally, by a discussion of these quantities, to
+     establish the general character of the law of the rotation of the
+     pole. It is now requisite to analyse the observations in a different
+     way, and discover whether the deviations from the general provisional
+     law, in the last column of Table II., are real, and also in what
+     manner the variation of the period is brought about. The outcome of
+     this discussion, which is to be presented in the present paper, is
+     extremely satisfactory. The real nature of the phenomenon is most
+     distinctly revealed, and may be described as follows:--
+
+     "1. The observed variation of the latitude is the resultant curve
+     arising from two periodic fluctuations superposed upon each other.
+     The first of these, and in general the more considerable, has a
+     period of about 427 days, and a semi-amplitude of about 0".12. The
+     second has an annual period with a range variable between 0".04 and
+     0".20 during the last half-century. During the middle portion of this
+     interval, roughly characterised as between 1860 and 1880, the value
+     represented by the lower limit has prevailed, but before and after
+     those dates, the higher one. The minimum and maximum of this annual
+     component of the variation occur at the meridian of Greenwich, about
+     ten days before the vernal and autumnal equinoxes respectively, and
+     it becomes zero just before the solstices.
+
+     "2. As the resultant of these two motions, the effective variation of
+     the latitude is subject to a systematic alternation in a cycle of
+     seven years' duration, resulting from the commensurability of the two
+     terms. According as they conspire or interfere, the total range
+     varies between two-thirds of a second as a maximum, to but a few
+     hundredths of a second, generally speaking, as a minimum.
+
+     "3. In consequence of the variability of the coefficient of the
+     annual term above mentioned, the apparent average period between 1840
+     and 1855 approximated to 380 or 390 days; widely fluctuated from
+     1855 to 1865; from 1865 to about 1885 was very nearly 427 days, with
+     minor fluctuations; afterwards increased to near 440 days, and very
+     recently fell to somewhat below 400 days. The general course of these
+     fluctuations is quite faithfully represented by the law of eq. (3),
+     (No. 267), and accurately, even down to the minor oscillations of
+     individual periods, by the law of eq. (15), hereafter given, and
+     verbally interpreted above. This law also gives a similarly accurate
+     account of the corresponding oscillations in the amplitude. The
+     closeness of the accordance between observation and the numerical
+     theory, in both particulars, places the reality of the law beyond
+     reasonable doubt."
+
+Those who cannot follow the details of the above statement will
+nevertheless catch the general purport--that the difficulties felt by
+Professor Newcomb have been surmounted; and this is made clearer by a
+later extract:--
+
+     "A very important conclusion necessarily follows from the agreement
+     of the values of the 427-day term, deduced from the intervals between
+     the consecutive values of T in Table XII., namely, that there has
+     been no discontinuity in the revolution, such as Professor Newcomb
+     regarded as so probable that he doubted the possibility of drawing
+     any conclusions from the comparison of observations before and after
+     1860 (_A. J._, 271, p. 50).
+
+     [Sidenote: Theory must go, if it will not fit observation.]
+
+     "The present investigation demonstrates that the way out of the
+     apparently irreconcilable contradiction of theory and observation in
+     this matter does not lie in the direction of discrediting the
+     observations, as he is inclined to do. On the contrary, the result is
+     a beautiful vindication of the trustworthiness of the latter, and, at
+     the same time, of the theory that demands an invariable rate of
+     motion; providing a perfectly fitting key to the riddle by showing
+     that another cause has intervened to produce the variability of the
+     period. I feel confident that Professor Newcomb will agree with the
+     reality of the explanation here set forth, and will reconsider his
+     view that the perturbations in the position of the Pole must be of
+     the nature of chance accumulations of motion, a view which he then
+     considered necessary to the maintenance of the constancy in the
+     period of latitude-variation."
+
+[Sidenote: The final paper.]
+
+The paper from which these words are taken appeared on November 4, 1892.
+The next paper on the main theme did not appear till a year later, though
+much work was being done in the meantime on the constant of aberration and
+other matters arising immediately after the discovery. On November 14,
+1893, Mr. Chandler winds up the series of eight papers "On the Variation
+of Latitude," which he had commenced just two years before. His work was
+by no means done; rather was it only beginning, for the torch he had lit
+illuminated many dark corners. But he rightly regarded his discovery as
+now so firmly established that the series of papers dealing with it as
+still under consideration might be terminated. In this final paper he
+first devotes the most careful attention to one point of detail. He had
+shown earlier in the series that the North Pole must be revolving from
+West to East, and not from East to West; but this was when the motion was
+supposed to be simple and not complex, and it was necessary to re-examine
+the question of direction for each of the components. After establishing
+conclusively that the original direction holds for each of the components,
+he almost apologises for the trouble he has taken, thus:--
+
+     "It is therefore proved beyond reasonable doubt that the directions
+     of the rotations is from West to East in both elements; whence the
+     general form of the equation for the variation of latitude adopted in
+     _A. J._, 284, p. 154, eq. (19). It may be thought that too much pains
+     have been here bestowed upon a point which might be trusted to theory
+     to decide. I cannot think so. One of the most salient results of
+     these articles has been the proof of the fact that theory has been a
+     blind guide with regard to the velocity of the Polar rotation,
+     obscuring truth and misleading investigators for a half a century.
