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Transcriber’s Notes
Obvious typographical errors have been silently corrected. Variations
in hyphenation has been standardised but all other spelling and
punctuation remains unchanged.
Italics are represented thus _italic_, =bold=, superscripts thus y^{en}
and subscripts thus x_{1}.
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[Illustration: The moon. From a photograph taken at the Lick Observatory.
[_Frontispiece._ ]
_THE UNIVERSITY SERIES_
A Short History
of
Astronomy
BY ARTHUR BERRY, M.A.
FELLOW AND ASSISTANT TUTOR OF KING’S COLLEGE, CAMBRIDGE;
FELLOW OF UNIVERSITY COLLEGE, LONDON
_Wagner._ Verzeiht! es ist ein gross Ergetzen
Sich in den Geist der Zeiten zu versetzen.
Zu schauen wie vor uns ein weiser Mann gebracht,
Und wie wir’s dann zuletzt so herrlich weit gebracht.
_Faust._ O ja, bis an die Sterne weit!
GOETHE’S _Faust_.
NEW YORK
CHARLES SCRIBNER’S SONS
1899
PREFACE.
I have tried to give in this book an outline of the history of
astronomy from the earliest historical times to the present day, and to
present it in a form which shall be intelligible to a reader who has no
special knowledge of either astronomy or mathematics, and has only an
ordinary educated person’s power of following scientific reasoning.
In order to accomplish my object within the limits of one small volume
it has been necessary to pay the strictest attention to compression;
this has been effected to some extent by the omission of all but
the scantiest treatment of several branches of the subject which
would figure prominently in a book written on a different plan or
on a different scale. I have deliberately abstained from giving any
connected account of the astronomy of the Egyptians, Chaldaeans,
Chinese, and others to whom the early development of astronomy is
usually attributed. On the one hand, it does not appear to me possible
to form an independent opinion on the subject without a first-hand
knowledge of the documents and inscriptions from which our information
is derived; and on the other, the various Oriental scholars who
have this knowledge still differ so widely from one another in the
interpretations that they give that it appears premature to embody
their results in the dogmatic form of a textbook. It has also seemed
advisable to lighten the book by omitting—except in a very few simple
and important cases—all accounts of astronomical instruments; I do not
remember ever to have derived any pleasure or profit from a written
description of a scientific instrument before seeing the instrument
itself, or one very similar to it, and I have abstained from attempting
to give to my readers what I have never succeeded in obtaining myself.
The aim of the book has also necessitated the omission of a number of
important astronomical discoveries, which find their natural expression
in the technical language of mathematics. I have on this account
only been able to describe in the briefest and most general way the
wonderful and beautiful superstructure which several generations of
mathematicians have erected on the foundations laid by Newton. For the
same reason I have been compelled occasionally to occupy a good deal
of space in stating in ordinary English what might have been expressed
much more briefly, as well as more clearly, by an algebraical formula:
for the benefit of such mathematicians as may happen to read the book
I have added a few mathematical footnotes; otherwise I have tried to
abstain scrupulously from the use of any mathematics beyond simple
arithmetic and a few technical terms which are explained in the text.
A good deal of space has also been saved by the total omission of, or
the briefest possible reference to, a very large number of astronomical
facts which do not bear on any well-established general theory; and for
similar reasons I have generally abstained from noticing speculative
theories which have not yet been established or refuted. In particular,
for these and for other reasons (stated more fully at the beginning
of chapter XIII.), I have dealt in the briefest possible way with the
immense mass of observations which modern astronomy has accumulated;
it would, for example, have been easy to have filled one or more
volumes with an account of observations of sun-spots made during the
last half-century, and of theories based on them, but I have in fact
only given a page or two to the subject.
I have given short biographical sketches of leading astronomers (other
than living ones), whenever the material existed, and have attempted
in this way to make their personalities and surroundings tolerably
vivid; but I have tried to resist the temptation of filling up space
with merely picturesque details having no real bearing on scientific
progress. The trial of Kepler’s mother for witchcraft is probably
quite as interesting as that of Galilei before the Inquisition, but I
have entirely omitted the first and given a good deal of space to the
second, because, while the former appeared to be chiefly of curious
interest, the latter appeared to me to be not merely a striking
incident in the life of a great astronomer, but a part of the history
of astronomical thought. I have also inserted a large number of
dates, as they occupy very little space, and may be found useful by
some readers, while they can be ignored with great ease by others; to
facilitate reference the dates of birth and death (when known) of every
astronomer of note mentioned in the book (other than living ones) have
been put into the Index of Names.
I have not scrupled to give a good deal of space to descriptions of
such obsolete theories as appeared to me to form an integral part of
astronomical progress. One of the reasons why the history of a science
is worth studying is that it sheds light on the processes whereby a
scientific theory is formed in order to account for certain facts, and
then undergoes successive modifications as new facts are gradually
brought to bear on it, and is perhaps finally abandoned when its
discrepancies with facts can no longer be explained or concealed. For
example, no modern astronomer as such need be concerned with the Greek
scheme of epicycles, but the history of its invention, of its gradual
perfection as fresh observations were obtained, of its subsequent
failure to stand more stringent tests, and of its final abandonment
in favour of a more satisfactory theory, is, I think, a valuable and
interesting object-lesson in scientific method. I have at any rate
written this book with that conviction, and have decided very largely
from that point of view what to omit and what to include.
The book makes no claim to be an original contribution to the subject;
it is written largely from second-hand sources, of which, however,
many are not very accessible to the general reader. Particulars of the
authorities which have been used are given in an appendix.
It remains gratefully to acknowledge the help that I have received
in my work. Mr. W. W. Rouse Ball, Tutor of Trinity College, whose
great knowledge of the history of mathematics—a subject very closely
connected with astronomy—has made his criticisms of special value, has
been kind enough to read the proofs, and has thereby saved me from
several errors; he has also given me valuable information with regard
to portraits of astronomers. Miss H. M. Johnson has undertaken the
laborious and tedious task of reading the whole book in manuscript
as well as in proof, and of verifying the cross-references. Miss F.
Hardcastle, of Girton College, has also read the proofs, and verified
most of the numerical calculations, as well as the cross-references. To
both I am indebted for the detection of a large number of obscurities
in expression, as well as of clerical and other errors and of
misprints. Miss Johnson has also saved me much time by making the Index
of Names, and Miss Hardcastle has rendered me a further service of
great value by drawing a considerable number of the diagrams. I am
also indebted to Mr. C. E. Inglis, of this College, for fig. 81; and I
have to thank Mr. W. H. Wesley, of the Royal Astronomical Society, for
various references to the literature of the subject, and in particular
for help in obtaining access to various illustrations.
I am further indebted to the following bodies and individual
astronomers for permission to reproduce photographs and drawings, and
in some cases also for the gift of copies of the originals: the Council
of the Royal Society, the Council of the Royal Astronomical Society,
the Director of the Lick Observatory, the Director of the Instituto
Geographico-Militare of Florence, Professor Barnard, Major Darwin, Dr.
Gill, M. Janssen, M. Loewy, Mr. E. W. Maunder, Mr. H. Pain, Professor
E. C. Pickering, Dr. Schuster, Dr. Max Wolf.
ARTHUR BERRY.
KING’S COLLEGE, CAMBRIDGE
CONTENTS.
PAGE
PREFACE v
CHAPTER I.
PRIMITIVE ASTRONOMY, §§ 1-18 1-20
§ 1. Scope of astronomy 1
§§ 2-5. First notions: the motion of the sun: the motion
and _phases_ of the moon: daily motion of the
stars 1
§ 6. Progress due to early civilised peoples: Egyptians,
Chinese, Indians, and Chaldaeans 3
§ 7. The _celestial sphere_: its scientific value: _apparent
distance_ between the stars: the measurement of _angles_ 4
§§ 8-9. The rotation of the celestial sphere: the _North_ and
_South poles_: the _daily motion_: the _celestial
equator_: _circumpolar stars_ 7
§§ 10-11. The _annual motion_ of the sun: _great circles_:
the _ecliptic_ and its _obliquity_: the _equinoxes_ and
_equinoctial points_: the _solstices_ and _solstitial
points_ 8
§§ 12-13. _The constellations_: _the zodiac_, _signs of the zodiac_,
and _zodiacal constellations_: the _first point of
Aries_ (♈), and the _first point of Libra_ (♎) 12
§ 14. The five _planets_: _direct_ and _retrograde_ motions:
_stationary points_ 14
§ 15. The order of nearness of the planets: _occultations_:
_superior_ and _inferior_ planets 15
§ 16. Measurement of time: the day and its division into
hours: the _lunar month_: the year: the week 17
§ 17. _Eclipses_: the _saros_ 19
§ 18. The rise of _Astrology_ 20
CHAPTER II.
