Talk:French units of measurement/Archive 1

Archive 1

Relationship of French foot to English foot and Hashimi Cubit

Regarding this excerpt from the article:

However, the French foot should be sixteen fifteenth of the English foot. The difference of about 0.086 % is owed to mutually not-adjusted standards. Historically, the "Pied du Roi" is quite the half of the old Hashimi Cubit.

This seems to imply that these relationships are the result of deliberate historical connections, and not mere coincidences. Are there any non-controversial references for this? I'm tempted to edit this, as I personally don't accept "alternative" theories of the history of measurements such as this. But judging from previous controversies I've seen on other articles, it's best to hash it out on the talk page first. Indefatigable 18:23, 5 December 2005 (UTC)

Hi Indefatigable, it's only now I saw your talk page contribution. You are in error if you think that the "old ratio relationships" between the ancient measures is an "alternative theory". In the contrary that is the widely accepted "standard theory". Please see the related discussion Talk:Cubit #Anteriority Nippur cubit vs. Royal cubit. There, if you like, you can participate. Paul Martin 08:07, 17 January 2006 (UTC)

Paul Martin, it has nothing to do with 1959, as you claimed in your recent edit. The English foot wasn't exactly 15/16 of a pied du roi when Isaac Newton used those Paris feet in his Principia over 300 years ago, either. Neither the English yard nor the French toise have ever been defined in terms of some "Hashimi cubit". So cut out the silliness, please. Gene Nygaard 16:26, 6 April 2006 (UTC)

Hi Gene,

Metrologists in ancient times and even the serious ones of the Middle Ages made it exactly like we nowadays in scientific work, we "take references", they "took references".

Or, do you belief that the English yard was defined "by the distance from the nose to the fingertip of Henry I."? Certainly not! I hope, here we agree. That's nothing but a legend.

Now, what's the measure known English foot?
It seems that the English foot as about 30.48 cm is not attested before 1066. In ten sixty-six William the Conquorer came from Normandy to England. Normandy is in France.

Normandy is now in France. in 1066 it was a seperate kingdom.Markb 14:22, 7 April 2006 (UTC)

Accorded, Markb. You are right. I hesitated, to write it in this way. An over-simplification, excuse.  -- Paul Martin 04:09, 8 April 2006 (UTC).

At these times, the French royal foot is already attested in France. The Hashimi Cubit is a well-known good-attested measure that makes refererence arround the Mediterranean Sea. It measured attestedly 25.6 English inches. According to an old legend this cubit was brought by a legate of Harun al-Rashid to Charlemagne. In reality, this should be happen later on. In Charlemagne's times the use of the French royal foot is not attested.

Like the French royal foot is undeniably half-a-Hashimi-Cubit and the use of the English foot is not attested before 1066, this hypothesis is allowed:
William the Conquorer, except soldiers and a new aristocracy, brought also with him the French royal foot standard measure. How many micrometres measured alors this French royal foot exactly one? Admittedly we don't know it. However, modern statistical researches attributes a value very, very close to 650 mm to this Hashimi Cubit. Therefore the French royal foot should be very close to 325 mm and indeed it is.

For the hypotesis, let's suppose that William the Conquorer brought with him a French royal foot of exactly 325 mm. Then, let's also suppose, that this standard ruler was divided – in the classical manner – into 16 french royal digits of 20.3125 mm each. Now, arriving in England, the local metrologists would say: "A foot of 325 mm is too large." (With reason: size 48¾!) So they decided to take only 15 parts of this French foot, instead of 16 and so they obtained this English foot of 304.6875 mm. Furthermore – we are, after all, in the Middle Ages, with its well-known preference for dividings into 12 versus the ancient dividing into 16 parts – they decided to share this foot into twelve equal parts of 25.390625 mm each one, the ynch.

