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
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, 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


<< previous page | next page >>

Jump to page: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 |