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.

DESCRIPTION OF THE ODOMETER FROM HERON

Below is a translation of the odometer¢s description from Heron:
"…..lets be manufactured a wooden wrapping like box, in the interior of which will be installed the entire manufacture that we will describe.
In the base of the box is placed cupreous disk [….] ABCD in which they have been adapted the (8) known as scytales (small jutting out pieces of timber. For them, as it becomes a (suitable) incision (opening) in the bottom of the box via which a bollard firmly attached to the bearing (to the ring round the shaft) of one of the wheels of the vehicle, after a rotation of the wheel, entering to the incision of the bottom of the box it will move a skytale, in order that the next skytale will receives the same, precisely, place and this is repeated continuously (as long as the vehicle moves).

Each time that the wheel makes 8 turns, the drum with the skytales will come back in his initial place. In the centre of the skytalian drum and vertically to this, is nailed firmly (at one of its side) an interminable screw, while in the other side of it, penetrates and fastened in the opposite wall¢s opening. Now next to the screw, places a cogged drum of which the cogs are involved, precisely, in the helix of the screw, that is to say it is vertical to the bottom of the box and has, similarly, a stable adapted axis, which¢s edges lead to the walls of the box. A part of the axis has, also, a helical incision so that makes it an interminable screw. Next to this screw is placed, again, a cogged drum parallel to the bottom and the other one has been adapted, firmly, an axis of which the one edge, leads to the bottom of the box, and the other embedded in the walls of the box, as (horizontal)bar. And this axis on its one edge has a helix (interminable screw) which also, is adapted again, to the cogs of another drum that is vertical to the bottom.

And this process as is repeated all times we wish, provided that there is enough available space of the box. Because as many drums and screws are placed as much bigger are the intervals which might be measured.

Thus, with each rotation of the screw the adjacent drum will be moved at one cog so in a way of length equal with 8 perimeters of the wheel, the fixed skytaled drum will do a rotation, while the adjacent drum will be promoted at 1 cog. For instance, if the adjacent drum has 30 cogs and be turned once by the screw, this will mean that the wheel of (the vehicle) made 30 x 8 = 240 turns. And when this cogged drum is turned once again, the adapted in this, screw makes a rotation, the adjacent in the screw drum will be moved at one cog. If this drum has 30 cogs too, (what of course could could also be more) and is turned once, then this will indicates that the wheel made 7200 (= 30 x 240) turns, so if the perimeter of the wheel is 10 piheis (ðÞ÷çò: length measure, 1pihis =64 cm), the covered interval it will be 72000 piheis (ðÞ÷çò: length measure, 1pihis =64 cm) that is to say (72000/400 =) 180 stadios. And these are marked on the second drum.

When these drums are more and at the same time has increased also the number of the cogs, then the length of the way it will be calculated much more bigger, when it is measured.

Therefore the appliance should be manufactured in such way so that couldn¢t show much bigger indication than the daily way that the vehicle makes. It is possible the daily way to be measured and the indicator of the meter to be placed again to the beginning for the measurement of another way.

However due to the fact that the rotation of each one of the screws does not turn the adjacent cogs with mathematic precision, we turn by trial the first screw until the adjacent, to this, cogged drum makes a complete rotation and we measure the number of his revolvers.

For instance, the adjacent drum in order to execute a complete rotation, are required 20 turns of screw which has 30 cogs. This means that the 20 turns of the skytaled drum has promoted 30 cogs of the adjacent to the screw drum. However the 20 turns, turn (20 x 8 =) 160 skytales. So many too they will be also the turns of the wheel. This amounts with interval of 1600 piheis (ðÞ÷çò: length measure, 1pihis =64 cm) (160 turns x 10piheis (ðÞ÷çò: length measure, 1pihis =64 cm)/turn). And if the 30 cogs correspond in way of 1600 piheis (ðÞ÷çò: length measure, 1pihis =64 cm) then 1 cog of the above cogged drum, corresponds in way of 53 x 1/3 piheis (ðÞ÷çò: length measure, 1pihis =64 cm). So if in the beginning of the daily way is found that the cogged drum has been moved at 15 cogs, this means a way of 800 (53 x 1/3 x 15) piheis (ðÞ÷çò: length measure, 1pihis =64 cm), that is to say 2 stadios.

