Talk:Ancient Roman units of measurement/Archive 1
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Good, but...
You should expand the introduction more and give better citations for the measurements - citations go on the bottom of the article, also. See the wikipedia style guidelines to see how it's done. Xaa 23:49, 5 August 2005 (UTC)
The Greek Orders of Architecture were copied by the Romans
Disputed
See User:Egil/Sandbox/rktect#Articles_under_attack -- Egil 15:31, 27 August 2005 (UTC) Egil has listed no grounds to dispute any fact in this article
Disputed, again
It seems we have now got the version from the previous pseudoscientific attack from 2004, which we managed to weed out, but because it remained long enough in the English version for an Italian version to be made, we are now experiencing a deja vu by having this Italian version re-imported back into English! My brain hurts. Really.
This version was from an editor that was a firm believer in the Megalithic Yard as an absolute measure of everything, and thus wrote things like:
- The "theoretical" value of the Nippur ell is: 518 616 µm exactly. Therefore Romain foot is 296 352 µm. This is around 29.64 cm.
Help! -- Egil 10:32, 19 September 2005 (UTC)
- Hi Egil,
- You are right, the so-called Megalithic Yard is very doubtful.
- But that the Roman foot has been picked up from Egyptians as 16/28th of the Nippur cubit is indeed non-controversial in science.
- With friendly greetings, Paul.
Roman foot
Hallo Rktect,
First a tip: If you use "Show prewiew" bottom before a final save, the history pages would be easier to consult.
- You can give only 296 mm for the conventional Roman foot, that's not false. One day soon, the recently proposed value of 296 352 µm as defined, practical, conventional value for the Roman foot will be largely accepted in science. Because, on the one hand, that's 2^5 * 3^3 * 7^3 µm and thus gives round values for other related ancient measures. On the other hand this defined, conventional value is inside the range of mean values empirically calculated by modern statistical methodes. Thitherto both 296 mm as well as 296.4 mm is okey.
- I removed your insertion:
- There is a direct relationship between ancient lengths and the weights. Roman and Egyptian measures are divided into digits, palms, feet, remen and cubits with the relatonship 16 digits to a foot and 18.5 Roman digitus = 18.75 Egyptian dj. Biblical and Greek measures are divided into hands so three Greek hands = 4 Roman palms = 1 foot 1 Biblical cubit = 18" Ancient English and French measures are derived from the Romans and ancient Germanic measures are derived from the Greeks.
- because this insertion is outside of of the topic. If you know a real relationship between both values, we can discus this here. Sure, the English foot is considered to be 36/35 Roman foot and the Austrian foot is identical to the Greek "Pous metrios" but this is without regard to the relationship between Roman lengths and Roman weights.
-- Paul Martin 11:48, 21 September 2005 (UTC)
Hi Rktect, you answered inside of my statements. For better lisibility I allowed me to separated your reply: (Paul)
- I am more comfortable without going to decimal mm for two reasons. First even the Romans had some inaccurate, less than ideal, conflicting standards which make it hard to claim an accuracy to decimals of a mm and secondly I like to avoid going to mean values when there is a clear mathematical relationship.
- The stadium of 185 m being 625 x 16 = 10000 digitus suggests a preference for ease of computation. The remen being the hypotenuse of the quarter and foot, the mile being 75 stadia = 111 km.
- Roman and Egyptian measures are divided into digits, palms, feet, remen and cubits with the relatonship 16 digits to a foot and 18.5 Roman digitus = 18.75 Egyptian dj. Biblical and Greek measures are divided into hands so three Greek hands = 4 Roman palms = 1 foot 1 Biblical cubit = 18" Ancient English and French measures are derived from the Romans and ancient Germanic measures are derived from the Greeks.
- Its the very essence of the topic. Without knowing those kinds of details it becomes very difficult to tell the difference between Greek and Roman feet. If you know that one is always divided into palms and the other is always divided into hands it makes it a lot easier to tell them apart.
- Aside from basing everything on the ratio of column diameters to height as a euphamism for the parallels and using the resultant pleasing ratio to define standards of measure the issue becomes one of defining pleasing and harmonious loadbearing proportions using the geography of Pi and Phi. (The only number which is its own reciprocal)
- The Roman Vitruvius considers 16 an ideal number for anything to do with architectural measurement. As an architect he thinks of the Greek orders from which Roman architecture is derived as not quite so perfect as his Roman ideals. There is a direct relationship between ancient lengths and the weights in that architectural proportions are designed to take loads and look god doing it. Vitruvious says that 16 is ideal because it is composed of 10 and 6. I would be happy to discuss that using Normand's Parallel Orders.
- The relationship that the square of the length is the area and the cube of the length is the volume and thus the weight depends on the material and unit is far more ancient than the Romans.
Rktect 18:05, 21 September 2005 (UTC)
The aim of this modern definition: one Roman foot equal 296 352 µm (or Nippur Ell = 518 616 µm or Punic foot = 294 000 µm it's all the same) is to highlight the real existing "clear mathematical relationships" between ancient measures. But it's also clear that in ancient times good measure standards could turn around about ± 0.17%. (294 × 1.0017 = 294.4998) This means that all Roman foot specimen between 295.849 and 296.855 mm are quite good enough. If you want continue to wear you by using other values than 296.352 mm, that's your right. Me, I decided to recognise and to adopte this definition discried and formulated by a friend of mine in 2003.
You said: "the mile being 75 stadia = 111 km" ??? The Romain mile equal 5000 Roman feet. 75 Roman miles equal 375 000 Roman feet equal 600 Roman-attic stadions or 625 stadions of Delphi or 578 stadions of Olympia. It's that, what you want to say? So, that's true.
