CHAPTER IX.. Universal Gravitation (from 1643 a.d. to 1727 a.d.),

UNIVERSAL GRAVITATION (FROM 1643 A.D. TO 1727 A.D.), §§ 164-195 210-246

§ 164. Division of Newton’s life into three periods 210

§ 165. Early life, 1643 to 1665 210

§ 166. Great productive period, 1665-87 211

§ 167. Chief divisions of his work: astronomy, optics, pure mathematics 211

§ 168. Optical discoveries: the reflecting telescopes of Gregory and Newton: the spectrum 211

§ 169. Newton’s description of his discoveries in 1665-6 212

§ 170. The beginning of his work on gravitation: the falling apple: previous contributions to the subject by Kepler, Borelli, and Huygens 213

§ 171. The problem of circular motion: acceleration 214

§ 172. The law of the inverse square obtained from Kepler’s Third Law for the planetary orbits, treated as circles 215

§ 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