GREEK ASTRONOMY (FROM ABOUT 600 B.C. TO ABOUT
400 A.D.), §§ 19-54 21-75
§§ 19-20. =Astronomy up to the time of Aristotle.= The
Greek calendar: _full_ and _empty_ months:
the _octaeteris_: _Meton’s cycle_ 21
§ 21. The Roman calendar: introduction of the
_Julian Calendar_ 22
§ 22. The _Gregorian Calendar_ 23
§ 23. Early Greek speculative astronomy: _Thales_
and _Pythagoras_: the spherical form of the
earth: the celestial spheres: the _music of
the spheres_ 24
§ 24. _Philolaus_ and other Pythagoreans: early believers
in the motion of the earth: _Aristarchus_
and _Seleucus_ 25
§ 25. _Plato_: uniform circular and spherical motions 26
§ 26. _Eudoxus_: representation of the celestial
motions by combinations of spheres: description
of the constellations. _Callippus_ 27
§§ 27-30. _Aristotle_: his spheres: the phases of the moon:
proofs that the earth is spherical: his
arguments against the motion of the earth:
relative distances of the celestial bodies:
other speculations: estimate of his astronomical
work 29
§§ 31-2. =The early Alexandrine school=: its rise: Aristarchus:
his estimates of the distances of the
sun and moon. Observations by _Timocharis_
and _Aristyllus_ 34
§§ 33-4. Development of _spherics_: the _Phenomena_ of
_Euclid_: the _horizon_, the _zenith_, _poles_ of a
great circle, _verticals_, _declination circles_, the
_meridian_, _celestial latitude_ and _longitude_,
_right ascension_ and _declination_. Sun-dials 36
§ 35. The division of the surface of the earth into
zones 37
§ 36. _Eratosthenes_: his measurement of the earth:
and of the obliquity of the ecliptic 39
§ 37. =Hipparchus=: his life and chief contributions to
astronomy. _Apollonius’s_ representation of
the celestial motions by means of circles.
General account of the theory of eccentrics
and epicycles 40
§§ 38-9. Hipparchus’s representation of the motion of
the sun, by means of an _eccentric_: _apogee_,
_perigee_, _line of apses_, _eccentricity_: _equation of
the centre_: the _epicycle_ and the _deferent_ 41
§ 40. Theory of the moon: _lunation_ or _synodic month_
and _sidereal month_: motion of the moon’s
_nodes_ and apses: _draconitic month_ and
_anomalistic month_ 47
§ 41. Observations of planets: eclipse method of connecting
the distances of the sun and moon:
estimate of their distances 49
§ 42. His star catalogue. Discovery of the _precession
of the equinoxes_: the _tropical year_ and the
_sidereal year_ 51
§ 43. Eclipses of the sun and moon: _conjunction_
and _opposition_: _partial_, _total_, and _annular_
eclipses: _parallax_ 56
§ 44. Delambre’s estimate of Hipparchus 61
§ 45. The slow progress of astronomy after the time of Hipparchus:
_Pliny’s_ proof that the earth is round:
new measurements of the earth by _Posidonius_ 61
§ 46. =Ptolemy.= The _Almagest_ and the _Optics_: theory of
_refraction_ 62
§ 47. Account of the _Almagest_: Ptolemy’s postulates:
arguments against the motion of the earth 63
§ 48. The theory of the moon: _evection_ and _prosneusis_ 65
§ 49. The _astrolabe_. Parallax, and distances of the
sun and moon 67
§ 50. The star catalogue: precession 68
§ 51. Theory of the planets: the _equant_ 69
§ 52. Estimate of Ptolemy 73
§ 53. The decay of ancient astronomy: _Theon_ and _Hypatia_ 73
§ 54. Summary and estimate of Greek astronomy 74
CHAPTER III.
THE MIDDLE AGES (FROM ABOUT 600 A.D. TO ABOUT
1500 A.D.), §§ 55-69 76-91
§ 55. The slow development of astronomy during this
period 76
§ 56. =The East.= The formation of an astronomical school
at the court of the Caliphs: revival of astrology:
translations from the Greek by _Honein ben Ishak_,
_Ishak ben Honein_, _Tabit ben Korra_, and others 76
§§ 57-8. The Bagdad observatory. Measurement of the
earth. Corrections of the astronomical data
of the Greeks: _trepidation_ 78
§ 59. _Albategnius_: discovery of the motion of the
sun’s apogee 79
§ 60. _Abul Wafa_: supposed discovery of the _variation_
of the moon. _Ibn Yunos_: the _Hakemite
Tables_ 79
§ 61. Development of astronomy in the Mahometan
dominions in Morocco and Spain: _Arzachel_:
the _Toletan Tables_ 80
§ 62. _Nassir Eddin_ and his school: _Ilkhanic Tables_:
more accurate value of precession 81
§ 63. Tartar astronomy: _Ulugh Begh_: his star catalogue 82
§ 64. Estimate of oriental astronomy of this period:
Arabic numerals: survivals of Arabic names
of stars and astronomical terms: _nadir_ 82
§ 65. =The West.= General stagnation after the fall of the
Roman Empire: _Bede_. Revival of learning
at the court of Charlemagne: _Alcuin_ 83
§ 66. Influence of Mahometan learning: _Gerbert_:
translations from the Arabic: _Plato of Tivoli_,
_Athelard of Bath_, _Gherardo of Cremona_.
_Alfonso X._ and his school: the _Alfonsine
Tables_ and the _Libros del Saber_ 84
§ 67. The schoolmen of the thirteenth century,
_Albertus Magnus_, _Cecco d’Ascoli_, _Roger
Bacon_. _Sacrobosco’s Sphaera Mundi_ 85
§ 68. _Purbach_ and _Regiomontanus_: influence of the
original Greek authors: the Nürnberg school:
_Walther_: employment of printing: conflict
between the views of Aristotle and of
Ptolemy: the celestial spheres of the Middle
Ages: the _firmament_ and the _primum mobile_ 86
§ 69. _Lionardo da Vinci_: _earthshine_. _Fracastor_ and
_Apian_: observations of comets. _Nonius._
_Fernel’s_ measurement of the earth 90
CHAPTER IV.
COPPERNICUS (FROM 1473 A.D. TO 1543 A.D.), §§ 70-92 92-124
§ 70. The Revival of Learning 92
§§ 71-4. Life of _Coppernicus_: growth of his ideas: publication
of the _Commentariolus_: _Rheticus_ and the
_Prima Narratio_: publication of the _De Revolutionibus_ 93
§ 75. The central idea in the work of Coppernicus:
relation to earlier writers 99
§§ 76-9. The =De Revolutionibus=. _The first book_: the
postulates: the principle of _relative motion_,
with applications to the apparent annual
motion of the sun, and to the daily motion
of the celestial sphere 100
§ 80. The two motions of the earth: answers to
objections 105
§ 81. The motion of the planets 106
§ 82. The seasons 108
§ 83. End of first book. _The second book_: decrease
in the obliquity of the ecliptic: the star
catalogue 110
§ 84. _The third book_: precession 110
§ 85. _The third book_: the annual motion of the earth:
_aphelion_ and _perihelion_. _The fourth book_:
theory of the moon: distances of the sun
and moon: eclipses 111
§§ 86-7. The _fifth_ and _sixth_ books: theory of the planets:
_synodic_ and _sidereal periods_ 112
§ 88. Explanation of the stationary points 118
§§ 89-90. Detailed theory of the planets: defects of the
theory 121
§ 91. Coppernicus’s use of epicycles 122
§ 92. A difficulty in his system 123
CHAPTER V.
THE RECEPTION OF THE COPPERNICAN THEORY AND THE PROGRESS
OF OBSERVATION (FROM ABOUT 1543 A.D.
TO ABOUT 1601 A.D.), §§ 93-112 125-144
§§ 93-4. The first reception of the _De Revolutionibus_:
_Reinhold_: the _Prussian Tables_ 125
§ 95. Coppernicanism in England: _Field_, _Recorde_, _Digges_ 127
§ 96. Difficulties in the Coppernican system: the need for
progress in dynamics and for fresh observations 127
§§ 97-8. The Cassel Observatory: the Landgrave _William
IV._, _Rothmann_, and _Bürgi_: the star catalogue:
Bürgi’s invention of the pendulum clock 128
§ 99. =Tycho Brahe=: his early life 130
§ 100. The new star of 1572: travels in Germany 131
§§ 101-2. His establishment in Hveen: Uraniborg and
Stjerneborg: life and work in Hveen 132
§ 103. The comet of 1577, and others 135
§ 104. Books on the new star and on the comet of 1577 136
§ 105. Tycho’s system of the world: quarrel with
_Reymers Bär_ 136
§ 106. Last years at Hveen: breach with the King 138
§ 107. Publication of the _Astronomiae Instauratae
Mechanica_ and of the star catalogue: invitation
from the Emperor 139
§ 108. Life at Benatek: co-operation of Kepler: death 140
§ 109. Fate of Tycho’s instruments and observations 141
§ 110. Estimate of Tycho’s work: the accuracy of his
observations: improvements in the art of
observing 141
§ 111. Improved values of astronomical constants.
Theory of the moon: the _variation_ and the
_annual equation_ 143
§ 112. The star catalogue: rejection of trepidation:
unfinished work on the planets 144
CHAPTER VI.
