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CHAPTER Ⅰ.PRIMITIVE ASTRONOMY, §§ 1-181

1.Scope of astronomy1

2-5.First notions:the motion of the sun:the motion and phases of the moon:daily motion of the stars1

6.Progress due to early civilised peoples:Egyptians,Chinese,Indians,and Chaldaeans3

7.The celestial sphere:its scientific value:apparent distance between the stars:the measurement of angles4

8-9.The rotation of the celestial sphere:the North and South poles:the daily motion:the celestial equator:circumpolar stars7

10-11.The annual motion of the sun:great circles:the ecliptic and its obliquity:the equinoxes and equinoctial points:the solstices and solstitial points8

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 points14

15.The order of nearness of the planets:occultations:superior and inferior planets15

16.Measurement of time:the day and its division into hours:the lunar mouth:the year:the week17

17.Eclipses:the saros19

18.The rise of Astrology20

CHAPTER Ⅱ.GREEK ASTRONOMY (FROM ABOUT 600 B.C.TO ABOUT 400 A.D.), §§ 19-5421

19-20.Astronomy up to the time of Aristotle.The Greek calendar:full and empty months:the octaeteris:Meton's cycle21

21.The Roman calendar:introduction of the Julian Calendar22

22.The Gregorian Calendar23

23.Early Greek speculative astronomy:Thales and Pythagoras:the spherical form of the earth:the celestial spheres:the music of the spheres24

24.Philolaus and other Pythagoreans:early believers in the motion of the earth:Aristarchus and Seleucus25

25.Plato:uniform circular and spherical motions26

26.Eudoxus:representation of the celestial motions by combinations of spheres:description of the constellations.Callippus27

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 work29

31-2.The early Alexandrine school:its rise:Aristarchus:his estimates of the distances of the sun and moon.Observations by Timocharis and Aristyllus34

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-dials36

35.The division of the surface of the earth into zones37

36.Eratosthenes:his measurement of the earth:and of the obliquity of the ecliptic39

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 epicycles40

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 deferent41

40.Theory of the moon:lunation or synodic month and sidereal month:motion of the moon's nodes and apses:draconitic month and anomalistic month47

41.Observations of planets:eclipse method of connecting the distances of the sun and moon:estimate of their distances49

42.His star catalogue.Discovery of the precession of the equinoxes:the tropical year and the sidereal year51

43.Eclipses of the sun and moon:conjunction and opposition:partial,total,and annular eclipses:parallax56

44.Delambre's estimate of Hipparchus61

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 Posidonius61

46.Ptolemy.The Almagest and the Optics:theory of refraction62

47.Account of the Almagest:Ptolemy's postulates:arguments against the motion of the earth63

48.The theory of the moon:evection and prosneusis65

49.The astrolabe.Parallax,and distances of the sun and moon67

50.The star catalogue:precession68

51.Theory of the planets:the equant69

52.Estimate of Ptolemy73

53.The decay of ancient astronomy:Theon and Hypatia73

54.Summary and estimate of Greek astronomy74

CHAPTER Ⅲ.THE MIDDLE AGES (FROM ABOUT 600 A.D.TO ABOUT 1500 A.D.), §§ 55-6976

55.The slow development of astronomy during this period76

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 others76

57-8.The Bagdad observatory.Measurement of the earth.Corrections of the astronomical data of the Greeks:trepidation78

59.Albategnius:discovery of the motion of the sun's apogee79

60.Abul Wafa:supposed discovery of the variation of the moon.Ibn Yunos:the Hakemite Tables79

61.Development of astronomy in the Mahometan dominions in Morocco and Spain:Arzachel:the Toletan Tables80

62.Nassir Eddin and his school:Ilkhanic Tables:more accurate value of precession81

63.Tartar astronomy:Ulugh Begh:his star catalogue82

64.Estimate of oriental astronomy of this period:Arabic numerals:survivals of Arabic names of stars and astronomical terms:nadir82

65.The West.General stagnation after the fall of the Roman Empire:Bede.Revival of learning at the court of Charlemagne:Alcuin83

