PAGEPrefacevCHAPTER I.Primitive Astronomy, §§ 1-181-20§ 1.Scope of astronomy1§§ 2-5.First notions: the motion of the sun: the motion andphasesof the moon: daily motion of the stars1§ 6.Progress due to early civilised peoples: Egyptians, Chinese, Indians, and Chaldaeans3§ 7.Thecelestial sphere: its scientific value:apparent distancebetween the stars: the measurement ofangles4§§ 8-9.The rotation of the celestial sphere: theNorthandSouth poles: thedaily motion: thecelestial equator:circumpolar stars7§§ 10-11.Theannual motionof the sun:great circles: theeclipticand itsobliquity: theequinoxesandequinoctial points: thesolsticesandsolstitial points8§§ 12-13.The constellations:the zodiac,signs of the zodiac, andzodiacal constellations: thefirst point of Aries(♈), and thefirst point of Libra(♎)12§ 14.The fiveplanets:directandretrogrademotions:stationary points14§ 15.The order of nearness of the planets:occultations:superiorandinferiorplanets15§ 16.Measurement of time: the day and its division into hours: thelunar month: the year: the week17§ 17.Eclipses: thesaros19§ 18.The rise ofAstrology20CHAPTER II.Greek Astronomy (from about 600 b.c. to about 400 a.d.),§§ 19-5421-75§§ 19-20.Astronomy up to the time of Aristotle.The Greek calendar:fullandemptymonths: theoctaeteris:Meton’s cycle21§ 21.The Roman calendar: introduction of theJulian Calendar22§ 22.TheGregorian Calendar23§ 23.Early Greek speculative astronomy:ThalesandPythagoras: the spherical form of the earth: the celestial spheres: themusic of the spheres24§ 24.Philolausand other Pythagoreans: early believers in the motion of the earth:AristarchusandSeleucus25§ 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 byTimocharisandAristyllus34§§ 33-4.Development ofspherics: thePhenomenaofEuclid: thehorizon, thezenith,polesof a great circle,verticals,declination circles, themeridian,celestial latitudeandlongitude,right ascensionanddeclination. 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’srepresentation 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 aneccentric:apogee,perigee,line of apses,eccentricity:equation of the centre: theepicycleand thedeferent41§ 40.Theory of the moon:lunationorsynodic monthandsidereal month: motion of the moon’snodesand apses:draconitic monthandanomalistic 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 theprecession of the equinoxes: thetropical yearand thesidereal year51§ 43.Eclipses of the sun and moon:conjunctionandopposition:partial,total, andannulareclipses:parallax56§ 44.Delambre’s estimate of Hipparchus61§ 45.The slow progress of astronomy after the time of Hipparchus:Pliny’sproof that the earth is round: new measurements of the earth byPosidonius61§ 46.Ptolemy.TheAlmagestand theOptics: theory ofrefraction62§ 47.Account of theAlmagest: Ptolemy’s postulates: arguments against the motion of the earth63§ 48.The theory of the moon:evectionandprosneusis65§ 49.Theastrolabe. Parallax, and distances of the sun and moon67§ 50.The star catalogue: precession68§ 51.Theory of the planets: theequant69§ 52.Estimate of Ptolemy73§ 53.The decay of ancient astronomy:TheonandHypatia73§ 54.Summary and estimate of Greek astronomy74CHAPTER III.The Middle Ages (from about 600 a.d. to about 1500 a.d.),§§ 55-6976-91§ 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 byHonein 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 thevariationof the moon.Ibn Yunos: theHakemite Tables79§ 61.Development of astronomy in the Mahometan dominions in Morocco and Spain:Arzachel: theToletan Tables80§ 62.Nassir Eddinand 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: theAlfonsine Tablesand theLibros del Saber84§ 67.The schoolmen of the thirteenth century,Albertus Magnus,Cecco d’Ascoli,Roger Bacon.Sacrobosco’s Sphaera Mundi85§ 68.PurbachandRegiomontanus: 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: thefirmamentand theprimum mobile86§ 69.Lionardo da Vinci:earthshine.FracastorandApian: observations of comets.Nonius.Fernel’smeasurement of the earth90CHAPTER IV.Coppernicus (from 1473 a.d. to 1543 a.d.),§§ 70-9292-124§ 70.The Revival of Learning92§§ 71-4.Life ofCoppernicus: growth of his ideas: publication of theCommentariolus:Rheticusand thePrima Narratio: publication of theDe Revolutionibus93§ 75.The central idea in the work of Coppernicus: relation to earlier writers99§§ 76-9.TheDe Revolutionibus.The first book: the postulates: the principle ofrelative 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:aphelionandperihelion.The fourth book: theory of the moon: distances of the sun and moon: eclipses111§§ 86-7.Thefifthandsixthbooks: theory of the planets:synodicandsidereal periods112§ 88.Explanation of the stationary points118§§ 89-90.Detailed theory of the planets: defects of the theory121§ 91.Coppernicus’s use of epicycles122§ 92.A difficulty in his system123CHAPTER V.The Reception of the Coppernican Theory and the Progress of Observation (from about 1543 a.d. to about 1601 