nd from the North Sea to Upper Egypt, it certainly seems
enigmatical--at first thought almost miraculous--that an observer
should have been able to measure the entire globe. That he should have
accomplished this through observation of nothing more than a tiny bit of
Egyptian territory and a glimpse of the sun's shadow makes it seem but
the more wonderful. Yet the method of Eratosthenes, like many another
enigma, seems simple enough once it is explained. It required but the
application of a very elementary knowledge of the geometry of circles,
combined with the use of a fact or two from local geography--which
detracts nothing from the genius of the man who could reason from such
simple premises to so wonderful a conclusion.

Stated in a few words, the experiment of Eratosthenes was this. His
geographical studies had taught him that the town of Syene lay directly
south of Alexandria, or, as we should say, on the same meridian of
latitude. He had learned, further, that Syene lay directly under the
tropic, since it was reported that at noon on the day of the summer
solstice the gnomon there cast no shadow, while a deep well was
illumined to the bottom by the sun. A third item of knowledge, supplied
by the surveyors of Ptolemy, made the distance between Syene and
Alexandria five thousand stadia. These, then, were the preliminary data
required by Eratosthenes. Their significance consists in the fact
that here is a measured bit of the earth's arc five thousand stadia in
length. If we could find out what angle that bit of arc subtends, a mere
matter of multiplication would give us the size of the earth. But how
determine this all-important number? The answer came through reflection
on the relations of concentric circles. If you draw any number of
circles, of whatever size, about a given centre, a pair of radii drawn
from that centre will cut arcs of the same relative size from all the
circles. One circle may be so small that the actual arc subtended by the
radii in a given case may be but an inch in length, while another circle
is so large that its corresponding are is measured in millions of miles;
but in each case the same number of so-called degrees will represent the
relation of each arc to its circumference. Now, Eratosthenes knew, as
just stated, that the sun, when on the meridian on the day of the summer
solstice, was directly over the town of Syene. This meant that at that
moment a radius of the earth projected from Syen