§ 151. Estimate of Kepler’s work and intellectual character 197 CHAPTER VIII. FROM GALILEI TO NEWTON (FROM ABOUT 1638 A.D. TO ABOUT 1687 A.D.), §§ 152-163 198-209 § 152. The general character of astronomical progress during the period 198 § 153. Scheiner’s observations of _faculae_ on the sun. _Hevel_: his _Selenographia_ and his writings on comets: his star catalogue. _Riccioli’s New Almagest_ 198 § 154. Planetary observations; _Huygens’s_ discovery of a satellite of Saturn and of its ring 199 § 155. _Gascoigne’s_ and _Auzout’s_ invention of the _micrometer_: _Picard’s_ telescopic “sights” 202 § 156. _Horrocks_: extension of Kepler’s theory to the moon: observation of a transit of Venus 202 §§ 157-8. Huygens’s rediscovery of the pendulum clock: his theory of circular motion 203 § 159. Measurements of the earth by _Snell_, _Norwood_, and Picard 204 § 160. The Paris Observatory: _Domenico Cassini_: his discoveries of four new satellites of Saturn: his other work 204 § 161. _Richer’s_ expedition to Cayenne: pendulum observations: observations of Mars in opposition: _horizontal parallax_: _annual_ or _stellar parallax_ 205 § 162. _Roemer_ and the velocity of light 208 § 163. _Descartes_ 208 CHAPTER IX. 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