You wrote: "Ancient English and French measures are derived from the Roman [...] measures." You can give me the good ratio between Roman foot and the "pied du Roy de France" of about 324.8394 mm i.e. about 109.6% of Roman foot? If yes, I'am highly interested to hear it(!!), because hitherto no one gave me a convincible ratio (like this is the case for many mediaeval measures, because in Middle-Ages metrologistes not always refer to already existing standards, like it is the case in Antiquity with their international trade relationships.)
You wrote: "The relationship that the square of the length is the area and the cube of the length is the volume and thus the weight depends on the material and unit is far more ancient than the Romans." I answer you: "The truth is concrete." This means: Which numbering relationship (= ratio) between Roman lenghts and weights? It's not the weight of water in a cube, that's sure, because four Roman digits cube gives about 406.67 ml or grams i.e. about 0.932% of the weight of a Greek mine. I don't know any concrete ratio. Do you know one, say? Spongy referring to "hands", don't help.
The problem with "ideals" is that ideals are not objective. What you or another juge ideal, a third one (with good arguments too) considers not-ideal. You know. But it's true, sixteen is both an old system and a very modern one (cf. there)
I don't read Charles Normand. I can't juge it and I don't think that I'll have time to read it. But I imagine that he treats systems like the mediaeval measure systems based to the Fibonacci suite: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...
This can be interesting with condition that you clearly distinguish them from the main and standard systems:
In the mediaeval standard system the palm has 36 lines, the foot 144 lines, the cubit 216 lines.
The mediaeval "Royal canna" has 555 lines composed by one "palmus minor" with 34 lines, one "palmus maior" with 55 lines, one "palma" with 89 lines, then: one foot equal to the foot of the standard system and one cubit 17 lines longer. It's a legitim system, but it's not the standard system.
It's important to discern this clearly. No confusions please.
-- Paul Martin 16:41, 22 September 2005 (UTC)
I agree that there were both "clear mathematical relationships" and great variations in standards. I don't like using decimal mm because of the variations but we are not in any essential dissagreement on these points.
Did I say that? The correct statement is that 75 Roman miles were taken as a degree. We can run the numbers 296 mm to a pes or foot, Each mile passum was 8 stadia of 625 pes and thus 5000 pes or 1000 passus to a mile passum or mile, 75 miles to a degree and get 111 km easily enough.
We can also mention that the Ionic Greeks used the same arrangement and the Attic Greeks used 600 pous of 308.4 mm to get a stadion that was the same 185 m as the Roman stadium. I also agree that there were other stadia. They all use pretty close to the same value for the degree but the value improves slightly over time. Mesopotamian 180 km, Egyptian,110.25 km, Greek and Roman, 111 km.
- Herodotus
- 608 miles = 81 schoenus
- 1 schoenus = 7.5 miles = 11.1 km
- 1 mile (mia chiloi, mylios, milos or milion) = 1480 m = 4800 pous of 308.33 mm
- 1 degree = 111 km = 10 schoeni, each schoenus is 11.1 km
- 11.1 km = 1 Egyptian itrw = 1 schoenus = 60 stadions
- 111 km = 600 stadions = 75 Roman milliare or miles.
These stadia were used to my knowledge 1 degree = 111 km = 500 stadia, each stadia is 222 m (stadia of Ptolemy and Marinus) 600 remen of 370 mm = 222 m (stadia of Ptolemy, Marinus and Posidonus) 500 x 360 = 180,000 stadia = 39,960 km
1 degree = 111 km = 600 stadia, each stadia is 185 m (Greek and Roman stadia) 600 pous of 308.4 mm or 625 pes of 296 mm = 185 m (Greek and Roman stadia) (This is the stadia Herodotus equates to the Egyptian itrw of 21,000 Egyptian royal cubits) 600 x 360 = 216,000 stadia = 39,960 km
1 degree = 111 km = 700 stadia, each stadia is 158.57 m (Persian stadia) 500 amma of 317.14 mm (Close to Athenian pous of 316 mm) = 158.57 m (Persian stadia) 1 degree = 110.25 km = 700 stadia each stadia is 300 Egyptian st3t = 157.5 m (Eratosthenes) 1 st3t = 100 royal cubits of 525 mm = 52.5 m
700 x 360 = 252,000 stadia = 39,690 km Egyptian, 39,960 km Persian
Aristotle gets a circumference of 400,000 stadia of 300 pous of 308.4 mm = 37,008 km Pythagorus used a chain of ten stadia at Miletus to get what became the nautical mile = 1850 m.