GALILEI (FROM 1564 A.D. TO 1642 A.D.), §§ 113-134 145-178
§ 113. Early life 145
§ 114. The pendulum 146
§ 115. Diversion from medicine to mathematics: his first
book 146
§ 116. Professorship at Pisa: experiments on falling
bodies: protests against the principle of
authority 147
§ 117. Professorship at Padua: adoption of Coppernican
views 148
§ 118. =The telescopic discoveries.= Invention of the telescope
by _Lippersheim_: its application to
astronomy by _Harriot_, _Simon Marius_, and
Galilei 149
§ 119. The _Sidereus Nuncius_: observations of the moon 150
§ 120. New stars: resolution of portions of the Milky
Way 151
§ 121. The discovery of Jupiter’s _satellites_: their importance
for the Coppernican controversy:
controversies 151
§ 122. Appointment at the Tuscan court 153
§ 123. Observations of Saturn. Discovery of the
phases of Venus 154
§ 124. Observations of _sun-spots_ by Fabricius, Harriot,
_Scheiner_, and Galilei: the _Macchie Solari_:
proof that the spots were not planets: observations
of the _umbra_ and _penumbra_ 154
§ 125. Quarrel with Scheiner and the Jesuits: theological
controversies: _Letter to the Grand Duchess
Christine_ 157
§ 126. Visit to Rome. The first condemnation: prohibition
of Coppernican books 159
§ 127. Method for finding longitude. Controversy on
comets: _Il Saggiatore_ 160
§ 128. =Dialogue on the Two Chief Systems of the World.=
Its preparation and publication 162
§ 129. The speakers: argument for the Coppernican
system based on the telescopic discoveries:
discussion of stellar parallax: the _differential
method of parallax_ 163
§ 130. Dynamical arguments in favour of the motion of
the earth: the _First Law of Motion_. The tides 165
§ 131. =The trial and condemnation.= The thinly veiled
Coppernicanism of the _Dialogue_: the remarkable
preface 168
§ 132. Summons to Rome: trial by the Inquisition:
condemnation, abjuration, and punishment:
prohibition of the _Dialogue_ 169
§ 133. Last years: life at Arcetri: _libration_ of the moon:
the _Two New Sciences_: _uniform acceleration_, and
the first law of motion. Blindness and death 172
§ 134. Estimate of Galilei’s work: his scientific method 176
CHAPTER VII.
KEPLER (FROM 1571 A.D. TO 1630 A.D.), §§ 135-151 179-197
§ 135. Early life and theological studies 179
§ 136. Lectureship on mathematics at Gratz: astronomical
studies and speculations: the _Mysterium Cosmographicum_ 180
§ 137. Religious troubles in Styria: work with Tycho 181
§ 138. Appointment by the Emperor Rudolph as successor
to Tycho: writings on the new star of 1604 and
on Optics: theory of refraction and a new form
of telescope 182
§ 139. Study of the motion of Mars: unsuccessful attempts
to explain it 183
§§ 140-1. The _ellipse_: discovery of the first two of _Kepler’s
Laws_ for the case of Mars: the _Commentaries
on Mars_ 184
§ 142. Suggested extension of Kepler’s Laws to the other
planets 186
§ 143. Abdication and death of Rudolph: appointment at
Linz 188
§ 144. The _Harmony of the World_: discovery of _Kepler’s
Third Law_: the “music of the spheres” 188
§ 145. _Epitome of the Copernican Astronomy_: its prohibition:
fanciful correction of the distance of
the sun: observation of the sun’s _corona_ 191
§ 146. Treatise on _Comets_ 193
§ 147. Religious troubles at Linz: removal to Ulm 194
§ 148. The _Rudolphine Tables_ 194
§ 149. Work Under Wallenstein: death 195
§ 150. Minor discoveries: speculations on gravity 195
§ 151. Estimate of Kepler’s work and intellectual character 197
CHAPTER VIII.
FROM GALILEI TO NEWTON (FROM ABOUT 1638 A.D. TO
ABOUT 1687 A.D.), §§ 152-163 198-209
§ 152. The general character of astronomical progress
during the period 198
§ 153. Scheiner’s observations of _faculae_ on the sun. _Hevel_:
his _Selenographia_ and his writings on comets:
his star catalogue. _Riccioli’s New Almagest_ 198
§ 154. Planetary observations; _Huygens’s_ discovery of a
satellite of Saturn and of its ring 199
§ 155. _Gascoigne’s_ and _Auzout’s_ invention of the _micrometer_:
_Picard’s_ telescopic “sights” 202
§ 156. _Horrocks_: extension of Kepler’s theory to the
moon: observation of a transit of Venus 202
§§ 157-8. Huygens’s rediscovery of the pendulum clock:
his theory of circular motion 203
§ 159. Measurements of the earth by _Snell_, _Norwood_, and
Picard 204
§ 160. The Paris Observatory: _Domenico Cassini_: his
discoveries of four new satellites of Saturn: his
other work 204
§ 161. _Richer’s_ expedition to Cayenne: pendulum observations:
observations of Mars in opposition: _horizontal
parallax_: _annual_ or _stellar parallax_ 205
§ 162. _Roemer_ and the velocity of light 208
§ 163. _Descartes_ 208
CHAPTER IX.
UNIVERSAL GRAVITATION (FROM 1643 A.D. TO 1727 A.D.),
§§ 164-195 210-246
§ 164. Division of _Newton’s_ life into three periods 210
§ 165. Early life, 1643 to 1665 210
§ 166. Great productive period, 1665-87 211
§ 167. Chief divisions of his work: astronomy, optics, pure
mathematics 211
§ 168. Optical discoveries: the _reflecting telescopes_ of
_Gregory_ and Newton: the _spectrum_ 211
§ 169. Newton’s description of his discoveries in 1665-6 212
§ 170. The beginning of his work on gravitation: the
falling apple: previous contributions to the
subject by Kepler, _Borelli_, and Huygens 213
§ 171. The problem of circular motion: _acceleration_ 214
§ 172. The _law of the inverse square_ obtained from Kepler’s
Third Law for the planetary orbits, treated as
circles 215
§ 173. Extension of the earth’s gravity as far as the moon:
imperfection of the theory 217
§ 174. _Hooke’s_ and _Wren’s_ speculations on the planetary
motions and on gravity. Newton’s second calculation
of the motion of the moon: agreement
with observation 221
§ 175-6. Solution of the problem of elliptic motion:
_Halley’s_ visit to Newton 221
§ 177. Presentation to the Royal Society of the tract _De
Motu_: publication of the _Principia_ 222
§ 178. The =Principia=: its divisions 223
§§ 179-80. The _Laws of Motion_: the First Law: acceleration
in its general form: _mass_ and _force_:
the Third Law 223
§ 181. Law of _universal gravitation_ enunciated 227
§ 182. The attraction of a sphere 228
§ 183. The general problem of accounting for the
motions of the solar system by means of
gravitation and the Laws of Motion:
_perturbations_ 229
§ 184. Newton’s lunar theory 230
§ 185. Measurement of the mass of a planet by means
of its attraction of its satellites 231
§ 186. Motion of the sun: _centre of gravity_ of the solar
system: relativity of motion 231
§ 187. The non-spherical form of the earth, and of Jupiter 233
§ 188. Explanation of precession 234
§ 189. The tides: the mass of the moon deduced from
tidal observations 235
§ 190. The motions of comets: _parabolic_ orbits 237
§ 191. Reception of the _Principia_ 239
§ 192. Third period of Newton’s life, 1687-1727: Parliamentary
career: improvement of the lunar
theory: appointments at the Mint and removal
to London: publication of the _Optics_ and of the
second and third editions of the _Principia_, edited
by _Cotes_ and Pemberton: death 240
§ 193. Estimates of Newton’s work by Leibniz, by Lagrange,
and by himself 241
§ 194. Comparison of his astronomical work with that of
his predecessors: “explanation” and “description”:
conception of the material universe
as made up of bodies attracting one another
according to certain laws 242
§ 195. Newton’s scientific method: “_Hypotheses non fingo_” 245
CHAPTER X.
OBSERVATIONAL ASTRONOMY IN THE EIGHTEENTH
CENTURY, §§ 196-227 247-286
§ 196. _Gravitational astronomy_: its development due
almost entirely to Continental astronomers: use
of _analysis_: English observational astronomy 247
§§ 197-8. _Flamsteed_: foundation of the Greenwich Observatory:
his star catalogue 249
§ 199. =Halley=: catalogue of Southern stars 253
§ 200. Halley’s comet 253
§ 201. _Secular acceleration of the moon’s mean motion_ 254
§ 202. Transits of Venus 254
§ 203. _Proper motions_ of the fixed stars 255
§§ 204-5. Lunar and planetary tables: career at Greenwich:
minor work 255
§ 206. =Bradley=: career 257
§§ 207-11. Discovery and explanation of _aberration_: the
_constant of aberration_ 258
§ 212. Failure to detect parallax 265
§§ 213-5. Discovery of _nutation_: _Machin_ 265
§§ 216-7. Tables of Jupiter’s satellites by Bradley and by
_Wargentin_: determination of longitudes,
and other work 269
§ 218. His observations: _reduction_ 271
§ 219. The density of the earth: _Maskelyne_: the _Cavendish
experiment_ 273
§ 220. The _Cassini-Maraldi_ school in France 275
§ 221. Measurements of the earth: the Lapland and
Peruvian arcs: _Maupertuis_ 275
§§ 222-4. _Lacaille_: his career: expedition to the Cape:
star catalogues, and other work 279
§§ 225-6. _Tobias Mayer_: his observations: lunar tables:
the longitude prize 282
§ 227. The transits of Venus in 1761 and 1769: distance
of the sun 284
CHAPTER XI.
