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28. The Relationship between the 0.729166667" digit and the Egyptian Royal Cubit of 20.625"

Updated: Feb 23, 2022

The 0.729166667" digit is an important unit. It goes 1,575,000,000 times into the circumference of the earth (the polar circumference of 24,857.95454545 miles to be exact), and it fits well with the remen of 14.583333", this remen consisting of 20 of these digits. But the 20.625" Egyptian Royal cubit seems not to fit, unless of course by means of the square root of 2. And this itself has to be taken as 99/70. So we have 20.625 x 7 / (2 x 99) = 0.729166667. The relationship between the digit and the Egyptian Royal Cubit, as 0.729166667" and 20.625" respectively, is of course as the side of a square is to it's diagonal.

However, the relationship between the 0.729166667" digit and the Egyptian Royal Cubit of 20.625" could also be though of as this: the digit goes in 1,400,000 x 4,374 / 4,375 times into a hypothetical 25,920 ancient metres unit of length (using the 39.375" conversion to metres). And the 20.625" cubit goes into this 25,920 mm unit 49,500 x 4374 / 4375 x 9,801 / 9,800 times. Royal Egyptian cubit and digit, as 20.625" and 0.729166667", are linked like this: cubit x 49,500 / 1,400,000 x 9,800/9,801 = digit.

This also has the advantage of linking up with the Neal / Michell value for the Egyptian Royal Cubit of 20.618181818", as 25,920 x 39.375 / 49,500 = 20.6181818181. This is because the link between these two cubits, the 20.6181818" one and the 20.625" one, is 9,801/9,800 x 4,375/4,374.

So we could define the digit of 0.7291666667" as simply 25,920 ancient metres divided by 49,500, and multiplied by 4,375/4,374 (ragisma) and 9,801/9,800.

This offers an intriguing connection between the digit, the inch and the ancient metre.

A hypothetical unit of 25,920 ancient metres in fact lends itself to many other possible connections. For example, 25,920 / 49,500 = 0.523636363..., and this is the value in metres of the Neal / Michell Royal Egyptian Cubit, otherwise known as 1,134/55 = 20.618181818 inches. The 1,134 part of this fraction is in fact 25,920 x 4,375 / 100,000. The 55 part of the fraction is 49,500 / 9, and also links up with an approximation of Phi or Phi squares using the Fibonacci numbers. For example 55/34 = 1.617647, and 144/55 = 2.618181818.

There is good reason to think of these values in metres, of the ancient kind at least, using the 39.375" conversion. For example, 25,920 / 49,500 = 0.523636363... is 2.618181818 + 3.141818181818, these last two numbers being values for Phi squared (144/55) and pi (144/55 x 6/5).

To convert from the ancient metre to the modern one, the 8,001/8,000 ratio works perfectly.

And so the digit of 0.7291666667" is 25,920 / 140 x 4,375 / 4,374 ancient mm, or 25,920 / 140 x 4,375 / 4,374 x 39.375 / 10,000 ancient mm, multiplied by 8,000/8,001 to obtain the modern metre value. (39.375 = 10,000 / 254 x 8,001/8,000)

The 39.375 conversion between ancient metre and inch is in fact 9 x 4,375.

The 0.729166667" digit is itself already connected to the ragisma 4,375/4,374, as it can also be written 9 x 9 x 9 / 1,000 x 4,375 / 4,374 . Curiously, 25,920 / 140 x 4,375 = 81 = 9 x 9. This means then that the digit expressed in ancient centimetres, 1.851851851851, is 9 x 9 / 4,374.

And expressed in inches, that's simply 9 x 9 x 9 x 4375/ 4,374 x 1/1,000.

The remen of 14.5833333", in relation to 25,920 ancient mm, is 25920 / 1,800 x 7,875 / 7,776, or 14.4 x 7,875/7,776. The remen is an Egyptian Royal Cubit of 20.625" divided by 99/70. This approximation of root 2 is also 25,920 / (2.618181818 x 7,000).

7,875/7,776 is an interesting ratio that comes up from time to time in metrology, and here it seems to bridge the values in inches and metres between the 25,920 mm unit and the 14.583333" remen. 7,875 inches are in fact 200 ancient metres. And 14.4 / 7,776 is in fact the digit in ancient metres: 0.0185185185....

The 0.7291666667" or 1.851851851 (ancient) cm digit is 2 (ancient) metres / 1,080.

The moon's radius is 1,080 miles.

I thought I might try and see if the 0.729166667" digit might connect to other units.

I went back to a text I was looking at a few months ago by Mauss, to see how the measures he gave fitted in with a 0.72916666" digit. The first unit he mentions is the Assyrian and Persian Royal Cubit, also referred to as the "grande Hachémique", which he assigns 658.285 mm to. The conversion rate for all his measures is 39.375" to the metre. We know this because he gives the value of the English yard in millimetres as 914.2857. This article is from 1892, so before the 1897 Weights and Measures Act, and long before 1930 when the 25.4 mm inch was adopted. The conversion rate is curious however as I've not been able to find any mentrion anywhere of this rate ever having been in existence. Still, it ties in perfectly with the 0.7291666667" digit.