+     And even if we were certain, which we are not, that the fourteen
+     months' term is the Eulerian period in a modified form. It would
+     still be necessary to settle by observation the direction of the
+     annual motion, with regard to which theory is powerless to inform us.
+     To save repetition of argument, I must refer to the statement in _A.
+     J._, 273, pp. 68, 70, of the principles adopted in beginning these
+     inquiries in 1891."
+
+Finally, he answers one of the few objectors of eminence who still
+lingered, the great French physicist Cornu:--
+
+     [Sidenote: Cornu answered.]
+
+     "The ground is now cleared for examination of the only topic
+     remaining to be covered, to establish, upon the foundation of fact,
+     every point in the present theory of these remarkable movements of
+     the earth's axis. This is the question of the possibility that these
+     movements are not real, but merely misinterpretations of the observed
+     phenomena; being in whole or in part an illusory effect of
+     instrumental error due to the influence of temperature. Such a
+     possibility has been a nightmare in practical astronomy from the
+     first, frightening us in every series of unexplained residuals,
+     brought to light continually in nearly all attempts at delicate
+     instrumental research. A source of danger so subtile could not fail
+     to be ever present in the mind of every astronomer and physicist who
+     has given even a superficial attention to the question of the
+     latitude variations, and there is no doubt that some are even now
+     thus deterred from accepting these variations as proved facts.
+     Perhaps the most explicit and forcible statement of the doubts that
+     may arise on this subject has been given very recently by Mr. Cornu.
+     The views of so distinguished a physicist, and of others who are
+     inclined to agree with him, call for careful attention, and cannot be
+     neglected in the present closing argument upon the theory presented
+     in these articles. It is unnecessary, for the purpose of disposing of
+     objections of the sort raised by Cornu, to insist that it is not
+     sufficient to show that the observed variations, attributed to the
+     unsteadiness of the Earth's Pole, are near the limit of precision
+     attainable in linear differential measures, and in the indication of
+     the direction of gravity by means of the air bubble of the level; or
+     to show that there are known variations in divided circles and in
+     levels, dependent on temperature and seasons. Nor need we require of
+     objectors the difficult, although essential, task--which they have
+     not distinctly attempted--of showing that these errors are not
+     eliminated, as they appear to be, by the modes in which astronomers
+     use their instruments. Neither need we even urge the fact that a
+     large portion of the data which have been utilised in the present
+     researches on the latitude were derived by methods which dispense
+     with levels, or with circles, a part of them indeed with both, and
+     yet that the results of all are harmonious. On the contrary, let us
+     admit, although merely for argument's sake, that all the known means
+     of determining the direction of gravity--including the plumb-line,
+     the level, and a fluid at rest, whether used for a reflecting surface
+     or as a support for a floating instrument--are subject to a common
+     law of periodical error which vitiates the result of astronomical
+     observation, obtained by whatever methods, and in precisely the same
+     manner. Now, the observed law of latitude variation includes two
+     terms, with periods of fourteen and twelve months respectively. Since
+     the phases of the first term are repeated at intervals of two months
+     in successive years, and hence in a series of years come into all
+     possible relations to conditions of temperature dependent on season,
+     the argument against the reality of this term, on this ground,
+     absolutely fails, and needs no further notice. As to the second, or
+     annual term, while the phases, as observed in any given longitude,
+     are indeed synchronical with the seasons, they are not so as regards
+     different longitudes. If, therefore, the times of any given phase, as
+     observed in the same latitude, but in successively increasing
+     longitudes, occurred at the same date in all of them, there would be
+     a fatal presumption against the existence of an annual period in the
+     polar motion. If, on the contrary, they occur at times successively
+     corresponding to the differences of longitude, the presumption is
+     equally fatal to the hypothesis that they can possibly be due to
+     temperature variation as affecting instrumental measurement. But the
+     facts given in the foregoing section correspond most distinctly to
+     the latter condition. Therefore, unless additional facts can be
+     brought to disprove successively these observed results, we may
+     dismiss for ever the bugbear which has undoubtedly led many to
+     distrust the reality of the annual component of the
+     latitude-variation, while they admit the existence of the 427-day
+     term."
+
+[Sidenote: Consequences of the discovery.]
+
+[Sidenote: Suspected observers acquitted.]
+
+At this point we must leave the fascinating account of the manner in which
+this great discovery was established, in the teeth of opposition such as
+might have dismayed and dissuaded a less clear-sighted or courageous man.
+It is my purpose to lay more stress upon the method of making the
+discovery than upon its results; but we may afford a brief glance at some
+of the consequences which have already begun to flow from this step in
+advance. Some of them have indeed already come before us, especially that
+large class represented by the explanation of anomalies in series of
+observations which had been put aside as inexplicable. We have seen how
+the observations made in Russia, or in Washington, or at Greenwich, in all
+of which there was some puzzling error, were immediately straightened out
+when Chandler applied his new rule to them. We in England have special
+cause to be grateful to Chandler; not only has he demonstrated more
+clearly than ever the greatness of Bradley, but he has rehabilitated Pond,
+the Astronomer Royal of the beginning of the nineteenth century; showing
+that his observations, which had been condemned as in some way erroneous,
+were really far more accurate than might have been expected; and further
+he has shown that the beautiful instrument designed by Airy, and called
+the Reflex Zenith Tube, which seemed to have unaccountably failed in the
+purpose for which it was designed, was really all the time accumulating
+observations of this new phenomenon, the Variation of Latitude. Instead of
+Airy having failed in his design, he had in Chandler's words "builded
+better than he knew."
