Talk:Ancient Roman units of measurement/Archive 3

Archive 1

Archive 2

Archive 3

Archive 4

This is, of course, the talk page of the article Ancient Roman units of measurement. However Jimp and me (Paul Martin) discussed here firstly the digital or hexadecimal foot. Later on, we decided to separate the two discussions, but some back-links refer also to here. If you are arriving from one of these pages, please see:  Talk:Hexadecimal metric system.

Please see ancient weights and measures for previous edit history and discussions wrt this article.

Newer discussions:

Archive I   (archived for making place for further talks.)   -- Paul Martin 18:39, 4 October 2005 (UTC)
Archive II   (Topo: Impossible precision, older replies.)   -- Paul Martin 12:02, 30 December 2005 (UTC)

Impossible precision

Suite:

Hi Jimp, eventually my reply on the topo. I put the first part of our talk into an archive.

What do you think about these notes under the table, by keeping your 296 mm value:

Notes:

The value: 296 millimetres for the Roman foot is a usual rounding to the closest integer millimetre precision. A correct usual value, nearby the length really used by ancient Romans.
However, the value of the historical Roman foot scientifically obtained by modern statistical methodes is 296.2 mm ± 0.5 mm or about ± 0.17 % (cf. Rottländer, Tübingen, Germany).
The widely accepted ratio of the Roman foot and the English foot is 36:35. The latter one is 16/28 Mesopotamian cubit and the ratio between this one and the Roman cubit is 20:24.
If the present English foot is taken as for reference, the Roman foot should be 296⅓ millimetres. That is within the margin obtained by R.C.A. Rottländer (cf. Ordo et Mensura, 2004).
The comparison of the Roman foot with the height of a sheet of A4 paper is descriptive, but with + 0.27 % out of range.

(End of the proposed notes)

Then I think we have clearly to distinguish the ancient measures in use by great European nations at the end of the 18th century and the ancient measures out of use at the arriving of the decimal metre definition.

To the first categorie belong next to the French foot, notably the Austrian foot, of course the English foot, a.s.o. more.

Excursus to your statement:

"Changing the definition of a unit doesn't redefine the units it was once based on. The older definition is abandoned and a new one adopted or are you going to insist that the length of the earth's meridian along a quadrant is exactly the distance travelled by light in vacuum during a time interval of 10 000 000/299 792 458 of a second?"

No, it's about 10 001 965.75 / 299 792 458, since we know that the decimal metre is defined about 0.02 % to short respectively to its conceptual idea.
Of course a measure once "definitively" defined (in 1799 for instance of the metre) and widely used in science like it is its case since about 150 years,
can not be redefined whensoever our cognition converge to the real value. That's evident and this, we have to accept.

With the measures not or no longer used in exact science such redefinitions – inside exiguous limits, of course – can be suitable, see the English compromise foot of 1959.
Example: If we know and if we accept that the Austrian "pous metrios" is 28/27 of the English foot and if we take for reference the present legal English foot, then we can say, retrospectively: The Austrian metrologues of 1872 were in "error" to define the Austrian fathom as 1.8965 metres exactly one (and not 1.8965,3, m).
If contrariwise we consider that the Austrian definition is the "best one", the modern one: Then the English foot should be 304.7946,428571, millimetres.
The difference of about ± 0.000879 % is a honorable older precision. A question of mutual according, just like between the English foot and the American foot before 1959. Those modern reasonable ajustments would yield problems with measures used in exact sciences; admittedly. But that's nothing as regards to an obsolete foot like the Austrian one, and an agonising one like the English foot. Sure, the historical definition laws (1872, 1959, etc.) and its values must always be mentioned.

However the best value of the Roman foot should really be the modern 296.352 mm definition. This has nothing to do with falsify history etc. Then afterwards we can say for example: this archaeological gratuated Roman foot stick found at that archaeological site dated to that epoch is with its, say, 296.5 mm is quite 100.05 % of the modern definition for the Roman foot. The only reason why – preliminary – I renounce to state this modern defined value into the current article is that this value is not yet "widely accepted". Just a question of time.

Happy New Year Jimp.  Cheers!  Paul Martin 16:02, 31 December 2005 (UTC)

Reply

Yes, happy new year Paul though it be late. No, I'm afraid that I still can't swallow your wording and, yes, it's the same old problem. No, your "modern 296.352 mm definition" is not widely accepted but nor contrary to what you claim is your 35 barleycorns definition. If you're going to be insisting otherwise in the article, let's see some references.

My argument is unchanged. No, the Austrians were not in error. They merely discarded one definition for another (if their foot had indeed been defined in this way to start with). We are not at liberty to redifine the Roman foot. It was what it was.

I've removed the following and done a little rewording. I hope you find this compromise acceptable. Jimp 16:43, 11 May 2006 (UTC)

---

Since the Roman cubit measures 17.5 English inches, the English foot is 16⁄28 of the Mesopotamian cubit. Thus the Roman foot measures 35 English barleycorns.

The widely accepted ratio of the Roman foot and the English foot is 36:35. The latter one is 16⁄28 Mesopotamian cubit and the ratio between this one and the Roman cubit is 20:24. If the present English foot is taken as for reference, the Roman foot should be 296+1⁄3 mm. That is within the margin obtained by R.C.A. Rottländer (see the references below).
For the modern conventional value of the Roman foot, please also see this general note.

General note

In 2003, the conventional value of the Roman foot was defined to be 296.352 mm exactly one by Michael Florencetime. This proposal is too recent to be already widely accepted.
However, the value of 2⁵ x 3³ x 7³ = 296 352 µm exactly one has the clear advantage to deliver always plain, easy and round values for the deduced units of the ancient Roman foot.

Like it is already widely accepted since long times, the Roman foot is 14 / 25 of the Egyptian Royal cubit, because one Egyptian remen equals five Roman palms.

In his definition M. Florencetime  – who also developed the twice-sixteen-hours hexadecimal time in 1989 –  set the Egyptian Royal cubit to 2¹ x 3³ x 5^-1 x 7²  =  529.2 mm or actually he defined the well-attested Carthagian foot  – five ninth of the Egyptian Royal cubit –  to equate the exact value of  2¹ x 3¹ x 7²  =  294 mm.

In concordance to modern statistical researches, he assumed a possible incertitude of 0.17%. Therefore, the Carthagian foot was defined by M. Florencetime: 294 mm ± 0.4998 mm.
This constitutes an "over-all rounding" for all the related ancient measures of length and therefore avoids odd values, resulting by arbitrary particular roundings of the ancient measures.

---

RE:RE

Hi Jimp,

Let's begin by your very first [citation needed]-tag.

PR = 16 / 28 NC

The Roman foot is defined to be 16⁄28 of the Nippur cubit.

If you read the given souce: On the Ancient Determination of Meridian Arc Length by Eratosthenes of Kyrene by acting Director of the Institute for Geodesy and Geo-Information Technology, TU Berlin Dieter Lelgemann, WS – History of Surveying and Measurement, Athens, Greece, May 22-27, 2004. Page 2 / 9 :

<quotation>
Our knowledge about the set of ancient non-metric length units (that are the cubit/foot or pechys/pous units) is mainly based on the Nippur cubit (NC = 518,5mm; museum in Istanbul), the so-called Gudea unit (GU = (20/28)(20/28) NC = 264,55 mm; ouvre / Paris) as well as the pes romanus or “Pous Romaikos” (pr = 16/28 NC = (28/24) GU = 296,3mm). All the ancient metric relations are governed by the very old Egyptian definition of a Remen (Pygon): 1 Remen = (20/28) royal cubits = (20/24) trade cubits = (20/16) “Pous”.
</quotation>

  (The important ratio given in this quotation was bolded by me.)

Your "fact"-tag is gratuitous, since for a better legibility an encyclopedia is not oblied to refer all banal assertions.

Mister Lelgemann is incidentally not alone with his assertion: PR = 16 / 28 NC. In the contrary, all the contemporary specialists in ancient measurement are unanimous.
I don't know any serious scientific for contesting it. Do you know one?

Hello Paul,

I'm afraid I don't agree that this assertion is banal. It's no less than a definition that you're giving here. Ian Cairns made the same point in January (below). A little number in square brackets directing us to the link is not about to interfere significantly with legibility. Moreover, can we not find something a little more concrete? I'm not disputing Lelgemann's authority. I'm refering to the fact that this paragraph doesn't explicitely state that the Pous Romaikos was defined as 16/28 NC. All we have is this ratio. Is this ratio something we find stated in ancient literature or was it something we find empirically by study of ancient buildings and artefacts? Jimp 2 June 2006 (UTC)

Hi Jimp,

Old Egypien metrologists defined the later called Roman digit when – in the early third millennium BC – they decided to share the prevalent Nippur cubit into 28 digits.
Sumeriens themself shared the cubit into 30 digits, cf. sexagesimal system. The egyptien geometers needed to use a good trigonometrical approximation: 20√2 ≥ 28.
Old Egyptian geometers could not calculate the square root of two, but they needed a round value for the hypotenuse. This one percent error was satifying in practice.

The attested raw Nippur cubit is 518.4 mm. This value divided by 28, then multiplied by 16 gives 296.22857142 mm, after an appropriated rounding, that is 296.2 mm.

Because all the ancient metrologists took reference by preexistent measures, (since they were metrologists and geometers, not bunglers), so: the ratio is the definition.