914.2857, which you could take as 6.4/7, multplied by 39.375 = 36, so 36 inches.

Interestingly, 6.4 m = 252", so 7 yards, is quite compatible with the 0.729166667" digit.

6.4 metres are obviously 54 x 0.72916667 x 6.4, or perhaps also 21.6 x 16 digits, 14.4 x 24 digits, 12.8 x 27 digits, etc.

This makes the yard 14.4 x 24 x 0.72916667 / 7 inches = 12 x 12 x 12 x 2 x 0.729166667 / 70", and the English foot = 115.2 / 7 x 0.729166667"

To go back to the Assyrian and Persian royal cubit that Mauss writes about, 658.285 mm, this is also a seventh division of something. 4608 / 7 = 658.2857142857 mm = 25,920 / 1,000 inches, which is 2.16 English feet, and also 248.832 / 7 digits, or 12⁵ / 7,000.

25.92" for an Assyrian cubit is an interesting number. In the article on weights and measures here, an Assyrian cubit is mentioned, "a royal cubit of 7/6 the U cubit, or 25.20, and four monuments show a cubit averaging 25.28 (...) we may take 25.24 as the nearest approach to the ancient Persian unit". (p 4 on the webpage)

The 25.2" value would work well with the 0.729166667" digit, being 2 x 12³ / 100 digits.

The same article gives the size of the "U" as 10.806 inches. If it were in fact 10.8 inches, that would also go well with the digit, as 12³ x 6/700 digits. (In fact in the little table below this sentence in the article the "U" is down as 10.80, 6 of these are a qanu, and there are more multiples of this, worth 129.6", 648", 7776" and 233,280", whose names are hard to read.)

The article then says there is a 2"U" unit of 21.6", and this ties in well with the Mauss article.

Mauss has a unit which is 5/6 of the royal Assyrian and Persian cubit, which he calls the worker's cubit, or Coudée ouvriere, worth, as he states it, 548.571 mm, which is also 3,840 / 7 mm, and which is also 21.6" exactly.

The 21.6" unit doesn't seem to work with the digit at first, but bring in the number 7 again and it does: 21.6" x 7 = 151.2" = 12⁴ x 0.729166667 / 100

And this logic links almost all the units Mauss talks about.

Royal assyrian cubit = 4,608 / 7 mm = 12⁵ / 7,000 digits = 25.92"

Worker's cubit = 3,840 / 7 mm = 12⁴ / 700 digits = 21.6"

This worker's unit of 548.57142 mm is also 3 digits x 144/55 x 6/5 x 22/7, so the two pis, 3.142857 and 3.141818181. Three digits are perhaps a tenth of Ezekiel's cubit, as Jim Alison says in his article: "Ezekiel’s cubit of 30 digits, which is contained 72,000,000 times in the polar circumference, or 18,000,000 times in the quarter circumference, or 200,000 times in one degree of latitude"

Royal foot = 2,304 / 7 mm = `12² x 16 / 7 mm = 6 x 12⁴ / 700 digits = 12.96"

`Royal foot x 7/8 = 288 mm = 11.34" = 55/100 x 20.6181818 (Michell / Neal Egyptian Egyptian cubit)

So the 20.6181818" cubit = 6 x 12⁴ / 440 digits = 28.8 / 55 = 0.52363636 metres = 2 x Phi squared / 10 = metres (with Phi squared as 144 / 55). This would make the metre an integral part of Neal and Michell's Egyptian cubit, via Phi squared. (And of course, as pointed out earlier, this unit of 0.52363636.. = 3.1418181818... - 2.618181818... metres, or (144/55 x 6/5) - (144/55) metres.)

Other units mentioned in the Mauss article include:

  • Dieulafoy's worker's cubit = 550 mm = 20.625 x 24/25 x 3/2 digits = 21.65625"

  • Dieulafoy's worker's foot = 330 mm = 20.625 x 24/25 x 18/20 digits = 12.99375"

  • Dieulafoy's royal cubit = 660 mm = 20.625 x 24/25 x 18/10 digits = 25.9875"

  • Watering cubit ("coudée de l'arroseur") = 576 mm = 126 x 12³ / 7,000 digits = 22.68"

  • Hand cubit ("coudée de la main") = 480 mm = 105 x 12³ / 7,000 = 18.9". This is also the quim cubit and divides into 24 digits of 0.7875".

  • Iron cubit / Black cubit ("coudée de fer / coudée noire") = 540 mm = 105 x 12³ x 9 / (8 x 7,000) digits = 21.2625". This is also the same as the "coudée des étoffes", the fabric cubit, which divides up into 27 digits. These digits would be of 0.7875", which is 0.729166667 x 1.08 inches, same as the hand cubit digits. After all, a digit of 0.729166667" or 1.851851851 ancient cm, is 2 / 108 ancient metres.

