CHAPTER XI.. Gravitational Astronomy in the Eighteenth Century,

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

§ 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