These values are confirmed not only by study of ancient buildings, but also by hundreds of graduated rulers, dating from very ancient times up to early modern time. (Since Bohemia, Oldenburg and Augsburg for example preserved the Roman foot up to the late 19th century with an excellent accuracy.) Some ratios we can find stated in ancient literature. This ratio is – to my knowledge – not related by ancient writs. Modern researches makes on evidence that the Nippur cubit was used since, at least, the middle of fourth millennium BC. However in Roman times – more than three millennia later – the Nippur cubit was replaced by more recent, deduced units. Ancient metrologists cann't refer to the Nippur cubit, because they ignored its older existence. Sadly, we don't have theoretical, metrological treatises before the first millennium BC.  Nevertheless:

•  The confirmed and preserved value of the Roman foot – in its five millennia tradition – proves the ancient ratio-definition.
•  None scientific specialist in ancient metrology, nowadays disputes the fact that the Roman foot is 16 / 28 Nippur cubit.

However, you are right: "A little number in square brackets directing us to the link is not about to interfere significantly with legibility."
Together we will find the way to make it clearer in the article.  -- Paul Martin 11:27, 5 June 2006 (UTC)

English ft. = 36 / 35 PR

Your current article version:
A far better simple modern conversion is 35⁄36 of an English foot.
If the idealistic value of the English foot with 304.8192 mm is indeed a modern value, the ratios are ancient, not modern!

In the other Lelgemann source, Lelgemann writes page 4 / 7:

<quotation>
Recognise the conservative and long tradition of this non-metric system from the relation English foot = (24/28) Pous basilikos = 304,75 mm.
</quotation>

You see "to err is human" even for a great university professor. Because just before he make the relationship: one pous basilikos = 6 / 5 roman cubit = 533.3 mm.
So he want say: one English foot = (16/28) Pous basilikos. That's an evidence.

Your quotation: "... but nor contrary to what you claim is your 35 barleycorns definition." If the Roman-English foot ratio 36:35 is widely accepted (give me a contemporary specialist, who contests, excepting yourself), then also the 35 barleycorns definition is widely recognised, since this is the same.

Michael Florencetime's (thus not mine) 296.352 mm definition for the "idealistic" Roman foot is not yet widely accepted, so we can let it out of the article. Meantime...

As for Michael Florencetime's definition, let's include it the day he's elected Emperor of Ancient Rome. The article is "Ancient Roman units of measurement" not "Modernised Roman units of measurement".

So ... Lelgemann didn't say this but this is what he meant to say ...?

You want a contemporary specialist who contests the ratio? I can give you better than a specialist, I give you logic. We have the metre, the Roman foot and the English foot. The metre was never based on either foot. The Roman foot came before the English one and before the metre so it was never based on either of these. The English foot is the one in question here.

It is the English foot that seems to be chopping and changing. If it had once been defined as 36/35 of a Roman foot, then this definition is no longer valid. One definition has been discarded for another. One definition was dumped and a different on adopted (the reality is of course more complex) just as with the Austrian foot. Jimp 2 June 2006

Reply to Jimp's objections:

•   I liked your "Emperor-humor". However in science a conventional definition can be accepted even afterwards. Especially in context of an obsolete measure with a spread of ± 0.17 %.

•   Yes, to err is human. Typos are not seldom even in serious scientific tracts. Did you never observe it? Sometimes one has to detect the obviously "meant sens".
     Since the well-known pous basilikos is about 533.4 mm, the English foot cann't be 24/28 PB = 457.2 mm, but must be 16/28 PB = 304.8 mm. Obviously a typo.

•   You are right. The decimal "metre was never based on either foot."  However, since the PB is 36/35 NC and the EF is 4/7 PB, the English foot is also 144/245 NC.
     (Because you don't accept the idealistic values, you will get an error of 1/2400 or about 0.04 %.)
     However, just like in communicating vessels, if you define one value, you define all values. The remain is all conceitedness of this or that standard institute.

•   No, the English foot has "never been defined as 36/35 of a Roman foot." Rather 15/16 French pied-du-roi.  However, since the french foot is (32x24 =) 768/1225 (= 25x49) of
     the Nippur Cubit, so the English foot is also (12x12 =) 144/245 (= 5x49) NC, like we already saw above. The remain is all conceitedness of this or that standard institute.
     Yes, in 1959 the legal standard institutes adopted a 127-smooth number definition for the English foot. One English foot is legally: 2³ x 3¹ x 127¹ tenth of millimetres.
     An odd definition, but the legal one!  The illegal, but elaborate 7-smooth (cf. A002473) definition is 2⁸ x 3⁵ x 7² tenth of µm, admittedly 1/15875 (≈0.0063%) more.
     Of course, this idealistic definition must be corrected by the factor  (2 x 5 x 19, 109 257)  /  (2¹⁸ x 3⁶)  to be scientifically correct, like I explained it there.  So the value of 1959 is good at about  99.99915 %.

-- Paul Martin 11:27, 5 June 2006 (UTC)

Other points

Your quotation: "[Austrians] merely discarded one definition for another." You are wrong. They didn't discarted an English foot definition, because in 1872 an official metre definition of the English foot didn't exist before 1959.

If they discarted a definition, this was the US survey definition 1866 for the yard 3600/3937, later on, for the foot 1200/3937, what's the same.

If the Austrians recognised this odd US survey definition their foot as 28:27 English foot would be 11200 / 35433 m. A very odd value. So they rounded their fathom to half a millimetre, about 0.001 958 % smaller than it would be accordingly to the US survey definition. One of both or both are in error!

That: "The Roman pound is exactly three quarters of the Greek mine." is also widely recognised.

Anyway, I rewoked the article, going in your sens.

-- Paul Martin 13:35, 14 May 2006 (UTC)

I'm not 100% sure of what you're driving at here. If the Austrians redefined their foot, then they redefined their foot. How can the definition of the English foot be dependant upon whether or not the Austrians recognised the odd definition of the US survey foot? It makes no sense. We're talking definitions here, how can a definition be in error? Jimp 06:35, 2 June 2006 (UTC)

The Austrians didn't "redefine" their foot, but they gave a legal metre value to their 6-feet "Klafter" with the aim to abandon the old measures.

The pragmatical, but ignorant austrian legislator defined this Klafter 5 x 3793 tenth of mm, id est 0.00176 % less than 6 x 28/27 x 304.8 mm. That's ridiculous.

If false national conceitedness not hindered, the European, North-Africain and Near-East nations, at least, in Renaissance times would have made a conference to harmonise their standards. Then, the ratio between the English and the Austrian foot must be 27 : 28, and not 18288 : 18965, i.e. about 54000 : 55999. The opus of modern botchers!
You are right: A definition is a definition. It can not be false or true. However it can be adequated or not.  No, those odd definitons  – even legal –  can not be adequated.
-- Paul Martin 11:27, 5 June 2006 (UTC)

Article tone

This article's tone sounds like a deranged scientist. Marked for cleanup. Ashibaka tock 03:40, 15 January 2006 (UTC)

Hi Ashibaka, it's possible that something what is new for you, in your ears "sounds like a deranged science". However, it's your subjective impression. Your sweeping adjudgement is not argued at all. The theory of diffusionism of ancient measures in the Fertile Crescent and in Mediterranean Basin is now the "standard theory" supported by doubtless serious scientists. Paul Martin 14:46, 16 January 2006 (UTC)

There are problems with the accuracy of the language in places. The cleanup tag was well-placed. I'll replace. Ian Cairns 11:56, 18 January 2006 (UTC)

Hi Ian, can you express your objections more explicitly, more detailed?  Regardful, Paul Martin 21:07, 18 January 2006 (UTC)

Thanks Paul. Yes, the language does not read as English. Most sections have a problem, and this would be a major revision to correct all this - hence my replacement of cleanup tag. For example:

Length - "The Roman foot is defined to be sixteen 28th of the Nippur cubit." a sweeping statement like that would need a source / footnote? It is also likely to be phrased differently ~ 16/28?

Mesopotamien -> Mesopotamian;

"The value: 296 millimetres for the Roman foot is a usual rounding to the closest integer millimetre precision" This is French. English would use 'the closest millimetre'.

Area - "This egal 14 400 square feet or about 0.126 hectares," - this is French. English is 'equals'?

more exactly one - not sure what this means

Volume - "Its almost 26.027 litres." -> It is

"The third part of this quadrantal is the Roman peck." - One third of a quandrantal is a Roman peck.

I could go on. However, I hope you see there is much to correct. The article also needs sources. A previous contributor produced this material and more, but his sources were not agreed by the majority of editors. Good sources for the current information must be supplied. Regards, Ian Cairns 23:02, 18 January 2006 (UTC)

• "It is also likely to be phrased differently ~ 16/28?"  No! Definitively no.  (We'll discuss this later.)
• "the closest (integer) millimetre precision"  Perhaps. No problem. Even if: you can also have a "closest tenth of millimetre precision.
• "equals"  Thanks, ok. m typo.
• "It is"  Item.
• "One third of a quandrantal is a Roman peck."  Why not, if you prefer, even if I don't see the fault in the initial phrase.
• "I could go on."  Aye, Ian, go on!
• For the sources and its agreement, let's stay in discussion.