32 of these digits of 0.7875", or 2 ancient cm, make up the Hachemi cubit of 0.64 metres = 25.2"

These 0.7875" digits connect back to the English foot as 320 / 21 digits of 0.7875". The Egyptian Royal cubit of 20.625" contains 550/21 of these digits. The Neal / Michell Egyptian cubit contains 10 x Phi squared of these cubits, or 10 x 144/55. The 14.58333" remen would contain 2000 / (3 x 36) of these 0.7875" digits. This remen is also 4/9 x 2.618181818 / 3.1418181818 metres. If you take 1,000 of these digits of 0.7875" that's also 20 metres.

It's actually surprisingly helpful to think of the digit and Egyptian / Royal Cubit in terms of metres, however much certain researchers might like to disagree. The idea of a hypothetical unit of 25,920 ancient metres is intriguing.

The 39.375" 'metre' is just another subdivision of the 1,575,000,000" meridian circumference, and a third of it is Jim Alison's Northern foot of 13.125", which is Jim Wakefield's 13.2" inch Saxon foot x 175/176, 13.2 x 100,000 x 10/3 x 360 = 1,584,000,000. The question is always going to be what was the value for the meridian circumference in the first place? the 12" English foot relates to the 1,575,000,000" circumference, as 1,575,000,000 x 9 x 176 / (360 x 12 x 250,000 x 1.1 x 175) = 12, and the 0.729166667" digit is the 12" foot multiplied by 1.1, 175/176, and divided by 18.

Are all units of measure linked? The idea has come up in the work of various researchers recently. It was also a common idea in 18th century France. Bailly, Letronne, and Gosselin found in their research that many units of measure could be traced back to an accurate survey of the size of the planet, in particular to the length of the polar meridian. Paucton, also from the same period, wrote about various types of feet being already integer parts of a degree. He also says if you're designing a new system, you should really take one particular length for a degree and stick to it, or else it will be too confusing when people travel abroad. And he says that the project of post-revolutionary France in implementing a universal system of measure based on an exact division of the earth's meridian arc is actually the very same project that was undertaken in the "remotest antiquity", when the units designed were based precisely on a meridian degree.

Quote Paucton Voilà préciſément quel étoit le ſyſtême métrique des peuples dans l'antiquité la plus reculée . Cette partie de la légiſlation leur avoit paru mériter une attention particuliere . Ils fixerent d'une maniere irrévocable leurs meſures en les rendant dépendantes de ta grandeur d'un degré du Méridien . Ils en prirent préciſément la quatre cent millieme partie qu'ils appellerent , tantôt pied & tantôt coudée (...)
This is precisely the measurement system of the peoples of the remotest antiquity. This part of their legislation seemed to warrant particular attention. They irrevocably fixed their measures making them dependant on the length of a meridian degree. They tool precisely the 400,000th part, which they sometimes called foor, sometimes cubit (...)

Jim Alison recently wrote on GHMB:

The heart of Washington DC is defined by the NS sections 3-6 and the EW sections B-D. This forms a perfect square of 3600 x 3600 meters, or 10,800 x 10,800 Northern feet, with an area of 116,640,000 square Northern feet. I wonder where L'enfant was coming from with that?

Jim has done some amazing work on the city of Washington D.C., see here. He has found that the metre, albeit in its ancient form of 39.375", comes up in surprising places, for example in the US, where the metre was never actually adopted, despite the closeness of the founders of the country with the French revolutionaries who implemented the metre in France as part of their design for a new country. L'Enfant, who was responsible for designing the city of Washington, was of course French, and both a revolutionary anda trained painter at the French Academy, and trained by his father who himself wa a court painter. Jim Alison has shown that L'Enfant used a grid defined in metres to place his design for the city in.

In the same post, Jim Alison also wrote:

If, instead of saying the proposed metric system was based on the most recent, most extensive and most accurate global survey in the history of the world, they had said their proposed metric system was the same as the oldest system of measurement in the history of the world, would the rest of the world, or even the French, have considered adopting it?

One of my webpages about the global alignment of Teotihuacan, Washington DC, Stonehenge, Troy, etc., has to do with the street plan of Washington DC that was designed by Pierre L'enfant. Although the U.S. rejected the metric system, Washington DC, despite the diagonal avenues, is based on a due NS-EW street grid, and a metric grid, with NS lengths of 900 meters, and EW lengths of 1200 meters, defines the locations of the main buildings and monuments and the slopes, angles and distances of the diagonal avenues.

See his webpage here.

I wondered if you could extend Jim's grid slightly to the east to include the hospital / prison site, which is at the apex of on of the huge triangles in the city's design. In another post, I wrote about how if you superimpose a picture of Orion's Belt onto L'Enfant's plan, it forms a nice little trio with the other two more important sites: the White House and the Capitol. In the mind of a revolutionary, perhaps the place where 'broken' citizens go to get 'fixed' should be placed in an almost equally important part of the city as the Congress and President's House, one which is directly linked to them.You can then get a nice 2:1 rectangle, with an area of 259,200 square km. Again this number: 25,920, that I was imagining as a possible unit of measure that might make sense of the relationship between the digit of 0.72916666" and the Royal cubit of 20.625".

Here is my variation on Jim Alison's grid.

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