GRAVITATIONAL ASTRONOMY IN THE EIGHTEENTH CENTURY,
§§ 228-250 287-322
§ 228. Newton’s problem: the _problem of three bodies_:
methods of approximation: _lunar theory_ and
_planetary theory_ 287
§ 229. The progress of Newtonian principles in France:
popularisation by Voltaire. The five great
mathematical astronomers: the pre-eminence of
France 290
§ 230. _Euler_: his career: St. Petersburg and Berlin:
extent of his writings 291
§ 231. _Clairaut_: figure of the earth: return of Halley’s
comet 293
§ 232. _D’Alembert_: his dynamics: precession and nutation:
his versatility: rivalry with Clairaut 295
§§ 233-4. The lunar theories and lunar tables of Euler,
Clairaut, and D’Alembert: advance on Newton’s
lunar theory 297
§ 235. Planetary theory: Clairaut’s determination of the
masses of the moon and of Venus: _Lalande_ 299
§ 236. Euler’s planetary theory: method of the _variation
of elements_ or _parameters_ 301
§ 237. _Lagrange_: his career: Berlin and Paris: the
_Mécanique Analytique_ 304
§ 238. _Laplace_: his career: the _Mécanique Céleste_ and the
_Système du Monde_: political appointments and
distinctions 306
§ 239. Advance made by Lagrange and Laplace on the
work of their immediate predecessors 308
§ 240. Explanation of the moon’s secular acceleration by
Laplace 308
§ 241. Laplace’s lunar theory: tables of _Bürg_ and _Burckhardt_ 309
§ 242. _Periodic_ and _secular_ inequalities 310
§ 243. Explanation of the mutual perturbation of Jupiter
and Saturn: _long inequalities_ 312
§§ 244-5. Theorems on the _stability_ of the solar system:
the _eccentricity fund_ and the _inclination fund_ 313
§ 246. The magnitudes of some of the secular inequalities 318
§ 247. Periodical inequalities: solar and planetary tables
_Mécanique Céleste_ 318
§ 248. Minor problems of gravitational astronomy: the
satellites: Saturn’s ring: precession and nutation:
figure of the earth: tides: comets: masses
of planets and satellites 318
§ 249. The solution of Newton’s problem by the astronomers
of the eighteenth century 319
§ 250. The _nebular hypothesis_: its speculative character 320
CHAPTER XII.
HERSCHEL (FROM 1738 A.D. TO 1822 A.D.), §§ 251-271 323-353
§§ 251-2. William Herschel’s early career: Bath: his
first telescope 323
§§ 253-4. The discovery of the planet Uranus, and its
consequences: Herschel’s removal to Slough 325
§ 255. Telescope-making: marriage: the forty-foot telescope:
discoveries of satellites of Saturn and of
Uranus 327
§ 256. Life and work at Slough: last years: _Caroline
Herschel_ 328
§ 257. Herschel’s astronomical programme: the study of
the fixed stars 330
§ 258. The distribution of the stars in space: _star-gauging_:
the “grindstone” theory of the universe: defects of the
fundamental assumption: its partial withdrawal. Employment of
brightness as a test of nearness: measurement of brightness:
“space-penetrating” power of a telescope 332
§ 259. _Nebulae_ and _star clusters_: Herschel’s great catalogues 336
§ 260. Relation of nebulae to star clusters: the “island
universe” theory of nebulae: the “shining fluid”
theory: distribution of nebulae 337
§ 261. Condensation of nebulae into clusters and stars 339
§ 262. The irresolvability of the Milky Way 340
§ 263. _Double stars_: their proposed employment for finding
parallax: catalogues: probable connection
between members of a pair 341
§ 264. Discoveries of the revolution of double stars:
_binary stars_: their uselessness for parallax 343
§ 265. The motion of the sun in space: the various
positions suggested for the _apex_ 344
§ 266. Variable stars: _Mira_ and _Algol_: catalogues of
comparative brightness: method of _sequences_:
variability of α _Herculis_ 346
§ 267. Herschel’s work on the solar system: new satellites:
observations of Saturn, Jupiter, Venus, and Mars 348
§ 268. Observations of the sun: _Wilson_: theory of the
structure of the sun 350
§ 269. Suggested variability of the sun 351
§ 270. Other researches 352
§ 271. Comparison of Herschel with his contemporaries:
_Schroeter_ 352
CHAPTER XIII.
THE NINETEENTH CENTURY, §§ 272-320 354-409
§ 272. The three chief divisions of astronomy, _observational_,
_gravitational_, and _descriptive_ 354
§ 273. The great growth of descriptive astronomy in the
nineteenth century 355
§ 274. =Observational Astronomy.= Instrumental advances:
the introduction of photography 357
§ 275. The method of _least squares_: _Legendre_ and _Gauss_ 357
§ 276. Other work by Gauss: the _Theoria Motus_: rediscovery
of the minor planet Ceres 358
§ 277. _Bessel_: his improvement in methods of reduction:
his table of refraction: the _Fundamenta
Nova_ and _Tabulae Regiomontanae_ 359
§ 278. The parallax of 61 _Cygni_: its distance 360
§ 279. _Henderson’s_ parallax of α _Centauri_ and _Struve’s_
of _Vega_: later parallax determinations 362
§ 280. Star catalogues: the photographic chart 362
§§ 281-4. The distance of the sun: transits of Venus:
observations of Mars and of the minor planets
in opposition: _diurnal method_: gravitational
methods, lunar and planetary: methods
based on the velocity of light: summary of results 363
§ 285. Variation in latitude: rigidity of the earth 367
§ 286. =Gravitational Astronomy.= Lunar theory: _Damoiseau_,
_Poisson_, _Pontécoulant_, _Lubbock_, _Hansen_,
_Delaunay_, Professor _Newcomb_, _Adams_, Dr.
_Hill_ 367
§ 287. Secular acceleration of the moon’s mean motion:
Adams’s correction of Laplace: Delaunay’s
explanation by means of _tidal friction_ 369
§ 288. Planetary theory: _Leverrier_, _Gyldén_, M. _Poincaré_ 370
§ 289. The discovery of Neptune by Leverrier and Dr.
_Galle_: Adams’s work 371
§ 290. Lunar and planetary tables: outstanding discrepancies
between theory and observation 372
§ 291. Cometary orbits: return of Halley’s comet in
1835: Encke’s and other periodic comets 372
§ 292. Theory of tides: analysis of tidal observations
by Lubbock, _Whewell_, Lord _Kelvin_, and
Professor _Darwin_: bodily tides in the earth
and its rigidity 373
§ 293. The stability of the solar system 374
§ 294. =Descriptive Astronomy.= Discovery of the _minor
planets_ or _asteroids_: their number, distribution,
and size 376
§ 295. Discoveries of satellites of Neptune, Saturn,
Uranus, Mars, and Jupiter, and of the _crape
ring_ of Saturn 380
§ 296. The surface of the moon: _rills_: the lunar atmosphere 382
§ 297. The surfaces of Mars, Jupiter, and Saturn: the
_canals_ on Mars: _Maxwell’s_ theory of Saturn’s
rings: the rotation of Mercury and of Venus 383
§ 298. The surface of the sun: _Schwabe’s_ discovery of
the periodicity of sun-spots: connection between
sun-spots and terrestrial magnetism:
_Carrington’s_ observations of the motion and
distribution of spots: Wilson’s theory of spots 385
§§ 299-300. _Spectrum analysis_: Newton, _Wollaston_, _Fraunhofer_,
_Kirchhoff_: the chemistry of the sun 386
§ 301. Eclipses of the sun: the _corona_, _chromosphere_,
and _prominences_: spectroscopic methods of
observation 389
§ 302. Spectroscopic method of determining motion to
or from the observer: _Doppler’s principle_:
application to the sun 391
§ 303. The constitution of the sun 392
§§ 304-5. Observations of comets: _nucleus_: theory of the
formation of their tails: their spectra: relation
between comets and _meteors_ 393
§§ 306-8. Sidereal astronomy: career of _John Herschel_: his
catalogues of nebulae and of double stars:
the expedition to the Cape: measurement of
the sun’s heat by Herschel and by _Pouillet_ 396
§ 309. Double stars: observations by Struve and
others: orbits of binary stars 398
§ 310. Lord _Rosse’s_ telescopes: his observations of
nebulae: revival of the “island universe”
theory 400
§ 311. Application of the spectroscope to nebulae:
distinction between nebulae and clusters 401
§ 312. Spectroscopic classification of stars by _Secchi_:
chemistry of stars: stars with bright-line
spectra 401
§§ 313-4. Motion of stars in the line of sight. Discovery
of binary stars by the spectroscope: eclipse
theory of variable stars 402
§ 315. Observations of variable stars 403
§ 316. Stellar _photometry_: _Pogson’s_ light ratio: the
Oxford, Harvard, and Potsdam photometries 403
§ 317. Structure of the sidereal system: relations of
stars and nebulae 405
§§ 318-20. Laplace’s nebular hypothesis in the light of
later discoveries: the sun’s heat: _Helmholtz’s_
shrinkage theory. Influence of tidal friction on
the development of the solar system: Professor
Darwin’s theory of the birth of the moon.
