now admitted that there is no evidence for this. Delambre
doubted, and most subsequent writers follow him here, whether
Hipparchus ever so much as visited Alexandria. In any event there
seems to be no question that Rhodes may claim the honor of being
the chief site of his activities.

It was Hipparchus whose somewhat equivocal comment on the work of
Eratosthenes we have already noted. No counter-charge in kind
could be made against the critic himself; he was an astronomer
pure and simple. His gift was the gift of accurate observation
rather than the gift of imagination. No scientific progress is
possible without scientific guessing, but Hipparchus belonged to
that class of observers with whom hypothesis is held rigidly
subservient to fact. It was not to be expected that his mind
would be attracted by the heliocentric theory of Aristarchus. He
used the facts and observations gathered by his great predecessor
of Samos, but he declined to accept his theories. For him the
world was central; his problem was to explain, if he could, the
irregularities of motion which sun, moon, and planets showed in
their seeming circuits about the earth. Hipparchus had the gnomon
of Eratosthenes--doubtless in a perfected form--to aid him, and
he soon proved himself a master in its use. For him, as we have
said, accuracy was everything; this was the one element that led
to all his great successes.

Perhaps his greatest feat was to demonstrate the eccentricity of
the sun's seeming orbit. We of to-day, thanks to Keppler and his
followers, know that the earth and the other planetary bodies in
their circuit about the sun describe an ellipse and not a circle.
But in the day of Hipparchus, though the ellipse was recognized
as a geometrical figure (it had been described and named along
with the parabola and hyperbola by Apollonius of Perga, the pupil
of Euclid), yet it would have been the rankest heresy to suggest
an elliptical course for any heavenly body. A metaphysical
theory, as propounded perhaps by the Pythagoreans but ardently
supported by Aristotle, declared that the circle is the perfect
figure, and pronounced it inconceivable that the motions of the
spheres should be other than circular. This thought dominated the
mind of Hipparchus, and so when his careful measurements led him
to the discovery that the northward and southward journeyings of
the sun did not divide the year into four equal parts, there was
nothing open to him but to either assume that the earth does not
lie precisely at the centre of the sun's circular orbit or to
find some alternative hypothesis.

In point of fact, the sun (reversing the point of view in
accordance with modern discoveries) does lie at one focus of the
earth's elliptical orbit, and therefore away from the physical
centre of that orbit; in other words, the observations of
Hipparchus were absolutely accurate. He was quite correct in
finding that the sun spends more time on one side of the equator
than on the other. When, therefore, he estimated the relative
distance of the earth from the geometrical centre of the sun's
supposed circular orbit, and spoke of this as the measure of the
sun's eccentricity, he propounded a theory in which true data of
observation were curiously mingled with a positively inverted
theory. That the theory of Hipparchus was absolutely consistent
with all the facts of this particular observation is the best
evidence that could be given of the difficulties that stood in
the way of a true explanation of the mechanism of the heavens.

But it is not merely the sun which was observed to vary in the
speed of its orbital progress; the moon and the planets also show
curious accelerations and retardations of motion. The moon in
particular received most careful attention from Hipparchus.
Dominated by his conception of the perfect spheres, he could find
but one explanation of the anomalous motions which he observed,
and this was to assume that the various heavenly bodies do not
fly on in an unvarying arc in their circuit about the earth, but
describe minor circles as they go which can be likened to nothing
so tangibly as to a light attached to the rim of a wagon-wheel in
motion. If such an invisible wheel be imagined as carrying the
sun, for example, on its rim, while its invisible hub follows
unswervingly the circle of the sun's mean orbit (this wheel, be
it understood, lying in the plane of the orbit, not at right-
angles to it), then it must be obvious that while the hub remains
always at the same distance from the earth, the circling rim will
carry the sun nearer the earth, then farther away, and that while
it is traversing that portion of the are which brings it towards
the earth, the actual forward progress of the sun will be
retarded notwithstanding the uniform motion of the hub, just as
it will be accelerated in the opposite arc. Now, if we suppose
our sun-bearing wheel to turn so slowly that the sun revolves but
once about its imaginary hub while the wheel itself is making the
entire circuit of the orbit, we shall have accounted for the
observed fact that the sun passes more quickly through one-half
of the orbit than through the other. Moreover, if we can
visualize the process and imagine the sun to have left a visible
line of fire behind him throughout the course, we shall see that
in reality the two circular motions involved have really resulted
in producing an elliptical orbit.

The idea is perhaps made clearer if we picture the actual
progress of the lantern attached to the rim of an ordinary
cart-wheel. When the cart is drawn forward the lantern is made to
revolve in a circle as regards the hub of the wheel, but since
that hub is constantly going forward, the actual path described
by the lantern is not a circle at all but a waving line. It is
precisely the same with the imagined course of the sun in its
orbit, only that we view these lines just as we should view the


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