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 Saber84

67.The schoolmen of the thirteenth century,Albertus Magnus,Cecco d' Ascoli,Roger Bacon.Sacrobosco's Sphaera Mundi85

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 mobile86

69.Lionardo da Vinci:earthshine.Fracastor and Apian:observations of comets.Nonius.Fernel's measurement of the earth90

CHAPTER Ⅳ.COPPERNICUS (FROM 1473 A.D.TO 1543 A.D.), §§ 70-9292

70.The Revival of Learning92

71-4.Life of Coppernicus:growth of his ideas:publication of the Commentariolus:Rheticus and the Prima Narratio:publication of the De Revolutionibus93

75.The central idea in the work of Coppernicus:relation to earlier writers99

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 sphere100

80.The two motions of the earth:answers to objections105

81.The motion of the planets106

82.The seasons108

83.End of first book.The second book:decrease in the obliquity of the ecliptic:the star catalogue110

84.The third book:precession110

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:eclipses111

86-7.The fifth and sixth books:theory of the planets:synodic and sidereal periods112

88.Explanation of the stationary points118

89-90.Detailed theory of the planets121

91.Coppernicus's use of epicycles122

92.A difficulty in his system123

CHAPTER Ⅴ.THE RECEPTION OF THE COPPERNICAN THEORY AND THE PROGRESS OF OBSERVATION (FGROM ABOUT 1543 A.D.TO ABOUT 1601 A.D.), §§ 93-112125

93-4.The first reception of the De Revolutionibus:Reinhold:the Prussian Tables125

95.Coppernicanism in England:Field,Recorde,Digges127

96.Difficulties in the Coppernican system:the need for progress in dynamics and for fresh observations127

97-8.The Cassel Observatory:the Landgrave William Ⅳ.,Rothmann,and Bürgi:the star catalogue:Bürgi's invention of the pendulum clock128

99.Tycho Brahe:his early life130

100.The new star of 1572:travels in Germany131

101-2.His establishment in Hveen:Uraniborg and Stjerneborg:life and work in Hveen132

103.The comet of 1577,and others135

104.Books on the new star and on the comet of 1577136

105.Tycho's system of the world:quarrel with Reymers Bar136

106.Last years at Hveen:breach with the King138

107.Publication of the Astronomiae Instauratae Mechanica and of the star catalogue:invitation from the Emperor139

108.Life at Benatek:co-operation of Kepler:death140

109.Fate of Tycho's instruments and observations141

110.Estimate of Tycho's work:the accuracy of his observations:improvements in the art of observing141

111.Improved values of astronomical constants.Theory of the moon:the variation and the annual equation143

112.The star catalogue:rejection of trepidation:unfinished work on the planets144

CHAPTER Ⅵ.GALILEI (FROM 1564 A.D.TO 1642 A.D.), §§ 113-134145

113.Early life145

114.The pendulum146

115.Diversion from medicine to mathematics:his first book146

116.Professorship at Pisa:experiments on falling bodies:protests against the principle of authority147

117.Professorship at Padua:adoption of Coppernican views148

118.The telescopic discoveries.Invention of the telescope by Lippersheim:its application to astronomy by Harriot,Simon Marius,and Galilei149

119.The Sidereus Nuncius:observations of the moon150

120.new stars:resolution of portions of the Milky Way151

121.The discovery of Jupiter's satellites:their importance for the Coppernican controversy:controversies151

122.Appointment at the Tuscan court153

123.Observations of Saturn.Discovery of the phases of Venus154

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 penumbra154

125.Quarrel with Scheiner and the Jesuits:theological controversies:Letter to the Grand Duchess Christine157

126.Visit to Rome.The first condemnation:prohibition of Coppernican books159

127.Method for finding longitude.Controversy on comets:Il Saggiatore160

128.Dialogue on the Two Chief Systems of the World.Its preparation and publication162

129.The speakers:argument for the Coppernican system based on the telescopic discoveries:discussion of stellar parallax:the differential method of parallax163

130.Dynamical arguments in favour of the motion of the earth:the First Law of Motion.The tides165

