§ 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 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