CHAPTER Ⅰ.PRIMITIVE ASTRONOMY, §§ 1-18 1
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 mouth: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
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 horison,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 aspses, 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
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
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 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 (FGROM ABOUT 1543 A.D.TO ABOUT 1601 A.D.), §§ 93-112 125
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 Bar 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
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 veild 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
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
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 Ausout'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
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 sequare 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 gravitatioon 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.Explanatioon 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
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 acceleratioon 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
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 Mecanique 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 based on the 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
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:siargauging: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 a 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
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 a 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:gtravitational 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.Poincare 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 282
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:Helmholis'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