On the day of the summer solstice, at the moment the sun was stationary in the meridian of Syene, he placed a style perpendicularly in the bottom of a half-concave sphere, which he exposed in open air to the sun at Alexandria. Now, if that style had cast no shade at Alexandria, it would have been precisely in the same circumstance with a style in the well in Syene; and the reason of its not casting the shade would have been, that the sun was directly vertical to it. But he found, on the contrary, this style at Alexandria did cast a shadow; and by measuring the distance of the top of this shadow from the foot of the style, he found, that, when the sun cast no shadow at Syene, by being in the zenith, at Alexandria he projected a shadow; which shewed he was distant from the vertical point, or zenith, 7 1/5° = 7° 12', which was 1/50th of the circumference of the whole heavens, or of a great circle.
This being settled, the conclusion was, that Alexandria and Syene must be distant from each other by the 50th part of the circumference of the whole earth.
Now 5000 stades was the distance already assumed between Alexandria and the well of Syene; and all that was to be done was to repeat 5000 stades fifty times, or multiply 5,000 stades by 50, and the answer was 250,000 stades, which was the total of the earth's circumference. This, admitting the French contents of the Egyptian stadium to be just, will amount to 11,403 leagues for the circumference of the earth sought; and as our present account fixes it to be 9000, the error will be 2403 leagues in excess, or more than one-fourth of the whole sum required.