+
+[Sidenote: Constant of Aberration improved.]
+
+Secondly, there is the modifying influence of this new phenomenon on other
+phenomena already known, such, for instance, as that of "aberration." We
+saw in the third chapter how Bradley discovered this effect of the
+velocity of light, and how the measure of it is obtained by comparing the
+velocity of light with that of the earth. This comparison can be effected
+in a variety of ways, and we should expect all the results to agree within
+certain limits; but this agreement was not obtained, and Chandler has been
+able to show one reason why, and to remove some of the more troublesome
+differences. It is impossible to give here an idea of the far-reaching
+consequences which such work as this may have; so long as there are
+differences of this kind we cannot trust any part of the chain of
+evidence, and there is in prospect the enormous labour of examining each
+separate link until the error is found. The velocity of light, for
+instance, may be measured by a terrestrial experiment; was there anything
+wrong in the apparatus? The velocity of the earth in its journey round the
+sun depends directly upon the distance of the sun: have we measured this
+distance wrongly, and if so what was the error in the observations made?
+These are some of the questions which may arise so long as the values for
+the _Constant of Aberration_ are still conflicting; but it requires
+considerable knowledge of astronomy to appreciate them fully.
+
+[Sidenote: Latitude Variation Tide.]
+
+[Sidenote: Earthquakes.]
+
+Another example will, perhaps, be of more general interest. If the axis of
+the earth is executing small oscillations of this kind, there should be an
+effect upon the tides; the liquid ocean should feel the wobble of the
+earth's axis in some way; and an examination of tidal registers showed
+that there was in fact a distinct effect. It may cause some amusement when
+I say that the rise and fall are only a few inches in any case; but they
+are unmistakable evidences that the earth is not spinning smoothly, but
+has this kind of unbalanced vibration, which I have compared to the
+vibrations felt by passengers on an imperfectly engineered twin-screw
+steamer. A more sensational effect is that apparently earthquakes are more
+numerous at the time when the vibration is greatest. We remarked that the
+vibration waxes and wanes, much as that of the steamer waxes and wanes if
+the twin-screws are not running quite together. Now the passengers on the
+steamer would be prepared to find that breakages would be more numerous
+during the times of vigorous oscillation; and it seems probable that in a
+similar way the little cracks of the earth's skin which we call great
+earthquakes are more numerous when these unbalanced vibrations are at
+their maximum; that is to say, about once every seven years. This result
+is scarcely yet worthy of complete confidence, for our observations of
+earthquakes have only very recently been reduced to proper order; but if
+it should turn out to be true, it is scarcely necessary to add any words
+of mine to demonstrate the importance of this rather unexpected result of
+the Latitude Variation.
+
+[Sidenote: The Kimura phenomenon.]
+
+Finally I will mention another phenomenon which seems to be at present
+more of a curiosity than anything else, but which may lead to some future
+great discovery. It is the outcome of observations which have been
+recently made to watch these motions of the Pole; for although there seems
+good reason to accept Mr. Chandler's laws of variation as accurate, it is
+necessary to establish their accuracy and complete the details by making
+observations for some time yet to come; and there could be no better proof
+of this necessity than the discovery recently made by Mr. Kimura, one of
+those engaged in this watch of the Pole in Japan. Perhaps I can give the
+best idea of it by mentioning one possible explanation, which, however, I
+must caution you may not be by any means the right one. We are accustomed
+to think of this great earth as being sufficiently constant in shape; if
+asked, for instance, whether its centre of gravity remains constantly in
+the same place inside it, we should almost certainly answer in the
+affirmative, just as only twenty years ago we thought that the North Pole
+remained in the same place. But it seems possible that the centre of
+gravity moves a few feet backwards and forwards each year--this would at
+any rate explain certain curious features in the observations to which Mr.
+Kimura has drawn attention. Whatever the explanation of them may be, or to
+settle whether this explanation is correct, we want more observations,
+especially observations in the Southern Hemisphere; and it is a project
+under consideration by astronomers at the present moment whether three
+stations can be established in the Southern Hemisphere for the further
+observation of this curious phenomenon. The question resolves itself
+chiefly into a question of money; indeed, most astronomical projects do
+ultimately resolve themselves into questions of money; and I fear the
+world looks upon scientific men as insatiable in this respect. One can
+only hope that on the whole the money is expended so as to give a
+satisfactory return. In this instance I have no hesitation in saying that
+an immediate return of value for a comparatively modest expenditure is
+practically certain, if only in some way we can get the means of making
+the observations.