There is a page on the French variations on the pied du Roy de France which seem to vary by Province and then by city. As mentioned above I'm of the opinion that a range of +/- 1 mm is about the limit to which you can hold standards precise, and at three decimals of mm they would begin to be affected by their coefficients of expansion
"For instance, in 1740 A.D., Anders Celsius, who was connected with the measurement of the arc of meridian in Lappland and for this reason was particularly concerned with the exact value of lineal units, states that the English foot is 1027/1000 of Swedish foot, which means 304.916 mm., by a Swedish foot of 296.9. Taking the same value of the Swedish foot and Celsius’ statement that it is 1000/1094 of Paris foot, the latter would be 324.808 mm. (The meridian was measured in Lappland with the definitive Paris foot of 1732 A.D., which is 324.839 mm.). Robert Young in discussing Scottish measures in 1740 A.D., states that the English foot is 1351.7 Paris lines or 304.920 mm." [Metrum]
When the system originated the accuracy and precision of standards was probably something simiar to that used by Archimedes to find the counterfeit coins. If you can define a foot to the nearest mm then you can define a finger to the nearest 1/16 mm. When you start talking about water in a cube there is a difference in specific gravity between say fresh water, salt water, wine and olive oil, and a further difference between them at different temperatures and sea levels, but does it amount to enough to be of any great importance in commerce? Since the Greeks all had different pous and there were both sacred Mina of 60 shekels and profane Mina of 50 shekels getting an exact table of equivalences can take a little work. "
- Mesopotamia
- 1 talent (GÚ.UN; biltu) = 60 mina = 3600 shekel = 30.00 kg
- 1 mina (MA.NA; manû) = 60 shekel = 500 gr
- 1 shekel (GÍN; šiqlu) = 8.333 gr
- Persia
- 1 Babylonian mina = 6 karšâ = 60 shekel = 499.80 gr
- 1 karšâ = 10 shekel = 83.33 gr
- 1 shekel = 8.33 gr
- Attic Greek
- 1 talent-weight = 60 mnai = 6000 drachm-weights = 27.47 kg
- 1 mna = 100 drachm-weights = 457.8 gr
- 1 drachm-weight (holkê) = 4.578 gr
- 1 talent-weight = 60 mnai = 6300 coin-drachms = 27.47 kg
- 1 mna = 105 coin-drachms = 457.8 gr
- 1 coin drachm = 4.36 gr
- 1 talent (to talanton) = 60 minae = 6000 drachms = 36,000 obols = 25.86 kg
- 1 mina (hê mnâ) = 100 drachms = 600 obols = 431 gr
- 1 drachm (hê drachmê) = 6 obols = 4.31 gr
- 1 obol (ho obolós) = 0.72 gr
- Alternative values:
- 1 talent = 21.45 kg
- 1 mina = 357.5 gr
- 1 drachm = 3.58 gr
- 1 obol = 0.60 gr
- 1 stater (ho statêr) or tetradrachm = 4 drachms = 17.24 gr
- 1 didrachm = 2 drachms = 12 obols = 8.62 gr (= 1 Babylonian shekel?)
- 1 obol = 8 chalkoi
- 1 deben silver (Ptolemaic demotic) = 20 drachms "
Yes, if you can tolerate a little ambiguity and make allowances for less than ideal accuracy then it becomes pretty easy to follow things like the above correspondence between weights and measures in Mesopotamia, Persia, Greece, Rome and Egypt
The Greek Orders of Architecture relate architectural proportions to column diameters and use diagonals to get the Fibonacci series from the Golden Section, but they also relate the diameter of the columns to their unsupported lengths (pi related to phi) and thus are related to the ability of the columns to take gravity seismic, and wind loads. I have no problem allowing that there are many different levels of related math problems involved but once you compare a shear and moment diagram for the three moments theorem or look at Hanskines formula and realize that the roof pitch is actually related to the vector at which the load is transfered from the roof to the columns by this really beautiful formula it makes what they are doing with the three problems of classical antiquity much easier to follow. Just at the point at which medieval belief is becoming Renaissance science, Andreas Palladio begins rediscovering Vitruvius.
I don't have a problem with that as far as it goes but can't resist a few confusions. For one thing there are several different Greek pous being used east of the Rhine and clearly they have different proportions than the Roman pes and for that matter the remen. Since feet can be divided into both palms and hands (not to mention fists, spans and quarters) there can be confusion as to whether the division is actually of a pes divided into 4 palmus and 16 digitus or a remen divided into 5 palms and 15 uncia or a pous based fote divided into 3 hands and 15 digits.
Clearly a foot divided into 144 lines has 12 lines to the inch and if there are 4 palms of 36 lines there are 9 lines to a finger. If we are talking a Greek foot divided into hands there are 150 lines to a foot and 10 lines to a finger. That leaves us wondering about the remen which may be in a Roman system five palms or 20 fingers and 180 lines or on a Greek system 18 fingers.
Rktect 15:28, 23 September 2005 (UTC)
Hi Rktect,
Before I will reply you later to the other topos, let's examine your statements concerning the French Foot. You say French Foot should be 1094/1027 English Foot.
Are you serious or it's a joke? Okey: (1094/1027) × 304.8 mm ≥ 324.6847 mm.
In 1799 the decimal meter was defined as 3 French feet and 11.296 lines exactly. This gives 324.839 385 mm to the Pied du Roy. The ratio 1094/1027 ???
1094=2*547 and 1027=13*79 No, surely not! This has nothing to do with classical very, very, easy primary ratio factors used in antiquity:
Mainly the factors two, three, five and seven. The factor eleven is only present in the Attic Foot and the English Mile. No other factor exists in ancient metrologie.
No! (2*547) / (13*79) is not a ratio, but these values are another way to say 109.4 and 102.7 %.
To illustrate you the very simply ratios in ancient metrologie, I made this table below:
| A range of ancient measures, with Nippur Cubit = 518.616 mm By definition: One Punic Foot (as 250/441 Nippur Cubit) equal 294 × 1021 yoctometers.