Summary 406
LIST OF AUTHORITIES AND OF BOOKS FOR STUDENTS 411
INDEX OF NAMES 417
GENERAL INDEX 425
LIST OF ILLUSTRATIONS.
FIG. PAGE
The moon _Frontispiece_
1. The celestial sphere 5
2. The daily paths of circumpolar stars _To face p._ 8
3. The circles of the celestial sphere 9
4. The equator and the ecliptic 11
5. The Great Bear _To face p._ 12
6. The apparent path of Jupiter 16
7. The apparent path of Mercury 17
8-11. The phases of the moon 30, 31
12. The curvature of the earth 32
13. The method of Aristarchus for comparing the distances of
the sun and moon 34
14. The equator and the ecliptic 36
15. The equator, the horizon, and the meridian 38
16. The measurement of the earth 39
17. The eccentric 44
18. The position of the sun’s apogee 45
19. The epicycle and the deferent 47
20. The eclipse method of connecting the distances of the sun
and moon 50
21. The increase of the longitude of a star 52
22. The movement of the equator 53
23, 24. The precession of the equinoxes 53, 54
25. The earth’s shadow 57
26. The ecliptic and the moon’s path 57
27. The sun and moon 58
28. Partial eclipse of the moon 58
29. Total eclipse of the moon 58
30. Annular eclipse of the sun 59
31. Parallax 60
32. Refraction by the atmosphere 63
33. Parallax 68
34. Jupiter’s epicycle and deferent 70
35. The equant 71
36. The celestial spheres 89
PORTRAIT OF COPPERNICUS _To face p._ 94
37. Relative motion 102
38. The relative motion of the sun and moon 103
39. The daily rotation of the earth 104
40. The solar system according to Coppernicus 107
41, 42. Coppernican explanation of the seasons 108, 109
43. The orbits of Venus and of the earth 113
44. The synodic and sidereal periods of Venus 114
45. The epicycle of Jupiter 116
46. The relative sizes of the orbits of the earth and of a superior
planet 117
47. The stationary points of Mercury 119
48. The stationary points of Jupiter 120
49. The alteration in a planet’s apparent position due to an
alteration in the earth’s distance from the sun 122
50. Stellar parallax 124
51. Uraniborg 133
52. Tycho’s system of the world 137
PORTRAIT OF TYCHO BRAHE _To face p._ 139
53. One of Galilei’s drawings of the moon „ 150
54. Jupiter and its satellites as seen on January 7, 1610 152
55. Sun-spots _To face p._ 154
56. Galilei’s proof that sun-spots are not planets 156
57. The differential method of parallax 165
PORTRAIT OF GALILEI _To face p._ 171
58. The daily libration of the moon 173
PORTRAIT OF KEPLER _To face p._ 183
59. An ellipse 185
60. Kepler’s second law 186
61. Diagram used by Kepler to establish his laws of planetary
motion 187
62. The “music of the spheres” according to Kepler 190
63. Kepler’s idea of gravity 196
64. Saturn’s ring, as drawn by Huygens _To face p._ 200
65. Saturn, with the ring seen edge-wise „ 200
66. The phases of Saturn’s ring 201
67. Early drawings of Saturn _To face p._ 202
68. Mars in opposition 206
69. The parallax of a planet 206
70. Motion in a circle 214
71. The moon as a projectile 220
72. The spheroidal form of the earth 234
73. An elongated ellipse and a parabola 238
PORTRAIT OF NEWTON _To face p._ 240
PORTRAIT OF BRADLEY „ 258
74, 75. The aberration of light 262, 263
76. The aberrational ellipse 264
77. Precession and nutation 268
78. The varying curvature of the earth 277
79. Tobias Mayer’s map of the moon _To face p._ 282
80. The path of Halley’s comet 294
81. A varying ellipse 303
PORTRAIT OF LAGRANGE _To face p._ 305
PORTRAIT OF LAPLACE „ 307
PORTRAIT OF WILLIAM HERSCHEL „ 327
82. Herschel’s forty-foot telescope 329
83. Section of the sidereal system 333
84. Illustrating the effect of the sun’s motion in space 345
85. _61 Cygni_ and the two neighbouring stars used by Bessel 360
86. The parallax of _61 Cygni_ 361
87. The path of Halley’s comet 373
88. Photographic trail of a minor planet _To face p._ 377
89. Paths of minor planets 378
90. Comparative sizes of three minor planets and the moon 379
91. Saturn and its system 380
92. Mars and its satellites 381
93. Jupiter and its satellites 382
94. The Apennines and the adjoining regions } _To face p._ 383
of the moon }
95. Saturn and its rings „ 384
96. A group of sun-spots „ 385
97. Fraunhofer’s map of the solar spectrum „ 387
98. The total solar eclipse of 1886 „ 390
99. The great comet of 1882 „ 393
100. The nebula about η _Argus_ „ 397
101. The orbit of ξ _Ursae_ 399
102. Spiral nebulae _To face p._ 400
103. The spectrum of β _Aurigae_ „ 403
104. The Milky Way near the cluster in Perseus „ 405
A SHORT HISTORY OF ASTRONOMY.
CHAPTER I.
PRIMITIVE ASTRONOMY.
“The never-wearied Sun, the Moon exactly round,
And all those Stars with which the brows of ample heaven are crowned,
Orion, all the Pleiades, and those seven Atlas got,
The close beamed Hyades, the Bear, surnam’d the Chariot,
That turns about heaven’s axle tree, holds ope a constant eye
Upon Orion, and of all the cressets in the sky
His golden forehead never bows to th’ Ocean empery.”
_The Iliad_ (Chapman’s translation).
1. Astronomy is the science which treats of the sun, the moon, the
stars, and other objects such as comets which are seen in the sky. It
deals to some extent also with the earth, but only in so far as it has
properties in common with the heavenly bodies. In early times astronomy
was concerned almost entirely with the observed motions of the heavenly
bodies. At a later stage astronomers were able to discover the
distances and sizes of many of the heavenly bodies, and to weigh some
of them; and more recently they have acquired a considerable amount of
knowledge as to their nature and the material of which they are made.
2. We know nothing of the beginnings of astronomy, and can only
conjecture how certain of the simpler facts of the science—particularly
those with a direct influence on human life and comfort—gradually
became familiar to early mankind, very much as they are familiar to
modern savages.
With these facts it is convenient to begin, taking them in the order in
which they most readily present themselves to any ordinary observer.
3. The sun is daily seen to rise in the eastern part of the sky, to
travel across the sky, to reach its highest position in the south in
the middle of the day, then to sink, and finally to set in the western
part of the sky. But its daily path across the sky is not always the
same: the points of the horizon at which it rises and sets, its height
in the sky at midday, and the time from sunrise to sunset, all go
through a series of changes, which are accompanied by changes in the
weather, in vegetation, etc.; and we are thus able to recognise the
existence of the seasons, and their recurrence after a certain interval
of time which is known as a year.
4. But while the sun always appears as a bright circular disc, the
next most conspicuous of the heavenly bodies, the moon, undergoes
changes of form which readily strike the observer, and are at once
seen to take place in a regular order and at about the same intervals
of time. A little more care, however, is necessary in order to observe
the connection between the form of the moon and her position in the
sky with respect to the sun. Thus when the moon is first visible soon
after sunset near the place where the sun has set, her form is a thin
crescent (cf. fig. 11 on p. 31), the hollow side being turned away
from the sun, and she sets soon after the sun. Next night the moon is
farther from the sun, the crescent is thicker, and she sets later; and
so on, until after rather less than a week from the first appearance of
the crescent, she appears as a semicircular disc, with the flat side
turned away from the sun. The semicircle enlarges, and after another
week has grown into a complete disc; the moon is now nearly in the
opposite direction to the sun, and therefore rises about at sunset
and sets about at sunrise. She then begins to approach the sun on the
other side, rising before it and setting in the daytime; her size
again diminishes, until after another week she is again semicircular,
the flat side being still turned away from the sun, but being now
turned towards the west instead of towards the east. The semicircle
then becomes a gradually diminishing crescent, and the time of rising
approaches the time of sunrise, until the moon becomes altogether
invisible. After two or three nights the new moon reappears, and the
whole series of changes is repeated. The different forms thus assumed
by the moon are now known as her =phases=; the time occupied by this
series of changes, the month, would naturally suggest itself as a
convenient measure of time; and the day, month, and year would thus
form the basis of a rough system of time-measurement.