+
+It would be natural, at the conclusion of this brief review of some types
+of astronomical discovery, to summarise the lessons indicated: but there
+is the important difficulty that there appear to be none. It has been
+pointed out as we proceeded that what seemed to be a safe deduction from
+one piece of history has been flatly contradicted by another; no sooner
+have we learnt that important results may be obtained by pursuing steadily
+a line of work in spite of the fact that it seems to have become tedious
+and unprofitable (as in the search for minor planets) than we are
+confronted with the possibility that by such simple devotion to the day's
+work we may be losing a great opportunity, as Challis did. We can scarcely
+go wrong in following up the study of residual phenomena in the wake of
+Bradley; but there is the important difficulty that we may be wholly
+unable to find a clue for the arrangement of our residuals, as is at
+present largely the case in meteorology. And, in general, human
+expectations are likely to be quite misleading, as has been shown in the
+last two chapters; the discoveries we desire may lie in the direction
+precisely opposite to that indicated by the best opinion at present
+available. There is no royal road to discovery, and though this statement
+may meet with such ready acceptance that it seems scarcely worth making,
+it is hoped that there may be sufficient of interest in the illustrations
+of its truth.
+
+The one positive conclusion which we may derive from the examples studied
+is that discoveries are seldom made without both hard work and conspicuous
+ability. A new planet, even as large as Uranus, does not reveal itself to
+a passive observer: thirteen times it may appear to such a one without
+fear of detection, until at last it encounters an alert Herschel, who
+suspects, tests, and verifies, and even then announces a comet--so little
+did he realise the whole truth. Fifteen years of unrequited labour before
+Astraea was found, nineteen years of observation before the discovery of
+nutation could be announced: how seldom do these years of toil present
+themselves to our imaginations when we glibly say that "Bradley discovered
+nutation," or "Hencke discovered Astraea"! That the necessary labour is so
+often forgotten must be my excuse for recalling attention to it somewhat
+persistently in these examples.
+
+But beyond the fact that he must work hard, it would seem as though there
+were little of value to tell the would-be discoverer. The situation has
+been well summarised by Jevons in his chapter on Induction in the
+"Principles of Science;" and his words will form a fitting conclusion to
+these chapters:--
+
+     "It would seem as if the mind of the great discoverer must combine
+     contradictory attributes. He must be fertile in theories and
+     hypotheses, and yet full of facts and precise results of experience.
+     He must entertain the feeblest analogies, and the merest guesses at
+     truth, and yet he must hold them as worthless till they are verified
+     in experiment. When there are any grounds of probability he must hold
+     tenaciously to an old opinion, and yet he must be prepared at any
+     moment to relinquish it when a clearly contradictory fact is
+     encountered."
+
+
+
+
+INDEX
+
+
+  Aberration, 105-109, 111, 112, 117, 118, 185, 188, 192, 214, 215
+
+  Accidental discovery, 15, 73, 121-154
+
+  Adams, 12, 45-85;
+    resolution, 55
+
+  Airy, 32, 40-85, 214
+
+  Algiers, 130
+
+  Alleghenia, 26
+
+  Almucantar, 180, 181
+
+  Alphabet used for planets, 27
+
+  Anderson, Dr. T. C., 8, 142, 143, 144, 146
+
+  Anthelm, 142
+
+  Apollo, 9
+
+  Argon, 109
+
+  Ascension, 34
+
+  Assumption, forgotten, 196
+
+  Astraea, 22, 23, 219
+
+  Astrographic chart, 122, 125, 130
+
+  _Astronomical Journal_, 177-217
+
+  _Astronomische Nachrichten_, 52, 158
+
+  Astrophil, 143
+
+  Auwers, 142
