Eratosthenes^{1} was the third chief librarian of the *Great Library of Alexandria*, which was the center of science and learning in the ancient world. In *On the Circular Motion’s of the Celestial Bodies, *Cleomedes credited him with having calculated the circumference of the Earth around 240 BCE. He was said to have done this by comparing the angle to the Sun at the summer solstice both in Alexandria and in Swenet near the current city of Aswan. He calculated the difference in the sun’s angle to be 7.2 degrees and the Pharaonic bookkeepers estimated the distance between the cities was 5000 stadia. This resulted in a circumference of 250,000 stadia which he rounded up to 252,000 stadia or 700 stadia per degree. Unfortunately no description of the length of the stadia was provided so the accuracy of this calculation is in doubt.

We can, however, retrace this calculation with the knowledge we have today.

From Google Earth^{2} we find that the north-south distance between the cities is close to 7.2 degrees or 432 arc-minutes while the diagonal distance between the cities is 7.7 degrees or 462 arc-minutes. The Earth according to WGS84^{3} gives the length of an arc-minute of latitude between the cities as 1846.73 m. The average length of an arc-minute over the total circumference of the Earth is 1852.216 m.

The length of the Egyptian^{4} foot, reman, cubit, and royal cubit were fixed in the third millennia BCE with the length of the reman at 375 mm and the Egyptian stadia of 500 reman at 187.5 meters. The north-south distance between the cities is 432 arc-seconds or 4268 Egyptian stadia.

If the Pharaonic bookkeepers had given the distance between the cities as 4268 Egyptian stadia Eratosthenes might have made the connection that this 2500 year old standard of length was very close to one tenth arc-minute and that the circumference had been measured in the days of the pyramids as 187.5 x 600 x 360 = 40,500 km which is 0.47 percent larger than the correct value.

An accurate measurement of the north-south distance between the cities would also have shown that many of the other existing standards of length were also related to the circumference of the Earth. This same calculation made with The Roman^{5} “sea mile” of 6250 Roman feet or with the Greek stadia^{6}of 600 Greek feet would have predicted the circumference of the Earth with an error of less than 0.1 percent.

We may never know the accuracy of the calculations made by Eratosthenes but accurate measurements of the circumference of the Earth had most certainly been made many centuries earlier.

References

References

1 Circumference: Eratosthenes and…. by Nicholas Nicastro St Martins Press 2008

2 Google Earth Coordinates of Alexandria and Swenet (Aswan)

3 (The earth according to WGS 84) http://en.wikipedia.org/wiki/World_Geodetic_System

4 http://en.wikipedia.org/wiki/Ancient_Egyptian_weights_and_measures

5 Historical Metrology by A.E. Berriman 1953 E.P. Dutton & CO,INC

6 The Acropolis Width and Ancient Geodesy Nicholas Kollerstrom, Ph.D. –http://www.dioi.org/kn/stade.pdf

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