5. From a few observations of the stars it could also clearly be seen
that they too, like the sun and moon, changed their positions in the
sky, those towards the east being seen to rise, and those towards
the west to sink and finally set, while others moved across the sky
from east to west, and those in a certain northern part of the sky,
though also in motion, were never seen either to rise or set. Although
anything like a complete classification of the stars belongs to a
more advanced stage of the subject, a few star groups could easily be
recognised, and their position in the sky could be used as a rough
means of measuring time at night, just as the position of the sun to
indicate the time of day.
6. To these rudimentary notions important additions were made when
rather more careful and prolonged observations became possible, and
some little thought was devoted to their interpretation.
Several peoples who reached a high stage of civilisation at an early
period claim to have made important progress in astronomy. Greek
traditions assign considerable astronomical knowledge to Egyptian
priests who lived some thousands of years B.C., and some of the
peculiarities of the pyramids which were built at some such period
are at any rate plausibly interpreted as evidence of pretty accurate
astronomical observations; Chinese records describe observations
supposed to have been made in the 25th century B.C.; some of the Indian
sacred books refer to astronomical knowledge acquired several centuries
before this time; and the first observations of the Chaldaean priests
of Babylon have been attributed to times not much later.
On the other hand, the earliest recorded astronomical observation the
authenticity of which may be accepted without scruple belongs only to
the 8th century B.C.
For the purposes of this book it is not worth while to make any attempt
to disentangle from the mass of doubtful tradition and conjectural
interpretation of inscriptions, bearing on this early astronomy, the
few facts which lie embedded therein; and we may proceed at once to
give some account of the astronomical knowledge, other than that
already dealt with, which is discovered in the possession of the
earliest really historical astronomers—the Greeks—at the beginning of
their scientific history, leaving it an open question what portions of
it were derived from Egyptians, Chaldaeans, their own ancestors, or
other sources.
7. If an observer looks at the stars on any clear night he sees an
apparently innumerable[1] host of them, which seem to lie on a portion
of a spherical surface, of which he is the centre. This spherical
surface is commonly spoken of as the sky, and is known to astronomy
as the =celestial sphere=. The visible part of this sphere is bounded
by the earth, so that only half can be seen at once; but only the
slightest effort of the imagination is required to think of the other
half as lying below the earth, and containing other stars, as well as
the sun. This sphere appears to the observer to be very large, though
he is incapable of forming any precise estimate of its size.[2]
Most of us at the present day have been taught in childhood that
the stars are at different distances, and that this sphere has in
consequence no real existence. The early peoples had no knowledge of
this, and for them the celestial sphere really existed, and was often
thought to be a solid sphere of crystal.
[Illustration: FIG. 1.—The celestial sphere.]
Moreover modern astronomers, as well as ancient, find it convenient
for very many purposes to make use of this sphere, though it has no
material existence, as a means of representing the directions in which
the heavenly bodies are seen and their motions. For all that direct
observation can tell us about the position of such an object as a star
is its _direction_; its distance can only be ascertained by indirect
methods, if at all. If we draw a sphere, and suppose the observer’s eye
placed at its centre O (fig. 1), and then draw a straight line from O
to a star S, meeting the surface of the sphere in the point _s_; then
the star appears exactly in the same position as if it were at _s_, nor
would its apparent position be changed if it were placed at any other
point, such as S′ or S″, on this same line. When we speak, therefore,
of a star as being at a point _s_ on the celestial sphere, all that we
mean is that it is in the same direction as the point _s_, or, in other
words, that it is situated somewhere on the straight line through O and
S. The advantages of this method of representing the position of a star
become evident when we wish to compare the positions of several stars.
The difference of direction of two stars is the angle between the lines
drawn from the eye to the stars; _e.g._, if the stars are R, S, it is
the angle R O S. Similarly the difference of direction of another pair
of stars, P, Q, is the angle P O Q. The two stars P and Q appear nearer
together than do R and S, or farther apart, according as the angle P
O Q is less or greater than the angle R O S. But if we represent the
stars by the corresponding points _p_, _q_, _r_, _s_ on the celestial
sphere, then (by an obvious property of the sphere) the angle P O Q
(which is the same as _p_ O _q_) is less or greater than the angle R O
S (or _r_ O _s_) according as the arc joining _p q_ on the sphere is
less or greater than the arc joining _r s_, and in the same proportion;
if, for example, the angle R O S is twice as great as the angle P O
Q, so also is the arc _p q_ twice as great as the arc _r s_. We may
therefore, in all questions relating only to the directions of the
stars, replace the angle between the directions of two stars by the arc
joining the corresponding points on the celestial sphere, or, in other
words, by the distance between these points on the celestial sphere.
But such arcs on a sphere are easier both to estimate by eye and to
treat geometrically than angles, and the use of the celestial sphere
is therefore of great value, apart from its historical origin. It is
important to note that this =apparent distance= of two stars, _i.e._
their distance from one another on the celestial sphere, is an entirely
different thing from their actual distance from one another in space.
In the figure, for example, Q is actually much nearer to S than it is
to P, but the apparent distance measured by the arc _q s_ is several
times greater than _q p_. The apparent distance of two points on the
celestial sphere is measured numerically by the angle between the lines
joining the eye to the two points, expressed in =degrees=, =minutes=,
and =seconds=.[3]
We might of course agree to regard the celestial sphere as of a
particular size, and then express the distance between two points on
it in miles, feet, or inches; but it is practically very inconvenient
to do so. To say, as some people occasionally do, that the distance
between two stars is so many feet is meaningless, unless the supposed
size of the celestial sphere is given at the same time.
It has already been pointed out that the observer is always at the
centre of the celestial sphere; this remains true even if he moves to
another place. A sphere has, however, only one centre, and therefore
if the sphere remains fixed the observer cannot move about and yet
always remain at the centre. The old astronomers met this difficulty
by supposing that the celestial sphere was so large that any possible
motion of the observer would be insignificant in comparison with
the radius of the sphere and could be neglected. It is often more
convenient—when we are using the sphere as a mere geometrical device
for representing the position of the stars—to regard the sphere as
moving with the observer, so that he always remains at the centre.
8. Although the stars all appear to move across the sky (§ 5), and
their rates of motion differ, yet the distance between any two stars
remains unchanged, and they were consequently regarded as being
attached to the celestial sphere. Moreover a little careful observation
would have shown that the motions of the stars in different parts of
the sky, though at first sight very different, were just such as would
have been produced by the celestial sphere—with the stars attached
to it—turning about an axis passing through the centre and through a
point in the northern sky close to the familiar pole-star. This point
is called the =pole=. As, however, a straight line drawn through the
centre of a sphere meets it in two points, the axis of the celestial
sphere meets it again in a second point, opposite the first, lying in
a part of the celestial sphere which is permanently below the horizon.
This second point is also called a pole; and if the two poles have to
be distinguished, the one mentioned first is called the =north pole=,
and the other the =south pole=. The direction of the rotation of the
celestial sphere about its axis is such that stars near the north pole
are seen to move round it in circles in the direction opposite to
that in which the hands of a clock move; the motion is uniform, and a
complete revolution is performed in four minutes less than twenty-four
hours; so that the position of any star in the sky at twelve o’clock
to-night is the same as its position at four minutes to twelve
to-morrow night.
The moon, like the stars, shares this motion of the celestial sphere
and so also does the sun, though this is more difficult to recognise
owing to the fact that the sun and stars are not seen together.
As other motions of the celestial bodies have to be dealt with, the
general motion just described may be conveniently referred to as the
=daily motion= or =daily rotation= of the celestial sphere.
9. A further study of the daily motion would lead to the recognition of
certain important circles of the celestial sphere.
Each star describes in its daily motion a circle, the size of
which depends on its distance from the poles. Fig. 2 shews the
paths described by a number of stars near the pole, recorded
photographically, during part of a night. The pole-star describes so
small a circle that its motion can only with difficulty be detected
with the naked eye, stars a little farther off the pole describe larger
circles, and so on, until we come to stars half-way between the two
poles, which describe the largest circle which can be drawn on the
celestial sphere. The circle on which these stars lie and which is
described by any one of them daily is called the =equator=. By looking
at a diagram such as fig. 3, or, better still, by looking at an actual
globe, it can easily be seen that half the equator (E Q W) lies above
and half (the dotted part, W R E) below the horizon, and that in
consequence a star, such as _s_, lying on the equator, is in its daily
motion as long a time above the horizon as below. If a star, such as
S, lies on the north side of the equator, _i.e._ on the side on which
the north pole P lies, more than half of its daily path lies above the
horizon and less than half (as shewn by the dotted line) lies below;
and if a star is near enough to the north pole (more precisely, if it
is nearer to the north pole than the nearest point, K, of the horizon),
as σ, it never sets, but remains continually above the horizon. Such a
star is called a (=northern=) =circumpolar= star. On the other hand,
less than half of the daily path of a star on the south side of the
equator, as S′, is above the horizon, and a star, such as σ′, the
distance of which from the north pole is greater than the distance of
the farthest point, H, of the horizon, or which is nearer than H to the
south pole, remains continually below the horizon.