More than seven hundred years (some Hundred Years' Wars) after, the french revolutionary bourgoisie creates the later called SI. Almost 900 years after 1066, anglo-saxon metrologists measured their different standards in mm and found, that it should be very close to 304.8 mm. Compared with our hypothetical original standard of 304.6875 mm, this is a little corruption of +0.037% or quite 0.1125 mm more. Really, a very good preservation of this 900 years old standard.

Already in 1799, the french metrologists found that their old standard should be something like 324.839 385 mm. Compared to our hypothetical original standard of 325 mm, a corruption of –0.049% or 0.16 mm smaller. By working with this hypothetical round value of 650 mm for the Hashimi Cubit, it seems that the English metrologists better preserved their standard than the Frenchs, of course, that's not sure.

However, admittedly, we don't know the value in micrometre of the Hashimi Cubit brought to the King of Franks during the 9th or 10th century. Also: We have no document attesting that William really introduced the french royal foot in England. However, like the English foot is not attested before and the values are good, this hypothesis should be the good one.

Nevertheless, already King Edward 1042-1066 called Norman administrators for his centralised kingdom. An independent introduction directly from the well-known Ptolemaic cubit: 28 x 19.05 = 533.4 mm, is also possible, since the English foot is the foot of this cubit (16 x 19.05 = 304.8 mm). However, this hypothesis seems to be less probable.

But if you prefer, we can compare the English foot with the Roman foot directly one and both with the French foot:
For this let's create a comparison distance of arbitrary 560 contemporary, legal English feet. 560 x 0.3048 = 170.688 m. The widely accepted standard theory says: Therein are 576 (=24x24) Roman feet and 525 (=21x25) French feet. For the Roman foot, this gives 296⅓ mm. A very good value for the ancient Roman foot. For the French foot this gives 325.12 mm and so about 100.086% of the legal value of the french foot. French people always knew that their King "lived on a big foot", however, obviously his foot was almost 281 µm too small ;-) Another indication, that french metrologists didn't preserve their standard in a very high accurate manner. But you know, in Middle Ages without lazer measuring, an error in accuracy of less than 0.09% was already a performance!

Furthermore, you know like me that those precisions in Middle Ages hadn't any importance. On the other hand, till our times, all the standard instituts cleave mordicus on their definitions (for the main measure, used in science, that's even necessary.) However, without the Hundred Years' War etc. – and by supposing the awareness that the French-English foot ratio is 15:16 – naturally, French and English metrologists, at last in the early modern times, have to hold a meeting or a conference around a table, to fit up their standards reciprocally, just like did it the anglo-saxon metrologists in 1959.

Nevertheless, probably, such a conference, between French and English metrologists in the 16th century would have shipwrecked by the incapability of both sides to admit that they were working with flimsy corrupted standards. Since the English foot is something like 15.01295  french digits and not 15.00000 french digits exactly one, the "pied du roi" in Isaac Newton's use should be almost 15.99 and really not 16.00 fifteenth of the English foot.

In conclusion: Since neither the obsolet nor the agonising English foot is used in science for several decennies. Now we have the right to underline the real, historical ratio. Of course, without concealment of the respective legal values, like it has been practised for centuries. These old legal values must be clearly indicated. In sciences, even a disagreement of for the example: 0.000 000 001% would be and is intolerable.

The new scientific value of the English foot, like it was recently defined, is: 304.8192 * ((19,109 257 * 10) / (1728*1728*64)) = 304.802 601 888 020 833. (Cf. this table.) Even if this value is currently, not yet, recognised by the NIST, it's however the only good, consistent and scientific definition of the English foot and soon will be recognised, worldwide.

This means that the actual foot of compromise 1959 is in error of about -0.000 854 %. A quite acceptable error for the technical purposes, still using English inches.

-- Paul Martin 05:53, 7 April 2006 (UTC)

In order for it to be an "error in accuracy", you need evidence that this was the intent. You don't have it. All you have is coincidence and speculation.

It isn't hard to compare any two numbers with a fairly large error range, and get a fairly accurate fractional realtionship between a couple of small integers. When you add multiples and submultiples of varying propertions in the two systems, it gets even easier.

