motions of the moon; treats of the first inequality,
of her eclipses, and the motion of the node. It then gives Ptolemy's own
great discovery--that which has made his name immortal--the discovery of
the moon's evection or second inequality, reducing it to the epicyclic
theory. It attempts the determination of the distances of the sun and
moon from the earth, with, however, only partial success, since it makes
the sun's distance but one-twentieth of the real amount. It considers
the precession of the equinoxes, the discovery of Hipparchus, the full
period for which is twenty-five thousand years. It gives a catalogue of
1,022 stars; treats of the nature of the Milky Way; and discusses, in
the most masterly manner, the motions of the planets. This point
constitutes Ptolemy's second claim to scientific fame. His determination
of the planetary orbits was accomplished by comparing his own
observations with those of former astronomers, especially with those of
Timochares on Venus.

[Sidenote: His geography.]

To Ptolemy we are also indebted for a work on Geography used in European
schools as late as the fifteenth century. The known world to him was
from the Canary Islands eastward to China, and from the equator
northward to Caledonia. His maps, however, are very erroneous; for, in
the attempt to make them correspond to the spherical figure of the
earth, the longitudes are too much to the east; the Mediterranean Sea is
twenty degrees too long. Ptolemy's determinations are, therefore,
inferior in accuracy to those of his illustrious predecessor
Eratosthenes, who made the distance from the sacred promontory in Spain
to the eastern mouth of the Ganges to be seventy thousand stadia.
Ptolemy also wrote on Optics, the Planisphere, and Astrology. It is not
often given to an author to endure for so many ages; perhaps, indeed,
few deserve it. The mechanism of the heavens, from his point of view,
has however, been greatly misunderstood. Neither he nor Hipparchus ever
intended that theory as anything more than a geometrical fiction. It is
not to be regarded as a representation of the actual celestial motions.
And, as might be expected, for such is the destiny of all unreal
abstractions, the theory kept advancing in complexity as facts
accumulated, and was on the point of becoming altogether unmanageable,
when it was supplanted by the theory of universal gravitation, which has
ever exhibited the inalienable attribute of a true theory--af