So we will write in the middle of this cogged drum, piheis (ðÞ÷çò: length measure, 1pihis =64 cm) 53 x 1/3. As we think the same thing, we will write the numbers on the rests cogged drums too, in order that from the number of the moved cogs will be known the executed way. And in order to we do not open the box of the instrument, each time we want to measure the length of the way by examining the cogs of each drum, we will show how it is possible to find the length of the way by seeing externally the indication of each corner indicator in the box. Because these cogged drums are placed so that they do not touch upon the sides of the box, while their axes at the exterior part, they penetrate the walls. The ledges of the axes now, lets have square cross-section, so that they can accept protractors of square reception. Thus when the drum is turned then it also rotates (at the same time) both the axis and the protractor.
The edge of the indicator of the protractor it will form at his rotation a circle on the exterior surface of the same wall, which we divide in as many equal arcs, as is the number of the cogged drum that is found in the interior. The indicator of the protractor, now, has such size so that could forms bigger circle and consequently the length of the arc of the region that corresponds per cog, it is bigger too.

This circle will have the same sign (that is to say the same numeration) with the one that brings the internal cogged drum. In this way with an observation in the interior of the box, we will check the length of the way. In, case it is impossible all the drums lean on the walls box, either because they are prevented by themselves or by the adjacent screws or by other cause, we remove each one of them in such distance, so that they are not prevented from anything at all.

Due to the fact that some of the cogged drums are parallel to the base and other are vertical to it, this results that the circles, that are written by the indicators of the protractors, some will be on the vertical walls and other on the cover (above side) of the box. Therefore, one of the vertical walls of the box that do not bring protractors, should become cover of the box, in order that this cover should be simultaneously wall……”

The calculation of the distance between Alexandria and Rome

Immediately afterwards the description of the odometer, Heron gives a method to calculate the distance Alexandria-Rome.
"Be it that it needs to be measured the straight line distance between Rome and Alexandria, that is to say the distance on the biggest circle of the region of the earth, taking into our account that the perimeter of earth is 252000 stadions (1 stadion=185m in approximately=606,95 english feet), as it was measured by Eratosthenes, with much more precision than all the others, who dealt with this subject, in his book with title "About the measuring of the earth "
1. It is observed the same eclipse of moon both in Rome and Alexandria. And if this eclipse is included in those that have been recorded, then we will use this. If not, then we can decide by doing the observation ourselves, since as eclipses of the moon become each 5 to 6 months
2. ???
Then Heron solves the problem by reporting elements as meridians, analemma of Rome (click here: http://www.perseus.gr/Astro-Solar-Analemma.htm ), observations by protractor, daily circle e.t.c and estimate the arc of the biggest circle, that is determined by the two cities, equal to 200. Considering, according to Eratosthenes that 1 degree corresponds in 700 stadios (or more precise according to Eparchus who proposed to get divided the meridian in 3600 and determined according to the measurements of Eratosthenes the length of one degree in 700 stadios), the distance Alexandria-Rome is 14000 stadios. However, due to the blanks that exist in the ancient text and in the important ill-treatments of the copyists, we cannot have an explicit picture of the method of calculation that was used.

Reference to the big distances makes also Ptolemaios in his eminent work "Geographic Narration", one of the most eminent and famous works of greek antiquity, which constitutes the beginning of projective cartography:
"? With the use of these instruments can be located very easily the place of the meridian, anywhere and anytime, and from this they can also be found with certainty the distances that have been covered in the travels. But even when it has been completed, the measuring with the stadios does not give us a sure information, because the travels seldom followed straight course. Because there were a lot of divergences so on the land as in the marine travels, therefore it is essential to calculate, in regard to a travel in land, the nature and the extent of the deviation and how much it deviates from the straight course, and afterwards to remove an amount from the number of stadios so that we change the course in straight.? The distance, which is found via an observation of the stars, shows with precision all these things and moreover shows which part of the region cut with their turn the parallel circles and the meridians that go through the various places. In other words, which part of the region of the parallel circles and Ecuador cut the meridians, or which part of meridians cut the parallel circles and Ecuador. After this, we easily can see how much interval there is between the two parts above the region of the big circle that goes through them and round the earth. This measuring with the stadios, after careful calculations, does not require the description of the travels to the various places of earth. Because, it is enough to assume that the perimeter of earth is divided in so many parts as we want to, and that some of them are contained in distances that were observed in the big circles that frame the earth. Dividing the entire perimeter of the earth or any part of its part, that has been observed by our measurements and is known as ?stadiasmoi?, it constitutes a not so much persuasive method? "