Paul Martin 00:00, 19 January 2006 (UTC)

Hi Ian, I hope meantime you found the time to check my added references. So, I delete the tags. If you see the need of further discussion on this topo: With you it's always with pleasure. If not, fine. Anyway we'll have occasion for exchanges, soon at Long and short scales/Discussion version. Paul Martin 21:07, 20 January 2006 (UTC)

Area Amendment

• I have modified you area table to reflect the true logic behind the basis of these measures:
  • The largest area used by the romans is 1 square mile or mille passuum.
  • All other area measures are fractions of this largest unit and must change accordingly.
  • If the foot is 12 inches the saltus becomes 57,600x57,600 inches which is not a mille-passum using your 11.667" roman foot. It is, however, a geodetic Greek foot which is 25/24th longer then the roman foot at 12.154"
  • The mille-passuum is therefore 8 x 7200 geodetic inch or 8 x 7500 conventional roman inch. The foot used for Roman Area is therefore Geodetic.
  • I have recalculated all of your area measures but left your figures remaining to show the difference in metric area between the two feet.

--Michael saunders 13:01, 19 March 2006 (UTC)

Hi Michael, I didn't see your talk contribution before my rv.

I only calculated: one Remen = 20/16 Pes Romanus = 0.37044 m. So, (100 Remen)² is indeed about 1372.25 m².

But this was not the definition of the Roman acre. But: (0.296352 x 120)² ≈ 1264.67 m², i.e. almost 8% less!  Ratio: 625:576.

The unusual Roman square mile was indeed 25 million Roman square feet. The customary saltus was 2304 Roman square perches.

-- Paul Martin 19:17, 23 March 2006 (UTC)

Hi Paul,

I am afraid you have completely missed the point..

• 1. ALL of the areas quoted are fractions of the saltus.
• 2. The lowest unit of measure is the square foot.
• 3. The dispute is not over the length of the square mille passus but over the length of the foot used.
• 4. All of the areas described are based on the 12.154" attic greek foot and not the 11.667" ionic greek foot.

The ratio between the saltus and square foot is (1/23040000th of the volume) or 1/4800th of the side length.

• ie. 1600 actus (saltus), 1/14,400th actus (square foot). 1600 * 14400 = 4800 * 4800

Never, ever has the roman mille passus been described as 4800 feet. You know as well as I that the roman foot was 5000 feet to the mile or 1000 x 5 feet (mille(1000) passus(5 pedes)). Therefore the foot used is not the roman foot but a foot that is 25/24th larger.

This foot is described by Herodotus Strabo and others:

• Great circle / 60
• Great circle / 60 / 60 = 1 schoene
• Great circle / 60 / 60 / 60 = 1 stade (600 feet according to herodotus)

The roman mille-passus is well defined as 75 miles of 60,000 uncia or 5000 pedes per degree. (60 * 60 * 60 * 600)/(360 * 75 * 5000) = 4800 greek feet : 5000 roman feet

Therefore all the area calculations defined as using the roman foot are inaccurate unless you accept the romans are using 2 foot length. 11.667" ionic greek and 12.154" attic greek. Either way, all of the area measures are based on the egyptian rmn or the roman palmipes (palm+pes) of 20 fingers. I really dont see how you can offer any alternative explanation. Can you please amend your information or restore my previous edit. If you do not wish to do so then the accuracy of this artical will be called into question.

Thanks --Michael saunders 21:29, 23 March 2006 (UTC)

Weight vs Volume discussion

If 20 ounce = 1 pint and the concept originates from somewhere....

"It will therefore be convenient to begin with the definition of the Standard of Weight by declaring, that nineteen cubic inches of distilled water, at the temperature of 50°, must weigh exactly ten ounces Troy, or 4,800 grains; and that 7,000 such grains make a pound avoirdupois; supposing, however, the cubic inches to relate to the measure of a portion of brass, adjusted by a standard scale of brass. This definition is deduced from some very accurate experiments of the late Sir George Shuckburgh, on the Weights and Measures of Great Britain; but we propose at a future period to repeat such of them as appear to be the most important.

We think it right to propose that these measures should again be reduced to their original equality; and at the same time, on account of the great convenience which would be derived from the facility of determining a gallon and its parts, by the operation of weighing a certain quantity of water, amounting to an entire number of pounds and ounces without fractions, we venture strongly to recommend, that the Standard Ale and Corn Gallon should contain exactly ten pounds Avoirdupois of distilled water, at 62° of Fahrenheit, being nearly equal to 277.2 cubic inches, and agreeing with the Standard pint in the Exchequer, which is found to contain exactly twenty ounces of water."

1819 Metrological Survey are we sure we shouldn't be using 20 uncia = 1 sextarius ??

• 40,007,862,917 mm Polar Circumference
• 875 Eratosthenes inch (1575000000) : 864 Greek inch (1555200000) : 900 Roman inch (1620000000) : Polar circumference
• 1/50th Earth of 5000 stade of 300 cubit of 21 inch (250,000 stade)
• 1/60th Earth of 60 schoene of 60 stade of 400 cubit of 18 inch = 252,000 stade of 300 cubits of 144 / 7 inch (700 stade per degree)
• 360 degrees of 75 roman miles of 60,000 inch
• 4/60th Earth to Egypts Border (24 degrees North) + 1/50th Earth to Alexandria (31.2 degrees North)

British and Eratosthenes Pound

• 12 * 24/25 = 11.52 inch
• 11.52 * 2 * root 2 = 32.583480
• 32.583480 * 2.54 = 82.762040
• 82.762040 ^3 = 566883.175282
• 566883.175282 / 125 = 4535.065402 This is 1cc short of 10 pound of distilled water using British inch

• 82.762040 * 1.00007178 = 82.767981
• 82.767981 ^3 = 567005.270044 Cubic megalithic yard
• 567005.270044 / 125 = 4536.042160 This is exactly 10 pound of distilled water using Eratosthenes inch

Pound Weight

Roman Libra

• 11.52 * 875 / 864 = 11.666'
• 11.666' * (864 / 275 / Pi) = 11.667504
• (11.667504 * 2.54 )^3 = 26027cc Quadrantal

• (11.667504 * 2 * square root 2 * 2.54) ^3 = 588938.610cc Cubic megalithic yard
• 588938.6101 / 1800 = 327.188cc Libra
• 588938.6101 / 21600 = 27.2656cc Uncia 360 * 60
• 588938.6101 / 172800 = 3.408cc Drachma 360 * 480

• cubed root (327.188 * 1800 / 567005.270044) = 1.0127313 (875 / 864)
• cubed root (327.495 * 1800 / 567005.270044) = 1.0130480
• cubed root (327.453 * 1800 / 567005.270044) = 1.0130047

Uncia and Sextarius

• 27.291 g * 20 sextarius * 8 = 4366.56
• 4536cc / 4366.56cc = 1.03880400
• cubed root 1.03880400 = 1.012770
• 875 / 864 = 1.012731

Hi Michael saunders, I see your talk contribution. I'll reply you soon. --Paul Martin 13:39, 14 May 2006 (UTC)

English Headwords?

Why is the leading information in each table an English word, and not the Latin name of the unit? It would seem to make more sense to use the names of the units themselves, rather than some translated terms that aren't necessarily informative anyway. Offhand, I have no idea what a peck is, let alone an arpent or a sester. These translated terms are only meaningful to those already familiar with a measurement system that is widely obsolete in the English-speaking world. I propose that the Latin term be placed in the first column, and where useful translations can be provided, they be listed in a comments column on the right end of the table. Rhialto 02:10, 2 June 2006 (UTC)

Hi Rhialto,
If you "have no idea what a peck is..."  You see like it is usefull to consult Wikipedia.
By your objections, I retain the justified reproach to wikify the terms. I'll do so within the next days.  -- Paul Martin 21:05, 5 June 2006 (UTC)

I guess its a valid point that I could look up these words, but my point was that in order to make sense of the Latin words into a system that I and most modern readers would be familiar with, the article as written essentially requires the reader to learn about a third set of units which are not at all relevant (except very tangentially) to either the topic of the article or the conventional systems in use today. It's almost like having an English-Latin dictionary which asks you to see the corresponding entry in a Russian dictionary to properly clarify the meanming of the terms being discussed. None of the other weights and measures articles in wikipedia have headwords that are not the actual term used in the original context, so it seems to me this is the article that should be changed to match the general pattern. Rhialto 04:12, 6 June 2006 (UTC)

I figure that the (widely decimal) old chinese units of measurement, often, don't have adequate English translations. In the case of roman units we can give these equivalences.

Take the units of length: eleven units. Eight of them are even etymologically the same word. Exemple: lat. leuga, eng. league. In the case of "pes", "gradus" and "actus", the English words are "foot", "step" and "arpent". Similary the nine weights are the literal traductions, helpful for the readers not familiar with the latin language. A "ligula" is also literaly a spoonful. The "semodius" can rightly be given by roman gallon, since the first one is about 4.67 litres and the English gallon quite a little less. These equivalences are helpfull for the readers.

Harmonisation in the lay-out between similar articles can be sensefull, nevertheless we can also have good reasons to make it different.
However, I appreciate your works in other systems of units, since many of them are in a bad state.  -- Paul Martin 14:35, 7 June 2006 (UTC)

You're right that those *modern* Chinese units don't have translations, only transliterations. As an aside, the Hong Kong units do have translations, which are the official translations used by the Hong Kong government. No such official translation exists for Roman units.

I have no problem with giving these etymologies of modern units, these translations if you will. My main issue is that these translations are given as the primary header on each line, as if they were the actual words used. This is not so.

