ERATOSTHENES, "THE SURVEYOR OF THE WORLD''
An altogether remarkable man was this native of
Cyrene, who came to Alexandria from Athens to be
the chief librarian of Ptolemy Euergetes. He was not
merely an astronomer and a geographer, but a poet and
grammarian as well. His contemporaries jestingly
called him Beta the Second, because he was said
through the universality of his attainments to be "a
second Plato'' in philosophy, "a second Thales'' in
astronomy, and so on throughout the list. He was also
called the "surveyor of the world,'' in recognition of his
services to geography. Hipparchus said of him, perhaps
half jestingly, that he had studied astronomy as
a geographer and geography as an astronomer. It is
not quite clear whether the epigram was meant as
compliment or as criticism. Similar phrases have been
turned against men of versatile talent in every age.
Be that as it may, Eratosthenes passed into history
as the father of scientific geography and of scientific
chronology; as the astronomer who first measured the
obliquity of the ecliptic; and as the inventive genius
who performed the astounding feat of measuring the
size of the globe on which we live at a time when
only a relatively small portion of that globe's surface
was known to civilized man. It is no discredit to approach
astronomy as a geographer and geography as an
astronomer if the results are such as these. What
Eratosthenes really did was to approach both astronomy
and geography from two seemingly divergent points
of attack—namely, from the stand-point of the geometer
and also from that of the poet. Perhaps no man
in any age has brought a better combination of observing
and imaginative faculties to the aid of science.
Nearly all the discoveries of Eratosthenes are associated
with observations of the shadows cast by the
sun. We have seen that, in the study of the heavenly
bodies, much depends on the measurement of angles.
Now the easiest way in which angles can be measured,
when solar angles are in question, is to pay attention,
not to the sun itself, but to the shadow that it
casts. We saw that Thales made some remarkable
measurements with the aid of shadows, and we have
more than once referred to the gnomon, which is the
most primitive, but which long remained the most important,
of astronomical instruments. It is believed
that Eratosthenes invented an important modification
of the gnomon 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° 42' 39''
of arc. One-half of this, or 23° 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, and 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
Syene 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° 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.
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.''