orld, 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, _Populaere 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: Durege, _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 Koenigsberg 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 Nac