131.The trial and condemnation.The thinly veild Coppernicanism of the Dialogue:the remarkable preface168

132.Summons to Rome:trial by the Inquisition:condemnation,abjuration,and punishment:prohibition of the Dialogue169

133.Last years:life at Arcetri:libration of the moon:the Two New Sciences:uniform acceleration,and the first law of motion.Blindness and death172

134.Estimate of Galilei's work:his scientific method176

CHAPTER Ⅶ.KEPLER (FROM 1571 A.D.TO 1630 A.D.), §§ 135-151179

135.Early life and theological studies179

136.Lectureship on mathematics at Gratz:astronomical studies and speculations:the Mysterium Cosmographicum180

137.Religious troubles in Styria:work with Tycho181

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 telescope182

139.Study of the motion of Mars:unsuccessful attempts to explain it183

140-1.The ellipse:discovery of the first two of Kepler's Laws for the case of Mars:the Commentaries on Mars184

142.Suggested extension of Kepler's Laws to the other planets186

143.Abdication and death of Rudolph:appointment at Linz188

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 corona191

146.Treatise on Comets193

147.Religious troubles at Linz:removal to Ulm194

148.The Rudolphine Tables194

149.Work under Wallenstein:death195

150.Minor discoveries:speculations on gravity195

151.Estimate of Kepler's work and intellectual character197

CHAPTER Ⅷ.FROM GALILEI TO NEWTON (FROM ABOUT 1638 A.D.TO ABOUT 1687 A.D.), §§ 152-163198

152.The general character of astronomical progress during the period198

153.Scheiner's observations of faculae on the sun.Hevel:his Selenographia and his writings on comets:his star catalogue.Riccioli's New Almagest198

154.Planetary observations:Huygens's discovery of a satellite of Saturn and of its ring199

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 Venus202

157-8.Huygens's rediscovery of the pendulum clock:his theory of circular motion203

159.Measurements of the earth by Snell,Norwood,and Picard204

160.The Paris Observatory:Domenico Cassini:his discoveries of four new satellites of Saturn:his other work204

161.Richer's expedition to Cayenne:pendulum observations:observations of Mars in opposition:horizontal parallax:annual or stellar parallax205

162.Roemer and the velocity of light208

163.Descartes208

CHAPTER Ⅸ.UNIVERSAL GRAVITATION (FROM 1643 A.D.TO 1727 A.D.), §§ 164-195210

164.Division of Newton's life into three periods210

165.Early life,1643 to 1665210

166.Great productive period,1665-87211

167.Chief divisions of his work:astronomy,optics,pure mathematics211

168.Optical discoveries:the reflecting telescopes of Gregory and Newton:the spectrum211

169.Newton's description of his discoveries in 1665-6212

170.The beginning of his work on gravitation:the falling apple:previous contributions to the subject by Kepler,Borelli,and Huygens213

171.The problem of circular motion:acceleration214

172.The law of the inverse sequare obtained from Kepler's Third Law for the planetary orbits,treated as circles215

173.Extension of the earth's gravity as far as the moon:imperfection of the theory217

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 observation221

175-6.Solution of the problem of elliptic motion:Halley's visit to Newton221

177.Presentation to the Royal Society of the tract De Motu:publication of the Principia222

178.The Principia:its divisions223

179-80.The Laws of Motion:the First Law:acceleration in its general form:mass and force:the Third Law223

181.Law of universal gravitation enunciated227

182.The attraction of a sphere228

183.The general problem of accounting for the motions of the solar system by means of gravitatioon and the Laws of Motion:perturbations229

184.Newton's lunar theory230

185.Measurement of the mass of a planet by means of its attraction of its satellites231

186.Motion of the sun:centre of gravity of the solar system:relativity of motion231