+
+
+  Ball, Sir R., 24
+
+  Balliol College, 87
+
+  Banks, Sir J., 9
+
+  Barnard, E. E., 146, 220
+
+  Berlin, 181, 183, 184, 188, 193
+
+  Berlin star-map, 45, 66, 83, 124
+
+  Bessel, 192
+
+  Bettina, 26, 27
+
+  Birmingham, 142
+
+  "Black Drop" (in transit of Venus), 30
+
+  Bliss, 114
+
+  Board of Visitors of Greenwich Observatory, 63
+
+  Bode, 11, 14, 15, 22
+
+  Bode's Law, 12, 13, 38, 43, 45, 52, 72, 76, 77, 84
+
+  Bourdeaux, 130
+
+  Bouvard, 39, 40, 42, 48, 49, 50, 61
+
+  Bradley, 39, 86-120, 188-192, 213, 214, 218, 219
+
+  Bradley, John, 115
+
+  Bremen, 20
+
+  Bridstow, 87, 88, 94
+
+  Briggs, 119
+
+  Brinkley, 192
+
+  British Association, 63
+
+  Bruennow, 193
+
+
+  California, 26
+
+  Cambridge (Mass.), 180, 184, 188
+
+  Cambridge Observatory, 23, 42, 49, 52, 63, 65, 66, 135, 193
+
+  Cambridge University, 68-71, 114
+
+  Cape Observatory, 123, 124, 130
+
+  Cards, 11
+
+  Cassini II., 156
+
+  Catania, 130
+
+  Ceres, 14-22
+
+  Chacornac, 124
+
+  Challis, 49-54, 63-68, 71, 85, 218
+
+  Chandler, S. C., 118, 177-217
+
+  Chapman's "Homer," 2
+
+  Chicago, 157
+
+  Chromosphere, 170
+
+  Clarke, C. C., 2
+
+  Coelostat, 94
+
+  Columbus, 63
+
+  Comet, 4-8, 88, 108, 117, 123, 125
+
+  Commission, planetary, 27
+
+  Common, A. A., 124, 127
+
+  _Compte Rendu_, 62
+
+  Comstock, 202
+
+  Conference, Astrographic, 125-136
+
+  Copernicus, 79, 95
+
+  Cordoba, 130, 199
+
+  Cornu, 210-213
+
+  Corona, 170-175
+
+  _Cosmos_ (Humboldt's), 160
+
+
+  Delambre, 157
+
+  Deviation of Pole, 187
+
+  Disc of Neptune, 44, 64, 79
+
+  Disc of Uranus, 4-7
+
+  Dorpat, 192
+
+  Doublet (photographic), 127-129
+
+  Draconis, [gamma], 96-104
+
+  Draconis, [beta], 193
+
+  Driessen, 23
+
+  Dry plate, 122
+
+  Dublin, 192
+
+
+  Earthquakes, 215
+
+  Earth's Pole, 177-217
+
+  Eccentricity, 41, 83
+
+  Eclipses, 170-176
+
+  Edinburgh, 143
+
+  Eduarda, 26
+
+  Egeria, 22
+
+  Endymion, 25
+
+  Eriphyla, 26
+
+  Eros, 25, 26, 28, 35, 37, 68
+
+  Eulerian, 200, 209
+
+  Evelyn, 26
+
+  Exposure, times of, 122, 131
+
+
+  Faculae, 170
+
+  Faraday, 201
+
+  Flamsteed, 39, 53, 115
+
+  Fleming, Mrs., 142
+
+  Flora, 22
+
+  Foulkes, Martin, 94
+
+  French Academy, 43, 51, 62
+
+
+  Galileo, 95, 163
+
+  Galle, 44, 45, 47, 66, 67, 83
+
+  Gasparis, 22
+
+  Gauge (railways), 56
+
+  Gauss, 17-20
+
+  Geminorum, H., 4
+
+  George III., 8, 10
+
+  "Georgian," 11
+
+  _Georgium Sidus_, 8, 10, 11
+
+  Gill, Sir D., 32, 34, 35, 123
+
+  Gilliss, 32
+
+  Gotha, 20
+
+  Gould, 32
+
+  Graham, 22, 23
+
+  Gravitation, law of, 38, 45, 59, 84, 105
+
+  Greaves, 119
+
+  Greenwich Observatory, 48-64, 88, 89, 114-117, 130, 160-169,
+      182, 192, 193, 206, 213
+
+  Gregory, 93, 119
+
+
+  Hale, G. E., 170, 171
+
+  Hall, A., 184, 185
+
+  Halley, 88-92, 108, 112-116, 119
+
+  Hansen, 41, 59
+
+  Harkness, 184
+
+  Hartwig, 142
+
+  Harvard College Observatory, 128, 142, 144, 145
+
+  Hebe, 22
+
+  Hegel, 15
+
+  Heidelberg, 145
+
+  Heliometer, 32, 34
+
+  Helium, 109
+
+  Helsingfors, 130
+
+  Hencke, 22, 23, 64, 153, 219
+
+  Henry brothers, 124-129
+
+  Herschel, Sir John, 63, 75, 83
+
+  Herschel, Sir William, 2-11, 39, 44, 82, 219
+
+  Herschel (Uranus), 11, 12
+
+  Hind, 22, 23, 25, 142
+
+  Hooke, 96, 97
+
+  Hubbard, 184
+
+  Humboldt, 160
+
+  Hussey, Rev. T. J., 40, 42
+
+  Hygeia, 22
+
+
+  Ilmata, 26
+
+  Industria, 26
+
+  Ingeborg, 26
+
+  Instruments at Greenwich, 114-116
+
+  Iris, 22, 23, 32, 35
+
+
+  Janson, 142
+
+  Jevons, 219
+
+  Johnson, M., 156, 160
+
+  Juno, 9, 21, 22
+
+  Jupiter, 9, 28, 43, 49, 50, 61;
+    satellites, 92, 117
+
+
+  Keats, 1-3, 7, 8
+
+  Keill, 94, 112, 119, 156
+
+  Kelvin, Lord, 196, 197
+
+  Kepler, 95, 142
+
+  Kew, 95, 96, 188, 190
+
+  Kiel, 141
+
+  Kimura, 216
+
+  Koenigsberg, 192
+
+  Kuestner, 118, 181, 183
+
+
+  Lalande, 7, 11, 107, 157
+
+  Lameia, 26
+
+  Laplace, 61
+
+  La Plata, 130
+
