"Stadia (unit of length)" redirects here. For the land surveyor's device, see Stadia rod. For other uses, see Stadion (disambiguation).

The stadion, Latinized as stadium and anglicized as stade, is an ancient Greek unit of length. According to Herodotus, one stade is equal to 600 feet. However, there were several different lengths of “feet”, depending on the country of origin.

Itinerary 157 m used in measuring the distance of a journey.[1]
Olympic 176 m 600 × 294 mm
Attic/Italic 185 m 600 × 308 mm
Babylonian-Persian 196 m 600 × 327 mm
Phoenician-Egyptian 209 m 600 × 349 mm

Which measure of the stadia is used can affect the interpretation of ancient texts. For example, the error in the calculation of the circumference of the Earth by Eratosthenes[2] or Posidonius is dependent on which stade is chosen to be appropriate.

## Conjectural origin of the standard Attic or Alexandrian stadion

Ignoring various conspicuous factors that experienced specialists are closely familiar with, special pleader speculations may never stop defending Eratosthenes's overlarge circumference of the earth by positing for him a shorter stadion than the Attic. But conventional[3] opinion has mostly accepted that Alexandrian science used a fixed constant Attic 185 meter stadion — though its origin has long remained unknown. Following the original definition of the meter, it has been tentatively proposed[4] that if Greek affinity for unit fractions and for sexagesimal fractioning were applied to terrestrial girth in early Alexandria, the natural result would have been a new standard length unit close enough to the hitherto parochially and generationally varying old stadion that it could still be called a "stadion". In modern sexagesimal notation — as a fraction of the earth's circumference — it would be precisely 00;00,00,01 which is 1/60th of 1/60th of 1/60th of the circumference. As as a unit fraction of the circumference it is 1/216000. That would define a stadion as 1/600th of degree which is not mentioned in surviving Greek sources. But in the successive divisions by 60, the crucial first step — which determines the size of all further quantities during the divisions — is testified to,[5] as is the only measuring method[6] not distorted by air bending, thus insuring a correct circumference. If the circumference of the earth was accurately measured by Ptolemy Soter's surveyors the hypothesized standard Alexandrian stadion would have been 1/216000th of 40 million meters or 185 meters. Its presumed early date of origin is necessitated by the subsequent dominance of persistent conflicts between 700 stadia per degree versus 500 — that followed erection of Sostratus's Alexandria Lighthouse under Ptolemy Philadelphus.

## References

1. ^ Hoyle, Fred Astronomy, Rathbone Books Limited, London 1962 LC 62-14108
2. ^ Walkup, Newlyn (2005). "Eratosthenes and the Mystery of the Stades". The MAA Mathematical Sciences Digital Library. Retrieved 2008-07-29.
3. ^ Engels, D. 1985 [see Further Reading]; Berggren, J. L. and Jones, A. Ptolemy's Geography, Princeton and Oxford 2000 pages 14 and 20-22; DIO Volume 14 page 11 shows that air's bending of horizontal light accounts within 1% for both Eratosthenes's 40800 stadion earth radius and Posidonius's greatly discrepant 180,000 stadion earth circumference — if the Pharos was used for local determinations via flame visibility experiment versus sunset experiment — but only if the 185 meter stadion was used for both measures.
4. ^ DIO Volume 20 page 4 footnote 2.
5. ^ Dividing earth's circumference by 60 not yet 360. Strabo Geography Book 2 Chapter 5 §7.
6. ^ Ptolemy Geographia Book 1 Chapter 3 §2 and §3.