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
§ 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