187.The non-spherical form of the earth,and of Jupiter233

188.Explanatioon of precession234

189.The tides:the mass of the moon deduced from tidal observations235

190.The motions of comets:parabolic orbits237

191.Reception of the Principia239

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:death240

193.Estimates of Newton's work by Leibniz,by Lagrange,and by himself241

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 laws242

195.Newton's scientific method:"Hypotheses non fingo"245

CHAPTER Ⅹ.OBSERVATIONAL ASTRONOMY IN THE EIGHTEENTH CENTURY, §§ 196-227247

196.Gravitational astronomy:its development due almost entirely to Continental astronomers:use of analysis:English observational astronomy247

197-8.Flamsteed:foundation of the Greenwich Observatory:his star catalogue249

199. Halley:catalogue of Southern stars253

200.Halley's comet253

201.Secular acceleratioon of the moon's mean motion254

202.Transits of Venus254

203.Proper motions of the fixed stars255

204-5.Lunar and planetary tables:career at Greenwich:minor work255

206.Bradley:career257

207-11.Discovery and explanation of aberration:the constant of aberration258

212.Failure to detect parallax265

213-5.Discovery of nutation:Machin265

216-7.Tables of Jupiter's satellites by Bradley and by Wargentin:determination of longitudes,and other work269

218.His observations;reduction271

219.The density of the earth:Maskelyne:the Cavendish experiment273

220.The Cassini-Maraldi school in France275

221.Measurements of the earth:the Lapland and Peruvian arcs:Maupertuis275

222-4.Lacaille:his career:expedition to the Cape:star catalogues,and other work279

225-6.Tobias Mayer:his observations:lunar tables:the longitude prize282

227.The transits of Venus in 1761 and 1769:distance of the sun284

CHAPTER Ⅺ.GRAVITATIONAL ASTRONOMY IN THE EIGHTEENTH CENTURY, §§ 228-250287

228.Newton's problem:the problem of three bodies:methods of approximation:lunar theory and planetary theory287

229.The progress of Newtonian principles in France:popularisation by Voltaire. The five great mathematical astronomers:the pre-eminence of France290

230.Euler:his career:St.Petersburg and Berlin:extent of his writings291

231.Clairaut:figure of the earth:return of Halley's comet293

232.D'Alembert:his dynamics:precession and nutation:his versatility:rivalry with Clairaut295

233-4.The lunar theories and lunar tables of Euler,Clairaut,and D'Alembert:advance on Newton's lunar theory297

235.Planetary theory:Clairaut's determination of the masses of the moon and of Venus:Lalande299

236.Euler's planetary theory:method of the variation of elements or parameters301

237.Lagrange:his career:Berlin and Paris:the Mécanique Analytique304

238.Laplace:his career:the Mecanique Céleste and the Système du Monde:political appointments and distinctions306

239.Advance made by Lagrange and Laplace on the work of their immediate predecessors308

240.Explanation of the moon's secular acceleration by Laplace308

241.Laplace's lunar theory:tables of Bürg and Burckhardt309

242.Periodic and secular inequalities310

243.Explanation of the mutual perturbation of Jupiter and Saturn:long inequalities312

244-5.Theorems on the stability of the solar system:the eccentricity fund and the inclination fund313

246.The magnitudes of some of the secular inequalities318

247.Periodical inequalities:solar and planetary tables based on the Mécanique Céleste318

248.Minor problems of gravitational astronomy:the satellites:Saturn's ring:precession and nutation:figure of the earth:tides:comets:masses of planets and satellites318

249.The solution of Newton's problem by the astronomers of the eighteenth century319

250.The nebular hypothesis:its speculative character320

CHAPTER Ⅻ.HERSCHEL (FROM 1738 A.D.TO 1822 A.D.), §§ 251-271323

251-2.William Herschel's early career:Bath:his first telescope323

253-4.The discovery of the planet Uranus,and its consequences:Herschel's removal to Slough325

255.Telescope-making:marriage:the forty-foot telescope:discoveries of satellites of Saturn and of Uranus327

256.Life and work at Slough:last years:Caroline Herschel328

257.Herschel's astronomical programme:the study of the fixed stars330

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 telescope332

259.Nebulae and star clusters:Herschel's great catalogues336

260.Relation of nebulae to star clusters:the"island universe"theory of nebulae:the"shining fluid"theory:distribution of nebulae337

