Happiness Interrupted

An Addendum To

Something Strange At The Parthenon

Table of Contents


Cubit Origins

Cubit Historic Record

A New Understanding of Metrology

Ancient Egyptian Reaction to this Metrological Confusion

Professional Remarks on Cubits

The Historical Record on Egyptian Digits

Coincidence with English Inches

The Architect Kha Rods

The Giza I Chambers

A Theoretical Ideal Cubit

The English Inch



STEP #1: Sometime in remote antiquity, somewhere in the Middle East, someone devised a method for dealing with circles:

He said there are 360 degrees, 21,600 minutes, 1,296,000 seconds in a circle.

This rule is true regardless of the size of the circle: one inch diameter or a million miles. As such it has no mathematical dimension.

STEP #2: Expressed mathematically, and true for all circles, the Circumference is equal to 2 Pi times the Radius, C = 2 Pi R, or, exchanging symbols, R = C/2 Pi.

If we divide this last number, 1,296,000, by 2 Pi, 6.28318531 . . ., we get a statement about the property of the radius of the circle:

The radius in length is 206,264.806 . . . units.

STEP #3: The number 206,265 is used by astronomers to estimate celestial objects that are at great distances. For example One Parsec is equal to 206,265 AU, where AU is the distance from the sun to the earth.

However, our interest is terrestrial, not celestial. We can take the number of units in the radius of a circle and massage it into a form that is much easier to manipulate. We do this by reducing the size of the number.

We can divide this number by 10,000.

The number 10,000 would not occur naturally, by itself. It is a number devised by intelligent mind.

STEP #4: The fact that 10,000 is so neatly suited to our goal makes it outstanding as an intelligent step in our process.

We get 20.626,480+ units.

This number is purely intellectual. It has no basis in the literal world. It is defined mathematically.

We should remember that this number is defined as a distance along the radius of the circle which constitutes our intellectual framework.

I shall now show why this is such a startling number.

STEP #5: 20.626+ is the length of a Royal Egyptian Cubit in English inches, now accepted in the scholarly world.

Within our ability to measure, the two numbers are identical, one an intellectual creation from long in the past, the other a measured length.

How could this be?

Such a coincidence can come about only if some created intellect put his finger into the mix many millennia ago. In other words, some superior intelligence in remote antiquity caused it to appear in this identity. It did not come about accidentally, strictly of its own ability. He defined the Egyptian royal cubit to be equal to this special length.

Note that this equality is recognizable only when defined by the English inch. (We also defined the radius of the earth by English inches. See Table at the bottom of this Paper.)

Cubit Origins

I had been using 20.625 inches for the length of the royal Egyptian cubit for decades. I cannot remember when I first started.

Other sources are:

Key to the Hebrew-Egyptian Mystery, James Ralston Skinner, David McKay Co., Philadelphia, 1876. He puts the Elephantine Nilometer cubit at 20.625 inches, page 27, but holds to 20.612 inches as his main authority. This last value (20.611) was published by Flinders Petrie as the measure of the Great Pyramid base, but that was in 1883, seven years later!

No better authority can be had than Flinders Petrie, who measured the Great Pyramid with exquisite care. As he says in his detailed report The Pyramids and Temples of Gizeh:

"On the whole we may take 20.62 ± .01 as the original value . . ." Note that this is a calculated average from his many measures, not a measured value.

In the December 1, 1887 issue of the American Journal of Archaeology H. G. Woods wrote an article on cubit dimensions displayed by an artist's palette. Although the palette was only 15 inches in length it was inscribed in such a way that he felt he could determine an actual cubit measure of 20.625 inches. He emphasized this dimension is his article.

Importantly, this is not a whole cubit but a cubit calculated from pieces that make up the palette.

In a book, A Popular Account of the Ancient Egyptians, in Two Volumes, J. Gardner Wilkenson, Harper and Brothers, New York, 1854, provides a list of cubits in Vol. Two:

We can see that Wilkenson provides 20.6250 inches for his measurement of the Elephantine Nilometer. But he differs from other sources, including that of Jomard. Woods uses Wilkenson as a backup to his claim of 20.625 inches for the length of the cubit, but we can see the disparity among the different sources.