In most cases, the translations aren't particularly useful anyway. Certainly, it is interesting that the cubit, step, arpent and so on are decent translations of the units in question, but at least in those three cases, they provide no useful information to a person not already familiar with them, as none of those three were ever used as a unit of measurement in an English speaking country. Similarly, other unit headers make use of extremely convolulted or archaic English to get their meaning across. "one aune of furrows" and "one double third-sester" spring to mind here. In some cases they are even misleading, as the Roman league was only about half the English unit, and teh English perch was almost twice the length of the Roman pertica.

I agree there are cases where an English translation is perfectly meaningful to modern readers, but there are enough places where the English translations are either meaningless or confusing that an attempt to clean the article's translations would result in too many holes in the table. This is why I proposed promoting the Latin names to the first column and demoting the translations to a comments column. This would allow us to add a proper explanation of etymologies where it is useful, and avoid contrived workaround phrases as a headword where there isn't a simple English translation of the unit.

I've added a sample table here of how I think this could be modified. It's not a radical change, but I think it is more logical. Let me know what you think.

Unit Name	Roman Feet	Metric value	Comments
digitus	1⁄16	18.5 mm	a digit
palmus	1⁄4	74 mm	a palm
pes	1	296 mm	a Roman foot
cubitus	1+1⁄2	444 mm	one cubit
gradus	2+1⁄2	0.74 m
passus	5	1.48 m	one pace
pertica	10	2.96 m	The old English perch is etymologically derived from this unit.
actus	120	35.5 m	The old French arpent is etymologically derived from this unit.
stadium	625	185 m
milliarium	5000	1.48 km	the Roman mile
leuga	7500	2.22 km	The old English league is etymologically derived from this unit.

Rhialto 01:39, 9 June 2006 (UTC)

League = 1.5 miles or 3 miles?

Just a question out of curiosity. The article states that 1 mile is equivalent in Ancient Rome to 5000 ft, while 1 league is 7500 ft. Hence: 1 league is 1.5 mile. However the article League states that 1 league is 3 miles in Ancient Rome (quote: "The league was used by Ancient Rome, which defined it as being 3 miles."). Which is true? Brynnar 14:42, 14 August 2006 (UTC)

The league was originally used by the Gauls, and later picked up by the Romans during their conquests. Their interpretation of it was that a league was about 1,500 paces, or 7,500 feet. I'm not entirely sure how it came to mean three miles, but I'm fairly certain it wasn't used that way in Rome. --Xanzzibar 23:23, 15 August 2006 (UTC)

Problem fixed at both pages.  League and League (unit).  Paul Martin 13:18, 17 August 2006 (UTC)

A Roman mille passus or thousand paces derives from the Greek mia chillios or one thousand. The thousand is a measure of a field (aroura) laid out boustrehedron or as the ox plows in ten rows of one hundred orquia. Greek measures have short median and long forms so mia chillio of 8 stadia, (4800 ft), one aroura (5000 ft) and one nauticle mile (6000 ft); are referenced in the literature. Roman degrees of 25 leauges, 75 milliare or 110 km, are the same length as Greek degrees of 600 stadia. 69.39.100.2 (talk) 14:21, 15 February 2008 (UTC)

The "3 mille" statement is also at the page for Furlong, referencing it as "the distance a man could walk in an hour" (on a good roman road, one presumes - the going may be 1.5mph over rough ground instead?). Something in the depths of my memory tells me the 7 league boots in the old story covered 21 miles at a time... but then again that might be per pace, with each boot taking 7 at a time? I think this is a good case of Citation Needed :) 193.63.174.10 (talk) 10:01, 9 January 2009 (UTC)

Mass units

Talent (weight) notes that the Roman talent was a cubic (Roman) foot of water, or about 25.99 kg. It goes on to state that there were 100 libra in a talent, making the Roman pound about 260 grams, much smaller than the figure in this article. Somethng needs fixing. Rhialto 01:53, 12 February 2007 (UTC)

Thanks Rhialto for your advice,

If the Greek talent (= 60 greek mines) was indeed of about 26 kg, this also indicates that Greeks, here, used the old, later-called Roman-digit for their talent-definition, since the third root of 26 gives 2.9625 dm. The Roman foot. The Roman libra was attestedly 3/4 Greek mina.

If the statement that Romans called 100 Roman libra a talent is true (sources?), this would mean, that this hypothetical Roman talent is 1/60 * 3/4 * 100 = 1.25 "water-foot" Greek talent.

I'll see what I can find out, Gluck 123 18:36, 11 June 2007 (UTC).

Mina in their ancient Mesopotamian form have both sacred and profane values so their volume varies. A [Talent] is the cube of a linear measure 69.39.100.2 (talk) 14:29, 15 February 2008 (UTC)

Roman foot and Nippur cubit

The Roman foot is defined to be 16⁄28 of the Nippur cubit.

"Is that their official definition, or simply a coincidental equivalent value?"

Neither, nor.

Western Roman Empire is dissolved for 476, Eastern for 1453. So, there is no one to give modern "official definition" for Roman measures.

It's nor a "simply a coincidental equivalent value", but the current, widely accepted standard theorie in the science of the historical metrologie.

According to newer – especially German – researches since WW2, we know nowadays that the Roman digit (=1/16 RF) results from
an old Egyptian division per 28 of the sumerian Nippur Cubit. They needed 28 parts, because 20 · √2 = 28.284...

Certainly, Egyptian geometers knew that with their construction-remen, the digit of their 20-digit-catheti was not strictly the same digit, than the digit in their 28-digit-hypotenuse, but the small error of 1% was satisfying in practice. [1].

However, the digits of the hypothenuse belong to the so-called "Old Egyptian Cubit" of about 523.9 mm. Whereas the digits of the catheti are the later-called Roman digits.
Ancient precisions are generally better than 0.17%.

Thus, the Roman foot is de facto and really defined 16/28 Nippur Cubit. I don't know any serious, contemporary scientist for contesting it. Everyone, like for example, Prof. Dr. Eberhard Knobloch for admitting it.-- Gluck 123 18:36, 11 June 2007 (UTC)

My point was that, unless the Romans themselves knowingly defined their foot in relation to the Nippur cubit (in which case there would be a historical document from Roman days to say so), it incorrect to call that the definition. I can accept that modern analysis of the two units can show there was a coincidental equivalance, but only a historical document from ancient times can be used to demonstrate a definition.

The sidetrack on the Egyptian geometers is fascinating, but we are talking about Romans, not Egyptians here. I don't see how talking about what the Egyptians did has any bearing on what the Romans did. Without a historical document to say the Romans defined their foot that way, you can't properly call it a definition, except post hoc, which isn't really the same thing at all. Rhialto 21:58, 11 June 2007 (UTC)

Old Romans and old Greeks knew relationships (ratios) between their measures. These ratios were, by the by, the only way of evaluation of their respective measures, since they ignored decimal fractions like 1.25; so, this was always expressed by, here, 5 to 4. The knowledge of these ratios was even necessary for international trading, already very developped in ancient times (even more than in Middle-Ages).

On the other hand:  If in ancient times a changement of a system of measures was operated, we can surely distinguish two different cases. 1. A great, already prosper, ascending state wished to ameliorate their measures and weights, so by studying the performed, established systems in their neighbourship, by adapting it, by creating other subdivisions w.r.t. their own tradition, but by keeping, by taking-over faithfully at least one main measure. 2. Or, a new system was imposed by a conqueror. The conquered state or the new vassal state was obliged to take-over the measure-system of the suzerain. Sometimes, by creating their own variants in subdivisions, at least centuries later, when they reinforced their own sovereign power.

However in no case, never, a measure was "invented". The legend "from the tip of his nose to the tip of his outstretched fingers" is a legend. Later invented for other reasons. Weights and measures, since ancient times, are a too serious topic. Those improbable and ridiculous proceedings, in reality, never existed. Weight and measure systems were always worked out by the souvereign's scientists, the metrologists. Since they were scientists, they took references by operative and existing systems. (Cf. e.g. Troy weights, the system of Troyes, France.)

"I don't see how talking about what the Egyptians did has any bearing on what the Romans did."

You must understand that what, now, we call "Roman digit" was a well-known measure in all the Near-East, Mediterranean region for millennia. Widely used thousands of years before the foundation of Rome.

So, we can't talk about this measure of length, without mentioning, that, attestedly, even Old Egyptians used this same and identical digit of about 18.525 mm, since the beginning of third millennnia BC with their 20-so-called-Roman-digit-construction-remen of about 37.05 cm. We must talk about.

"[... that] the Romans defined their foot that way"

No, of course they didn't!  The Romans defined nothing. The Egyptian geometers did it !  This was thousands of years before the first Roman citizen was ever born! Romans only choised one of the plenty digits already in use for long times, by declaring this digit as their "national" digit. The digit of the Roman Empire.

Romans knew for example, that their foot was exactly 1/25 smaller than the greek foot used in the stadion of Athens. So, to have just the same length of race-track as in the greek capital, they decided to construct, at Rome, a stadion of 625 Roman feet equals 600 Athens feet.

Many other ratios are related by ancient authors. But the term "Nippur Cubit", Romans and Greeks ignored it. You have to realise that the Nippur measure was the domiant measure in Mesopotania and in Egypt 3000 years before Caesar's time. Archivation of memory was not too easy during these times. At the beginning of 3rd Millennary BC writing (archaic cuneiforme and hieroglyphes) existed but rather limited to epigraphs or writings relating some political or economic facts. There are no written scientific workings in no science dating from 30th c. BC. So, Romans, naturally, had forgotten this old relationship. But we, nowadays, thanks to long scientific researches, we rediscovered it. We know it, now.