Note: Only five basic primary numbers (2, 3, 5, 7 & 11) enter into the ratios. | |||||||||||||||||||
| Symb. | Units of length | Ratio | Millimeters | ‰ of P.F. | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| HC | Hashimi Cubit | 384 / 175 | 650. 280 96 | 2211 21/25 | |||||||||||||||
| Guard Cubit (arab.: ammatu rabitu) | 15 / 8 | 555. 660 00 | 1890 0/5 | ||||||||||||||||
| Arabic Nil-Cubit | 175 / 96 | 540. 225 00 | 1837 1/2 | ||||||||||||||||
| Pechys basilikos | 9 / 5 | 533. 433 60 | 1814 2/5 | ||||||||||||||||
| RC | Egytian Royal cubit | 25 / 14 | 529. 200 00 | 1800 0/5 | |||||||||||||||
| Pergamon cubit | 225 / 128 | 520. 931 25 | 1771 7/8 | ||||||||||||||||
| NC | Nippur cubit | 7 / 4 | 518. 616 00 | 1764 0/5 | |||||||||||||||
| BC | Babylonian cubit | 375 / 224 | 496. 125 00 | 1687 1/2 | |||||||||||||||
| Salamis cubit | 49 / 30 | 484. 041 60 | 1646 2/5 | ||||||||||||||||
| Pechys metrios | 8 / 5 | 474. 163 20 | 1612 4/5 | ||||||||||||||||
| BTC | Babylonian Trade Cubit | 675 / 448 | 446. 512 50 | 1518 3/4 | |||||||||||||||
| Cubitus Romanus | 3 / 2 | 444. 528 00 | 1512 0/5 | ||||||||||||||||
| R | Egyptian Remen (pygon romaikos) | 5 / 4 | 370. 440 00 | 1260 0/5 | |||||||||||||||
| PB | Pous basilikos (pygme metrios) | 6 / 5 | 355. 622 40 | 1209 3/5 | |||||||||||||||
| Pous of Egypt (2/3 Royal Cubit) | 25 / 21 | 352. 800 00 | 1200 0/5 | ||||||||||||||||
| Ionian foot (pygme Kyrenaika) | 75 / 64 | 347. 287 50 | 1181 1/4 | ||||||||||||||||
| Pes Drusianus (pygme romaikos) | 9 / 8 | 333. 396 00 | 1134 0/5 | ||||||||||||||||
| Pous Ptolemaikos (pygon Italikos) | 125 / 112 | 330. 750 00 | 1125 0/5 | ||||||||||||||||
| Vintage French Foot | 192 / 175 | 325 .140 48 | 1105 23/25 | ||||||||||||||||
| Pous Philetairikos (pygme Italikos) | 15 / 14 | 317. 520 00 | 1080 0/5 | ||||||||||||||||
| PM | Pous metrios | 16 / 15 | 316. 108 80 | 1075 1/5 | |||||||||||||||
| Attic-olympic foot | 11 / 10 | 311. 169 60 | 1058 2/5 | ||||||||||||||||
| Pous of Kyrenaika | 25 / 24 | 308. 700 00 | 1050 0/5 | ||||||||||||||||
| EF | English foot (uncial division) | 36 / 35 | 304. 819 20 | 1036 4/5 | |||||||||||||||
| Egyptian Royal Foot (« Shaku ») | 50 / 49 | 302. 400 00 | 1028 4/7 | ||||||||||||||||
| Haraion (Hebraic) foot | 225 / 224 | 297. 675 00 | 1012 1/4 | ||||||||||||||||
| PR | Pes Romanus | 1 | 296. 352 00 | 1008 0/5 | |||||||||||||||
| PF | Punic foot | 125 / 126 | 294. 000 00 | 1000 0/5 | |||||||||||||||
| « Baumaß » (uncial division) | 35 / 36 | 288. 120 00 | 0980 0/5 | ||||||||||||||||
| Nippur foot (or « Waterfoot ») | 14 / 15 | 276. 595 20 | 0940 4/5 | ||||||||||||||||
| Pous Nikomedesios | 625 / 672 | 275. 625 00 | 0937 0/5 | ||||||||||||||||
| PI | Pous Italikos | 25 / 28 | 264. 600 00 | 0900 0/5 | |||||||||||||||
| Foot of Hipparch (16 BTC Units) | 45 / 56 | 238. 140 00 | 0810 0/5 | ||||||||||||||||
| « Soilfoot » (10 inches of Nippur foot) | 7 / 9 | 230. 496 00 | 0784 0/5 | ||||||||||||||||
| Dorans Romanus | 3 / 4 | 222. 264 00 | 0756 0/5 | ||||||||||||||||
| « Natural span » | 2 / 3 | 197. 568 00 | 0672 0/5 | ||||||||||||||||
| Palmus Romanus | 1 / 4 | 074. 088 00 | 0252 0/5 | ||||||||||||||||
| Uncia romana (« pollex ») | 1 / 12 | 024. 696 00 | 0084 0/5 | ||||||||||||||||
| DR | Digitus Romanus | 1 / 16 | 018. 522 00 | 0063 0/5 | |||||||||||||||
| Roman length of grain (theoretical) | 1 / 36 | 008. 232 00 | 0021 0/5 | ||||||||||||||||
| |||||||||||||||||||
Like, currently, you seem to prefer a RP in ASC0, you choose also a Pous of Kyrenaika in Accuracy Standard Class 0 with 308.4 instead of the better value of 308.7 mm. One day soon, even the legal English Foot Standard will change.
0.006 299 %. For technical even high-level accuracy, it's nothing, but for a good and correct theorie, these new defined values are very useful and important. In science, the English foot is not used any more since a long time.
For your other topics, I will answer you soon.
-- Paul Martin 16:19, 24 September 2005 (UTC)
That's a cite that Metrum attributes to Celcius. Like the Greeks the French sem to have had a variety of foot measures. I wasn't there so I don't know for sure, but that seems reasonable. Not all measures in use will always be a part of the same system. I'll go to Klein for an illustration. p 70 he puts The Belgic foot at about 336 mm or 13.22". p 72, he puts the Paris foot at 12.785" or 325 mm.
While I would agree there was a system, you also have to allow for the fact that in the Middle ages many people were busy reinventing the wheel. I would also allow there are many more integer values than what you allow and quite a few not integer values. There are a lot of questions about the correct value for the Nippur cubit. Is it correctly measured from the end of the rod or the last mark on the rod? is it divided into hands or palms? is it divided into 15 fingers or 16? Are its increments intended to be equal or does it have sets of different widths as Egyptian rulers do?
