e would point directly
towards the sun. Meanwhile, of course, the zenith would represent the
projection of the radius of the earth passing through Alexandria. All
that was required, then, was to measure, at Alexandria, the angular
distance of the sun from the zenith at noon on the day of the
solstice to secure an approximate measurement of the arc of the
sun's circumference, corresponding to the arc of the earth's surface
represented by the measured distance between Alexandria and Syene.

The reader will observe that the measurement could not be absolutely
accurate, because it is made from the surface of the earth, and not from
the earth's centre, but the size of the earth is so insignificant in
comparison with the distance of the sun that this slight discrepancy
could be disregarded.

The way in which Eratosthenes measured this angle was very simple. He
merely measured the angle of the shadow which his perpendicular gnomon
at Alexandria cast at mid-day on the day of the solstice, when, as
already noted, the sun was directly perpendicular at Syene. Now a glance
at the diagram will make it clear that the measurement of this angle
of the shadow is merely a convenient means of determining the precisely
equal opposite angle subtending an arc of an imaginary circle passing
through the sun; the are which, as already explained, corresponds with
the arc of the earth's surface represented by the distance between
Alexandria and Syene. He found this angle to represent 7 degrees 12',
or one-fiftieth of the circle. Five thousand stadia, then, represent
one-fiftieth of the earth's circumference; the entire circumference
being, therefore, 250,000 stadia. Unfortunately, we do not know which
one of the various measurements used in antiquity is represented by the
stadia of Eratosthenes. According to the researches of Lepsius, however,
the stadium in question represented 180 meters, and this would make the
earth, according to the measurement of Eratosthenes, about twenty-eight
thousand miles in circumference, an answer sufficiently exact to justify
the wonder which the experiment excited in antiquity, and the admiration
with which it has ever since been regarded.

{illustration caption = DIAGRAM TO ILLUSTRATE ERATOSTHENES' MEASUREMENT
OF THE GLOBE

FIG. 1. AF is a gnomon at Alexandria; SB a gnomon at Svene; IS and JK
represent the sun's rays. The angle actually measured by Eratosthenes
is KFA, as determined by the shadow cast by the g