§ 257. Herschel’s astronomical programme: the study of the fixed stars 330 § 258. The distribution of the stars in space: _star-gauging_: the “grindstone” theory of the universe: defects of the fundamental assumption: its partial withdrawal. Employment of brightness as a test of nearness: measurement of brightness: “space-penetrating” power of a telescope 332 § 259. _Nebulae_ and _star clusters_: Herschel’s great catalogues 336 § 260. Relation of nebulae to star clusters: the “island universe” theory of nebulae: the “shining fluid” theory: distribution of nebulae 337 § 261. Condensation of nebulae into clusters and stars 339 § 262. The irresolvability of the Milky Way 340 § 263. _Double stars_: their proposed employment for finding parallax: catalogues: probable connection between members of a pair 341 § 264. Discoveries of the revolution of double stars: _binary stars_: their uselessness for parallax 343 § 265. The motion of the sun in space: the various positions suggested for the _apex_ 344 § 266. Variable stars: _Mira_ and _Algol_: catalogues of comparative brightness: method of _sequences_: variability of α _Herculis_ 346 § 267. Herschel’s work on the solar system: new satellites: observations of Saturn, Jupiter, Venus, and Mars 348 § 268. Observations of the sun: _Wilson_: theory of the structure of the sun 350 § 269. Suggested variability of the sun 351 § 270. Other researches 352 § 271. Comparison of Herschel with his contemporaries: _Schroeter_ 352 CHAPTER XIII. THE NINETEENTH CENTURY, §§ 272-320 354-409 § 272. The three chief divisions of astronomy, _observational_, _gravitational_, and _descriptive_ 354 § 273. The great growth of descriptive astronomy in the nineteenth century 355 § 274. =Observational Astronomy.= Instrumental advances: the introduction of photography 357 § 275. The method of _least squares_: _Legendre_ and _Gauss_ 357 § 276. Other work by Gauss: the _Theoria Motus_: rediscovery of the minor planet Ceres 358 § 277. _Bessel_: his improvement in methods of reduction: his table of refraction: the _Fundamenta Nova_ and _Tabulae Regiomontanae_ 359 § 278. The parallax of 61 _Cygni_: its distance 360