IN Sky and Telescope of September, under the heading “Saluting an Astronomer”, Joseph R. Habes has an article which describes the method adopted by Eratosthenes for measuring the circumference of the earth. He knew that the sun threw no shadow at the summer solstice at Syene (the modern Assuan) and at the same hour at Alexandria the pointers of the sundials threw shadows, because Alexandria is north of Syene. He found that the arc of the shadow in the hemispherical bowl of the sundial was 1/50 of its circle, and hence concluded that the arc of the earth between Syene and Alexandria, which was 5,000 stadia, was 1/50 of the great circle of the earth. By this means he found that the circumference of the earth was 250,000 stadia, according to Cleomedes, but Strabo says that it was 252,000 stadia. A discrepancy arises when we come to consider the length of the stadium. The Greek stadium was 606-75 ft., and if Eratosthenes used this he was obviously very much in error in his computation. On the other hand, Pliny in his “Naturalis Historia” claims that Eratosthenes made 40 stadia equal to the Egyptian schoinus, and if this be so, taking the schoinus as 12,000 royal cubits of 0-525 metres each, the length of the stadium was 516 o 73 ft. If we accept the account of Strabo that Eratosthenes measured the circumference of the earth as 252,000 stadia, the circumference would be 24,662 miles, and the polar diameter 7,850 miles-only 50 miles short of the true polar diameter. This is considered to be one of the first great triumphs of scientific calculation.
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Eratosthenes and the Circumference of the Earth. Nature 152, 473 (1943). https://doi.org/10.1038/152473a0