May I call your attention to the fact, that also, for example, Dieter Lelgemann pdf, former Director of Berlin's Institute for Geodesy uses well the term: definition.

If Rolf Rottländer for 40-50 years recollected especially ancient, archaeological, graduated rule sticks for his statistical researches, Dieter Lelgemann, several years ago, measured with his students, six race-tracks of preserved ancient Greek stadions.

According to Lelgemann, in this context, especially eight old measures are important.
With old highly composite number-orientated measures 7-smooth-numbers are very important. See: de:Historische Metrologie. Because old systems used selected numbers (never all in the same system) e.g. in the suite 16, 18, 20, 21, 24, 27, 28, 30, 32 digits = 2 feet, I prefered the defined, modern 7-smooth-value for the length of the Nippur Cubit, an over-all-rounding.

Symbol	Name of the measure	Deduction	Idealistic value	× 10-7 metre
NC	Nippur Cubit	by 7-smooth:	=  518.6160 mm	=  24 × 33 × 51 × 74
R	Remen	(20 / 28)  NC	=  370.4400 mm	=  24 × 33 × 52 × 73
ORC	Old Royal Cubit	Root 2  ×  R	~  523.8813 mm	=  25 × 33 × 52 × 73  × √2
OTC	Old Trade Cubit	(24 / 28)  ORC	~  449.0411 mm	=  26 × 34 × 52 × 72  × √2
RTC	Remen Trade Cubit	(20 / 28)  OTC	~  320.7436 mm	=  26 × 34 × 53 × 71  × √2
RC	Royal Cubit	(50 / 49)  NC	=  529.2000 mm	=  25 × 34 × 53 × 72
BC	Babylonian Cubit	(30 / 32)  RC	=  496.1250 mm	=  21 × 34 × 54 × 72
BTC	Babylonian Trade Cubit	(27 / 32)  RC	=  446.5125 mm	=  20 × 36 × 53 × 72
All the idealistic values  – excepting of course ORC, OTC and RTC –  are plain values, not-rounded, because the Nippur Cubit is a defined 7-smooth value, inside the scientific coefficient of variation.

Stadion	Measured	Length of the stadion	Deduction of the foot	Ideal length of the foot	Ideal length of the stadion	Relative deviation
Olympia	192.27 m	= 600 Remen trade cubits	(20/28) OTC	~ 320.7436 mm	~ 192.4462 m	– 0.092 %
Epidauros	181.30 m	= 600 Epidauros feet	(16/28) RC	= 302.4000 mm	= 181.4400 m	– 0.077 %
Priene	191.39 m	= 600 Priene feet	(20/28) BTC	= 318.9375 mm	= 191.3625 m	+ 0.014 %
Milet	177.36 m	= 600 Milet feet	(5/6)(20/28) BC	= 295.3125 mm	= 177.1875 m	– 0.097 %
Delphi	177.55 m	= 600 Roman feet	(16/28) NC	= 296.3520 mm	= 177.8112 m	– 0.147 %
Athens	184.96 m	= 600 Kyrenaika feet	(20/24) R	= 308.7000 mm	= 185.2200 m	– 0.140 %

One knows that in ancient times a lack of precision of ± 0.17 % must be considered as normal, without any problem. (Nowadays often (tolerances in industrial production, building construction, etc.) not better than this. Of course, now, much better in very high-level accuracy and with top-level scientific measures.)  So, all the values are good.

This can not be, like you said, a "coincidental equivalance", but arises from the well-known deduction of these measures, ones from the others. Example: You took on a 18-digit-pygme, but you decide to use – exactly this measure – as a 16-digit-standard-foot. So, your new digit is exactly 18/16 old digits. It grew-up by exactly 12.5 %.-- Gluck 123 11:33, 13 June 2007 (UTC)

Since these ancient metrologists apparently knew the precise relationships, no doubt there should be a cite from at least one of them to state the mathematical relationship between them, yes? You provide over 2 screens full of data, but without a single cite to show that the Romans (as opposed to more modern metrologists) were aware of the relationship, it just isn't relevant. Rhialto 14:13, 13 June 2007 (UTC)

I saw during my necessary corrections, you replied. I'll answer you soon. Gluck 123 15:16, 13 June 2007 (UTC)

PS. Just a thing, later more, it isn't that a fact is ignored by s.o. at a specific time (here, the ignorance of Romans), this doesn't prouve that a fact is not true. No? There are many ancient authors like Eratosthenes, Heron and Ptolemy describing well-known ratios. But all these ancients ignored the Nippur cubit. The first specimen was found by archeological excavations in 1916, but, meantime, we have understood its high importance.  *  It isn't because Columbus thought to be in India, that the Americas are identical to India. The knowledge progresses. Sometimes even, old, entombed cognitions must be regained. (Cf. Copernicus). In short:  It is not because s.o. at a specific time isn't aware of s.th. (here, the ignorance of the Romans) that it isn't true. If, now, we know that the definition of the "Roman foot" is via the Egytian Remen, 16/28 of the Nippur measure, it doesn't matter that the Romans ignored it. It is so, anyway!

((This was my prepared continuation before your reply below. I'll write you s.th. later on w.r.t. your new arguments. Thanks.))

Just to answer that specific point... you're right that absence of evidence isn't proof that something is not true. But equally, it isn't proof that something is true. And the official standard of wikipedia is to only say something is proved to be true if you can actually provide a cite which says so. I'm more than happy to acknowledge that modern metrologists have noted the relationship between the various ancient units. But this is froma time period in which written records are reasonably common.

If the Romans were directly aware of the relationship between their units of measurement and the Nippur/Egyptian/etc units of measurement, why are there no cites from notable Romans to demonstrate this? For example, we can say the metre was defined as xyz because someone somewhere made a formal statement about its relationship with xyz. For us to say that the Romans defined their foot as 16/28 of a Nippur cubit, somewhere there needs to be a Roman metrologist making a formal statement about its relationship with the Nippur cubit. Since I haven't seen any cite to say that the Romans defined it, I strongly feel the most we can say is that modern metrologists have found the Roman found to be 16/28 of a Nippur cubit.

Also in your long text, you noted that the Romans had in fact lost information about the Nippur cubit, as written records from taht long ago no longer existed. If the Romans really had no direct knowledge of the Nippur cubit, I put forward the hypothesis that the claim that they defined their foot as 16/28 of a Nippur cubit MUST be obviously untrue. You can't define something relative to something you don't know about. Although in this case, I would accept that there must be some intermediary unit whioch there were aware of, and that the Romans presumably defined their foot relative to that intermediary unit.

Rhialto 15:53, 13 June 2007 (UTC)

Here, my reply to your new thoughts:

1. Not an "absence of evidence", but an absence of knowledge, of cognition.  But you are right  – the other way round –  also, this must be proofed. At least as "to be the current, widely accepted standard theory."  That's the case.  (By Lelgemann, Knobloch, Huber, BI-SMH  a.m.o.m.)
2. You are right:  "Modern metrologists have found the Roman found to be 16/28 of a Nippur cubit." After long trials and tribulations especially at the end of 19th c. beginning of the 20th century with alltoo complicated, very doubtful theories (cf. Pseudoscientific metrology), now for several decades it is standard theorie in the historical metrology, that the Near-East, Fertile Crescent, Mediterranean weights and measures are all related by easy 7-smooth  – also called humble numbers –  deductions. Since 2003, the hexadecimal BI-SMH  – as the antagonist to the decimal BIPM –  even proposes a conventional, 7-smooth over-all-rounding of the values themselves. But if these modern metrologists are right, not only themself, we nowadays know that the later called Roman foot is defined 16/28 NC, but also these old Egyptian geometers operating this definition about 5000 Jears ago were aware using a mesopotamian measure to define a new measure, a new digit by 16/28 NC. This is it, what really counts. We contemporary human beings know it. Old Egyptian geometers knew it. Between long time of ignorancy. Nevertheless it is so.
3. One more:  Not the Romans, but the old Egyptian geometers defined the  – later called –  Roman foot 16/28 NC.
4. "that the Romans presumably defined their foot relative to that intermediary unit"  You are partially, widely right. Romans passed by an "intermediary unit". But they never defined anything, they simply took over a well-known  – since millennia –  already and widely used unit.
5. Ancient scientists referred  – of course –  to the various Greek measures, than also to the Egyptian measures. But old metrologists ignored the lost missing link, the Nippur cubit.

A personal question: Where you are Rhialto?  Me, roughly at 48° 52′ N, 02° 21′E.-- Gluck 123 18:09, 13 June 2007 (UTC)

((First, here above, my older prepared reply. Later on, w.r.t. your new arguments below, with these funny postpostements ;-))  However have a good day to you, Rhialto.

"If, now, we know that the definition of the "Roman foot" is via the Egytian Remen, 16/28 of the Nippur measure, it doesn't matter that the Romans ignored it. It is so, anyway!"

That is a spurious argument. By that logica, we can say, with teh benefit of some future historian, that the metre, far from being defined as a cfertain fraction of the teh distance light travels in a second, is in fact some fraction of the diameter of Pluto. It woudl of course be technically correct to define it that way, just as it is technically correct to say the metre is defined as slighlt less than half my height. But that would not be the definition that modern scientists use.

