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Bematists were specialists in ancient Greece who were trained to measure distances by counting their steps.


Measurements of Alexander's bematists

Bematists accompanied Alexander the Great on his campaign in Asia. Their measurements of the distances traveled by Alexander's army show a high degree of precision to the point that it had been suggested that they must have used an odometer, although there is no direct mentioning of such a device:

The overall accuracy of the bematists’ measurements should be apparent. The minor discrepancies of distance can be adequately explained by slight changes in the tracks of roads during the last 2300 years. The accuracy of the measurements implies that the bematists used a sophisticated mechanical device for measuring distances, undoubtedly an odometer such as describes by Heron of Alexandria.[1]

The table below lists distances of the routes as measured by two of Alexander's bematists, Diognetus and Baeton. They were recorded in Pliny's Naturalis Historia (NH 6.61-62). Another similar set of measurements is given by Strabo (11.8.9) following Eratosthenes.[2]

Pliny 6.61-62 Strabo 11.8.9 Actual Distance
Route Milia passum 1) English Miles Deviation Stadia 2) English Miles Deviation English Miles
Northern Caspian Gates - Hecatompylos 3) 1960 225 0.8% 227 main road
Southern Caspian Gates - Hecatompylos 133 122 2.4% 125 main road
Hecatompylos -Alexandria Areion 575 529 0.4% 4530 521 1.9% 531 Silk Route
Alexandria Areion - Prophtasia 199 183 3.2% 1600 184 2.6% 189 Herat-Juwain
Prophtasia - Arachoti Polis 565 520 1% 4120 474 9.7% 525 Juwain - Kelat-i-Ghilzai
Arachoti Polis - Hortospana 250 230 0.4% 2000 230 0.4% 231 main road Kelat-i-Ghilzai - Kabul
Hortospana - Alexandria ad Caucasum 50 46 2.1% 47 Kabul -Begram
Alexandria ad Caucasum - Peucolatis 237 218 3.2% 211 Begram - Charsada
Peucolatis - Taxila 60 55 20% 69 Charsada - Taxila
Taxila - Hydaspes (Jhelum) 120 110 4.8% 105 Aurel Stein-s route
Alexandria Areion - Bactra – Zariaspa4) 3870 445 1.6% 438 via Kala Nau, Bala Murghab, Maimana and Andkhui
Average 4.2% 2.8%
Median 2.8% 1.9%


Notes:

1) 1 mille passus = 1,480 meters or 1618.5 yards

2) 1 Attic stadion = 606’10’’

3) No entries: Data not specified (n.s.)

4) The route is not recorded to have been followed by Alexander himself.

Addenda: Leaving out the highest outlier each, the average deviation of the rest of the bematists's measurements would be 1.9% with Pliny and 1.5% with Strabo at a measured distance of 1958 respectively 1605 miles.


References

  1. ^ Donald W. Engels: Alexander the Great and the Logistics of the Macedonian Army, Los Angeles 1978, p.158
  2. ^ All data from: Donald W. Engels: Alexander the Great and the Logistics of the Macedonian Army, Los Angeles 1978, p.157.

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