Pre-metric lengths

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Vormetrische length measures include all measures of length , which at different times and in different countries before the introduction of meter used. Many of these measures were already described in antiquity by various scholars - including Herodotus , Heron and the Alexandrian Didymos. According to these sources, many measures of antiquity had a fixed numerical relationship, a so-called ratio , to one another.

As far as pre-metric systems of measurement are concerned, two opposing research opinions have long been opposed. On the one hand, there is the view that in antiquity - as is well known in the Middle Ages - there were a large number of different sizes from city to city. These dimensions were originally independent of one another, i.e. not related to one another. Only later, in order to facilitate trade, will the units of measurement be related to one another and adjusted in order to achieve simple conversion ratios, or new dimensions will be introduced. This view is far underrepresented in the research literature of the last decades, but not in the number of its representatives. On the other hand, some researchers from the field of historical metrology believe that all linear measures of antiquity - first those of the fertile crescent , as well as the entire Mediterranean , the Near and Middle East and later also all of Europe - refer to each other. If a new system of measurement was created, those who defined it would always have oriented themselves to the existing measurements of the region. This research opinion is followed by the further explanations of the article.

Research into ancient systems of measurement has been undertaken since the Renaissance . Today most of the ancient measures are known, recorded statistically and their arithmetic derivation explained for many. Many length measures of the European Middle Ages either seem to be identical to the measures of antiquity or can be interpreted as simple derivatives of them. The tradition, however, does not give any clues as to how this agreement could have come about. Historical traditions can usually be ruled out, so many equations remain questionable. Some of the ancient dimensions are now very well established through archaeological finds of around a thousand ancient standards, above all of the Roman foot, as well as building and stadium lengths.

introduction

The metrology is one of the oldest sciences . Measure and weight have been of extremely great economic importance since ancient times. They were therefore always part of the regalia . The international trade already in antiquity required that the dimensions were comparable in simple fractions.

If an area was conquered or brought into a relationship of dependency, the dimensions could be imposed. On the other hand, metrologists could voluntarily go to a city that shone with excellent standards - Troyes for weights in the Middle Ages - to "take measurements" there.

In both cases, it could not be ruled out that the basic measure adopted was divided or multiplied differently, depending on the local tradition. Even within a rulership it was customary to use different measures, which in turn always maintained fixed, known ratios consisting of highly complex numbers .

For example, Heron of Alexandria describes one of the Greek systems of measurement in his Geometria : “The stadium has 6 plethren , 60 measure rods, 400 cubits, 600 Philetarian feet and 720 Italic feet.”   The two - in the following even more frequently mentioned - the Philetarian foot , Greek pous philetairikos , and the Italian foot, pous italikos , already maintain the exact ratio of 10:12 according to Heron, whereby the pous italikos that in the agricultural measure yoke, the iugerum , due to the higher divisibility - 28,800 compared to 20,000 square feet -, was preferred.

Another reason for different dimensions, even within a domain, was taxation . In the case of real estate, it was quite common to grant a tax rebate per unit area in regions with soils that, for topographical or geological reasons, produced a low yield per area. For this purpose, the tax-relevant field sizes were modified and the local measuring rods were adjusted, but it was always ensured that they were in a simple relationship to the main size of the country.

So many of these ratios have been known and handed down for ages. The ancient stadium in Athens measures 600 Kyrenean feet , which can still be measured today , which, as was also known in ancient times, corresponds to exactly 625 Roman feet. The latter, for example , has a 15:16 ratio to the pous metrios , another important Greek foot measure.

The first six foot measurements

From the two basic dimensions - the Mesopotamian nippurelle and the Egyptian royal elephant - the following six, directly derived foot dimensions (dimensions in millimeters) were formed:
 

Division type:
Metrological name:
Length in finger width :
foot
Pous
16
Macedonian
cubit
Pygms
18th
Cretan
cubit
Pygon
20th
Classic
cubit
Pechys
24
Egyptian
cubit
Neilos
28
Mesopotamian
cubit
Mesopotamos
30th
Nubian
cubit
  Nibw *
32
   The "Nubian Nippur Foot" 259,308 291.7215 324.135 388,962 453.789 486.2025 518.616
   The Mesopotamian Nippur Foot 276.5952 311.1696 345.744 414.8928 484.0416 518.616 553.1904
   The Egyptian Nippur Foot (Roman Foot) 296,352 333,396 370.44 444.528 518.616 555.66 592.704
   The "Nubian King's Foot" 264.6 297.675 330.75 396.9 463.05 496.125 529.2
   The "Mesopotamian King's Foot" 282.24 317.52 352.8 423.36 493.92 529.2 564.48
   The Egyptian king's foot 302.4 340.2 378 453.6 529.2 567 604.8
* The old, Greek nomenclature of dimensions does not have a separate name for the double. The 32-digit cubit is called nibw (pronounced: nibu ) because in Nubia the cubit was always divided into 32 finger-widths.


