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 between the tropics less than 53 deg. 6’, and greater than 52 deg. 96’, which gives a mean of 23 deg. 51’ for the obliquity of the ecliptic.  The observations of Hipparchus (who flourished at Alexandria about 140 years before Christ, and whom we shall have occasion to mention more particularly afterwards) coincided with those of Eratosthenes.  Plutarch, however, who died A.D. 119, informs us, that, in his time, the gnomons at Syene were no longer shadowless on the day of the summer solstice.  As the interval between Eratosthenes and Plutarch was only about 512 years, Bishop Morsley has very naturally expressed his doubts of the accuracy of Plutarch’s assertion.  He says, that the change in the obliquity of the ecliptic in this interval was only 2’ 36”.  “A gnomon, therefore, at Syene, of the length of twelve inches, if it cast no shadow on the day of the solstice in the time of Eratosthenes, should have cast a shadow in the time of Plutarch of the length only of 9/1000th, or not quite 1/100th part of an inch.  The shadow of a perpendicular column of the height of 100 feet would have been 9/10ths of an inch.”  As, however, the ancients do not appear to have constructed gnomons of such a size, and as gnomons of inferior size would have given a shadow scarcely perceptible, it is probable that Plutarch is mistaken in his assertion; or, at any rate, that the very small variation which did take place between his time and that of Eratosthenes (if it were observed at all) was ascertained by means of the well itself, which would point it out much more distinctly and accurately than any gnomon the ancients can be supposed to have used.