Looking Down a Well in Egypt to Measure the Size of the Earth
How Eratosthenes calculated his surprisingly accurate value for the Earth’s circumference
After writing about some of the most exciting current and future experiments around the world, I decided to look all the way back to around 240 B.C., when Eratosthenes became the first person to measure the circumference of the Earth. Although by this time many Greeks believed that the Earth was round, they had found no way of measuring its size.
That is until Eratosthenes, who had been appointed chief librarian of the library of Alexandria, heard from travellers about a well in Syene (now Aswan, Egypt), which was unobstructed by shadows at local noon on the summer solstice, indicating that the Sun was directly overhead. Eratosthenes was a Greek polymath, but was called “Beta” (the second letter of the Greek alphabet) by his contemporaries, as his work was never quite first rate in any area of study.
He planned to create a map of the world, which first required him to conduct an experiment to measure its circumference. He calculated the angle of elevation of the Sun at high noon on the summer solstice in Alexandria by using trigonometry, with a vertical rod and its shadow as two sides of a triangle. This angle was found to be about 7º, or roughly 1/50th of a full circle.
Using the (incorrect, but acceptable for the equipment available at the time) assumptions that the light rays from the Sun were parallel and that Alexandria was due north of Syene, Eratosthenes reasoned that the angle of elevation would provide the fraction of the Earth’s circumference covered by the distance between Syene and Alexandria.
He therefore needed an estimate for the distance between the two cities, but measuring large distances was not an easy process at the time. Records suggest that the lands around the Nile were measured every year, as the flooding of the river changed the landscape and created disputes over property lines. Professional distance walkers, known as bematists, were employed to count their very regular paces in order to measure long distances, and lengths of knotted rope were used for shorter distances.
Eratosthenes used a value of 5,000 stadia in his calculations, which was likely taken from measurements that used these methods. Multiplying this value by 50 gave the circumference of the Earth as 250,000 stadia. The obvious question now is “how long is a stade?”, but the answer is not as straightforward as you might expect. Without an International Bureau of Weights and Measures, it is unclear how much the definition of the stade varied between regions. The unit most commonly accepted for Eratosthenes’ measurements is the 185 metre stade, which would give a percentage difference of +15.3% from the accepted modern value for the equatorial circumference of the Earth of 40,075 km. However, Carl Friedrich Lehmann-Haupt, a scholar of Greek antiquity, claims that there were at least six variations of the stade, each giving a different error on Eratosthenes’ measurement. Nevertheless, the experiment had produced surprisingly accurate results.
Using his newfound knowledge about the size and shape of the Earth, Eratosthenes mapped the entire known world in a three-volume work known as “Geography”. The work has since been lost, but he had invented terminology and concepts still used today, as well as the discipline of geography itself.
The measurement of the Earth’s circumference was repeated several decades later by Posidonius. He used the cities of Rhodes and Alexandria as his two locations, but confusion regarding the distance between them and the length of a stade resulted in a much lower value being reported for the circumference of the Earth. This value of about 29,000 km was used by Christopher Columbus when planning his journey. It would have been unfeasible to cover the real distances between Europe and Asia with a 15th century ship, so the incorrect results of the experiment may have been the reason that the voyage went ahead in the first place.