If the foot, later called Roman, can safely be called the Egyptian nippur foot , the three other names must be put in quotation marks.
In the table above, they stand for: the foot of the Nubian divided Nippurelle, the foot of the Nubian divided royal cell and the foot of the Mesopotamian divided royal cell.

The classic 24- daktyloi cubit is also called pechys ephtymetrikos . The Neilos also pechys neilos and the Mesopotamos also pechys histonikos . The 34-finger width pechys thrakikos, also cited in ancient literature , is no longer taken into account by today's metrological research. In fact, it cannot be proven as a multiple within a system. The ratio 17:16 can actually appear as the ratio between different, mutually derived measures.

The correct ratio must be 1701: 1600. The number 1701 is three to the power of five times seven. The prime numbers 17 and 13 never appear in the old systems, the prime number 11 almost never. So two, three, five and seven remain, that is, the seven-even numbers .

Exactly for this reason one opts for seven-smooth, conventional absolute values today . Calculating with seven- even values ​​does not mean, however, that the ancient metrologists determined their length measures with a precision of fractions of a micrometer, nor that modern historical metrology today could determine this value with the same precision. Seven-even values ​​only represent a practical rounding of all measures derived from one another , but also clearly within the coefficient of variation determined for the old length measures, so that you do not have to constantly round arbitrarily decimally.

Derived or derived measures

Derivations from the Nippurelle

The nippurelle was divided into 30 fingers in Mesopotamia - the region of origin of the sexagesimal system . Sixteen of these fingers form the Mesopotamian nippur foot, or simply called the nippur foot for short . Dimensions that are close to it are the Attic-Olympic foot , the Indus foot and the Salamis elephant .

At the beginning of the third millennium BC, the ancient Egyptians took over the Nippurelle, but divided them into only 28 equal parts. This is how the Egyptian nippur foot was created, to which the Roman foot corresponds as a value . Related or derived measures are the Drusian foot , the Roman cubitus and the so-called guard cubit .

Derivations from the royal cell

The Egyptian royal cell was divided into 28 parts by the ancient Egyptian geometers. The Egyptian king foot is the corresponding foot of this cubit. It is possible that this foot - as Shaku - also reached Japan. The pous italikos, which was used by the Greeks who settled in southern Italy, corresponds to the foot of the Nubian-divided royal cell . The Heraion foot stands close to it . a comparable measure was used as the Latin foot in Latium until modern times . The Babylonian cubit also belongs in this context.

If you divide the Egyptian royal cell directly by thirty, you get the little used foot of the Mesopotamian divided royal cell . In their environment belongs the Pous Philetairikos , the Philetarian Foot known since Heron . He reached China as "Tschi" - via the Silk Road - perhaps. A widespread derivation is associated with the Pous Ptolemaikos , the Ptolemaic foot.

Further length measures of antiquity

  • The Sami cubit and the important dimensions derived from it play a special role - not least in historical building research .
    The Sami cubit stands at 80:81 and measures a conventional 522 ⅔ mm. In the first half of the 20th century, the building researcher Armin von Gerkan postulated an Ionic foot that was two thirds of the Sami cubit, i.e. about 348     4/9   millimeters. With an "alleged Ionic foot" of about this length, however - according to the contemporary building researcher de Zwarte - "little to do".
  • The Doric foot, widespread both in antiquity and in the Middle Ages, also called the pheidonic foot since Herodotus (Works VI, 127) , is the pygon of the Sami cubit. Occasionally the Doric foot is also referred to as the "Attic foot", but this contradicts the widely recognized nomenclature.
  • In modern historical building research, the so-called ionic foot is no longer considered to be the foot of the Sami cubit as Pechys (see above), but a measure of around 298 ⅔ millimeters. This Ionic foot is also evident in the dimensions of the excavations in Didyma .
  • A lot of confusion was caused in historical metrology by the approx. 294 mm dimension that can be found in the entire Mediterranean region. Since this measure was also widespread in Italy, the Attic foot was confused with the Roman foot, especially by Paul Guilhiermoz at the end of the 19th century. Due to its frequent presence in Italy, Letronne  - forming a mean between this measure and the Roman pes monetalis - was only able to establish itself at around 295 mm for the Roman foot. Other historical metrologists also call this foot the “neo-Punic foot” because it can also be found in the area of ​​Carthage after the Roman settlement of North Africa. During excavations, both in Greek Asia Minor and on the Greek mainland, the Attic foot of 294 mm is very common.
  • The Kyrenean foot .
  • The Pechys basilikos, literally: "large cubit"; its conventional value is 533.43 mm. Its foot, the so-called pous basilikos , is 355.62 mm long.