It seems likely to me that the Romans would copy the Greeks as exactly as they could but the limits of accuracy and precision are probably not correct to 3 decimals of mm across the board. Rktect 16:54, 24 September 2005 (UTC)
- I well understood that this was a quotation of metrum.org. However: The French Foot equal 1094/1027 English Foot is not a ratio in the ancient sense of term.
- No, I'am formally, there is not a "variety of French foot measures", there is only one foot since the early Middle-Ages, even if in 1668 it was modified by about 0.5 % (the old, exposed main public standard, disaggregate, was replaced by a longer one). Belgium didn't exist between the end of Roman times and 1830 A.D.
- In ancient times, except a few measures derived from the Old Royal Cubit and hence irrational, I don't have knowledge of any ancient measure without easy ratio. Do you know any measure of antiquity not derived from the Nippur Cubit by simple ratio. If yes, say it, which archaeological graduated ruler stick? This case would be really very interisting for me and the colleagues.
- Yes, in the European Middle-Ages (much less scientific than the Antiquity) local princes and their metrologists didn't hesistate to officialise a local (currupt) measure standard without references to neighbour states or other well-known standards. The excellent metrologists of the Antiquity did'nt tolerate suchlike proceedings.
- Nevertheless, an important minority of mediaeval states in Europe conserved either the Roman foot or one of the different Greek feet or they have chosen a deduced foot measure just like the English-Russian Foot for example.
- For the measures of the Nippur Ell, see for example this link.
- What do you don't seem to understand, that the modern definition of the Roman foot do not pretend that Roman or Greek metrologists has been able to determinate pico-, atto- or yoctometer measures. It's a modern definition ! Definitions are not true or false, it can be adequate or not for the purpose for which it has been aimed. Beyond they can be widely recognised or not.
-- Paul Martin 19:02, 24 September 2005 (UTC)
It seems likely to me that the Romans would copy the Greeks as exactly as they could but the limits of accuracy and precision are probably not correct to 3 decimals of mm across the board.
| Standard | Finger | Thumb | Palm | Hand | Foot | Remen | kus | cubit | nibw |
| Sumerian | 16.7 | 25 | 75 | 100 | 300 | 400 | 500 | 600 | |
| Nipur | 17.7 | 23.6 | 70.7 | 106 | 318 | 424 | 530 | 601 | |
| Assyrian | 20.58 | 27.4 | 82.3 | 247 | 329.3 | 411.7 | 494 | 576 | |
| Egyptian | 18.75 | 25 | 75 | 100 | 300 | 375 | 450 | 525 | 600 |
| Hittite | 19.2 | 24 | 76.8 | 96 | 288 | 384 | 480 | 576 | 672 |
| Persian | 20 | 25 | 75 | 100 | 300 | 400 | 500 | 600 | |
| Greek | 19.3 | 25.7 | 77.1 | 102.8 | 308.4 | 411.2 | 514 | 616.8 | |
| Roman | 18.5 | 24.7 | 74 | 98.67 | 296 | 370 | 444 | 518 | |
| Palestine | 18.3 | 24.4 | 73.3 | 91.57 | 274.7 | 366.2 | 458 | 549 | 641 |
| Talmudic | 18.5 | 24.7 | 74 | 92.5 | 277.5 | 370 | 462.5 | 555 | 647.5 |
| Biblical | 18.3 | 22.9 | 73.2 | 91.44 | 274.7 | 365.8 | 457.2 | 548.6 | 640.1 |
| Arabic | 18 | 24 | 72 | 90 | 288 | 384 | 460 | 537.6 | 614.4 |
- Greek Feet: Miletus 318, Athens and Etruria 316, Aegina 314, Attic Short 308.4, Ionian 296.The important thing is that all palms, hands, feet, remenm cubits and elles are integral multiples of fingers, palms are 4 fingers, hands are five fingers feet are 3 hands or 4 palms, remen are or 5 palms, cubits are 5 hands or 6 palms, great cubits are 6 hands or 7 palms, nibw or elles are 8 palms.
Rktect 21:40, 24 September 2005 (UTC)
| Main multiples and submultiples for some ancient measures. The main value is defined (PR = 296.352 mm). Not a single deduced value is rounded. | ||||||||||
| In digits: | 1 | 4 | 16 | 18 | 20 | 24 | 28 | 30 | 32 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Ratio | Main Measure | Digit | Palm | Foot | Pygme | Pygon | Commun Cubit |
Pechys neilos |
Mesop. division |
Pechys histonikos |
| 25/24 | Pous of Kyrenaika | 019. 293 75 | 077. 175 00 | 308. 700 00 | 347. 287 50 | 385. 875 00 | 463. 050 00 | 540. 225 00 | 578. 812 50 | 617. 40<0 00 |
| 9/5 | Pechys basilikos | 019. 051 20 | 076. 204 80 | 304. 819 20 | 342. 921 60 | 381. 024 00 | 457. 228 80 | 533. 433 60 | 571. 536 00 | 609. 638 40 |
| 25/14 | Royal Cubit | 018. 900 00 | 075. 60>0 00 | 302. 400 00 | 340. 200 00 | 378. 000 00 | 453. 600 00 | 529. 200 00 | 567. 000 00 | 604. 800 00 |
| 1 | Pes Romanus | 018. 522 00 | 074. 088 00 | 296. 352 00 | 333. 396 00 | 370. 440 00 | 444. 528 00 | 518. 616 00 | 555. 660 00 | 592. 704 00 |
| 175/96 | Arabic Nil-Cubit | 018. 007 50 | 072. 030 00 | 288. 120 00 | 324. 135 00 | 360. 150 00 | 432. 180 00 | 504. 210 00 | 540. 225 00 | 576. 240 00 |
| 375/224 | Babylonian Cubit | 017. 718 75 | 070. 875 00 | 283. 500 00 | 318. 937 50 | 354. 375 00 | 425. 250 00 | 496. 125 00 | 531. 562 50 | 567. 000 00 |
| 9/8 | Pes Drusianus | 016. 669 80 | 066. 679 20 | 266. 716 80 | 300. 056 40 | 333. 396 00 | 400. 075 20 | 466. 754 40 | 500. 094 00 | 533. 433 60 |
| Some well-known measures are formated in green font color, not exhaustive. The important Nippur Ell measure like the English Foot marked in blue font color. For comparison : The irrational Egyptian Old Royal and Old Trade Cubit. (Here, of course, the values are rounded in the fifth right decimal position.) | ||||||||||
| 5√2/4 | Old Royal Cubit | 018. 710 05 | 074. 840 18 | 299. 360 07 | 336. 780 82 | 374. 200 91 | 449. 041 09 | 523. 881 27 | 561. 301 36 | 598. 721 45 |
| 15√2/14 | Old Trade Cubit | 016. 037 18 | 064. 148 73 | 256. 594 91 | 288. 669 27 | 320. 743 64 | 384. 892 36 | 449. 041 09 | 481. 115 45 | 513. 189 82 |
In your "Egyptian Finger" of 18.75 mm exactly one, I recognise the Old Royal Cubit in a quite bad standard (ASC-1), at least 0.213% longer than its modern definition.