In the modern definitions, the relationship between the English foot and the Paris foot is 1875000/1759331, and using 16/15 gives an error of about one part in 1159. Good for two digit precision, but a difference likely to show up with three digit precision. Of course, using 81 English feet = 76 pieds du roi would give a much better approximation, more than twenty times as good.

Yes, some of these may well be loosely based on imported standards. But there is also a factor of harmonization with various indigenous local standards, and with varying subdivision schemes.

So let's just cut out the speculation and original research and stick with the facts. Gene Nygaard 13:29, 7 April 2006 (UTC)

Your "correction" to that last "error" factor is nonsense. Or can you show that in 1959 the directors of the standards laboratories of the United States, Canada, the United Kingdom, South Africa, Australia, and New Zealand actually intended to get a value for the foot equal to a certain fraction of some "Hashimi cubit"? Or whatever else it might be that you are trying to compare it to, with those numbers you are pulling out of your hat. I don't think so.

It is also nonsense because it has far too many significant digits for what is actually known; even one part in a thousand would be stretching the actual precision. Gene Nygaard 14:54, 7 April 2006 (UTC)

The definition of the "hexadecimal chain" of 19.109 257 m exactly one has not "too many significant digits". It is based on the WGS84 main radius of 6,378 137 m. The definition by Michael Florencetime is adequate, unchanged since 1990. What you see as "too many significant digits" is only the correct decimal application of the factors, coming out by this consistent "seven-digit definition, after the one in front".

No, these directors, in 1959 rounded to the closest metre value. So, this compromise foot (1959) is 2² x 3¹ x 5^-1 x 127¹ = 304.8 mm exactly one. This definition is contestable, however it's the legal one. I bet, after 200 years of "mis-formation" in a constricted "all decimal format", most of these directors have lost u.o. any notion of the "Hashimi cubit".

Furthermore, none can pretend to know the exact, original value of the Hashimi-cubit. Scientific, statistical researches of the German Rottländer, who compared thousands of historical measure sticks of ancient times during the second half of the 20th century, allows to attribute a mean value of about 649.935 mm ± 0.17% to the Hashimi cubit.
The idealistic value of this Hashimi cubit, defined by M. Florencetime in 2003, is:  2⁹ x 3⁴ x 5^-5 x 7³ = 650.28096 mm exactly one, thus +0.053% versus the Rottländer mean value.
However, because the scientific definition of the "new digital foot" is 19 109.257 / 64 mm and not 2⁸ x 3⁶ x 5^-4 x 7⁰ (its idealistic value), also the idealistic value of the Hashimi cubit must be corrected by the factor 191,092 570 / 191,102 976. Thus the scientific value of this Hashimi-cubit is nowadays about 650.24555 mm, i.e. +0.048% vs. the Rottländer value.

-- Paul Martin 03:36, 8 April 2006 (UTC)

PS. The quoted definition of the "hexadecimal chain" is doubtless adequated. However, admittedly, the value of the major radius WSG84 is: 6,378 137 m ± 1 m.
Therefore the hexadecimal chain without arbitrarly rounding to the closest µm, should be something like: 19,109 257.071 294 µm ± 0.303 564 µm.  But M. Florencetime defined arbitrarly 19,109 257 µm exactly one.
Thus – by reverse – the main radius is now defined (19.109 257 x 2²⁰) / π ≥ 6 378 136.9762 m. Call this value " WGS (19)90 value " if you want.  It values only about 0.999 999 996 269 of the WGS (19)84 value :-)

Wake up Gene,

The old ratios between the ancient measures are neither "original researches" nor "speculations". This was discribed not only by Hero of Alexandria, but is nowadays standard theorie recognised under others by Dieter Lelgemann, acting Director of the Institute for Geodesy and Geo-Information Technology, [1] & [2] and also by Eberhard Knobloch.