a.d.),§§ 93-112125-144§§ 93-4.The first reception of theDe Revolutionibus:Reinhold: thePrussian 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 LandgraveWilliam IV.,Rothmann, andBürgi: 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 withReymers Bär136§ 106.Last years at Hveen: breach with the King138§ 107.Publication of theAstronomiae Instauratae Mechanicaand 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: thevariationand theannual equation143§ 112.The star catalogue: rejection of trepidation: unfinished work on the planets144CHAPTER VI.Galilei (from 1564 a.d. to 1642 a.d.),§§ 113-134145-178§ 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 byLippersheim: its application to astronomy byHarriot,Simon Marius, and Galilei149§ 119.TheSidereus Nuncius: observations of the moon150§ 120.New stars: resolution of portions of the Milky Way151§ 121.The discovery of Jupiter’ssatellites: 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 ofsun-spotsby Fabricius, Harriot,Scheiner, and Galilei: theMacchie Solari: proof that the spots were not planets: observations of theumbraandpenumbra154§ 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: thedifferential method of parallax163§ 130.Dynamical arguments in favour of the motion of the earth: theFirst Law of Motion. The tides165§ 131.The trial and condemnation.The thinly veiled Coppernicanism of theDialogue: the remarkable preface168§ 132.Summons to Rome: trial by the Inquisition: condemnation, abjuration, and punishment: prohibition of theDialogue169§ 133.Last years: life at Arcetri:librationof the moon: theTwo New Sciences:uniform acceleration, and the first law of motion. Blindness and death172§ 134.Estimate of Galilei’s work: his scientific method176CHAPTER VII.Kepler (from 1571 a.d. to 1630 a.d.),§§ 135-151179-197§ 135.Early life and theological studies179§ 136.Lectureship on mathematics at Gratz: astronomical studies and speculations: theMysterium 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.Theellipse: discovery of the first two ofKepler’s Lawsfor the case of Mars: theCommentaries on Mars184§ 142.Suggested extension of Kepler’s Laws to the other planets186§ 143.Abdication and death of Rudolph: appointment at Linz188§ 144.TheHarmony of the World: discovery ofKepler’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’scorona191§ 146.Treatise onComets193§ 147.Religious troubles at Linz: removal to Ulm194§ 148.TheRudolphine Tables194§ 149.Work Under Wallenstein: death195§ 150.Minor discoveries: speculations on gravity195§ 151.Estimate of Kepler’s work and intellectual character197CHAPTER VIII.From Galilei to Newton (from about 1638 a.d. to about 1687 a.d.),§§ 152-163198-209§ 152.The general character of astronomical progress during the period198§ 153.Scheiner’s observations offaculaeon the sun.Hevel: hisSelenographiaand his writings on comets: his star catalogue.Riccioli’s New Almagest198§ 154.Planetary observations;Huygens’sdiscovery of a satellite of Saturn and of its ring199§ 155.Gascoigne’sandAuzout’sinvention of themicrometer:Picard’stelescopic “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 bySnell,Norwood, and Picard204§ 160.The Paris Observatory:Domenico Cassini: his discoveries of four new satellites of Saturn: his other work204§ 161.Richer’sexpedition to Cayenne: pendulum observations: observations of Mars in opposition:horizontal parallax:annualorstellar parallax205§ 162.Roemerand the velocity of light208§ 163.Descartes208CHAPTER IX.Universal Gravitation (from 1643 a.d. to 1727 a.d.),§§ 164-195210-246§ 164.Division ofNewton’slife 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: thereflecting telescopesofGregoryand Newton: thespectrum211§ 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.Thelaw of the inverse squareobtained 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’sandWren’sspeculations 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’svisit to Newton221§ 177.Presentation to the Royal Society of the tractDe Motu: publication of thePrincipia222§ 178.ThePrincipia: its divisions223§§ 179-80.TheLaws of Motion: the First Law: acceleration in its general form:massandforce: the Third Law223§ 181.Law ofuniversal gravitationenunciated227§ 182.The attraction of a sphere228§ 183.The general problem of accounting for the motions of the solar system by means of gravitation 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 gravityof the solar system: relativity of motion231§ 187.The non-spherical form of the earth, and of Jupiter233§ 188.Explanation of precession234§ 189.The tides: the mass of the moon deduced from tidal observations235§ 190.The motions of comets:parabolicorbits237§ 191.Reception of thePrincipia239§ 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 theOpticsand of the second and third editions of thePrincipia, edited byCotesand 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”245CHAPTER X.Observational Astronomy in the