261.Condensation of nebulae into clusters and stars339

262.The irresolvability of the Milky Way340

263.Double stars:their proposed employment for finding parallax:catalogues:probable connection between members of a pair341

264.Discoveries of the revolution of double stars:binary stars:their uselessness for parallax343

265.The motion of the sun in space:the various positions suggested for the apex344

266.Variable stars:Mira and Algol:catalogues of comparative brightness:method of sequences:variability of a Herculis346

267.Herschel's work on the solar system:new satellites:observations of Saturn,Jupiter,Venus,and Mars348

268.Observations of the sun:Wilson:theory of the structure of the sun350

269.Suggested variability of the sun351

270.Other researches352

271.Comparison of Herschel with his contemporaries:Schroeter352

CHAPTER ⅩⅢ.THE NINETEENTH CENTURY, §§ 272-320354

272.The three chief divisions of astronomy,observational,gravitational,and descriptive354

273.The great growth of descriptive astronomy in the nineteenth century355

274.Observational Astronomy.Instrumental advances:the introduction of photography357

275.The method of least squares:Legendre and Gauss357

276.Other work by Gauss:the Theoria Motus:rediscovery of the minor planet Ceres358

277.Bessel:his improvement in methods of reduction:his table of refraction:the Fundamenta Nova and Tabulae Regiomontanae359

278.The parallax of 61 Cygni:its distance360

279.Henderson's parallax of a Centauri and Struve's of Vega:later parallax determinations362

280.Star catalogues:the photographic chart362

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 results363

285.Variation in latitude:rigidity of the earth367

286.Gravitational Astronomy.Lunar theory:Damoiseau,Poisson,Pontécoulant,Lubbock,Hansen,Delaunay,Professor Newcomb,Adams,Dr.Hill367

287.Secular acceleration of the moon's mean motion:Adams's correction of Laplace:Delaunay's explanation by means of tidal friction369

288.Planetary theory:Leverrier,Gyldén,M.Poincare370

289.The discovery of Neptune by Leverrier and Dr.Galle:Adams's work371

290.Lunar and planetary tables:outstanding discrepancies between theory and observation372

291.Cometary orbits:return of Halley's comet in 1835:Encke's and other periodic comets372

292.Theory of tides:analysis of tidal observations by Lubbock,Whewell,Lord Kelvin,and Professor Darwin:bodily tides in the earth and its rigidity373

293.The stability of the solar system374

294.Descriptive Astronomy.Discovery of the minor planets or asteroids:their number,distribution,and size376

295.Discoveries of satellites of Neptune,Saturn,Uranus,Mars,and Jupiter,and of the crape ring of Saturn380

296.The surface of the moon:rills:the lunar atmosphere282

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 Venus383

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 spots385

299-300.Spectrum analysis:Newton,Wollaston,Fraunhofer,Kirchhoff:the chemistry of the sun386

301.Eclipses of the sun:the corona,chromosphere,and prominences:spectroscopic methods of observation389

302.Spectroscopic method of determining motion to or from the observer:Doppler's principle:application to the sun391

303.The constitution of the sun392

304-5.Observations of comets:nucleus:theory of the formation of their tails:their spectra:relation between comets and meteors393

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 Pouillet396

309.Double stars:observations by Struve and others:orbits of binary stars398

310.Lord Rosse's telescopes:his observations of nebulae:revival of the"island universe"theory400

311.Application of the spectroscope to nebulae:distinction between nebulae and clusters401

312.Spectroscopic classification of stars by Secchi:chemistry of stars:stars with bright-line spectra401

313-4.Motion of stars in the line of sight.Discovery of binary stars by the spectroscope:eclipse theory of variable stars402

315.Observations of variable stars403

316.Stellar photometry:Pogson's light ratio:the Oxford,Harvard,and Potsdam photometries403

317.Structure of the sidereal system:relations of stars and nebulae405

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.Summary406

LIST OF AUTHORITIES AND OF BOOKS FOR STUDENTS411

INDEX OF NAMES417

GENERAL INDEX425