Eratosthenes’s experiment

“They all laughed at Christopher Columbus
When he said the world was round”

George and Ira Gershwin were responsible for some of the most memorable songs of the last century, but this particular line highlights a common misconception. In 1492, when Columbus’ small fleet sailed from Palos de la Frontera in Spain, it had been the best part of two millennia since any serious scholar had believed that the world was flat.

The ancient Greeks were not only aware that the Earth was spherical, but around 240 BC they made an estimate of the circumference and obtained a surprisingly accurate result. Eratosthenes of Cyrene (276 – 194 BC) was a Greek polymath who held the post of Chief Librarian at the Library of Alexandria. He had heard that in Syrene (now Aswan), the noontime Sun on the day of the summer solstice lit up a well, casting no shadow on the side and implying that it was directly overhead. At Alexandria, however, the Sun did not quite reach the zenith and therefore did cast a shadow. By measuring the length of the shadow cast by a vertical rod of known height, the angular distance of the Sun from the zenith in Alexandria at noon could be determined. Of course, Eratosthenes couldn’t simply look at his watch to see when it was noon, so he would have relied on the shadow being at its minimum length at noon.

Eratosthenes found that the angular distance was a fiftieth of a whole circle (i.e. 50/360 = 7.2 degrees) and that the distance from Alexandria to Syrene was therefore a fiftieth of the circumference of the Earth. He then used a value of 5,000 stadia for the distance between the two cities (clearly a rough estimate) to obtain a value of 250,000 stadia for the Earth’s circumference.

Unfortunately, we don’t know the exact value of the stadion Eratosthenes used. The stadion (from which we get the word ‘stadium’) was defined as 600 Greek feet, but different values of the foot were used in different parts of the Greek world and Eratosthenes’ stadion is thought to have been anywhere between 150 and 158 meters (492 and 519 feet), making the distance from Alexandria to Aswan 750 -790 km (466 – 490 miles). We thus obtain a value of 37,500 – 39,500 km (23,300 – 24,500 miles) for the Earth’s circumference, which is very close to the accepted value of 40,075 km (24,901 miles). The actual distance from Alexandria to Aswan is 843 km (524 miles), giving a value of 42,150 km (26,200 miles).

Eratosthenes made the following assumptions: firstly, the Sun is so distant that rays of light reaching Alexandria and Syrene are effectively parallel; secondly that Syrene is located on the Tropic of Cancer (the latitude where the Sun is directly overhead on the summer solstice); and thirdly that Alexandria lies on the same meridian as Syrene.

Eratosthenes’ first assumption was correct, but the other two were not entirely accurate. The Tropic of Cancer is currently located at latitude 23°26′12.7″ N, but in Eratosthenes’ day, it was lay at approximately latitude 23°43′ N. Syrene lies at 24°05′ N 32°54 E, 22 minutes of an arc north of the Tropic of Cancer as it then was; and three degrees further east than Alexandria, which lies at 31°12′ N 29°55′ E.

Essentially, Eratosthenes’s experiment entailed simultaneous measurements the sun’s altitude at two separate locations on the same meridian. The experiment was simplified by choosing the solstitial sun at noon, and a second location that he either believed or approximated to be due south and at the latitude of the Tropic of Cancer. Had both been the case, he would have obtained an answer of 41,600 km (25,850 miles) based on a second location 7°29′ due south of Alexandria. Today we could easily replicate the experiment with two observers equipped with clinometers at John O’ Groats and Weston Super Mare, which are very close to sharing a common meridian and are 810 km (503 miles) apart. The experiment demonstrates how fundamental data can sometimes be obtained from a subtle but easy to measure phenomenon.

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Author: prehistorian

Prehistorian & author

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