jointed bars there spoken of for describing the circles were supposed
to be real. This is no more the case than that the spheres of Eudoxus
and Callippus were supposed to be real. Both were introduced only to
illustrate the mathematical conception upon which the solar,
planetary, and lunar tables were constructed. The epicycles
represented nothing more nor less than the first terms in the Fourier
series, which in the last century has become a basis of such
calculations, both in astronomy and physics generally.

[Illustration: "QUADRANS MURALIS SIVE TICHONICUS." With portrait of
Tycho Brahe, instruments, etc., painted on the wall; showing
assistants using the sight, watching the clock, and recording. (From
the author's copy of the _Astronomiae Instauratae Mechanica._)]


FOOTNOTES:

[1] For definition see p. 22.

[2] _Ibid_.

[3] For definition see p. 18.

[4] For definition see p. 18.

[5] In his great book Copernicus says: "The movement of the heavenly
bodies is uniform, circular, perpetual, or else composed of circular
movements." In this he proclaimed himself a follower of Pythagoras
(see p. 14), as also when he says: "The world is spherical because the
sphere is, of all figures, the most perfect" (Delambre,