which
was elaborated afterwards by Hipparchus and called an armillary sphere.
This consists essentially of a small gnomon, or perpendicular post,
attached to a plane representing the earth's equator and a hemisphere in
imitation of the earth's surface. With the aid of this, the shadow
cast by the sun could be very accurately measured. It involves no new
principle. Every perpendicular post or object of any kind placed in the
sunlight casts a shadow from which the angles now in question could be
roughly measured. The province of the armillary sphere was to make these
measurements extremely accurate.

With the aid of this implement, Eratosthenes carefully noted the longest
and the shortest shadows cast by the gnomon--that is to say, the shadows
cast on the days of the solstices. He found that the distance between
the tropics thus measured represented 47 degrees 42' 39" of arc.
One-half of this, or 23 degrees 5,' 19.5", represented the obliquity of
the ecliptic--that is to say, the angle by which the earth's axis dipped
from the perpendicular with reference to its orbit. This was a most
important observation, and because of its accuracy it has served modern
astronomers well for comparison in measuring the trifling change due to
our earth's slow, swinging wobble. For the earth, be it understood, like
a great top spinning through space, holds its position with relative but
not quite absolute fixity. It must not be supposed, however, that
the experiment in question was quite new with Eratosthenes. His merit
consists rather in the accuracy with which he made his observation than
in the novelty of the conception; for it is recorded that Eudoxus, a
full century earlier, had remarked the obliquity of the ecliptic. That
observer had said that the obliquity corresponded to the side of a
pentadecagon, or fifteen-sided figure, which is equivalent in modern
phraseology to twenty-four degrees of arc. But so little is known
regarding the way in which Eudoxus reached his estimate that the
measurement of Eratosthenes is usually spoken of as if it were the first
effort of the kind.

Much more striking, at least in its appeal to the popular imagination,
was that other great feat which Eratosthenes performed with the aid
of his perfected gnomon--the measurement of the earth itself. When we
reflect that at this period the portion of the earth open to observation
extended only from the Straits of Gibraltar on the west to India on
the east, a