n of as the theory of Ptolemy.
We have sufficiently detailed the theory in speaking of Hipparchus. It
should be explained, however, that, with both Hipparchus and Ptolemy,
the theory of epicycles would appear to have been held rather as a
working hypothesis than as a certainty, so far as the actuality of
the minor spheres or epicycles is concerned. That is to say, these
astronomers probably did not conceive either the epicycles or the
greater spheres as constituting actual solid substances. Subsequent
generations, however, put this interpretation upon the theory,
conceiving the various spheres as actual crystalline bodies. It is
difficult to imagine just how the various epicycles were supposed to
revolve without interfering with the major spheres, but perhaps this is
no greater difficulty than is presented by the alleged properties of
the ether, which physicists of to-day accept as at least a working
hypothesis. We shall see later on how firmly the conception of
concentric crystalline spheres was held to, and that no real challenge
was ever given that theory until the discovery was made that comets
have an orbit that must necessarily intersect the spheres of the various
planets.

Ptolemy's system of geography in eight books, founded on that of Marinus
of Tyre, was scarcely less celebrated throughout the Middle Ages than
the Almagest. It contained little, however, that need concern us here,
being rather an elaboration of the doctrines to which we have already
sufficiently referred. None of Ptolemy's original manuscripts has come
down to us, but there is an alleged fifth-century manuscript attributed
to Agathadamon of Alexandria which has peculiar interest because it
contains a series of twenty-seven elaborately colored maps that are
supposed to be derived from maps drawn up by Ptolemy himself. In these
maps the sea is colored green, the mountains red or dark yellow, and the
land white. Ptolemy assumed that a degree at the equator was 500 stadia
instead of 604 stadia in length. We are not informed as to the grounds
on which this assumption was made, but it has been suggested that the
error was at least partially instrumental in leading to one very
curious result. "Taking the parallel of Rhodes," says Donaldson,(5) "he
calculated the longitudes from the Fortunate Islands to Cattigara or the
west coast of Borneo at 180 degrees, conceiving this to be one-half the
circumference of the globe. The real distance is only 125 degr