Important European measures of length

  • The English foot was set to exactly 304.8 mm in 1959. The different definitions before that, in the United Kingdom , in the Commonwealth and in the United States, were a little larger or smaller.
  • The French foot was defined in 1799 by the decimal meter definition at 443.296 Paris lines with 144 Paris lines at 2.25583 mm, i.e. 324.83952 mm.
  • The Austrian foot measures 316.1088 mm and was empirically determined in 1871 .
  • The Bavarian foot was officially set to exactly 291,859,206 millimeters under King Ludwig II in 1869 .
  • The Rhenish foot , which is very widespread in Europe , also became the Prussian foot in 1793 . Its dimension is 313.85 mm. It was abandoned in 1872.
  • The Austrian foot, introduced by Maria Theresa in 1760, was also legally valid in Prague . In practice, Bohemia held on to a foot, which should be set at 296.380 mm.
  • In Lazio , a foot of 297.675 mm was used by surveyors until 1863, which was mistaken for the Roman foot by many historical metrologists in the early modern period and up until the 19th century.

The diversification of length measures in the Middle Ages

The diversification of the various length measurement systems, especially in the European Middle Ages, means that not all systems have been fully understood from this period. The sovereignty over measure and weight had increasingly passed to smaller political administrative units. There was a common system of measurements. B. not or only partially in the Holy Roman Empire , cf. Mark (weight) . Smaller principalities and cities with market rights often had their own regional systems of measurement. Also craftsmen associations sat firmly their local dimensions. Examples of this are the various tailoring positions and the dimensions used by the cathedral builders.

In quite a few regions, the old dimensions from antiquity were simply preserved and used. In other areas new measures emerged, the derivations of which have not yet been clarified. In some cases, trigonometric derivatives are proven. In other cases, inaccuracies in the transfer or preservation of the dimensions are suspected, namely whenever an assumption of error brings the measure into a simple ratio to a known length measure, otherwise either none at all, or only an extremely complicated, and therefore highly improbable Derivation can be found. For the most important length measures, including those of the Middle Ages, this is practically without exception not the case.

Cases of misinterpretation or deliberate adaptation to a main system are also known in historical metrology. B. an obviously very differently derived cloth measure, while accepting a considerable alteration of the original measure, was brought into a simpler relationship to the main length measure of the country.

There is also evidence, especially from the 19th century, of laws about adapting the old dimensions, either to the geographical mile or to the decimal meter itself, with more or less large deviations from the old dimensions.

See also

literature

  • Friedrich Hultsch : Greek and Roman metrology. 2nd Edition. Berlin 1882.
  • Eberhard Knobloch , Dieter Lelgemann , Andreas Fuls: On the Hellenistic method of determining the circumference of the earth and on the map of Asia by Klaudios Ptolemaios. In: Journal of Geodesy, Geoinformation and Land Management . Volume 128 Issue 3, 2003, pp. 211-217.

Web links

Individual evidence

  1. ↑ Heron of Alexandria, Geometria, Heiberg, 1912, ISBN 3-519-01416-5 , p. 403, paragraph 12. See also Heron's table fragment, fragments 2, 2 and a work Περὶ μαρμάρων καὶ, which was slipped under Didymos Chalkenteros of Alexandria παντοίων ξύλων ( About all types of marble and wood ) 16.
  2. ↑ Heron von Alexandria, Geometria, Heiberg, 1912, ISBN 3-519-01416-5 , p. 413, paragraph 67 ff.
  3. ↑ R. de Zwarte: The Ionic foot and the relationship between the Roman, Ionic and Attic foot measurements . In: Bulletin Antieke Beschaving . Vol. 69, 1994, p. 131.
  4. ↑ Wolfgang Torge : History of geodesy in Germany. De Gruyter, Berlin et al. 2007, ISBN 978-3-11-020719-4 , p. 68 f.
  5. ↑ MARTINI, Angelo, Manuale di metrologia ossia misure, pesi e monete, Torino, Loescher, 1883. P. 577: Prague.
  6. ↑ MARTINI, Angelo, manuals di metrologia ossia misure, pesi e monete, Torino, Loescher, 1883. S. 596: Rome.
  7. ↑ MARTINI, Angelo, manuals di metrologia ossia misure, pesi e monete, Torino, Loescher, 1883. S. 783: Turin.