Beg pardon. The meter was defined as being a fraction of the size of the earth. Later it was changed to a number of wavelengths of a certain colour of light. Estimates can vary about the size of the earth, but wavelenths of light are assumed to be constant. The distance light travels in a second is a secondary measure, and comes out at an awkward amount, usually rounded off to 300 m/sec.Mariya Oktyabrskaya 04:18, 5 October 2007 (UTC)

Similarly, although with hindsight, we can say the Roman foot was some fraction of teh Nippur cubit, that would not be teh definition that they used. Rhialto 16:50, 13 June 2007 (UTC)

This argumentation is invalidated by the fact (and only, if that theorie is true):  The old Egyptian geometers consciously took the Nippur measure to create their construction-remen digit. Later called Roman digit. They knew what they did. If this is true, we modern human beings, we rediscover. So, if this is the case, your argumentation above is invalid.-- Gluck 123 18:23, 13 June 2007 (UTC)

If it is true that they consciously took that Nippur cubit, we should be able to come up with a Roman scholar on record as saying as much. It's not as if written records from Roman times are lost to modern day scholars. I see your point that the Romans were using a unit that was defined by the Egyptians. But that simply pushes the date and culture of the people doing the defining. If we can't find a historical document saying it was defined as such, the best we can do is reconstruct the definition from the evidence available, and make a best guess as to the definition.

I am going to amend the article to note that modern scholars have found (re-discovered?) that 16/28 relationship. Rhialto 19:34, 13 June 2007 (UTC)

According to Rottländer this digit is attested at least since the third dynasty of Egypt, i.e. roughly 2650 BC. From this time, by the preserved hieroglyphic textes we only know the names of the pharaons, some few political facts. In no case there exist e.g. philosophical, theoretical textes, nor any scientific dissertation. However in practice, we know that the Old Egyptians were good and competent geometers.

More than 2000 years later, scholars like Eratosthenes were content to discribe relationships with the measures in use during their life-time, including those used in the hellenistic Egypt.

In conclusion:  I can live with your current amendement and I thank you for our interesting discussion.-- Gluck 123 07:18, 14 June 2007 (UTC)

Am I the only person bothered by "16/28"? What is wrong with 4/7? --76.185.116.56 (talk) 14:16, 7 August 2011 (UTC)

I mean, I understand the 7-smooth numbers, but it doesn't mean that 16/28 doesn't equal 4/7. --76.185.116.56 (talk) 14:20, 7 August 2011 (UTC)

Important Error.

There is an important error in this article, in the table of ancient Roman dodecimal fraction-names. Semis means not 2/12 but 6/12. Sextans means not 6/12 but 2/12. I'm sure about this, but I suppose I should find a reference-- here we go: Gullberg, Jan: Mathematics from the Birth of Numbers, Norton, 1997, p. 16. Mjhrynick (talk) 18:13, 5 April 2008 (UTC)

Mjhrynick is correct. 1/2 is called semis which is short for "semi as" where the "as" is the Roman unit for weight and a monetary unit. The sextans the name of 1/6. A stronger reference supporting this is that of Friedlein¹ at SICD Universities of Strasbourg - Digital old books. Note that this site did provide an enlarged view of each page but lately this fails. A large copy can be seen here Tafel.

¹ Friedlein, Gottfried - Die Zahlzeichen und das elementare Rechnung der Griechen und Römer

Shekel

What is this "Roman unit" (sicilicus) doing in the article? 85.113.253.229 (talk) 18:42, 23 November 2008 (UTC)

Why wouldn't it be in this article? It was used by Pliny. See here. Note that this is not the same as a shekel, which is called a siclus in Latin. Rwflammang (talk) 09:37, 24 November 2008 (UTC)

Then shouldn't sicilicus article reflect this usage? Because as it sits it has nothing to do with measurement. Sicilicus is written about a theoretical usage of a diacritical mark... --76.185.116.56 (talk) 14:09, 7 August 2011 (UTC)

Ancient Roman field divisions preserved?

I heard once in a class of mine that the ancient Roman agricultural field divisions are occasionally preserved in modern fields. Specifically, I have an aerial picture of fields near Pula that claims to show square divisions of 20 actus per side. I can't post the picture because I have no idea of it's copyright. Does anybody know anything about this?--SkiDragon (talk) 11:25, 14 December 2008 (UTC)

Actually, here is the picture. [2] --SkiDragon (talk) 11:30, 14 December 2008 (UTC)

"Mass?"

First off, they weren't measures of mass. They were measures of weight. Second, I followed at least one hatch link here that broke because the #weight section had been removed. Changed, pending some rationale on changing the terminology to something more erroneous and less user-friendly. — LlywelynII 22:00, 24 February 2011 (UTC)

Presumably they used balances for measurement rather than springs, so they were measuring mass and not weight. Not that they, or anybody else really, cared. Rwflammang (talk) 13:48, 29 June 2011 (UTC)

This question comes up so frequently that there should be a rule that no one be allowed to edit a weights-and-measures article until they understand that "weight" in legal and commercial usage has, since the 18th century, meant "mass" in the physics sense. Before that, going back to the Bronze Age, it meant that property measured by a balance scale in conjunction with a standard reference mass, thus de facto "mass."Zyxwv99 (talk) 14:59, 15 November 2011 (UTC)

OK, we know it is called "mass" in physics and a few other sciences (not including, for example, medicine and chemistry). But the Romans didn't have Newtonian physics, so to call it mass in this article seems an anachronism. This isn't an article title, but I suggest that it should anyway be moved to its common name, weight. I'll do that in a day or two, unless there is opposition to such a move? Justlettersandnumbers (talk) 15:15, 12 December 2011 (UTC)

Actually, calling it "weight" is an anachronism too, since the ancient Romans didn't speak English. But I agree, "weight" is the common name. I just wish we had an article entitled "Weight (mass)." Eventually, I hope to get around to writing it, if only so that articles such as this one could have a Wikilink to it. Many other articles are struggling with the same issue. Weight is the right word, but it really needs to be distinguished from "weight" in the physics sense. This is motivating me to hurry up and write the article Zyxwv99 (talk) 15:45, 12 December 2011 (UTC)

They definitely were not measuring weight in the physics sense. I won't object to a name change as long as that is made clear. Perhaps with parentheses? The Roman units of weight (i.e., "mass" in the sense of modern Physics) were... The weight (mass) article would help. Rwflammang (talk) 23:42, 12 December 2011 (UTC)

The weights were, I believe, called pondera, which roughly translates into English as "weights". I'm personally fully prepared to respect the redefinition of "mass" to mean what ordinary people call "weight", and "weight" to mean something else, but only in those contexts where that redefinition has occurred. I don't believe that this is one of them. Yes, some clarification, perhaps in parentheses as suggested, would be necessary. Unless there are any objections, I'll go ahead and make the change tomorrow. Justlettersandnumbers (talk) 23:57, 12 December 2011 (UTC)

I like the way NIST handles this: When used in this law (or regulation), the term “weight” means “mass.” (See paragraphs V. and W. in Section I., Introduction, of NIST Handbook 130 for an explanation of these terms.) Zyxwv99 (talk) 00:50, 13 December 2011 (UTC)

Justlettersandnumbers, no redefinition of mass is needed, nor appropriate. English speaking physicists redefined the word weight for pedagogical reasons at some point in the 19th or twentieth centuries. This redefinition is anachronistic when applied to ancient times. When Romans spoke of pondera, they meant what modern day physics teachers call masses. Of course, everyone else calls them weights, including most translators of ancient Latin. In modern high-school physics English-based jargon, weight is used to mean a type of force, but everywhere else it is just a synonym for mass. Rwflammang (talk) 01:13, 13 December 2011 (UTC)

More info on time?

I know nothing of the subject matter, but the section on units of time seems incomplete without some mention of how the romans sub-divided the day. Either they had no common unit on the order of hours and minutes, or they did, and the answer to this question ought to be mentioned in the article. Flies 1 (talk) 14:52, 7 September 2011 (UTC)

Expanded the time section a bit. I based everything on my memory; I'll add references when I can look them up. In the mean time, most of the linked articles have references in them. Rwflammang (talk) 08:23, 8 September 2011 (UTC)

Great work! Seems like a big improvement to me. Flies 1 (talk) 20:20, 13 September 2011 (UTC)

Mass Section Proposal

I don't know the history of this article and was not sure whether "be bold" would lead to flames, so I decided to ask first: The mass section has a couple of things that I feel would benefit from attention.

