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Odometer (οδόμετρο)(“Taximeter”)

An odometer is a device used for indicating distance traveled by a vehicle, like a taximeter. Vitruvius around 27 and 23 BC describes such a device although the actual invention may have been by Archimedes during the First Punic War. Hero also describes an odometer in chapter 34 of his Dioptra. Chariots with wheels of 4 feet diameter turns exactly 400 times in one Roman mile. For each revolution, a pin on the axle engage a 400 tooth cogwheel, thus making one complete revolution per mile. This engages another gear with holes along the circumference, where pebbles (calculus) are located, that drop one by one into a box. The number of miles traveled is given simply by counting the number of pebbles. Whether this instrument was actually built is disputed. Leonardo da Vinci tried to build it according to the description, but failed.

Book 10, Vitruvius

André Wegener Sleeswyk, "Vitruvius' Odometer", Scientific American 245(4) October, 1981, pp. 188-200
http://www.database.com/~lemur/rb-rolling-ball.html

See also

Bematist

Odometer for Ships of Archimedes according to Heron

The naval log mentioned by Hero in paragraph 38 of his "Dioptra" was a variation on this device. A paddlewheel on a float fitted to the outside of the hull was connected to a mechanism like that described for the odometer, located inside the vessel. The final wheel in the series made a full revolution every Roman mile, or about 1400 metres. Both these instruments were important and very useful inventions, especially the naval variant, which improved the measurement of distances at sea. The naval log was replicated by K. N. Rados in wood and brass and exhibited at the International Exhibition in Bordeaux in 1907. From the Technology Museum of Thessaloniki, Greece

Quotations

989 BC. Daedalus and his nephew Talus invent the saw, the turning-lath, the wimble, the chipax, and other instruments of Carpenters and Joyners, and thereby give a beginning to those Arts in Europe. Daedalus also invented the making of Statues with their feet asunder, as if they walked. Sir Isaac Newton, A short chronicle: From the First Memory of things in Europe to the Conquest of Persia by Alexander the Great