For your so-called "Sumerian" and "Nippur" Standard you say "Foot", but you divise into 18 digits. So it's a Pygme.
For your so-called "Palestine", "Talmudic", "Biblical", "Hittite" and "Persian" standards you divide into 15 fingers, what even the Sumerians great inventors of the sexagesimal system never did.
Also for your so-called "Arabic standard" (correctly divided into 16 digits), please check your sources. It seems to be less "Arabic" then "arabesque". What you call "Arabic Remen" it's 64/3 digits or 1.333 feet. Okey. But it becomes "better", futher. What you call "Arabic Kus" and "Arabic Cubit", it's 230/9 digits equal 25.555 digits and, hold you tight, 1344/45 digits or 1.8666 feet. Isn't it? Your "Arabic Nibw" is 512/15 digits or 2.1333 feet. My God. You should be much more careful with your sources, by avoiding doubtful publications which immingle conspicuously sundry systems.
Likewise your "Greek Remen" and "Greek Kus" is 1.333 and 1.666 feet respectly, ok. But can you say me what's your "Greek Cubit" with 616.8 mm?? 1.9974 feet or what?
-- Paul Martin 13:34, 25 September 2005 (UTC)
The Egyptian royal cubit certainly has more than one artifact from which conclusions about its intended standard length in different periods may be argued. Fingers, palms, feet, cubits, remen, great cubits and nibw can all be evaluated separately or collectively with rulers, rods, inscription grids, building stones, nilometers and other artifacts all contribution to the discussion. Wilkenson cites James who measured the royal cubit ay 525 mm and Jomard who measured the cubit of Mephis at 20.4729" (520 mm);that of Turin at 20.57869", (523 mm); anothe 523 mm, another 524 mm, that of the Nileometer at 527 mm but Wilkenson himself measured the cubit of Nileometers as 20.625" (523.9 mm)per royal cubit and .736"(18.7 mm) to each digit. Wilkenson also mentions a 2 cubit rule of 41.3" found in a pylon at Karnak making its cubit 20.65" (524.5 mm)Wilkenson also found a cubit carved in stone at E'sooan about 21" 533.4 mm)((The most commonly cited values today would be IES Edwards, SRK Glanville and Petries ideal of 20.62" (523.8 mm) which is cited in Gardiner sixth edition despite the 3rd edition gives 20.59" and Gillings who goes with Gardiner at 20.59 (523 mm)and Stecchinis 525 mm.
The Sumerian cubit and Nipur cubit can be divided into 18 fingers (pygon) or 12 thumbs (foot) The Greek pygon is sometimes taken as 20 fingers (daktylos)[pygon]but it really ranges from palm based remen (370 mm)= 5 palms of 74 mm to hand based remen (416 mm)5 hands of 104 mm.
The division into 15 fingers is quite natural if you are measuring in hands of 5 fingers rather than palms of 4 fingers. Mesopotamians and Greeks tend to use hands, Egyptians use palms, hands and fists and Romans tend to use palms. There are a couple of points to make here in that in addition to measuring in different numbers of fingers some rules use different sizes of fingers for palms and hands and use thumbs when dividing into 12 parts.
- 1 finger = 16.67 mm Sumer
- 1 finger = 17.67 mm Nipur
- 1 finger = 18 mm Semitic
- 1 finger = 18.5 mm used with Roman fists and palms
- 1 finger = 18.75 mm used with Egyptian palms
- 1 finger = 19.275 mm used with Hittite and Greek hands
- 1 finger = 20 mm used with Mesopotamian hands
- 1 thumb = 24.67 mm used with Roman foot
- 1 thumb = 25 mm used with Egyptian and Mesopotamian foot
The most common divisions of the cubit are
4 fingers = 1 palm = 75 mm digit = 18.75 mm 5 fingers = 1 hand = 100 mm digit = 20 mm 6 fingers = 1 fist = 111 mm digit = 18.5 mm 10 fingers = 2 hands = 1 span = 200 mm = 20 mm 12 fingers = 3 palms = 2 fists = 222 mm 12 thumbs = 1 foot = 300 mm 15 fingers = 3 hands = 1 foot = 300 mm 16 fingers = 4 palms = 1 foot = 300 mm 18 fingers = 3 fists = 1 pygon = 333 mm 20 fingers = 5 palms = 1 remen = 375 mm 20 fingers = 4 hands = 1 remen = 400 mm 24 fingers = 6 palms = 1 cubit = 450 mm 24 fingers = 4 fists = 1 cubit = 444 mm 25 fingers = 5 hands = 1 cubit = 400 mm 28 fingers = 7 palms = 1 royal cubit = 525 mm 30 fingers = 5 fists = 1 great cubit = 555 mm 30 fingers = 6 hands = 1 great cubit = 600 mm 32 fingers = 8 palms = 1 nibw or elle = 600 mm
The nibw or elle is literally 2 feet. Two Greek feet of 308.4 mm = 616.8 mm The Germanic allen, or ellen come from the Greek by way of the Egyptian nibw and or the Mesopotamian great cubit.
