urse of the
sun in its orbit, only that we view these lines just as we should view
the lantern on the wheel if we looked at it from directly above and not
from the side. The proof that the sun is describing this waving line,
and therefore must be considered as attached to an imaginary wheel, is
furnished, as it seemed to Hipparchus, by the observed fact of the sun's
varying speed.

That is one way of looking at the matter. It is an hypothesis that
explains the observed facts--after a fashion, and indeed a very
remarkable fashion. The idea of such an explanation did not originate
with Hipparchus. The germs of the thought were as old as the Pythagorean
doctrine that the earth revolves about a centre that we cannot see.
Eudoxus gave the conception greater tangibility, and may be considered
as the father of this doctrine of wheels--epicycles, as they came to
be called. Two centuries before the time of Hipparchus he conceived a
doctrine of spheres which Aristotle found most interesting, and which
served to explain, along the lines we have just followed, the observed
motions of the heavenly bodies. Calippus, the reformer of the calendar,
is said to have carried an account of this theory to Aristotle. As new
irregularities of motion of the sun, moon, and planetary bodies were
pointed out, new epicycles were invented. There is no limit to the
number of imaginary circles that may be inscribed about an imaginary
centre, and if we conceive each one of these circles to have a proper
motion of its own, and each one to carry the sun in the line of that
motion, except as it is diverted by the other motions--if we can
visualize this complex mingling of wheels--we shall certainly be able to
imagine the heavenly body which lies at the juncture of all the rims,
as being carried forward in as erratic and wobbly a manner as could be
desired. In other words, the theory of epicycles will account for all
the facts of the observed motions of all the heavenly bodies, but in
so doing it fills the universe with a most bewildering network of
intersecting circles. Even in the time of Calippus fifty-five of these
spheres were computed.

We may well believe that the clear-seeing Aristarchus would look
askance at such a complex system of imaginary machinery. But Hipparchus,
pre-eminently an observer rather than a theorizer, seems to have been
content to accept the theory of epicycles as he found it, though his
studies added to its complexities; and H