Eighteenth Century,§§ 196-227247-286§ 196.Gravitational astronomy: its development due almost entirely to Continental astronomers: use ofanalysis: 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 acceleration of the moon’s mean motion254§ 202.Transits of Venus254§ 203.Proper motionsof the fixed stars255§§ 204-5.Lunar and planetary tables: career at Greenwich: minor work255§ 206.Bradley: career257§§ 207-11.Discovery and explanation ofaberration: theconstant of aberration258§ 212.Failure to detect parallax265§§ 213-5.Discovery ofnutation:Machin265§§ 216-7.Tables of Jupiter’s satellites by Bradley and byWargentin: determination of longitudes, and other work269§ 218.His observations:reduction271§ 219.The density of the earth:Maskelyne: theCavendish experiment273§ 220.TheCassini-Maraldischool 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 sun284CHAPTER XI.Gravitational Astronomy in the Eighteenth Century,§§ 228-250287-322§ 228.Newton’s problem: theproblem of three bodies: methods of approximation:lunar theoryandplanetary 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 thevariation of elementsorparameters301§ 237.Lagrange: his career: Berlin and Paris: theMécanique Analytique304§ 238.Laplace: his career: theMécanique Célesteand theSystème 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 ofBürgandBurckhardt309§ 242.Periodicandsecularinequalities310§ 243.Explanation of the mutual perturbation of Jupiter and Saturn:long inequalities312§§ 244-5.Theorems on thestabilityof the solar system: theeccentricity fundand theinclination fund313§ 246.The magnitudes of some of the secular inequalities318§ 247.Periodical inequalities: solar and planetary tablesMécanique 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.Thenebular hypothesis: its speculative character320CHAPTER XII.Herschel (from 1738 a.d. to 1822 a.d.),§§ 251-271323-353§§ 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: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 telescope332§ 259.Nebulaeandstar 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 theapex344§ 266.Variable stars:MiraandAlgol: catalogues of comparative brightness: method ofsequences: variability of αHerculis346§ 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:Schroeter352CHAPTER XIII.The Nineteenth Century,§§ 272-320354-409§ 272.The three chief divisions of astronomy,observational,gravitational, anddescriptive354§ 273.The great growth of descriptive astronomy in the nineteenth century355§ 274.Observational Astronomy.Instrumental advances: the introduction of photography357§ 275.The method ofleast squares:LegendreandGauss357§ 276.Other work by Gauss: theTheoria Motus: rediscovery of the minor planet Ceres358§ 277.Bessel: his improvement in methods of reduction: his table of refraction: theFundamenta NovaandTabulae Regiomontanae359§ 278.The parallax of 61Cygni: its distance360§ 279.Henderson’sparallax of αCentauriandStruve’sofVega: 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: gravitational 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, ProfessorNewcomb,Adams, Dr.Hill367§ 287.Secular acceleration of the moon’s mean motion: Adams’s correction of Laplace: Delaunay’s explanation by means oftidal friction369§ 288.Planetary theory:Leverrier,Gyldén, M.Poincaré370§ 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, LordKelvin, and ProfessorDarwin: bodily tides in the earth and its rigidity373§ 293.The stability of the solar system374§ 294.Descriptive Astronomy.Discovery of theminor planetsorasteroids: their number, distribution, and size376§ 295.Discoveries of satellites of Neptune, Saturn, Uranus, Mars, and Jupiter, and of thecrape ringof Saturn380§ 296.The surface of the moon:rills: the lunar atmosphere382§ 297.The surfaces of Mars, Jupiter, and Saturn: thecanalson Mars:Maxwell’stheory of Saturn’s rings: the rotation of Mercury and of Venus383§ 298.The surface of the sun:Schwabe’sdiscovery of the periodicity of sun-spots: connection between sun-spots and terrestrial magnetism:Carrington’sobservations 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: thecorona,chromosphere, andprominences: 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 andmeteors393§§ 306-8.Sidereal astronomy: career ofJohn Herschel: his catalogues of nebulae and of double stars: the expedition to the Cape: measurement of the sun’s heat by Herschel and byPouillet396§ 309.Double stars: observations by Struve and others: orbits of binary stars398§ 310.LordRosse’stelescopes: 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 bySecchi: 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.Stellarphotometry:Pogson’slight 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:Helmholtz’sshrinkage theory. Influence of tidal friction on the development of the solar system: Professor Darwin’s theory of the birth of the moon. Summary406List of Authorities and of Books for Students411Index of Names417General Index425