+  Latitude variation, 99, 100, 117, 118, 177-217
+
+  Lemonnier, 39, 53, 157
+
+  Le Verrier, 12, 43-85
+
+  Libussa, 26
+
+  Lick Observatory, 152
+
+  _Liouville's Journal_, 73
+
+  Lisbon, longitude of, 92
+
+  London, 23, 25, 96
+
+  Long, 157
+
+  Longitude, 92, 117
+
+  Lowth, Bishop, 119
+
+  Lyrae, [alpha], 184, 196
+
+
+  Macclesfield, Earl of, 94, 113
+
+  Maedler, 192
+
+  Magnetic observations, 161, 164, 174
+
+  Magnitude equation, 135
+
+  Markree, 23
+
+  Mars, 9, 28, 32, 34, 35, 91
+
+  Mayer, 39
+
+  Measurement of plates, 132-135
+
+  _Mecanique Celeste_, 61
+
+  Melbourne, 130, 193
+
+  Memorandum (Adams), 55
+
+  Mercury, 9
+
+  Messier, 7
+
+  Meteorites, 59
+
+  Meteors (November), 60
+
+  Metis, 22, 23
+
+  Micrometer, 5, 133
+
+  Milky Way, 125
+
+  Minerva, 9
+
+  Minor planets, 13-28
+
+  Minor planets tables, 22, 24, 26
+
+  Mistakes, 71-83
+
+  Molyneux, Samuel, 94-96, 101, 104
+
+  Monte Video, 130
+
+  Moon, tables of, 117
+
+
+  Names of minor planets, 22-28
+
+  Nasmyth, 162
+
+  "Nautical Almanac," 11
+
+  Nebula, 124, 146-152
+
+  Neptune, 11, 12, 38-85, 124
+
+  New College Lane, 112
+
+  Newcomb, Simon, 81, 183, 184, 195-202, 207, 208
+
+  New stars, 121, 140-154
+
+  Newton, 38, 84, 90-95, 105, 113
+
+  New York, longitude, 92
+
+  Ninina, 26
+
+  Northleach, 87
+
+  Northumberland, 65
+
+  Nova Geminorum, 141, 145, 146
+
+  Nova Persei, 143, 146-152
+
+  Nutation, 99, 100, 110, 115, 117, 118, 188, 219
+
+
+  _Observatory_ (magazine), 26
+
+  Ocllo, 26
+
+  Olbers, 20-22
+
+  Olympic games, 119
+
+  Oriani, 15
+
+  Ornamenta, 26
+
+  Oxford University, 87-89, 94, 105-119
+
+  Oxford University Observatory, 121, 130, 132, 136, 142, 145, 154
+
+
+  Palermo, Observatory of, 18
+
+  Palisa, 26
+
+  Pallas, 9, 21, 22
+
+  Parallax, 34, 91, 95-98, 109, 185
+
+  Paris, 130
+
+  Parkhurst, J. A., 145
+
+  Parthenope, 22
+
+  Peirce, 73, 80-83
+
+  Pendulum, 117
+
+  Perseus, 8, 143
+
+  Personal equation, 31, 134, 135, 185
+
+  Perth, 130
+
+  Perturbations of Uranus, 12, 42, 51, 54, 55, 61, 75
+
+  Peters, 188, 192
+
+  Phaetusa, 26
+
+  Philosopher, 201, 219
+
+  _Philosophical Transactions_, 3, 4, 9
+
+  Photographica, 26
+
+  Photographic methods, 24, 33, 36, 121-139;
+    lenses, 125, 126
+
+  Photographs of sun, 163, 170-173
+
+  Piazzi, 13-18, 22
+
+  Pickering, E. C., 128, 144
+
+  Pittsburghia, 26
+
+  Plana, 61
+
+  Planetary distances, 13;
+    commission, 27;
+    numbering, 27
+
+  Planets by photography, 24
+
+  Pole Star (_Polaris_), 177, 178, 192, 193
+
+  Pond, 192, 213
+
+  Potsdam, 130, 181
+
+  Pound, Mrs., 104, 110-112
+
+  Pound, Rev. James, 89-94, 104, 115
+
+  Prague, 181
+
+  Precession, 96, 178
+
+  Prymno, 26
+
+  Puiseux, 32
+
+  Pulfrich, 154
+
+  Pulkowa, 181-188, 213
+
+
+  Quadrants at Greenwich, 116
+
+
+  Radium, 175
+
+  Radius vector, 52-58, 60-62, 79, 83
+
+  Rayleigh, Lord, 109
+
+  Records before discovery, 144
+
+  Reflector, 93, 127, 128
+
+  Reflex zenith tube, 192, 214
+
+  Refraction, 96, 101-103, 117
+
+  Refractor, 93, 128
+
+  Reseau, 133
+
+  Residual phenomena, 108-110, 118, 120, 218
+
+  Rigaud, S. P., 87, 115, 119
+
+  Rome, 130
+
+  Rothschild, 27
+
+  Royal Astronomical Society, 40, 47, 68, 74, 124, 155, 157
+
+  Royal Society, 4, 9, 10, 92, 94
+
+
+  Sampson, R. A., 74-76, 84
+
+  San Fernando, 130
+
+  Santiago, 130
+
+  Sappho, 32, 35
+
+  Saturn, 9, 43, 61, 149, 150
+
+  Savile, Sir H., 119
+
+  Savilian professorship, 87-94, 108-119
+
+  Schmidt, Julius, 142, 160
+
+  Schuster, A., 169
+
+  Schwabe, 155-163, 176, 177
+
+  Sheldonian Theatre, 119
+
+  Sherbourn, 87
+
+  Solar eclipse, 26, 170-176
+
+  Spectro-heliograph, 170, 171
+
+  Star-maps, 45, 65, 83, 124
+
+  "Star-trap," 24
+
+  Stereo-comparator, 154
+
+  Stone, E. J., 32
+
+  Struve, 184, 188, 192
+
+  Sun's distance, 28-37
+
+  Sun-spots, 155-176
+
+  Sydney Observatory, 130
+
+
+  Tacubaya Observatory, 130