[Illustration:
FIG. 2.—The paths of circumpolar stars, shewing their movement during
seven hours. From a photograph by Mr. H. Pain. The thickest line is
the path of the pole star. [_To face p. 8._ ]
10. A slight familiarity with the stars is enough to shew any one
that the same stars are not always visible at the same time of night.
Rather more careful observation, carried out for a considerable time,
is necessary in order to see that the aspect of the sky changes in a
regular way from night to night, and that after the lapse of a year the
same stars become again visible at the same time. The explanation of
these changes as due to the motion of the sun on the celestial sphere
is more difficult, and the unknown discoverer of this fact certainly
made one of the most important steps in early astronomy.
[Illustration: FIG. 3.—The circles of the celestial sphere.]
If an observer notices soon after sunset a star somewhere in the
west, and looks for it again a few evenings later at about the same
time, he finds it lower down and nearer to the sun; a few evenings
later still it is invisible, while its place has now been taken by
some other star which was at first farther east in the sky. This star
can in turn be observed to approach the sun evening by evening. Or
if the stars visible after sunset low down in the east are noticed
a few days later, they are found to be higher up in the sky, and
their place is taken by other stars at first too low down to be seen.
Such observations of stars rising or setting about sunrise or sunset
shewed to early observers that the stars were gradually changing their
position with respect to the sun, or that the sun was changing its
position with respect to the stars.
The changes just described, coupled with the fact that the stars do not
change their positions with respect to one another, shew that the stars
as a whole perform their daily revolution rather more rapidly than the
sun, and at such a rate that they gain on it one complete revolution
in the course of the year. This can be expressed otherwise in the
form that the stars are all moving westward on the celestial sphere,
relatively to the sun, so that stars on the east are continually
approaching and those on the west continually receding from the sun.
But, again, the same facts can be expressed with equal accuracy and
greater simplicity if we regard the stars as fixed on the celestial
sphere, and the sun as moving on it from west to east among them (that
is, in the direction _opposite_ to that of the daily motion), and at
such a rate as to complete a circuit of the celestial sphere and to
return to the same position after a year.
This =annual motion= of the sun is, however, readily seen not to be
merely a motion from west to east, for if so the sun would always rise
and set at the same points of the horizon, as a star does, and its
midday height in the sky and the time from sunrise to sunset would
always be the same. We have already seen that if a star lies on the
equator half of its daily path is above the horizon, if the star is
north of the equator more than half, and if south of the equator less
than half; and what is true of a star is true for the same reason of
any body sharing the daily motion of the celestial sphere. During the
summer months therefore (March to September), when the day is longer
than the night, and more than half of the sun’s daily path is above the
horizon, the sun must be north of the equator, and during the winter
months (September to March) the sun must be south of the equator. The
change in the sun’s distance from the pole is also evident from the
fact that in the winter months the sun is on the whole lower down in
the sky than in summer, and that in particular its midday height is
less.
11. The sun’s path on the celestial sphere is therefore oblique to the
equator, lying partly on one side of it and partly on the other. A good
deal of careful observation of the kind we have been describing must,
however, have been necessary before it was ascertained that the sun’s
annual path on the celestial sphere (see fig. 4) is a =great circle=
(that is, a circle having its centre at the centre of the sphere).
This great circle is now called the =ecliptic= (because eclipses take
place only when the moon is in or near it), and the angle at which it
cuts the equator is called the =obliquity= of the ecliptic. The Chinese
claim to have measured the obliquity in 1100 B.C., and to have found
the remarkably accurate value 23° 52′ (cf. chapter II., § 35). The
truth of this statement may reasonably be doubted, but on the other
hand the statement of some late Greek writers that either Pythagoras
or Anaximander (6th century B.C.) was the _first_ to discover the
obliquity of the ecliptic is almost certainly wrong. It must have been
known with reasonable accuracy to both Chaldaeans and Egyptians long
before.
[Illustration: FIG. 4.—The equator and the ecliptic.]
When the sun crosses the equator the day is equal to the night, and the
times when this occurs are consequently known as the =equinoxes=, the
=vernal equinox= occurring when the sun crosses the equator from south
to north (about March 21st), and the =autumnal equinox= when it crosses
back (about September 23rd). The points on the celestial sphere where
the sun crosses the equator (A, C in fig. 4), _i.e._ where ecliptic
and equator cross one another, are called the =equinoctial points=,
occasionally also the equinoxes.
After the vernal equinox the sun in its path along the ecliptic
recedes from the equator towards the north, until it reaches, about
three months afterwards, its greatest distance from the equator, and
then approaches the equator again. The time when the sun is at its
greatest distance from the equator on the north side is called the
=summer solstice=, because then the northward motion of the sun is
arrested and it temporarily appears to stand still. Similarly the sun
is at its greatest distance from the equator towards the south at the
=winter solstice=. The points on the ecliptic (B, D in fig. 4) where
the sun is at the solstices are called the =solstitial points=, and are
half-way between the equinoctial points.
12. The earliest observers probably noticed particular groups of stars
remarkable for their form or for the presence of bright stars among
them, and occupied their fancy by tracing resemblances between them
and familiar objects, etc. We have thus at a very early period a rough
attempt at dividing the stars into groups called =constellations= and
at naming the latter.
In some cases the stars regarded as belonging to a constellation form a
well-marked group on the sky, sufficiently separated from other stars
to be conveniently classed together, although the resemblance which
the group bears to the object after which it is named is often very
slight. The seven bright stars of the Great Bear, for example, form
a group which any observer would very soon notice and naturally make
into a constellation, but the resemblance to a bear of these and the
fainter stars of the constellation is sufficiently remote (see fig.
5), and as a matter of fact this part of the Bear has also been called
a Waggon and is in America familiarly known as the Dipper; another
constellation has sometimes been called the Lyre and sometimes also the
Vulture. In very many cases the choice of stars seems to have been made
in such an arbitrary manner, as to suggest that some fanciful figure
was first imagined and that stars were then selected so as to represent
it in some rough sort of way. In fact, as Sir John Herschel remarks,
“The constellations seem to have been purposely named and delineated
to cause as much confusion and inconvenience as possible. Innumerable
snakes twine through long and contorted areas of the heavens where no
memory can follow them; bears, lions, and fishes, large and small,
confuse all nomenclature.” (_Outlines of Astronomy_, § 301.)
[Illustration: FIG. 5.—The Great Bear. From Bayer’s _Uranometria_
(1603). [_To face p. 12._]
The constellations as we now have them are, with the exception of a
certain number (chiefly in the southern skies) which have been added
in modern times, substantially those which existed in early Greek
astronomy; and such information as we possess of the Chaldaean and
Egyptian constellations shews resemblances indicating that the Greeks
borrowed some of them. The names, as far as they are not those of
animals or common objects (Bear, Serpent, Lyre, etc.), are largely
taken from characters in the Greek mythology (Hercules, Perseus, Orion,
etc.). The constellation Berenice’s Hair, named after an Egyptian
queen of the 3rd century B.C., is one of the few which commemorate a
historical personage.[4]
13. Among the constellations which first received names were those
through which the sun passes in its annual circuit of the celestial
sphere, that is those through which the ecliptic passes. The moon’s
monthly path is also a great circle, never differing very much from
the ecliptic, and the paths of the planets (§ 14) are such that they
also are never far from the ecliptic. Consequently the sun, the moon,
and the five planets were always to be found within a region of the
sky extending about 8° on each side of the ecliptic. This strip of the
celestial sphere was called the =zodiac=, because the constellations
in it were (with one exception) named after living things (Greek ζῷον,
an animal); it was divided into twelve equal parts, the =signs of the
zodiac=, through one of which the sun passed every month, so that the
position of the sun at any time could be roughly described by stating
in what “sign” it was. The stars in each “sign” were formed into a
constellation, the “sign” and the constellation each receiving the
same name. Thus arose twelve =zodiacal constellations=, the names of
which have come down to us with unimportant changes from early Greek
times.[5] Owing, however, to an alteration of the position of the
equator, and consequently of the equinoctial points, the sign Aries,
which was defined by Hipparchus in the second century B.C. (see chapter
II., § 42) as beginning at the vernal equinoctial point, no longer
contains the constellation Aries, but the preceding one, Pisces: and
there is a corresponding change throughout the zodiac. The more precise
numerical methods of modern astronomy have, however, rendered the signs
of the zodiac almost obsolete: but the =first point of Aries= (♈), and
the =first point of Libra= (♎), are still the recognised names for the
equinoctial points.
