# How Did the Ancient Greeks Measure the Circumference of the Earth?

*Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.*

The first recorded mention of the Earth’s length around its middle comes from Aristotle, who claimed it was 400,000 stadia in his __On the Heavens II__. That unit is mentioned by Pliny when he equated 40 of them to 12,000 royal cubits, of which each is about 0.525 meters. Therefore, 1 stadia is 300 cubits which is 157.5 meters which is about 516.73 feet. Therefore, Aristotle had the Earth’s circumference at about 39,146 miles, assuming this was the stadia he referenced. Turns out many different people considered a stadia to be different lengths, so we are not 100% sure Aristotle meant the modern value we find. He didn’t mention *how* he arrived at this number, but it is likely a Greek source since we don’t know of any Egyptian or Chaldean measurements of the sort at that time and also because no historians can see Aristotle being influenced by outside sources for this measurement. Another value we are not certain about comes from Archimedes who stated a value of 300,000 stadia, or about 29,560 miles. He most likely used some distance data of features in the Mediterranean compiled by Dicaearchus of Messana but again we are not sure as to his method (Dreyer 173, Stecchini).

The first known mathematical method was done by Eratosthenes of Alexandria, who lived from 276-194 BC. While his original work has been lost, Kleomedes has the event recorded. He looked at the position of the Sun at the Summer Solstice at different locations along the same meridian. When at Cyrene (which is south of Egypt), Eratosthenes looked at a vertical pit in the ground and saw it had no shadow, indicating that the Sun was directly at the zenith (which is directly above you), but at Alexandria (north of Cyrene the distance of the shadow in the pit implied that the arc difference from the zenith was 1/50 “the circumference of the heavens,” aka the sky. Using the Sun’s rays as roughly parallel lines, one can show that the angle between the two locations must be the same as the angle measured in Cyrene. Coupling this with the distance between the two cities at about 5,000 stadia gives a circumference of 250,000 stadia, or roughly 24,466 miles. Not bad, considering that the actual value is about 24,662 miles! Kleomedes was later able to show that a similar figure was reached when using the Winter Solstice, surprise surprise. It should be mentioned many scholars doubt the veracity of Eratosthenes and to this day no consensus has been reached on if Eratosthenes was truthful or a liar about his measurements. Why is this the case? Some details do not line up in regards to latitude and longitude and the supposed error that was taken into account could not have been found with the tools Eratosthenes had at the time. More than likely, Eratosthenes knew of the value and retroactively wanted to show that a mathematical model would also provide the same number (Dreyer 174-5, Pannekock 124).

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An alternate method used was implemented by Rosidonius and also recorded by Kleomedes. Here, the star Canopus was recorded at the time it hit the horizon when at Rhodes. Comparing this to where the star was at the same time at Alexandra (7.5 degrees above) and using some right triangle trigonometry implied that the difference was in fact the change in latitude and then using the distance between the two locations led to a value of 240,000 stadia, or 23,488 miles (Pannekock 124).

Not bad for cultures without modern technology. We see time and time again that with some foresight and perseverance, we can find relatively accurate results of some difficult numbers. Now, what else can we do…

## Works Cited

Dreyer, J.L.E. __A History of Astronomy__. Dover, New York: 1901. Print. 173-5

Pannekick, A. __A History of Astronomy__. Barnes & Noble, New York: 1961. Print. 124.

Stecchini, Livio C. *Metrum.org*. Metrum, n.d. Web. 25 Nov. 2016.

**© 2017 Leonard Kelley**