| 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 |
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| §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 |
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| 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 |
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| §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 |
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| 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 |
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| §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 |
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| 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 |
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| §§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 |
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| 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 |
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| 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 |
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| §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 |
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| 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 |
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| §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 |
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| 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 |
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| 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 |
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| §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 |
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| §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 |
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| 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 |
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| §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 |
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| 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 |
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| §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 |
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| 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 |
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| 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 |
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| §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 |