Note: The idea of the size of earth appears to occupy the Greeks from very early. In the Nefeles of Aristophanes, he gives the definition of geometry as the science that deals with the measurement of earth. Horace calls Archyta as the counter of earth and sea. Aristotle gives the first rate for the earth perimeter, 400.000 stadios, referring that it was calculated by mathematicians without mention them by name, it is speculated that he refers to Eudoxus the Knidian and his students. The next rate, 300.000 stadios was given by Archimedes in his work Sandstone (Øáììßôçò), which is attributed ôï Dikaiarhus the Messenian or according to others, Aristarchus the Samian. After that follows the stricter measurement and calculation from Eratosthenes, and later from Posidonius.
The width of a place can be calculated by the measurements of the corner of the height of the celestial pole and by the measurements of the shade of the sun with the help of protractor.
More convenient would be the measurements of the height corners of the sun in the afternoon equinox, because then the beams of sun are parallel to the route of Ecuador. The problem of length is more difficult. Hipparchus says that the difference of the length between two places it cannot be found by any other way than by means of the differences between the local times that are calculated from the eclipse of moon. Later, Ptolemaios has the same opinion with Hipparchus, considering that what results from the application of astronomical methods, should be preferred than the narrations of the travellers. Despite those references, the length remains an uncertain quantity almost up to the modern era.

THE ODOMETER IS ATTRIBUTED TO ARCHIMEDES

And now, the altimate legitimate question: "how are we sure that Archimedes is the “father” of the odometer;;;;; Since they have been lost many of his works, among them and that, that is referred to the construction and operation of odometer!!!!"
The only direct philological testimony emanates from history researcher Ioannis Tzetzis, among what he refers to for Archimedes, he writes also the following:
"Geometry is useful in many mechanic constructions……… and measuring via machines the sea covered intervals, and the land via the odometers and many other things are work of geometry, omniscient art"
E. Stamatis in his "Archimedes¢ complete works" reports that the odometer is attributed to Heron, but according to Tzetzis¢ testimony, is invention of Archimedes, although the information of Tzetzis is vague and does not name Archimedes but it just implies him.

The attribution of the invention of odometer to Archimedes, apart from the literary reminders, is also supported in relative correlations. For instance, the opinion of Sleeswyk, in assistance with the researches of Hill, the relative ones with the hydraulic clock, is remarkable. He reports that the odometer was mainly used in order to measures the distances of the large roman streets, and in each roman mile (in approximately 1400m) that was completed, a round pebble fell causing an acoustic signal that warned that had been covered the same distance, which they also pointed out with a marble column (miliario) that had written on the distances in miles at serial number, a habit that is used until today with the plates of kilometric distances and he also marks: "Moreover this attribution of the odometer to Archimedes is adapted chronically and coincides with the political economic situations. Syracuses, a city where Archimedes was citizen, from 262 B.C, during the reign of Hieron the II and until his death in 215 B.C, they were a respectable ally of Rome. So is not impossible Archimedes invented the odometer for the Roman allies of Syracuses after the end of the first Punic war. In that era, Archimedes was 46 years old, age that fits with the attribution of the odometer to him, and of course no one could then forecast that afterthe battle of Cannes (in 216 B.C) and the death of Hieron II would come political change in Syracuses, that would lead to the siege of the city from the Marcelus and to the death of Archimedes in 212 B.C.".

This system of warning is precisely the same with what is described in an arabic manuscript of 1150 A.D and refers the hydraulic clock, which is attributed to Archimedes by the Arabs. According to this logic, and since the system of cogwheels that was used had been found in the middle, between the common branch of the cogged mechanism and the interminable screw, which according to Athenian (3rd century B.C) is attributed to Archimedes. The sub system of cogwheels of odometer can consequently take a logically place in the technological achievements of Archimedes.

THE DESIGNING OF THE ODOMETER FROM LEONARDO DA VICHI AND ITS RECONSTRUCTION BY SLEESWYK

The first efforts of the reconstruction of the mechanism became from Leonardo Da Vinchi, in 1490, he should have in his possession a copy of the work of Vitruvius.

