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
Hipparchus was the dominant scientific personality of his
century. What he believed became as a law to his immediate
successors. His tenets were accepted as final by their great
popularizer, Ptolemy, three centuries later; and so the
heliocentric theory of Aristarchus passed under a cloud almost at
the hour of its dawning, there to remain obscured and forgotten
for the long lapse of centuries. A thousand pities that the
greatest observing astronomer of antiquity could not, like one of
his great precursors, have approached astronomy from the
stand-point of geography and poetry. Had he done so, perhaps he
might have reflected, like Aristarchus before him, that it seems
absurd for our earth to hold the giant sun in thraldom; then
perhaps his imagination would have reached out to the
heliocentric doctrine, and the cobweb hypothesis of epicycles,
with that yet more intangible figment of the perfect circle,
might have been wiped away.

But it was not to be. With Aristarchus the scientific imagination
had reached its highest flight; but with Hipparchus it was
beginning to settle back into regions of foggier atmosphere and
narrower horizons. For what, after all, does it matter that
Hipparchus should go on to measure the precise length of the year
and the apparent size of the moon's disk; that he should make a
chart of the heavens showing the place of 1080 stars; even that
he should discover the precession of the equinox;--what, after
all, is the significance of these details as against the
all-essential fact that the greatest scientific authority of his
century--the one truly heroic scientific figure of his
epoch--should have lent all the forces of his commanding
influence to the old, false theory of cosmology, when the true
theory had been propounded and when he, perhaps, was the only man
in the world who might have substantiated and vitalized that
theory? It is easy to overestimate the influence of any single
man, and, contrariwise, to underestimate the power of the
Zeitgeist. But when we reflect that the doctrines of Hipparchus,
as promulgated by Ptolemy, became, as it were, the last word of
astronomical science for both the Eastern and Western worlds, and
so continued after a thousand years, it is perhaps not too much
to say that Hipparchus, "the lover of truth," missed one of the
greatest opportunities for the promulgation of truth ever
vouchsafed to a devotee of pure science.

But all this, of course, detracts nothing from the merits of
Hipparchus as an observing astronomer. A few words more must be
said as to his specific discoveries in this field. According to
his measurement, the tropic year consists of 365 days, 5 hours,
and 49 minutes, varying thus only 12 seconds from the true year,
as the modern astronomer estimates it. Yet more remarkable,
because of the greater difficulties involved, was Hipparchus's
attempt to measure the actual distance of the moon. Aristarchus
had made a similar attempt before him. Hipparchus based his
computations on studies of the moon in eclipse, and he reached
the conclusion that the distance of the moon is equal to 59 radii
of the earth (in reality it is 60.27 radii). Here, then, was the
measure of the base-line of that famous triangle with which
Aristarchus had measured the distance of the sun. Hipparchus must
have known of that measurement, since he quotes the work of
Aristarchus in other fields. Had he now but repeated the
experiment of Aristarchus, with his perfected instruments and his
perhaps greater observational skill, he was in position to


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