xxii Contents 



PAGE 



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 . . . -2,75 

 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. UAlembert'. his dynamics: precession and nuta- 

 tion : 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 . . . . 3 O1 



237. Lagrange : his career : Berlin . and Paris : the 



Mecanique Analytique 304 



238. Laplace : his career : the Mecanique Celeste and the 

 Systeme du Monde : political appointments and 

 distinctions 36 