+
+  Telescopes, 92, 124-129
+
+  Thames River, 105
+
+  Themistocles, 119
+
+  _Theoria Motus_, 17
+
+  Theory and observation, 208
+
+  Thomson, Sir W., 196, 197
+
+  Tides, 215
+
+  Titius, 13
+
+  Toulouse Observatory, 130
+
+  Tycho Brahe, 95, 140, 142
+
+
+  Uranus, 2-14, 25, 38-85, 144, 219
+
+
+  Variable stars, 140
+
+  Variation of latitude, 99, 100, 117, 118, 177-217
+
+  Venus, 9, 79;
+    diameter of, 92;
+    transit of, 28-32, 34
+
+  Vesta, 21, 22
+
+  Victoria, 22, 25, 32, 35
+
+  Von Zach, 20
+
+
+  Wallace, 119
+
+  Wansted, 88-94, 104, 110, 115, 188, 190
+
+  Ward, 119
+
+  Washington Observatory, 184-188, 193, 196, 213
+
+  Weather and sun-spots, 161, 167-169
+
+  Weyer, 193
+
+  Whiteside, 112
+
+  Williams, Mrs. E., 110, 111
+
+  Wind-vane, revolutions, 167-169
+
+  Winnecke, 32
+
+  Wolf, Dr. Max, 145
+
+  Wolf, Rudolf, 163
+
+  Wren, Sir C., 119
+
+
+  Yerkes Observatory, 145, 146, 152, 157, 170, 176
+
+
+  Zeiss, 154
+
+  Zodiac, 64, 124, 137
+
+
+THE END
+
+
+Printed by BALLANTYNE, HANSON & CO.
+
+Edinburgh & London
+
+
+
+
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+LEONARD HILL, M.B., F.R.S., Lecturer on Physiology, London Hospital
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+Illustrations, xii + 484 pages. Crown 8vo., cloth, 6s.
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+Polytechnic Institute, London. With nearly 150 Illustrations. 3s. 6d.
+
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+M.I.M.E., Professor of Mechanical Engineering and Applied Mathematics in
+the City and Guilds of London Technical College, Finsbury. With 173
+Illustrations. Demy 8vo., 10s. 6d. net.
+
+=THE STRENGTH AND ELASTICITY OF STRUCTURAL MEMBERS.= By R. J. WOODS, Master
+of Engineering, Royal University of Ireland, Fellow of the Royal Indian
+Engineering College, and Assistant Professor of Engineering Cooper's Hill
+College. Demy 8vo. 10s. 6d. net.
+
+=TRAVERSE TABLES.= With an Introductory Chapter on Coordinate Surveying. By
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+G. W. CAUNT, M.A. Demy 8vo., 4s. 6d. net.
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+of Mechanics and Mathematics in the Royal College of Science, etc. Crown
+8vo., cloth, 7s. 6d.
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+the Electrical Engineering Department in the University College, Sheffield,
+viii + 380 pages. Demy 8vo., 10s. 6d. net.
+
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+Ph.D., F.R.S., Professor of Physics at the University of Manchester. With
+numerous Diagrams. Demy 8vo., 15s. net.
+
+=ASTRONOMICAL DISCOVERY.= By H. H. TURNER, Savilian Professor of Astronomy
+in the University of Oxford. With Diagrams. Demy 8vo., 10s. 6d. net.
+
+=VECTORS AND ROTORS.= With Applications. Being Lectures delivered at the
+Central Technical College By Professor O. HENRICI, F.R.S. Edited by G. C.
+TURNER, Goldsmith Institute. Crown 8vo., cloth. 4s. 6d.
+
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+Engineering Department of the Northern Polytechnic Institute, Holloway.
+Crown 8vo., cloth, 3s. 6d.
+
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+Lecturer on Mathematics at King's College, London. For use in Schools,
+Colleges, and Technical Classes. 304 pages, Crown 8vo., 3s. 6d.
+
+=FIVE-FIGURE TABLES OF MATHEMATICAL FUNCTIONS.= By J. B. DALE, M.A. Camb.,
+B.A. Lond., late Scholar St. John's College, Cambridge, Lecturer on Pure
+and Applied Mathematics, King's College, University of London. Demy 8vo.,
+3s. 6d. net.
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+Demonstrator of Mechanical Engineering and Applied Mathematics in the
+Technical College, Finsbury. Crown 8vo., cloth, 3s. 6d.
+
+=PRELIMINARY PRACTICAL MATHEMATICS.= BY S. G. STARLING, A.R.C.Sc., B.Sc.,
+Head of the Mathematics and Physics Department of the West Ham Municipal
+Technical Institute; and F. C. CLARKE, A.R.C.Sc., B.Sc.
