§ 173. Extension of the earth’s gravity as far as the moon: imperfection of the theory 217 § 174. _Hooke’s_ and _Wren’s_ speculations on the planetary motions and on gravity. Newton’s second calculation of the motion of the moon: agreement with observation 221 § 175-6. Solution of the problem of elliptic motion: _Halley’s_ visit to Newton 221 § 177. Presentation to the Royal Society of the tract _De Motu_: publication of the _Principia_ 222 § 178. The =Principia=: its divisions 223 §§ 179-80. The _Laws of Motion_: the First Law: acceleration in its general form: _mass_ and _force_: the Third Law 223 § 181. Law of _universal gravitation_ enunciated 227 § 182. The attraction of a sphere 228 § 183. The general problem of accounting for the motions of the solar system by means of gravitation and the Laws of Motion: _perturbations_ 229 § 184. Newton’s lunar theory 230 § 185. Measurement of the mass of a planet by means of its attraction of its satellites 231 § 186. Motion of the sun: _centre of gravity_ of the solar system: relativity of motion 231 § 187. The non-spherical form of the earth, and of Jupiter 233 § 188. Explanation of precession 234 § 189. The tides: the mass of the moon deduced from tidal observations 235 § 190. The motions of comets: _parabolic_ orbits 237 § 191. Reception of the _Principia_ 239 § 192. Third period of Newton’s life, 1687-1727: Parliamentary career: improvement of the lunar theory: appointments at the Mint and removal to London: publication of the _Optics_ and of the second and third editions of the _Principia_, edited by _Cotes_ and Pemberton: death 240 § 193. Estimates of Newton’s work by Leibniz, by Lagrange, and by himself 241 § 194. Comparison of his astronomical work with that of his predecessors: “explanation” and “description”: conception of the material universe as made up of bodies attracting one another according to certain laws 242 § 195. Newton’s scientific method: “_Hypotheses non fingo_” 245 CHAPTER X. OBSERVATIONAL ASTRONOMY IN THE EIGHTEENTH CENTURY, §§ 196-227 247-286