The values of Arabic measures come from Klein. The measures themselves probably came from Arabata along with Hindu (Arabic numerals) c 200 BC. From my own experience there are several different kinds of Arabic with Egyptian arabic, Persian arabic and Farsi not necessarily closely related. Arabic measures draw from a huge mixture of different standards from all over the Ancient near east. Mesopotamia, Egypt, Persia, Baluchistan, Pakistan, North Africa and Spain get involved in the mix. Wikipedia says Arabic measures are based on the Persian system, but the Persian empire was huge.
- 1 finger,wa:hid assbaa = ¼ palm
- 1 palm, 'arba`ah assbaa = 1 cabda = ¼ foot
- 1 foot 1 thala:thah (3 hands) ='arba`ah cabda = 1 'arba`ah ≈ 0.32 m (Thats a median Greek foot)
- 1 cubit, sittah cabda = 1 arsh
- 1 great cubit, sab`ah cabda
- 1 thama:niyyah cabda = ithna:n thala:thah
- 1 pace, xamsah = xamsah thala:thah
- 1 sittah orgye = sittah thala:thah (The orquia is Greek)
- 1 cane, qasab = thama:niyyah thala:thah
- 1 stadion, seir = sittah `asharah `asharah thala:thah (The stadion is Greek)
- 1 ghalva = sab`ah ithna:n `asharah thala:thah
- 1 league, farasakh = ithna:n tis`ah thala:thah `asharah thala:thah ≈ 5.76 km, from parasang
- 1 barid = 'arba`ah farasakh
- 1 marhala = ithna:n'arba`ah farasakh
Rktect 16:07, 25 September 2005 (UTC)
- First, excuse, you are right: If in reality you count with 19.275 mm (=ASC0) for the digit of the Pous of Kyrenaika, than it's right, nibw = pechys histonikos = 2×308.4 mm = 616.8 mm. It's my fault. I divised 616.8 mm by your 19.3 mm finger value.
- For the Egyptian values one can say since the third dynastie, Egyptian surveyors used the Old Royal Cubit of about 524 mm with Remen sides of 20 (later called) Roman Feet. Afterwards they complety abandoned the Old Royal Cubit, but used a construction Remen with sides of 20 digits of the Old Royal Cubit. Since, the digit of the Royal Cubit is 100/98 digiti Romani exactly one. There are not a multitude of "artifacts" of Royal Cubits, but two exactly one. Well separated in time.
If Wilkenson found 20.625" for the ORC, he found a specimen of ASC7 a top-level Accuracy Standard Class. If this value is confirmed by Edwards, Glanville and Petries (with 20.62") and if even Gillings and Gardiner value of 20.59" is quite -0.17% of the modern defined value, why you privilege the Stecchinis value of 525 mm? Note, +0.2 %, it's not a catastrophe. Outside of your "Cubit of Memphis" everyone confirms the good value of about 523.9 mm, where is the problem? - It's useful to employ terms unambiguous. The pygon is the "20-digits-unit" (and so 5 palms), like the pygme is a "18-digits-unit". Perhaps you found a metrologist, who use the term "pygon" for a 18-digits-unit. Not me like the other colleagues. The 25 digits measure (5 hands) can exist, but it's inappropiated to call it pygon too.
- The Nippur Ell was divided into 30 digits by the Sumerians. This is 518.616 ÷ 30 = 17.2872 mm. But even the Sumerians considerd that the foot is 16 digits, so there are 1 7/8 feet in the Sumerian Nippur Cubit, like there are 1 3/4 Roman feet in the NC and 1.75 Egyptian Feet in both Egyptian Royal Cubit. The museums are fully of pretty specimen illustring this without doubt. For your "Nipur Finger" of 17.7 mm give me references please! This should be the 29.3th part of the Nippur Cubit if I've well calculated. Fanciful, abstruse, completly absurd! *
- Please, grace! No long paragraphs like your "4 fingers = 1 palm = 75 mm digit = 18.75 mm..." It's not useful! Because you change always references. First a bad ORC-digit, than a digit of 2 cm, than a Roman digit a.s.o. I'am horrified!
- If Klein really wrotes "a huge mixtures" of heavy non-sense, it's not profitably to quote it, or on the contrary you have to quote it faithfully. But I absolutly exclude that this "came from Arabata" which I know as a great and reasonable mathematician.
-- Paul Martin 19:28, 25 September 2005 (UTC)
* PS: I see: What you wrongly call "Nippur digit" is actually the "digit of the Babylonian Cubit" of indeed 17.7(1875) mm. I will immediately integrate it the table above.
Hi Rktect,
I integrated your so-called "Sumerian Finger" of about 16.67 mm (better 16.669 80 mm) into the second table. It's the Pes Drusianus taken as a pygon or - that's the same - the Pechys basilikos as a nibw.
For your multiples of hand systems, let's discuss this later. But you see, we already identified your "Sumerian Finger", your misnamed "Nippur Finger" (the Nippur digit is 518.616 / 30 = 17.187 20 mm), your Old "Egyptian Finger" (even if 18.75 mm is a bad ASC-1, I halfly understand you, because 18 750 µm is in primary factors is however 2^1 * 3^1 * 5^5.), then of course the Roman digit and many other values you used. We will finish by clear it up.