John Perring became field manager for Operations Carried on at the Pyramids of Giseh in 1837, Howard Vyze, in Three Vol., James Fraser, London, 1840. However, I do not draw on his tabulations; I do not trust them as accurate. 

Cubit Historic Record

In spite of the numerous attestations nothing could be more troublesome to modern scholarship than the search for the source of the ancient cubit measure. The answers go from human body parts to catalogues of numerous guesses.

In a work entitled Arithmetical Books, From the Invention of Printing Till the Present Time, Taylor and Walton, London, 1847, written by Augustus De Morgan. He neatly defined the primary cause of modern confusion regarding ancient metrology. He stated:

"There runs through all these national systems a certain resemblance in the measures of length; and, if a bundle of rods were made of foot rules, one from every nation, ancient and modern, there would not be a very unreasonable difference in the lengths of the sticks."

I am indebted to John Neal for bringing this work to my attention. John published a treatise on www.world-mysteries.com, 2003, which expressed his effort to capture this mass of metrological confusion from the past. Unfortunately, John is also lost in this confusion. In a private exchange with him he refused to discuss the possibility of ancient Egyptian higher level of knowledge displayed in logarithms. http://www.egyptorigins.org/antecham.htm. Smoke and mirrors is a metaphor for a deceptive, fraudulent or insubstantial explanation or description. All Done With Mirrors, his personal explanation, http://www.secretacademy.com/, is published by Secret Academy, John's private outlet.

In support of De Morgan's remark Tim Lovett published a work on the Internet in April 2004. Tim is currently working for http://www.answersingenesis.org in Petersburg, Kentucky USA. His mailing address is  PO Box 510, Hebron, KY 41048. Here is his tabulation of the ancient cubit measure.

Approx Date

Greek Short










Roman "Cubitum"





Hebrew "Common"




1, 5






Egyptian (short)










Greek "Prechys"





Olympic (Greek)















Babylon "Ammatu"





Babylon (old) "kush"

"2000 - 1600" BC

500 (approx)



Nippur (Sumer)

2000 BC




English (Druid)





Hebrew (Ezekiel 40:5)





Hebrew (Jerusalem)

1 AD




Egyptian Royal "Original"


523.75 ± .25

20.62 ± .01


Egyptian Royal "Average"


524.00 ± .51

20.63 ± .02


Egyptian Royal





Mexico Aztec





Babylonian "kus" 

1500 BC  









Arabic (Black)

800 AD





700 BC  














Persian (Royal)





Arabic (Hashimi)





Germany (Prussian)





Northern Europe

"3000" to 1800 BC




1 = Henry Morris "The Genesis Record", 2 = Werner Gitt "The Most Amazing Ship in the History of the World", 3 = www.footrule.com, 4 = Encyclopedia Britannica, 5 = Revell Bible Dictionary, 6 = W M Flinders Petrie, 7 = http://it.stlawu.edu/%7Edmelvill/mesomath/obmetrology.html

Numerous other individuals have contributed to this discourse.

Tables of Ancient Coins, Weights, and Measures, John Arbuthnot, J. Tonson, London, 1727. (Arbuthnot was a close friend to Jonathan Swift, author of Gulliver's Travels.)

A State of the English Weights and Measures of Capacity, as They Appear from the Laws as Well Ancient as Modern; With Some Considerations Thereon; Being an Attempt to Prove That the Present Avoirdepois Weight Is the Legal and Ancient Standard for the Weights and Measures of This Kingdom, Samuel Reynardson, January 1, 1753.

The Ancient Cubit, Charles Warren, The Committee of the Palestine Exploration Fund, London, 1903.

Metrology and mathematics in ancient Mesopotamia', in Civilizations of the ancient Near East III (ed. J. M. Sasson), Powell, New York, Scribners, 1941-1958.

Weights and Measures, Their ancient origins and development in Great Britain up to 1855, F. G. Skinner, HMSO, 1967

Dictionary of English Weights and Measures, R. E. Zupko, University of Wisconsin Press, 1968.

