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