The Odometer By Vitruvius And Heron, (an invention of Archimedes) Options

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THE ODOMETER BY VITRUVIUS AND HERON

(an invention of Archimedes)


The odometer is considered the precursor of current speedometer, the instrument that measures the kilometric distance, and his inventor was the bigger mathematician of antiquity, Archimedes. The odometer that describes the Roman architect and mechanic Vitrouvius was manufactured in 1st century B. C and is a mechanism that was adapted in a coachman¢s wheels that measures the distance that it had covered. Includes wooden cogged wheels and this is its basic difference from the odometer that describes Heron, which uses worm - screws.

First reference, however, to the odometer makes Vitruvius, who dedicates a special part for this without having a picture of it. With the reading of this part becomes immediately obvious that the writer describes an instrument that it is previous his era, of which he probably had seen only the remains of and therefore he did not portray it. Perhaps it was some form of a coach that allocated a disproportionately big wheel, necessary for the odometer and probably was not a utilitarian instrument, opinion with which also agrees D. Price in his relative essay. This ambiguity about the description and the non-existence of some drawing are some of the causes that have delayed the research about this mechanism. Although Vitrouvius has not named somebody as the inventor and constructor of the mechanism, nevertheless the modern research has attributed the invention of the instrument to Archimedes, since there is also a report from the historian Tzetzis relatively to the invention of the Syracousian.

We precisely know about the instrument because of Heron¢s the Alexandrian description, a great mathematician and engineer of the Hellenistic period, which had incorporated in his treatise (when he had been director of the eminent Museum of Alexandria, a scientific centre as good as the current technical universities.

The report of Heron to the odometer and his relative description are written hundred years roughly after that of Vitruvius and are contained in his work, "Spectacles" or "About Spectacles" (“Dioptra” or “Peri Dioptras”). As the most of the work of Heron, so this too, had an adventurous life. The "Dioptra" were for first time published in West in 1814, in Italy, from Venduri, while the Greek text was published with corresponding Italian once again in Italy from Vicentio 1858.
The french translation of the work made from Vincent in 1862, while in german a first publication made in 1897 from Schone, in order to be republished later in 1903.
There are two copies of the original Greek text, in the National Library of Paris with the name, Mynas Codex, which used by Vincent for his own publication, and a second one in the Library of Strasbourg. Finally, a third (in few extracts) exists in the library of Vienna.

The work of Heron "Dioptra" has become occasionally subject of important studies, particularly from writers that deal with the ancient greek and roman mechanics. The most important from all was that of A. G. Drachmann, substantially the work describes the manufacture of a geodesic instrument, spectacles (dioptre) that was the ancestor of the astrolabe and current theodolite.

Note: This instrument existed unique manufacture of Hellenistic period, after it gave the possibility of precise measurements, earthy and astronomical. In his book Heron stresses that his treatise is useful in the manufacture of aqueducts, reconstruction of walls, ports and generally any technical work. It is also useful in the astronomy, after it provides a lot of potentials for the measurement of angular distances of stars, the research of their mass, the distances and eclipses of the sun and moon. Still it is useful in the geographers, because it can measure the intervals between various places from distance, without the existing obstacles that surrounds them to degrade those measurements.

In the text of "Dioptras", in paragraph 34, there is an extensive report in the odometer, the introduction of which is as follows (in translation of the ancient text):
"And we believe that consequence of the assiduous research of the dioptrics is the measurement of the earth intervals with the so called odometer, so that we were not tired and lose time measuring it with the chain or the rope, but found on a moving vehicle we could determine with precision the already mentioned intervals, with the turning of the wheels. And other before us exposed certain methods with which becomes this, you will have the possibility of judging/comparing the instrument that we describe and those that was described by the previous."
From this extract we conclude that the odometer was not invention of Heron, but that the last one improved it considerably and described it with great clarity.Because the work of Heron, "Dioptra", was rescued, we consider his testimony as an additional clue that places the discovery of odometer much more behind, before Heron and Vitruvius.

The mechanic odometer or "dromometre”, is constituted by a cluster of cogged wheels, that with the help of helixes transport the movement of vehicle and change it in units of measurement. Thus it is easy to anyone to be informed for the distance that has covered the vehicle, consulted the graded plate that exists in the above side of the box which encompasses the mechanism, a mechanism that the modern researchers named "taximeter" (ôáîßìåôñï).

In regard to the corresponding instrument that could be used in the sea, the naval odometer, the description that Heron makes is roughly the same, beyond certain changes, that are essential for the adaptation of odometer in the boats with the help of a pontoon. The brief description of this transformation exists in the paragraph 38 of "Dioptra" and is presented suddenly without some introduction. We can sketch out concisely this instrument:
Outside the boat is placed a helix that is connected in the interior of boat with the same system of cogged wheels, as in the initial dromometer. The final wheel makes a complete turn each 100 roman passus (unit of measurement that has been lost the precise equivalence).

The odometer of Heron is technologically more elegant than that which describes Vitruvius. The initial movement is transmitted via a spike in the hub of tyre of vehicle, which promotes a disk that it brings eight joints, from a joint per rotation. From then and after the movement is spreaded to a row of screws and cogwheels. The shafts that have the screws and the cogwheels are successively vertical and horizontal and they lead to indicators on marked disks to the above part and the sides of the box that encloses all this system.
Similar is also the naval dromometer that Heron describes in the end of his book, where a bladed wheel, adapted in the external of the boat, it replaces the wheel of the vehicle. The movement is transmitted in a marked disk via a system of cogged wheels, similar to the odometer. Nevertheless, so its place in the text (immediately afterwards the description of the lifting mechanism, the whinch, that it does not have any relation to dioptric) as the different way of the writing makes the researchers believe that this part does not belong to Heron, but to later copyists.

Source :

• A.G.D Drachmann, “The Mechanical Technology of Greek and Roman Antiquity”
• Derek de Solla Price, “On The Origin of Clockwork, perpetual motion devices and the compass”
• A.J.H Vincent, “Notices et Extraits des Manuscrits relatives a la geometrie practique des Grecs, Paris 1862
• Heron¢s Dioptra: Text Herons von Alexandria Vermessungslehre und Dioptra, Griechisch und Deutsch von Hermann Schone