+
+=THE EVOLUTION THEORY.= By AUGUST WEISMANN, Professor of Zoology in the
+University of Freiburg-im-Breisgau. Translated by Professor J. ARTHUR
+THOMSON. With numerous Illustrations and Coloured Plates. Two Vols. Royal
+8vo., 32s. net.
+
+     The importance of this work is twofold. In the first place, it sums
+     up the teaching of one of Darwin's greatest successors, who has been
+     for many years a leader in biological progress. As Professor Weismann
+     has from time to time during the last quarter of a century frankly
+     altered some of his positions, this deliberate summing up of his
+     mature conclusions is very valuable. In the second place, as the
+     volumes discuss all the chief problems of organic evolution, they
+     form a reliable guide to the whole subject, and may be regarded as
+     furnishing--what is much needed--a Text-book of Evolution Theory.
+
+=ANIMAL BEHAVIOUR.= By C. LLOYD MORGAN, LL.D., F.R.S., Principal of
+University College Bristol, author of 'Animal Life and Intelligence,' etc.
+With numerous Illustrations. Large crown 8vo., 10s. 6d.
+
+=HABIT AND INSTINCT.= By C. LLOYD MORGAN, LL.D., F.R.S. With Photogravure
+Frontispiece. viii + 352 pages. Demy 8vo., cloth, 16s.
+
+=A TEXT-BOOK OF ZOOLOGY.= By G. P. MUDGE, A.R.C.Sc. Lond., Lecturer on
+Biology at the London School of Medicine for Women, and the Polytechnic
+Institute, Regent Street. With about 200 original Illustrations. Crown
+8vo., cloth, 7s. 6d.
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+Tonbridge School. With numerous Illustrations and Diagrams. Crown 8vo.,
+cloth, 4s. 6d.
+
+=A CLASS-BOOK OF BOTANY.= By G. P. MUDGE, A.R.C.Sc. Lond., F.Z.S., and
+A. J. MASLEN, F.L.S., Lecturer on Botany at the Woolwich Polytechnic. With
+over 200 Illustrations. Crown 8vo., 7s. 6d.
+
+=THE BECQUEREL RAYS AND THE PROPERTIES OF RADIUM.= By the Hon. R. J.
+STRUTT, Fellow of Trinity College, Cambridge. With Diagrams. Demy 8vo. 8s.
+6d. net.
+
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+G. MATTHEWS, F.I.C., F.C.S., etc. Fully Illustrated. Crown 8vo., cloth,
+7s. 6d. net.
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+Timbers of Commerce. By G. S. BOULGER, F.L.S., F.G.S. Fully Illustrated.
+Crown 8vo., 7s. 6d. net.
+
+=PSYCHOLOGY FOR TEACHERS.= By C. LLOYD MORGAN, LL.D., F.R.S. xii + 251
+pages. Crown 8vo., 3s. 6d.
+
+=ANIMAL SKETCHES.= By C. LLOYD MORGAN, LL.D., F.R.S. viii + 312 pages, with
+52 Illustrations (many of them full-page). Crown 8vo., cloth, 3s. 6d.
+
+
+_LONDON: EDWARD ARNOLD, 41 & 43 MADDOX STREET, W._
+
+
+
+
+Footnotes:
+
+[1] The inferior planet Venus comes closer, but is not visible throughout
+the night.
+
+[2] The facts were collected with great care and ability by S. P. Rigaud,
+and published by the Oxford University Press in 1832 as "Miscellaneous
+Works and Correspondence of the Rev. James Bradley."
+
+[3] Since the light must travel from the sun to Saturn _and back again to
+the earth_, the interval would be more nearly 150 minutes.
+
+[4] Monthly Notices of the Royal Astronomical Society, vol. xvii. p. 126.
+
+[5] This should be Cambridge, _Mass._
+
+[6] The distances do not represent the _total_ displacement, but only the
+displacement towards Washington in one case and towards Pulkowa in the
+other.
+
+
+
+
+Transcriber's Notes:
+
+Passages in italics are indicated by _italics_.
+
+Passages in bold are indicated by =bold=.
+
+Subscripted letters are indicated by {subscript}.
+
+The original text includes the Greek a, b, and g. For this text version
+these letters are presented as [alpha], [beta], and [gamma].
+
+All side notes belonging to a single paragraph have been moved to the
+beginning of the paragraph.
+
+Sidenotes split across pages have been joined together.
+
+Punctuation has been corrected without note.
+
+Corrections in the "Errata" have been made in this text version.
+
+The following misprints have been corrected:
+  "Hencke'" corrected to "Hencke's" (page 23 sidenote)
+  "annouced" corrected to "announced" (page 45 sidenote)
+  "are are" corrected to "are" (page 119)
+  "Konigsberg" corrected to "Koenigsberg" (Index)
+
+Other than the corrections listed above, inconsistencies in spelling and
+hyphenation have been retained from the original.
+
+
+
+
+
+
+End of Project Gutenberg's Astronomical Discovery, by Herbert Hall Turner
+
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