• First, the libra is defined using grams, but only one unit, Centum podium is then defined in librae, leaving the reader to do fairly complex math (x/12 to get uncia then do a multiple or fraction of that) in his or her head. Since it appears that everything in the section is defined in reference to the uncia, could we define that in modern grams instead of the libra?
• Next, the parenthetical "oz" after the gram-equivalence of the libra doesn't really fit WP:WORLDVIEW guidelines, since an "ounce" is defined with various gram-equivalences even in its own article. It should be clarified by linking it to the International avoirdupois ounce using oz.
• The uncia link takes you to a page that defines the coin, and that article uses a gram-equivalence range that differs from the one in this article. If the coin is a defining baseline for this unit, can we adjust the libra sentence to, "The modern mass of the libra is estimated to range from 273 to 327 grams..."? If not, we need to drop the link to the coin (or fix the coin article).
• Overall, the mass section could certainly use a tabular layout similar to the Length section. If there is consensus that we could use ~324 for the libra and ~27 grams for the uncia, we could create a chart like this:

Unit of mass	Unciae	Imperial	Metric
Centum podium	1,200	~71.5 lb	~32.4 kg
Mina	20	~1.2 lb	~540 g
Libra (podium)	12	~11.4 oz	~324 g
Deunx	11	~10.5 oz	~297 g
Dextans	10	~9.5 oz	~270 g
Dodrans	9	~8.6 oz	~243 g
Bes	8	~7.6 oz	~216 g
Septunx	7	~6.7 oz	~189 g
Semis	6	~5.7 oz	~162 g
Quincunx	5	~4.8 oz	~135 g
Triens	4	~3.8 oz	~108 g
Quadrans	3	~2.9 oz	~81 g
Sextans	2	~1.9 oz	~54 g
Uncia (ounce)	1	~0.95 oz	~27 g
Semuncia	1⁄2	~0.5 oz	~13.5 g
Duella	1⁄3	~139 gr	~9 g
Sicilium	1⁄4	~104 gr	~6.75 g
Miliaresium	1⁄5	~83 gr	~5.4 g
Solidus (sextula)	1⁄6	~69 gr	~4.5 g
Denarius	1⁄7	~60 gr	~3.857 g
Denier	1⁄8	~52 gr	~3.375 g
Scripulum	1⁄3 denier	~17 gr	~3 g

Putting in gram equivalents sounds good. Note, however, that I've revised the figure for the libra to 328.9 grams. (The question of "How many grains to a Roman pound?" is one that I've been following for many years. The accepted figure used to be 5040 British Imperial grains, but after comparing the weights of a great number of coins, specifically the denarius, they've arrived at 5076 grains.) Next, the bronze coin known as uncia is, to the best of my knowledge, not the defining baseline for this unit. I'm pretty sure it's the denarius. Also, you can't go by other Wikipedia articles, since they are likely to have been as poorly researched as this one, in which case it's the blind leading the blind. I would drop the link to the uncia coin.

Finally, the chart as it currently stands is a confused mess. It looks like it was lifted verbatim from a single source, a book by an author who is apparently a metrologist but not much of a historian. Mixing all those units together is like someone two thousand years from now mixing shoe sizes, points, picas, miles, furlongs, meters, Angstroms, light-years, and hands, and calling it "linear measurements system of the USA 1500 - 3000 AD."

Also, ancient Roman units should not include Republic or pre-Republcan, except in the way of historical background information. Starting with Constantinople, we're talking units of the Byzantine Empire.

By the way, I'm new here too. Zyxwv99 (talk) 17:58, 10 December 2011 (UTC)

The chart below is based on your sources for 328.9g equivalence. I am SOOOOO not a historian OR a metrologist, and you mention that some of the units (or possibly their definitions?) are incorrect or inappropriate in context. Can you identify the items in this chart that are ill-suited to this article, please? Kevin/Last1in (talk) 19:03, 10 December 2011 (UTC)

Unit of mass	Unciae	Imperial	Metric
Centum podium	1,200	~72.5 lb	~32.89 kg
Mina	20	~1.2 lb	~548.2 g
Libra (podium)	12	~11.6 oz	~328.9 g
Deunx	11	~10.6 oz	~301.5 g
Dextans	10	~9.7 oz	~274.1 g
Dodrans	9	~8.7 oz	~246.7 g
Bes	8	~7.7 oz	~219.3 g
Septunx	7	~6.8 oz	~191.9 g
Semis	6	~5.8 oz	~164.5 g
Quincunx	5	~4.8 oz	~137 g
Triens	4	~3.9 oz	~109.6 g
Quadrans	3	~2.9 oz	~82.2 g
Sextans	2	~1.9 oz	~54.8 g
Uncia	1	~0.97 oz or ~423 gr	~27.41 g
Semuncia	1⁄2	~0.48 oz or ~211 gr	~13.7 g
Duella	1⁄3	~141 gr	~9.14 g
Sicilium	1⁄4	~106 gr	~6.85 g
Miliaresium	1⁄5	~85 gr	~5.48 g
Solidus (sextula)	1⁄6	~70 gr	~4.57 g
Denarius	1⁄7	~60 gr	~3.92 g
Denier	1⁄8	~53 gr	~3.43 g
Scripulum	1⁄3 denier	~18 gr	~1.14 g

Without spending a great deal of time on further research, I am not qualified so say at this time which ones don't belong on the list. Since what you are proposing would be an improvement over what we have now, I would say go ahead and put it in. Zyxwv99 (talk) 20:37, 10 December 2011 (UTC)

Just off hand, I'd say Denier looks questionable. The closest I can think of is the Frankish silver penny (French denier) which would be Carolingian Empire, not ancient Rome.

Mina looks suspicious. Of course the Mina was probably by used by Greeks and Jews living in the Roman Empire, but I don't think it was ever official except locally (in which case we should at least mention that).

Solidus should go under Byzantine Empire, and probably not here. The Denarius was 1/6 of an ounce, not 1/7, so maybe (after further research) it could be linked to sextula. Zyxwv99 (talk) 01:09, 11 December 2011 (UTC)

One thing that has puzzled me about these Roman units is this. Should sextans, triens, quadrans, and so be considered actual units or simply specialised words on a par with pair, trio, quartet (ie are they counting words rather than measuring words)? Are there convincing arguments for or against? Rhialto (talk) 08:20, 12 December 2011 (UTC)

I believe they are uncial divisions of an as or whole, not units as such, and mean just a sixth, a third, and a quarter respectively. It looks as if the pes, the libra and the jugerum, and probably others too, were divided into "ounces" in this way. Justlettersandnumbers (talk) 10:35, 12 December 2011 (UTC)

Yes, I agree with this. It is what I was taught. Uncia, etc. apply to all Roman measures: weight, length, area, and volume. Rwflammang (talk) 01:46, 14 December 2011 (UTC)

OK, I know this section has just had work done on it and possibly doesn't need more. I'm wondering, though, whether in the interests of full referencing and of consistency of format and of source it might not be better to base this table too on those in Smith (who breaks it down into two parts, the uncial divisions of the libra and the subdivisions of the uncia). He gives a value of 5050 grains for the libra, which seems to be more or less in the right range. And no, I don't have shares in his company! - he just gives clear detail, and is a respected if well outdated source. What do others think about this? Justlettersandnumbers (talk) 23:27, 17 December 2011 (UTC)

One of the differences between plagiarism and not plagiarism is "consistency of source." I don't mean copyright violation, since that's not an issue, but just responsible scholarship. On the one hand, I can understand wanting to keeping units consistent within the same category, e.g., an inch should be 1/12th of a foot because that is it's definition. Similarly, it makes sense (I think) to have the capacity measures calibrated to the Roman foot, since that appears to have been the legal definition. However, I still lean towards the 296 mm figure for the foot and the 5057 grains figure for the pound, not only because it represents the latest scholarship, but also to get away from blindly following a single source. After all, we will, at some point, want to revise any items where contemporary scholarship has gone beyond Smith's work. Just my opinion. Zyxwv99 (talk) 23:53, 17 December 2011 (UTC)

The problem I would like to resolve is that the current table is completely unreferenced. I believe that taking Smith as a source for the names of the units (and, for now, eliminating any he does not name until references for those too can be found) would solve that problem. Whether the conversion to metric, in any case only a guide, is done at the value he uses as we have done for the measures of capacity, or using an accepted figure from a modern source as we have done for length and area, seems to me secondary; I would be agreeable to either. The difference between 5050 grains (Smith) and 5057 is anyway minute. How reliable are the sources that give 5057, in your opinion? Justlettersandnumbers (talk) 13:45, 18 December 2011 (UTC)

Since you are the one doing the work on the Smith project, and I'm just criticizing, maybe we should invite input from other users. My own opinion is that Smith has done a great deal of footwork for us, and that we should take full advantage of his generosity. However, I am dubious about modern-day equivalents from 19th century sources. For example, look at the first table in this article. It lists three sources for the Roman foot, all three of them now discredited (the third one apparently fraudulent). Nowadays historical metrologists use large numbers of sources, laser telemetry, computer statistical models, etc. Personally I'd like to eventually replace ALL of Smith's numbers with something more contemporary, taking care to ensure that our newer sources are actually better and supported by peer-reviewed scholarship. But then again, that's just my opinion. Zyxwv99 (talk) 00:29, 18 December 2011 (UTC)

Criticism is welcome, thank you. And yes, I hope that others will comment, particularly Kevin/Last1in who started this thread. As above, I have no objection whatsoever to using referenced values from reliable modern sources rather than 19th C ones, indeed agree that it is preferable. The first step, I believe, is to get everything referenced, and then fine-tune the details. Do you think the first table, summarising Greaves's findings, should not be there? I find his to be a remarkable example of 17th C scholarship; but perhaps that has led me to giving it undue weight? I'm puzzled by "fraudulent", which is about the last word I would apply to his account. Is it believed that the congius of Vespasian was a fake? By the way, if the "PX" in the inscription on that object is read as "pondo X" or 10 librae, the libra can be calculated from the Roman foot; a pes of 296 mm gives a libra of about 324 g or 5003 grains. Justlettersandnumbers (talk) 13:45, 18 December 2011 (UTC)

I'm not suggesting Greaves was guilty of fraud, but rather whoever sold the congius to the House of Farnese, which is where Villalpandus got it in the first place. For details, see my recent additions to the article congius and follow the references under "Congius of Vespasian." Those references lead to Google Books where you can read the referenced text.