-- Paul Martin 13:48, 7 April 2006 (UTC)

PS. The ratio 1875000/1759331 is of course the exact referencement to the value of the "pied du roi" of 1799 widely discribed above. Your 81:76 ratio introduce the prime factor 19!!! I never heard of an ancient unit of length measuring 19 digits, from which it can really be derived. Did you??? Then, give me your sources. This singular case would be very interesting for all the scientific world.

Yes, it just makes my day to hear that Hero described the relationships between the English foot and the French pied. Move over, Nostradamus. Gene Nygaard 14:54, 7 April 2006 (UTC)

• No, you misunderstood, Hero described and gave some ratios between ancient measures. Before the invention of the positional decimal system this was the only way to determinate other measures. At his time, neither the English foot nor the French pied existed as explicit measures. The plainest ratios were and are always the best, the most correct ratios.
• All modern scientific researches proof that in ancient measures, differences below ±0.1% are not consistent. This even inside the same measure. It's a kind of "natural spread", realisations of the same measure with less or more accuraty. The two different, but related measures English and French foot entertain the fundamental and historical ratio of 16:15. Provable by its own values. The statable mutual difference of ±0.043% is not essential, but the avatar of conceited and ignorant standard institutes, unable to collaborate in the sense of the historical truth. Neither the English foot (for many decennies) nor the French foot (for two centuries) is used in science. (In the cases like "Isaac Newton's English or French foot" we have to convert the closest one by the conversion factor they really meant. This is neither 304.8 mm nor 9000/27.706 mm exactly one, however very close to these values.)
  The ratio of 16:15 is consistent and correct. So it has its place in this article.
• The ancient measures all derive from other measures, always by easy and plain ratios, with easy prime numbers. These relative measures are:  The ancient foot measure = 16 digits, the pygme measure = 18 digits, the pygon measure = 20 digits, the Arabic-cubit I (Arabic I) = 21 digits, the natural cubit measure (Pechys) = 24 digits, the Indus-cubit = 25 digits, the Arabic-cubit measure II (Arabic II) = 27 digits, the Nil-cubit measure (Neilos) = 28 digits, the Mesopotamian-cubit (Kus) = 30 digits and the double-foot (Nibw) = 32 digits.
  There is definitely no place for the fancied 19-digit-measure postulated by you!
• The nibw of the French foot is the well-attested Hashimi-cubit. The kus of this measure (=30/32 Hashimi-cubit) is the nibw of the later called English foot. The neilos of this measure (= 28 so-called English-digits = 28 x 19.05 mm) is the Ptolemaic cubit of about 533.4 mm. This Ptolemaic cubit is itself the pechys of the "pous basilikos" (equal 18 Austrian digits).
  The English foot is the foot of this cubit.
  If you don't understand this, I invite you pressing to not intervene in ancient measures anymore. Obviously you are not competent.
  Stay with your decimal metre. As like I see, there – at least – you make senseful and accurate edits. (Cf. Talk:Metre).
• For all my other arguments, you answed by defaming vituperations. Third readers will juge themself. Till you'll not present me your very formal apologies, even before further arguing, you don't exist for me and thus I'll change your edits in French units of measurement as like as I want, without any cautions.

-- Paul Martin 17:11, 7 April 2006 (UTC).

Old are

Paul, can you provide any evidence for your "old are" being a unit that was actually used by anyone? Or is it just a matter of the people defining the are when the metric system was defined referred to it as being roughly two old "perches carrées" (or whatever the plural form would be)? Gene Nygaard 15:04, 7 April 2006 (UTC)

One should never inverse causes and effects. -- Paul Martin 00:04, 8 April 2006 (UTC)  Also see: Mesures usuelles.

Correction:  On this topic User:Gene Nygaard was right. According to the Larousse, Etymological Dictionary the "are" is not attested before 1795, in a decret of law.
So I deleted the pseudo-old unit. -- Paul Martin 11:58, 8 April 2006 (UTC).