Bematist

Bematists or bematistae (Ancient Greek βηματισταί, from 'pace'), were specialists in ancient Greece who were trained to measure distances by counting their steps.

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 2,300 years. The accuracy of the measurements implies that the bematists used a sophisticated mechanical device for measuring distances, undoubtedly an odometer such as described by Heron of Alexandria.

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.

Notes:
¹⁾ 1 mille passus = 1,480 meters or 1,618.5 yards
²⁾ 1 Attic stadion = 606’10’’
³⁾ 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 1,958 respectively 1,605 miles.

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