I like people like Greaves and think we would feature their work, so long as it is made clear to the reader that we are discussing history of Roman metrology and not current scholarship. The table seems to suggest that these three sources are still taken seriously, which they are not.

Is this valid objection answered by the caption I've put on the table, or would you prefer to see the table removed and the content as running text? If so, I'd have no objection - I thought table format would be clearer, that's all. Justlettersandnumbers (talk) 22:25, 19 December 2011 (UTC)

As for whether the Roman pound was 5050 grains or 5057, it could go either way, as there are plenty of competent sources to back up either number. That's why I would include something like this in the references. I'm actually impressed with how close Smith's numbers are to the latest scholarship (a point we should probably mention in the text). I'm just trying to get away from over-reliance on a single source. — Preceding unsigned comment added by Zyxwv99 (talk • contribs) 15:25, 18 December 2011 (UTC)

Indeed that would appear to be just the sort of source we need, nice find!; did you have any luck tracking down the various sources that it in turn cites? I have not tried to. As no-one else seems to have immediately responded here, I'd like to suggest a part-way solution: convert the table to show the units as Smith does, but using the current conversion value, with Skinner as reference for that. In that way the whole section as it stands will at least be referenced, which seems to me an essential starting-point. The metric conversions can always (and easily) be modified if consensus leads to using a different value for the libra. Justlettersandnumbers (talk) 22:25, 19 December 2011 (UTC)

In response to "Is this valid objection answered..." it looks fine. Thanks. Zyxwv99 (talk) 23:34, 19 December 2011 (UTC)

Capacity Measures

I just changed the metric equivalents for the capacity measures. I added a reference at the top of the section.

Incidentally, this article mentions something called the Congius of Vespasian.

The article on Congius has the following sentence:

There is a congius in existence, called the "congius of Vespasian", or the "Farnese congius", bearing an inscription stating it was made in the year 75, according to the standard measure in the capitol, and that it contained, by weight, ten pounds (3.4 kg). This congius is one of the means by which an attempt has been made to fix the weight of the Roman pound (Libra).

This is obviously lifted verbatim from a very old text. (Try doing a Google search on "There is a congius in existence". I tried to follow up on this. Apparently there is no longer such a congius in existence. Plus scholars who examined it had serious doubts about the interpretation of the inscription. Zyxwv99 (talk) 03:00, 13 December 2011 (UTC)

I wondered if this object still existed. It was measured and compared with a quadrantal constructed for the purpose by Greaves in 1639, not in order to fix the Roman pound but to obtain a value for the Roman foot. He wasn't too happy with the results. Justlettersandnumbers (talk) 17:00, 13 December 2011 (UTC)

The congius is illustrated in Daremberg and Saglio, Dictionnaire des antiquités grecques et romaines. Apparently it was by then in Dresden ...

How much confidence do we have in Zupco? I can't see what he says about the size of the sextarius (it isn't on the snippet Google gives me), but I'm a little concerned that the dry and liquid measures now no longer reflect the apparently well-documented equivalence of the quadrantal to a cubic Roman foot. IF the Roman foot was about 0.296 m then the quadrantal should have been about 25.9 l, and the sextarius 1/48 of that, or about 0.54 l; Smith gives 0.96 pint, or about 0.546 l. That's quite a big discrepancy from Zupco's figure. If Zupco is well supported by other sources then I'd suggest perhaps putting both sets of equivalences into the table, those derived from theory and the estimated length of the pes, and those from actual measurement of surviving containers; if not, perhaps the earlier values should be restored? Justlettersandnumbers (talk) 21:55, 13 December 2011 (UTC)

Zupko's British Weights and Measures has about 2 or 3 pages on Roman weights and measures. Apparently the Encyclopedia Britannica had enough confidence in him to use those 2 or 3 pages as their article for Roman Weights and Measures. (See Encyclopedia Britannica Online) Zyxwv99 (talk) 22:47, 13 December 2011 (UTC)

On the other hand, you raise a good point about the cubic foot issue. My guess is that our knowledge of Roman linear measurements in better than for capacity, just because capacity is much harder to measure, harder still for the Romans. How about if we went with 295.9 mm for the Roman foot, then figured out what sort of amphora that would give us? I know this sounds like "original research" but if that was Roman law, then maybe our tables should reflect the law. On the other hand, we could also add a paragraph about actual measurements from surviving amphorae, etc. Zyxwv99 (talk) 04:04, 14 December 2011 (UTC)

Okay, maybe 296 mm. (Wanting to put a number after the decimal point is my Asperger syndrome talking.) Zyxwv99 (talk) 22:36, 14 December 2011 (UTC)

I just made some changes to the capacity measures, mentioning a range of accepted values for the sextarius (.53 - .58 l) and the equivalence of the cubic foot with the amphora quadrantal. I then changed the figures for the liquid measures but don't have time (at this moment) to change the figures for dry measures. I think one of the issues here is that early-modern metrologists from the time of the Renaissance went overboard in constructing grand schemes on flimsy evidence. The 20th century witnessed a strong reaction to that sort of thing (not only in metrology but also in the field of archaeology). Thus, historical metrologists sometimes ignore systems, focusing merely on individual units. Zyxwv99 (talk) 16:05, 15 December 2011 (UTC)

I see that a lot of work has been done, and don't want to seem to criticise or undervalue it. However, I'm concerned that this section of the article (or at least the tables) continues to be completely unreferenced. What I suggest is that we redo the tables from a reasonably reliably source, removing (for now) all unreferenced English equivalents and Roman units; and put all discussion of alternative values for the equivalences into the text; there are a LOT of those. The only source I know of that gives a (fairly) full table is Smith, the 19th C source already used for length and area and for the related Greek article. I'm sure there are many others, but using that particular one might give a degree of consistency to the article as a whole; however, I don't want to push it unduly. There would of course be nothing to stop people putting the bits he doesn't mention back in as and when alternative sources for them are found. Smith's value for the congius is about 3.27 l, which is slightly over the theoretical equivalent calculated from his Roman foot, and possibly (I hazard a guess) chosen more because 5.76 pints divides neatly by 288 than for any other reason. IMO a referenced table that differs slightly from modern thinking is still preferable to a totally unreferenced one that doesn't. Any thoughts?

I have to admit to a twinge of anxiety that our source for both the minimum and the maximum value of the sextarius is from the same publisher. Can't they make up their minds? Justlettersandnumbers (talk) 22:55, 16 December 2011 (UTC)

I'm looking at Smith's tables right now. What I'd like to do is check some of the information against contemporary sources to get an overall feel for Smith's reliability. As for the Encyclopedia Britannica, they have about as many contributing editors as the Wikipedia, so of course they can't make up their minds. The only difference is that their editors have PhDs, are considered among the world's leading experts in their respective fields, and the gist of their articles has passed peer review. Also, I cited Zupko directly, not his encyclopedia entry. But basically I'm just asking you to hold off for at least a several hours so I can take a serious look at Smith. Right now I'm looking at these pages:

Smith's tables — Preceding unsigned comment added by Zyxwv99 (talk • contribs) 00:34, 17 December 2011 (UTC)

Smith's figures are a bit off from currently accepted values, but not by much. Considering the current state of this article, Smith's tables would probably be a big improvement. And thanks ahead of time for all the work you are about to do. Zyxwv99 (talk) 01:19, 17 December 2011 (UTC)

Astronomy versus astrology

An editor recently changed the word astrologer to astronomer in the sentence describing minutae. I don't really have a preference for which term is used; in this historical context, it was six or one, half dozen of the other. But I think whichever term we use, we should use it consistently. If we use astronomers to describe those who divided the day into minutae, then we should use astronomers to describe the those who grouped the days into weeks, since it was the same community of professionals doing both of these things. We should also replace astrological with astronomical. Rwflammang (talk) 14:07, 23 June 2012 (UTC)

Even though it was the same community, and usually the same individuals (Ptolemy for example) the divisions weren't necessarily used for the same purposes. I'll look into this and see what I can find. And sorry about putting "astronomers" into a sentence that had "astrologers" later in the same sentence. I'll just self-revert for now. Zyxwv99 (talk) 15:52, 23 June 2012 (UTC)

Well, that's very polite of you, but the more I think about it, the more I like your change and think we should follow it through. The term "astrologers" carries a very negative connotation these days that did not apply to the mathematical community of ancient Rome when it adopted the practice of the more scientifically advanced east in following a 7 day week. It would be like saying the metric system has become more popular now since it has been adopted by those who don't know how to divide by 12 or 16, rather than because it has been adopted by the prestigious medical and scientific communities. Rwflammang (talk) 17:46, 23 June 2012 (UTC)

I would be careful about making it all one or the other. Sometimes it was one, sometimes it was the other. The 7-day week, for example, seems to have been astrological. The division of the day into hours, on the other hand, was apparently astronomical. Zyxwv99 (talk) 22:22, 23 June 2012 (UTC)

Libra sign ₤

According to the article about the record label Parlophone, their trademark sign ₤ is for Libra (and also for Lindström, the German founder). --HelgeStenstrom (talk) 13:22, 10 August 2012 (UTC)

You bring up a good point. The Pound sign article does not explain the origins or early history of the symbol. However, I seriously doubt that it goes back to ancient times. Further discussion on this topic should probably take place on the Pound sign talk page, or better yet, someone should just look it up and fix the article. Zyxwv99 (talk) 15:13, 10 August 2012 (UTC)