ch precision as the concentricity of two circles,
provided the circles be neither very nearly equal, nor the inner circle
very small in proportion to the outer."

Eratosthenes observed, that at the time of the summer solstice this well
was completely illuminated by the sun, and hence he inferred that the sun
was, at that time, in the zenith of this place. 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. It is
immediately apparent that these various measures have some relation to each
other, and probably express the same extent; measured in different stadia;
and this probability is greatly increased by comparing the real distances
of several places with the ancient itinerary distances.

The observation of Eratosthenes respecting the obliquity of the ecliptic
(though undoubtedly not so immediately or essentially connected with our
subject as his observation of the circumference of the earth) is too
important to be passed over entirely without notice. He found the distance