Most probably he should have some prototype text that is unknown to us, repeating the same story with the atmotilevolo of Archimedes, the arhitronito, as he had named it. In any case and beyond these affairs, the attempt of Da Vinchi was decisive, after all in his own drawings was supported a modern researcher, the Dutch A.W.Sleeswyk, in order to reconstruct the odometer. As he also marks for the attempt of Da Vinchi:
"His efforts for the reconstruction of (odometer), even if they were unsuccessful, they existed very instructive. When finally in 1979 was achieved a reconstruction that was found in agreement so much with the texts as much with the technological credibility, this result became achievable, mostly, via the developed approach of Leonardo”






THE RECONSTRUCTION OF THE NAVAL DROMOMETRE FROM Mr N. RADO

It would be unfair for the Greek science if does not be written that in 1910 Mr N. Rados, one of the scientists that "crossed their swords" intensely afterwards the discovery and study of the eminent computer of Antikithira, reconstructed in the frames of this conflict the naval dromometro based on the description of Heron.
The writer formulated the opinion that naval dromometro was evolved mainly in Alexandria, naval capital of that era, where took action Heron, and claimed that the current odometers have small difference from the ancient one.

On the basis of Heron¢s description, Mr N. Rados manufactured a similar instrument from timber and copper, which exposed in the International Report of Bordeaux in 1907, with other objects related to the history of Greek navy and Greek shipping, from the ancient years. That collection extracted big praise.



These are all that we know about the odometer ("taximetro") of Heron and the relative naval odometer (or dromometer). We owe him the initially rescue all the existing clues for this mechanism, which probably was discovered by Archimedes, and secondly we owe him the significant improvement of the instrument but also its adaptation for use in sea. The naval dromometro, with Heron¢s improvements, became a functional and necessary mechanism for the measurement of the naval distances and it contributed in the knowledge of the naval art. And all these from the 1st century A.D, a period at which was found in development a big number of commercial and expeditionary missions on behalf of Greeks in East, West, North and South. It is the first period of explorations and discoveries, which is dated between the 300 B.C – 300A.D and extended the limits of the known world of that era.

CULTURAL OSMOSIS TO CHINA

It is useful by many views to be reported a paradoxical resemblance between the greek odometer, as it was described by Vitrouvius and Heron, and an equivalent chinese, that was theoretically discovered about at the same era. The fact was pointed out by Derek de Solla Price, which in his relative work underlines:
«It is important to be marked that the chinese odometer is modern of that of Heron and Vitruvius ones and very similar in form. There is not any clue to shows that there was a certain transfusion of this invention or even a "brilliant spread"»
The whole matter is particularly interesting, because we distinguish a "parallel" course in certain inventions. For example, the transmission of some movement via cogwheels begins from Archimedes, while is believed that it has ancienter origin. The same happens also in China, where this phenomenon is pointed out to be existed from the 4th B. C century, according to western researchers and historians but also with Chineses. Despite any notifications, the only certain is that Archimedes manufactures the odometer, as have been proved by the recent researches, and a planetarium too, forerunner form of the eminent computer of the Antikythira, as well as other.

The odometer is greek invention that is attributed to Archimedes and of course precedes chronically the chinese one, and if some they seek certain cultural osmosis, this begins from Greece. Without receding in cheap nationalistic gadflies, I would want to point out that in the interval between 320 B.C - 700 A.D, at least in India was presented an important greek influence in arts, letters and science, that has remained indelible up to today. With regard to China, I. Needhman himself in the first volume of his work mentions the information that the bigger doctor of Islam, the Ampou Bakr Moameth Impn Zakrinia Al Razi (850 - 932), known as Razis, that was named "the Galinos of the Arabs", dictated the some of the texts of the work of Galinos in a Chinese scholar that had visited Baghdad, a fact of which until recently we had a complete ignorance in our country, because the bibliography in the subject of the greek-arabian effects is very limited.

If, so, Razis in Baghdad practises Greek cultural osmosis to China, how many rather bigger and more intense should practised the Greeks in India, that borders on China! Important clue in favour of this greek effect constituted the publication for the discovery of a greek city in China, which is known for many years, but had not been announced, because the archaeologists could not believe that this city was greek and that the greek presence had reached so much far!!


NOTE: In China, there is the big town of Giou-nan which means Ionia (Éùíßá). In the East Giounan means Greek


Click here:
http://www.thermopilai.org/content/pelasgi...mides-sten-kina
http://tovima.dolnet.gr/default.asp?pid=46...mp;artId=248196