xx Contents 



PAGE 



167. Chief divisions of his work : aon'onomy, optics, pure 



mathematics 21 1 



1 68. 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 calcu- 

 lation of the motion of the moon : agreement 



with observation 221 



I75~6. Solution of the problem of elliptic motion : 



Halleys 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 



I79~8o. The Laws of Motion : the First Law : accelera- 

 tion 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 



