Eratosthenes (276-194 BC) was good. But being just 2% off the true value of the earth's circumference at a time when there aren’t precise instruments meant that he also got lucky.
There are two sources of errors in any measurement – systemic and random.
Systemic errors are associated with a particular instrument or experimental technique (e.g., a faulty ruler, inaccurate instruments, misaligned gun sights, etc.). And these errors always bias the results in one direction, either too high or too low.
Random errors on the other hand are unbiased as they come from unpredictable sources (e.g., quiver while holding the device, lab technician getting tired, inconsistent gunpowder quality, etc.). The results obtained are likely to be too high or too low.
The four scenarios above show the interplay between the two (click on image to enlarge).
In Eratosthenes’ experiment, we can presume that it had large systemic errors (e.g., the distance between the column in Alexandria & the well in Syene was measured via the crude pacing method, and that at a huge distance of 800 km!). Thus it’s probably Scenario B or D that happened.
Scenario B is out given the very accurate result obtained - leaving us with Scenario D. Erastosthenes’ measurement must then be that hole right beside the center.
Eratosthenes used two variables only. The measurement error in the first must have cancelled the error in the second. One lucky fellow indeed.
One can likewise guess which hole in Scenario D was Aristarchus’ (310-230 BC) somewhat off moon size estimate. Luck of the draw?
Related post: Eratosthenes and mathematical elegance
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