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>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
198-209
§ 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
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
§ 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
§ 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
247-286
§ 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
§ 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
287-322
§ 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 MĂ©canique Analytique
304
§ 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
§ 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 MĂ©canique CĂ©leste
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
323-353
§§ 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
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
§ 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
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