Concerning the measurement of the Earth's circumference by Eratosthenes

Question

I. In an episode of his Cosmos series, Carl Sagan discussed the brilliant argument whereby Eratosthenes purportedly estimated the circumference of our planet. At one point of the episode, Carl Sagan seemed to imply that one of the first observations of Eratosthenes in this matter was that the surface of the Earth had to be curved. However, Carl Sagan didn't elaborate on how it was that Eratosthenes deduced, from what he had concluded about the curvature of the surface of the Earth, that the planet had to have a spherical shape (a point which is essential to the rest of Eratosthenes's argument). So, either the hypothesis on the sphericity of the Earth was rather commonplace in the days of Eratosthenes or the popular accounts on the Eratosthenes's exploit under consideration omit one of the principal ingredients in his determination of the circumference of the planet. What can you people tell me about this?

II. Among the modern accounts on the measurement of the Earth's circumference by Eratosthenes, what is in your opinion the most accurate one?

Thanks in advance for your insightful replies!

Answer 1

Certainly that the Earth is spherical was a commonplace (among the educated people) at the time of Eratosthenes. Once you start traveling on sea (or climbing mountains) you immediately notice that the Earth is curved. Observations of the sky from different places confirm that and tell you that it is spherical, at least approximately (before that there were also theories that is is conical or cylindrical). The opinion that Earth is spherical is traditionally credited to Pythagoras (who lived 3 centuries before Eratosthenes), and there is no doubt that it was universally accepted by the Greek and Alexandrian scientists for long time before Eratosthenes.

All this is described in many books. (Including the details of Eratosthenes measurement). With really great detail in Delambre, Histoire d'Astronomie ancienne, vol. I. This is in French and not very modern:-) But very comprehensive. A more popular book is Dreyer, History of planetary theories. Later editions are called History of astronomy from Thales to Kepler.

We cannot evaluate Eratosthenes accuracy because he gives the dimensions in stadia, and there were many different stadia used at that time, and there is no way to tell how long his stadium exactly was. In any case, the analysis shows that it could not be very accurate, but gave the right order of magnitude. The main source of error was the distance measurement on Earth which could be done only very approximately: a courier walked on a road and counted steps. (It is not even known whether there was a special expedition to measure this distance, which is unlikely, or Eratosthenes just relied on travelers accounts). At the time of Eratosthenes (and later in antiquity) there were no precise measurements of the size of the Earth. Much later calculations of Posidonius are even less accurate than those of Eratosthenes. But again, this is a speculation because we do not know how Posidonius measured the distances on the Earth, and what his length unit exactly was.

As I mentioned in another post, even Newton in his youth thought that one degree is 60 (British) miles. This is probably what he was taught in the university in 17 century!

Remark. The books I mentioned are those which on my opinion are the best. But they can be hardly called "modern". On the other hand, if you type "Eratosthenes measurement" on Google, you obtain many expositions to choose from.