The consideration of Sir John Herschel's Cape observations brings us to the close of the period we are just now engaged in studying. They were given to the world, as already stated, three years before the middle of the century, and accurately represent the condition of sidereal science at that date. Looking back over the fifty years traversed, we can see at a glance how great was the stride made in the interval. Not alone was acquaintance with individual members of the cosmos vastly extended, but their mutual relations, the laws governing their movements, their distances from the earth, masses, and intrinsic lustre, had begun to be successfully investigated. _Begun to be_; for only regarding a scarcely perceptible minority had even approximate conclusions been arrived at. Nevertheless the whole progress of the future lay in that beginning; it was the thin end of the wedge of exact knowledge. The principle of measurement had been substituted for that of probability; a basis had been found large and strong enough to enable calculation to ascend from it to the sidereal heavens; and refinements had been introduced, fruitful in performance, but still more in promise. Thus, rather the kind than the amount of information collected was significant for the time to come--rather the methods employed than the results actually secured rendered the first half of the nineteenth century of epochal importance in the history of our knowledge of the stars. FOOTNOTES: [Footnote 58: Bessel, _Populäre Vorlesungen_, pp. 6, 408.] [Footnote 59: Fitted to the old transit instrument, July 11, 1772.] [Footnote 60: _Briefwechsel mit Olbers_, p. xvi.] [Footnote 61: R. Wolf, _Gesch. der Astron._, p. 518.] [Footnote 62: Bessel, _Pop. Vorl._, p. 22.] [Footnote 63: A new reduction of the observations upon which they were founded was undertaken in 1896 by Herman S. Davis, of the U.S. Coast Survey.] [Footnote 64: Bessel, _Pop. Vorl._, p. 440.] [Footnote 65: Durège, _Bessel's Leben und Wirken_, p. 28.] [Footnote 66: _Bonner Beobachtungen_, Bd. iii.-v., 1859-62.] [Footnote 67: Bessel, _Pop. Vorl._, p. 238.] [Footnote 68: The heads of the screws applied to move the halves of the object-glass in the Königsberg heliometer are of so considerable a size that a thousandth part of a revolution, equivalent to 1/20 of a second of arc, can be measured with the utmost accuracy. Main, _R. A. S. Mem._, vol. xii., p. 53.] [Footnote 69: _Specola Astronomica di Palermo_, lib. vi., p. 10, _note_.] [Footnote 70: _Monatliche Correspondenz_, vol. xxvi., p. 162.] [Footnote 71: _Astronomische Nachrichten_, Nos. 365-366. It should be explained that what is called the "annual parallax" of a star is only half its apparent displacement. In other words, it is the angle subtended at the distance of that particular star by the _radius_ of the earth's orbit.] [Footnote 72: _Astr. Nach._, Nos. 401-402.]