His Next Object Was To
Ascertain The Altitude Of The Sun, At The Same Solstice, And On The Very
Same Day, At Alexandria.
This he effected by a very simple contrivance:
He
employed a concave hemisphere, with a vertical style, equal to the radius
of concavity; and by means of this he ascertained that the arch,
intercepted between the bottom of the style and the extreme point of its
shadow, was 7 deg. 12'. This, of course, indicated the distance of the sun from
the zenith of Alexandria. But 7 deg. 12' is equal to the fiftieth part of a
great circle; and this, therefore, was the measure of the celestial arc
contained between the zeniths of Syene and Alexandria. The measured
distance between these cities being 5000 stadia, it followed, that 5000 X
50 = 250,000, was, according to the observations of Eratosthenes, the
extent of the whole circumference of the earth.
If we knew exactly the length of the stadium of the ancients, or, to speak
more accurately, what stadium is referred to in the accounts which have
been transmitted to us of the result of the operations of Eratosthenes,
(for the ancients employed different stadia,) we should be able precisely
to ascertain the circumference which this philosopher ascribed to the
earth, and also, whether a nearer approximation to the truth was made by
any subsequent or prior ancient philosopher. The circumference of the earth
was conjectured, or ascertained, by Aristotle, Cleomedes, Posidonius, and
Ptolemy respectively, to be 400, 300, 240, and 180 thousand stadia.
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