[Footnote 198: Second ed., p. 7. See Bode, _Von dem neuen Hauptplaneten_, p. 43, _note_.] [Footnote 199: The representative numbers are obtained by adding 1 to the following series (irregular, it will be observed, in its first member, which should be 1/2 instead of 0); 0, 3, 6, 12, 24, 48, etc. The formula is a purely empirical one, and is, moreover, completely at fault as regards the distance of Neptune.] [Footnote 200: _Monat. Corr._, vol. iii., p. 596.] [Footnote 201: Wolf, _Geschichte der Astronomie_, p. 648.] [Footnote 202: Such reversals of direction in the apparent movements of the planets are a consequence of the earth's revolution in its orbit.] [Footnote 203: _Dissertatio Philosophica de Orbitis Planetarum_, 1801. See Wolf, _Gesch. d. Astr._, p. 685.] [Footnote 204: Observations on Uranus, as a supposed fixed star, went back to 1690.] [Footnote 205: He had caught a glimpse of it on December 7, but was prevented by bad weather from verifying his suspicion. _Monat. Corr._, vol. v., p. 171.] [Footnote 206: Planetary fragments, hurled _in any direction_, and _with any velocity_ short of that which would for ever release them from the solar sway, would continue to describe elliptic orbits round the sun, all passing through the scene of the explosion, and thus possessing a common line of intersection.] [Footnote 207: _Phil. Trans._, vol. xcii., part ii., p. 228.] [Footnote 208: _Ibid._, p. 218. In a letter to Von Zach of June 24, 1802, he speaks of Pallas as "almost incredibly small," and makes it only seventy English miles in diameter. _Monat. Corr._, vol. vi., pp. 89, 90.] [Footnote 209: Olbers, _Monat. Corr._, vol. vi., p. 88.] [Footnote 210: _Conn. d. Tems_ for 1814, p. 218.] [Footnote 211: _Popular Astronomy_, p. 327.] [Footnote 212: _Month. Not._, vol. vii., p. 299; vol. viii., p. 1.] [Footnote 213: _Ibid._, p. 146.] [Footnote 214: Airy, _Mem. R. A. S._, vol. xvi., p. 386.] [Footnote 215: See Newcomb's _Pop. Astr._, p. 359. The error of Uranus amounted, in 1844, to 2'; but even the tailor of Breslau, whose extraordinary powers of vision Humboldt commemorates (_Kosmos_, Bd. ii., p. 112), could only see Jupiter's first satellite at its greatest elongation, 2' 15". He might, however, possibly have distinguished two objects of _equal_ lustre at a lesser interval.] [Footnote 216: J. W. L. Glaisher, _Observatory_, vol. xv., p. 177.] [Footnote 217: _Mem. R. A. S._, vol. xvi., p. 399.] [Footnote 218: For an account of D'Arrest's share in the detection see _Copernicus_, vol. ii., pp. 63, 96.] [Footnote 219: _Mem. R. A. S._, vol. xvi., p. 412.] [Footnote 220: He had recorded the places of 3,150 stars (three of which were different positions of the planet), and was preparing to map them, when, October 1, news of the discovery arrived from Berlin. Prof. Challis's _Report_, quoted in Obituary Notice, _Month. Not._, Feb., 1883, p. 170.] [Footnote 221: See Airy in _Mem. R. A. S._, vol. xvi., p. 411.]