PS. I added now the Arabic Nil-Cubit, which gives us the Arabic digit of 18.007 50 mm. In your table I don't see a difference between your Palestine and your Biblical Measures if this is not a thumb of 1.333 versus 1.250 digit. The values are quite the same. This hands should be 1/10 English yard, i.e. one digit of 54/875 Roman Foot = 18.289 152 mm.
I also deleted the hand measure in the second table. I don't say that this measure is not important, but I decided to add the mesopotamian division (30 digits). Hands and their multiples can come back in another new table.
-- Paul Martin 12:16, 26 September 2005 (UTC)
comments
I apologize for not getting back to you sooner, my pc is in the shop. I think we may be getting there. Its nice to enter into discussion with someone who recognizes there is a connection. In the case of Palestine it depends where and when but to mention just a few, you might have Mesopotamian Sumerian, Akkadian, Hurrian, Elamite, Ebalite, Kassite, Dilmanite, Caananite, Syrian, Mittani, Assyrian, Egyptian, Hebrew, Mycenean or Minoan or Sea People Greek, Persian, Phillistine, Phoenician, Roman, Hittite, or Arabic people all living in the same general neighborhood and borrowing and adapting each others standards of measure by adding a finger, a palm, a hand or a span to a rod. I'm still bothered by carrying things out to too many decimal points and would rather focus on the big picture items first, ie; There are short, median and long Greek feet, which it seems may be divided up differently into different numbers and sizes of fingers and or thumbs, and into hands or palms, so it would seem logical that there are also different stadia. Rktect 16:29, 29 September 2005 (UTC)
I think that there are systems of body measures used to measure lengths and systems of agricultural measures used to measure distances and that at some point they are merged into the same system so that for example we have feet as a component of yards, paces and fathoms or orquia/
Stadia measures are used in a similar manner by the Greeks, Persians, Romans and Egyptians
- 1 Greek stadion = 600 pous = 185 m, the pous used is 308.4 mm
- 1 Roman stadium = 625 pes = 185 m, the pes used is 296 mm
- 75 Roman miles or 600 stadia = 1 degree = 111 km
- The Greeks have a measure they call mia chilioi (my or mi lios) (one thousand orquia)
- The Romans call this a milion and it becomes their mille passus (one thousand paces)
- Eight stadia egual a mile and 10 stadia equal a nautical mile or chain the Greeks call the agros
- The Agros is used to lay out the side of the aroura or one thousand of land (from the Egyptian)
- The distance and area a yoke of oxen can plow in a day=10 furrows an orquia wide by a stadia long
- Herodotus says 1 Egyptian itrw equals (or closely approximates) 60 Greek stadia = 11.1 km
- We know the Egyptian Royal cubit is more 28 fingers of about 18.75 mm and 7 palms of about 75 mm
- Allowing the Egyptian Royal cubit is 525 mm 21,000 royal cubits is 11.025 km
- Herodotus has told us something that is in the right range to be taken as a correct statement.
- Marinus and Ptolomy take 500 stadia as equal to a degree
- Their stadia is thus 222 m or 600 remen of 370 mm
- The Persians and Egyptians use 700 stadia to a degree
- Their stadia is thus 157.5 m or 300 Egyptian royal cubits of 525 mm
- The Egyptians have 70 stadia of 300 royal cubits = 60 stadia of 600 pous
- Archimedes, Posideonos, Marinus, Ptolomy, Eratosthenes, Herodotus and the Egyptians all agree.
Rktect 16:29, 29 September 2005 (UTC)
Since some have questioned the Egyptians having a stadia as described above, I found the following interesting and worth citing. I think their schoenus was as Herodotus describes it but otherwise the statement goes the same place we are moving toward.
"Some figures given by the ancients for the circumference of the earth: Aristotle (384-322 B.C.)--400,000 stadia; Archimedes (287-212 B.C.)--300,000 stadia.
Eratosthenes of Alexandria (276-194 B.C.). In a book on the subject, now lost, he stated that at Syeffe (Aswan), 500 stadia due South of Alexandria, a gnomon (pointer on a sundial) threw no shadow on the day of the summer solstice, while the shadow at Alexandria was 1/50 of the circumference of the heavens (7.2 degrees of arc). Consequently, the circumference of the earth was 250,000 stadia. Later, 252,000 stadia was used, probably in order to get a round number (700 stadia) for the length of one degree of latitude. This figure was ado ' pted by Hipparchus (2nd c. B.C.), Strabo (63 B.C.-A.D. 21), and Pliny the Elder (23-79), and passed on to all educated people in Europe.
How long is a stadium? One Egyptian schoenus = 40 stadia. An Egyptian schoenus = 12,000 royal Egyptian cubits = .525 meters for each cubit. So one stadium = 300 cubits = 157.5 meters = 517 feet, which makes the earth 24,662 miles around and 7,850 miles in diameter (very close to modern calculations). "
[stadia]
Rktect 17:06, 29 September 2005 (UTC)
Rktect's proposals
We are making good progress with this page. To add on something more besides it would be nice to see some of the variations on Roman units as for example.
architectural units
The Corinthian orders of architecture, possibly as compared to the Greek orders they derived from.
measures of area
Roman areas compared to Greek and European areas as the use of the horse as a plow animal led to changes in crop rotation. The origin of the agros or chain and the nautical mile.
===industrial measures === measures related to industrial specilization in Roman mills such as board and cloth measure, the size of ingots for metals, barrels for beer, ale and wine, and amphorae for oil and wine, and the Roman use of the talent, mina and shekel as well as the Roman coinage and Biblical Imperial measures such as the bushel, quart, pint and gallon.