In some cases individual stars also received special names, or were
called after the part of the constellation in which they were situated,
_e.g._ Sirius, the Eye of the Bull, the Heart of the Lion, etc.; but
the majority of the present names of single stars are of Arabic origin
(chapter III., § 64).
14. We have seen that the stars, as a whole, retain invariable
positions on the celestial sphere,[6] whereas the sun and moon change
their positions. It was, however, discovered in prehistoric times that
five bodies, at first sight barely distinguishable from the other
stars, also changed their places. These five—Mercury, Venus, Mars,
Jupiter, and Saturn—with the sun and moon, were called =planets=,[7] or
wanderers, as distinguished from the =fixed stars=. Mercury is never
seen except occasionally near the horizon just after sunset or before
sunrise, and in a climate like ours requires a good deal of looking
for; and it is rather remarkable that no record of its discovery should
exist. Venus is conspicuous as the Evening Star or as the Morning Star.
The discovery of the identity of the Evening and Morning Stars is
attributed to Pythagoras (6th century B.C.), but must almost certainly
have been made earlier, though the Homeric poems contain references to
both, without any indication of their identity. Jupiter is at times as
conspicuous as Venus at her brightest, while Mars and Saturn, when well
situated, rank with the brightest of the fixed stars.
The paths of the planets on the celestial sphere are, as we have seen
(§ 13), never very far from the ecliptic; but whereas the sun and moon
move continuously along their paths from west to east, the motion of
a planet is sometimes from west to east, or =direct=, and sometimes
from east to west, or =retrograde=. If we begin to watch a planet when
it is moving eastwards among the stars, we find that after a time
the motion becomes slower and slower, until the planet hardly seems
to move at all, and then begins to move with gradually increasing
speed in the opposite direction; after a time this westward motion
becomes slower and then ceases, and the planet then begins to move
eastwards again, at first slowly and then faster, until it returns to
its original condition, and the changes are repeated. When the planet
is just reversing its motion it is said to be =stationary=, and its
position then is called a =stationary point=. The time during which a
planet’s motion is retrograde is, however, always considerably less
than that during which it is direct; Jupiter’s motion, for example, is
direct for about 39 weeks and retrograde for 17, while Mercury’s direct
motion lasts 13 or 14 weeks and the retrograde motion only about 3
weeks (see figs. 6, 7). On the whole the planets advance from west to
east and describe circuits round the celestial sphere in periods which
are different for each planet. The explanation of these irregularities
in the planetary motions was long one of the great difficulties of
astronomy.
[Illustration:
FIG. 6.—The apparent path of Jupiter from Oct. 28, 1897, to Sept. 3,
1898. The dates printed in the diagram shew the positions of Jupiter.]
15. The idea that some of the heavenly bodies are nearer to the
earth than others must have been suggested by eclipses (§ 17) and
=occultations=, _i.e._ passages of the moon over a planet or fixed
star. In this way the moon would be recognised as nearer than any
of the other celestial bodies. No direct means being available for
determining the distances, rapidity of motion was employed as a test
of probable nearness. Now Saturn returns to the same place among the
stars in about 29-1∕2 years, Jupiter in 12 years, Mars in 2 years, the
sun in one year, Venus in 225 days, Mercury in 88 days, and the moon in
27 days; and this order was usually taken to be the order of distance,
Saturn being the most distant, the moon the nearest. The stars being
seen above us it was natural to think of the most distant celestial
bodies as being the highest, and accordingly Saturn, Jupiter, and Mars
being beyond the sun were called =superior planets=, as distinguished
from the two =inferior planets= Venus and Mercury. This division
corresponds also to a difference in the observed motions, as Venus and
Mercury seem to accompany the sun in its annual journey, being never
more than about 47 and 29° respectively distant from it, on either
side; while the other planets are not thus restricted in their motions.
[Illustration:
FIG. 7.—The apparent path of Mercury from Aug. 1 to Oct. 3, 1898. The
dates printed in capital letters shew the positions of the sun; the
other dates shew those of Mercury.]
16. One of the purposes to which applications of astronomical knowledge
was first applied was to the measurement of time. As the alternate
appearance and disappearance of the sun, bringing with it light and
heat, is the most obvious of astronomical facts, so the day is the
simplest unit of time.[8] Some of the early civilised nations divided
the time from sunrise to sunset and also the night each into 12 equal
hours. According to this arrangement a day-hour was in summer longer
than a night-hour and in winter shorter, and the length of an hour
varied during the year. At Babylon, for example, where this arrangement
existed, the length of a day-hour was at midsummer about half as long
again as in midwinter, and in London it would be about twice as long.
It was therefore a great improvement when the Greeks, in comparatively
late times, divided the whole day into 24 equal hours. Other early
nations divided the same period into 12 double hours, and others again
into 60 hours.
The next most obvious unit of time is the =lunar month=, or period
during which the moon goes through her phases. A third independent unit
is the year. Although the year is for ordinary life much more important
than the month, yet as it is much longer and any one time of year is
harder to recognise than a particular phase of the moon, the length of
the year is more difficult to determine, and the earliest known systems
of time-measurement were accordingly based on the month, not on the
year. The month was found to be nearly equal to 29-1∕2 days, and as a
period consisting of an exact number of days was obviously convenient
for most ordinary purposes, months of 29 or 30 days were used, and
subsequently the calendar was brought into closer accord with the moon
by the use of months containing alternately 29 and 30 days (cf. chapter
II., § 19).
Both Chaldaeans and Egyptians appear to have known that the year
consisted of about 365-1∕4 days; and the latter, for whom the
importance of the year was emphasised by the rising and falling of the
Nile, were probably the first nation to use the year in preference to
the month as a measure of time. They chose a year of 365 days.
The origin of the week is quite different from that of the month or
year, and rests on certain astrological ideas about the planets. To
each hour of the day one of the seven planets (sun and moon included)
was assigned as a “ruler,” and each day named after the planet which
ruled its first hour. The planets being taken in the order already
given (§ 15), Saturn ruled the first hour of the first day, and
therefore also the 8th, 15th, and 22nd hours of the first day, the 5th,
12th, and 19th of the second day, and so on; Jupiter ruled the 2nd,
9th, 16th, and 23rd hours of the first day, and subsequently the 1st
hour of the 6th day. In this way the first hours of successive days
fell respectively to Saturn, the Sun, the Moon, Mars, Mercury, Jupiter,
and Venus. The first three are easily recognised in our Saturday,
Sunday, and Monday; in the other days the names of the Roman gods have
been replaced by their supposed Teutonic equivalents—Mercury by Wodan,
Mars by Thues, Jupiter by Thor, Venus by Freia.[9]
17. =Eclipses= of the sun and moon must from very early times have
excited great interest, mingled with superstitious terror, and the hope
of acquiring some knowledge of them was probably an important stimulus
to early astronomical work. That eclipses of the sun only take place
at new moon, and those of the moon only at full moon, must have been
noticed after very little observation; that eclipses of the sun are
caused by the passage of the moon in front of it must have been only a
little less obvious; but the discovery that eclipses of the moon are
caused by the earth’s shadow was probably made much later. In fact even
in the time of Anaxagoras (5th century B.C.) the idea was so unfamiliar
to the Athenian public as to be regarded as blasphemous.
One of the most remarkable of the Chaldaean contributions to astronomy
was the discovery (made at any rate several centuries B.C.) of the
recurrence of eclipses after a period, known as the =saros=, consisting
of 6,585 days (or eighteen of our years and ten or eleven days,
according as five or four leap-years are included). It is probable that
the discovery was made, not by calculations based on knowledge of the
motions of the sun and moon, but by mere study of the dates on which
eclipses were recorded to have taken place. As, however, an eclipse of
the sun (unlike an eclipse of the moon) is only visible over a small
part of the surface of the earth, and eclipses of the sun occurring
at intervals of eighteen years are not generally visible at the same
place, it is not at all easy to see how the Chaldaeans could have
established their cycle for this case, nor is it in fact clear that the
saros was supposed to apply to solar as well as to lunar eclipses. The
saros may be illustrated in modern times by the eclipses of the sun
which took place on July 18th, 1860, on July 29th, 1878, and on August
9th, 1896; but the first was visible in Southern Europe, the second in
North America, and the third in Northern Europe and Asia.
18. To the Chaldaeans may be assigned also the doubtful honour of
having been among the first to develop =astrology=, the false science
which has professed to ascertain the influence of the stars on human
affairs, to predict by celestial observations wars, famines, and
pestilences, and to discover the fate of individuals from the positions
of the stars at their birth. A belief in some form of astrology has
always prevailed in oriental countries; it flourished at times among
the Greeks and the Romans; it formed an important part of the thought
of the Middle Ages, and is not even quite extinct among ourselves
at the present day.[10] It should, however, be remembered that if
the history of astrology is a painful one, owing to the numerous
illustrations which it affords of human credulity and knavery, the
belief in it has undoubtedly been a powerful stimulus to genuine
astronomical study (cf. chapter III., § 56, and chapter V., §§ 99, 100)