[Footnote 4: Out of eighty stars compared, fifty-seven were found to have changed their places by more than 10". Lesser discrepancies were at that time regarded as falling within the limits of observational error. _Tobiæ Mayeri Op. Inedita_, t. i., pp. 80, 81, and Herschel in _Phil. Trans._, vol. lxxiii., pp. 275-278.] [Footnote 5: _Posthumous Works_, p. 701.] [Footnote 6: Arago in _Annuaire du Bureau des Longitudes_, 1842, p. 313.] [Footnote 7: Bradley to Halley, _Phil. Trans._, vol. xxxv. (1728), p. 660. His observations were directly applicable to only two stars, Gamma Draconis and Eta Ursæ Majoris, but some lesser ones were included in the same result.] [Footnote 8: Holden, _Sir William Herschel, his Life and Works_, p. 17.] [Footnote 9: _Phil. Trans._, vol. ci., p. 269.] [Footnote 10: Caroline Lucretia Herschel, born at Hanover, March 16, 1750, died in the same place, January 9, 1848. She came to England in 1772, and was her brother's devoted assistant, first in his musical undertakings, and afterwards, down to the end of his life, in his astronomical labours.] [Footnote 11: Holden, _op. cit._, p. 39.] [Footnote 12: _Memoir of Caroline Herschel_, p. 37.] [Footnote 13: See Holden's _Sir William Herschel_, p. 54.] [Footnote 14: _An Original Theory or New Hypothesis of the Universe_, London, 1750. See also De Morgan's summary of his views in _Philosophical Magazine_, April, 1848.] [Footnote 15: _Allgemeine Naturgeschichte und Theorie des Himmels_, 1755.] [Footnote 16: _Cosmologische Briefe_, Augsburg, 1761.] [Footnote 17: _The System of the World_, p. 125, London, 1800 (a translation of _Cosmologische Briefe_). Lambert regarded nebulæ as composed of stars crowded together, but _not_ as external universes. In the case of the Orion nebula, indeed, he throws out such a conjecture, but afterwards suggests that it may form a centre for that one of the subordinate systems composing the Milky Way to which our sun belongs.] [Footnote 18: _Opera Inedita_, t. i., p. 79.] [Footnote 19: _Phil. Trans._, vol. lxxiii. (1783), p. 273. Pierre Prévost's similar investigation, communicated to the Berlin Academy of Sciences four months later, July 3, 1783, was inserted in the _Memoirs_ of that body for 1781, and thus _seems_ to claim a priority not its due. Georg Simon Klügel at Halle gave about the same time an analytical demonstration of Herschel's result. Wolf, _Gesch. der Astronomie_, p. 733.] [Footnote 20: _Phil. Trans._, vol. xcv., p. 233.] [Footnote 21: _Ibid._, vol. xcvi., p. 205.] [Footnote 22: "Ingens bolus devorandus est," Kepler admitted to Herwart in May, 1603.] [Footnote 23: Described in "Præfatio Editoris" to _De Revolutionibus_, p. xix. (ed. 1854).] [Footnote 24: _Opere_, t. i., p. 415.] [Footnote 25: _Phil. Trans._, vol. xvii., p. 848.] [Footnote 26: _Ibid._, vol. lxxii., p. 97.] [Footnote 27: Doberck, _Observatory_, vol. ii., p. 110.] [Footnote 28: _Phil. Trans._, vol. lvii., p. 249.]