Bematist

Bematist (Ancient Greek: βηματιστής), plural bematists or bematistae (Ancient Greek: βηματισταί), meaning 'step measurer' (from βῆμα bema, meaning 'step, pace'), were specialists in ancient Greece and ancient Egypt who measured distances by pacing.

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 accuracy 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 Hero of Alexandria.

The table below lists distances of the routes as measured by two of Alexander's bematists, Baeton and Diognetus [ca]. 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. Eratosthenes calculated the circumference of the Earth based on work of Egyptian bematists.

Notes:
¹⁾ 1 mille passus = 1,480 meters (1,620 yd)
²⁾ 1 Attic stadion = 606 feet 10 inches (184.96 m)
³⁾ The route is not recorded to have been followed by Alexander himself.