Contents
Chapter I
§§ 2-5. First notions: the motion of the sun: the motion and phases of the moon: daily motion of the stars 1
§ 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
The annual motion of the sun: great circles: the ecliptic and its obliquity: the equinoxes and equinoctial points: the solstices and solstitial points
The constellations: the zodiac, signs of the zodiac, and zodiacal constellations: the first point of Aries (♈), and the first point of Libra (♎)
§ 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
Chapter II
§§ 19-20. Astronomy up to the time of Aristotle. The Greek calendar: full and empty months: the octaeteris: Meton’s cycle 21
§ 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
§ 26. Eudoxus: representation of the celestial motions by combinations of spheres: description of the constellations. Callippus 27
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
§§ 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
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. Eratosthenes: his measurement of the earth: and of the obliquity of the ecliptic 39
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
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
§ 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
§ 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
§ 47. Account of the Almagest: Ptolemy’s postulates: arguments against the motion of the earth 63
Chapter III
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
§§ 57-8. The Bagdad observatory. Measurement of the earth. Corrections of the astronomical data of the Greeks: trepidation 78
§ 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
§ 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
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
§ 67. The schoolmen of the thirteenth century, Albertus Magnus, Cecco d’Ascoli, Roger Bacon. Sacrobosco’s Sphaera Mundi 85
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
§ 69. Lionardo da Vinci: earthshine. Fracastor and Apian: observations of comets. Nonius. Fernel’s measurement of the earth 90
Chapter IV
§§ 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
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
§ 83. End of first book. The second book: decrease in the obliquity of the ecliptic: the star catalogue 110
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
§§ 86-7. The fifth and sixth books: theory of the planets: synodic and sidereal periods 112
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
§ 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
§§ 101-2. His establishment in Hveen: Uraniborg and Stjerneborg: life and work in Hveen 132
§ 107. Publication of the Astronomiae Instauratae Mechanica and of the star catalogue: invitation from the Emperor 139
§ 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
Chapter VI
§ 116. Professorship at Pisa: experiments on falling bodies: protests against the principle of authority 147
§ 118. The telescopic discoveries. Invention of the telescope by Lippersheim: its application to astronomy by Harriot, Simon Marius, and Galilei 149
§ 121. The discovery of Jupiter’s satellites: their importance for the Coppernican controversy: controversies 151
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
§ 125. Quarrel with Scheiner and the Jesuits: theological controversies: Letter to the Grand Duchess Christine 157
§ 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
Last years: life at Arcetri: libration of the moon: the Two New Sciences: uniform acceleration, and the first law of motion. Blindness and death
Chapter VII
§ 136. Lectureship on mathematics at Gratz: astronomical studies and speculations: the Mysterium Cosmographicum 180
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
§§ 140-1. The ellipse: discovery of the first two of Kepler’s Laws for the case of Mars: the Commentaries on Mars 184
§ 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
Chapter VIII
From Galilei to Newton (from about 1638 a.d. to about 1687 a.d.), §§ 152-163 198-209
§ 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
§ 156. Horrocks: extension of Kepler’s theory to the moon: observation of a transit of Venus 202
§ 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
Chapter IX
§ 170. The beginning of his work on gravitation: the falling apple: previous contributions to the subject by Kepler, Borelli, and Huygens 213
§ 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
§ 177. Presentation to the Royal Society of the tract De Motu: publication of the Principia 222
§§ 179-80. The Laws of Motion: the First Law: acceleration in its general form: mass and force: the Third Law 223
§ 183. The general problem of accounting for the motions of the solar system by means of gravitation and the Laws of Motion: perturbations 229
§ 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
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
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
Chapter X
§ 196. Gravitational astronomy: its development due almost entirely to Continental astronomers: use of analysis: English observational astronomy 247
§§ 216-7. Tables of Jupiter’s satellites by Bradley and by Wargentin: determination of longitudes, and other work 269
§§ 222-4. Lacaille: his career: expedition to the Cape: star catalogues, and other work 279
§ 227. The transits of Venus in 1761 and 1769: distance of the sun 284
Chapter XI
§ 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
§§ 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
§ 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
§§ 244-5. Theorems on the stability of the solar system: the eccentricity fund and the inclination fund 313
§ 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
Chapter XII
§§ 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
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
§ 260. Relation of nebulae to star clusters: the “island universe” theory of nebulae: the “shining fluid” theory: distribution of nebulae 337
§ 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
Chapter XIII
§ 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
§ 279. Henderson’s parallax of α Centauri and Struve’s of Vega: later parallax determinations 362
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
§ 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
§ 291. Cometary orbits: return of Halley’s comet in 1835: Encke’s and other periodic comets 372
Theory of tides: analysis of tidal observations by Lubbock, Whewell, Lord Kelvin, and Professor Darwin: bodily tides in the earth and its rigidity
§ 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
§ 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
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
§ 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
§§ 304-5. Observations of comets: nucleus: theory of the formation of their tails: their spectra: relation between comets and meteors 393
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
§ 310. Lord Rosse’s telescopes: his observations of nebulae: revival of the “island universe” theory 400
§ 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
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