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
gnomon AF. This angle is equal to the opposite angle JFL, which
measures the sun's distance from the zenith; and which is also
equal to the angle AES--to determine the Size of which is the
real object of the entire measurement.

FIG. 2 shows the form of the gnomon actually employed in
antiquity. The hemisphere KA being marked with a scale, it is
obvious that in actual practice Eratosthenes required only to set
his gnomon in the sunlight at the proper moment, and read off the
answer to his problem at a glance. The simplicity of the method
makes the result seem all the more wonderful.}

Of course it is the method, and not its details or its exact
results, that excites our interest. And beyond question the
method was an admirable one. Its result, however, could not have
been absolutely accurate, because, while correct in principle,
its data were defective. In point of fact Syene did not lie
precisely on the same meridian as Alexandria, neither did it lie
exactly on the tropic. Here, then, are two elements of
inaccuracy. Moreover, it is doubtful whether Eratosthenes made
allowance, as he should have done, for the semi-diameter of the
sun in measuring the angle of the shadow. But these are mere
details, scarcely worthy of mention from our present stand-point.
What perhaps is deserving of more attention is the fact that this
epoch-making measurement of Eratosthenes may not have been the
first one to be made. A passage of Aristotle records that the
size of the earth was said to be 400,000 stadia. Some
commentators have thought that Aristotle merely referred to the
area of the inhabited portion of the earth and not to the
circumference of the earth itself, but his words seem doubtfully
susceptible of this interpretation; and if he meant, as his words
seem to imply, that philosophers of his day had a tolerably
precise idea of the globe, we must assume that this idea was
based upon some sort of measurement. The recorded size, 400,000
stadia, is a sufficient approximation to the truth to suggest
something more than a mere unsupported guess. Now, since
Aristotle died more than fifty years before Eratosthenes was
born, his report as to the alleged size of the earth certainly
has a suggestiveness that cannot be overlooked; but it arouses
speculations without giving an inkling as to their solution. If
Eratosthenes had a precursor as an earth-measurer, no hint or
rumor has come down to us that would enable us to guess who that
precursor may have been. His personality is as deeply enveloped
in the mists of the past as are the personalities of the great
prehistoric discoverers. For the purpose of the historian,
Eratosthenes must stand as the inventor of the method with which
his name is associated, and as the first man of whom we can say
with certainty that he measured the size of the earth. Right
worthily, then, had the Alexandrian philosopher won his proud
title of "surveyor of the world."


HIPPARCHUS, "THE LOVER OF TRUTH"

Eratosthenes outlived most of his great contemporaries. He saw
the turning of that first and greatest century of Alexandrian
science, the third century before our era. He died in the year
196 B.C., having, it is said, starved himself to death to escape
the miseries of blindness;--to the measurer of shadows, life
without light seemed not worth the living. Eratosthenes left no
immediate successor. A generation later, however, another great
figure appeared in the astronomical world in the person of
Hipparchus, a man who, as a technical observer, had perhaps no
peer in the ancient world: one who set so high a value upon
accuracy of observation as to earn the title of "the lover of
truth." Hipparchus was born at Nicaea, in Bithynia, in the year
160 B.C. His life, all too short for the interests of science,
ended in the year 125 B.C. The observations of the great
astronomer were made chiefly, perhaps entirely, at Rhodes. A
misinterpretation of Ptolemy's writings led to the idea that
Hipparchus, performed his chief labors in Alexandria, but it is


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