Men and Measures, Edward Nicholson, Smith Elder and Co., London, 1912. He had this nonsense to say:

The readiest of these measures were those offered by the length of the forearm, and by parts of the hand; these formed a natural series of far-reaching importance. These arm-measures were --

    1. The Cubit, the length of the bent forearm from elbow-point to finger-hp, about 18 to 19 inches. 2. The Span, the length that can be spanned between the thumb-tip and little finger-tip of the outstretched hand It is nearly half of the cubit, about 9 inches. 3. The Palm, the breadth of the four fingers, one-third of the span, one-sixth of the cubit, about 3 inches. 4. The Digit or finger-breadth at about the middle of the middle huger, one-twelfth of the span, one-twenty-fourth of the cubit = 3/4 inch.

This idiocy has carried around the world by virtually all people who cannot accept a brilliant race were implanted here upon earth to guide primitive man from his animal origins to the higher levels we enjoy today. Because we lost that divine guidance we search for the origins that still abide with us. The ancient Egyptians were along that path of cultural travel. Charles Darwin led everyone to believe that man was a purely evolutionary creature who could think technically only in terms of human appendages. But Darwin did not give due credit to the fact that in ancient times, after mankind lost his divine guidance, the human race engaged in a wide intercontinental exchange of grains, jewels, food, hardware, and assorted other commodities. Economics forced him to come to common understanding of linear measure, along with weights, and so on. This morass gave us a metrological nightmare.

A New Understanding of Metrology

Peter Tompkins, now deceased, discussed the amazing coincidence of the 20.626,480+ mathematical number and the 20.625 inches per cubit in his book, Secrets of the Great Pyramid, Harper and Row, New York, 1971.

Even so (John) Taylor and (Piazzi) Smyth may have been on the track of a solution. Taylor suggested that the circumference of the earth had been measured in Ptolemaic feet and common cubits, whereas the polar axis had been measured in inches and sacred cubits. In his recent Historical Metrology Algernon Berriman supports Taylor's hypothesis by showing that whereas a "sacred" cubit of 25.064 inches is the ten millionth part of the earth's polar radius, a "royal" cubit of 20.6265 inches is a fraction of the circumference of the earth in that it is 206,265 sexigesimal seconds of arc: in other words the radius laid along a circumference of 1,296,000 seconds becomes a radian of 206,265 seconds. Page 207

In my original paper I pointed out that the polar radius of the earth was 250,000,000 inches. Berriman specified ten million polar "cubits" of 25,064 inches. Berriman agreed more closely with the astronomical data I had provided in my Table (250,265,313). I had used the word "Greek" feet whereas Taylor had specified "Ptolemaic" feet. Thompkins confuses matters in that he discusses the fraction of a circumference of the earth when he invokes 20.6265 inches, or 206,265 sexigesimal seconds, while I invoke radial distance, not radian seconds. I posit that the ancients recognized the difference between circumferential distance (Greek feet) and radial distance (Egyptian cubits). Thompkins does not discuss the reduction by 10,000 to reconcile the two numbers, which are identical. In fact, Thompkins may have had this connection revealed to him by some other unidentified person, who did not know about the difference between radian seconds and radial inches, and thus could not specify the fact of the 10,000 reduction.

Berriman wrote a very terse volume on metrology, sketching the similarity among ancient societies. (Algernon Berriman, Historical Metrolgy, Greenwood Press, New York, 1956, 1969.)

A reader may fault the nomenclature I use. When dealing with the dimensions of a circle I use "seconds"; when comparing distances found with measuring sticks I use "cubits" or "inches."

I would not ordinarily discuss the fact that the coincidence of weights and measures from deep in the past comes to haunt modern man. At one time on this planet we had a standard that was given to us from celestial planetary supervisors. With the breakup of that world administration we lost the common standard, each society groping to regain it but with no master rudder to carry us forward. Because weights and measures are a very practical business there was a cultural force that pushed us forward with a similarity from one segment of society to another. But the common understanding of metrology was lost.

Ancient Egyptian Reaction to this Metrological Confusion

The ancient Egyptians had an awareness of the intellectually defined radial distance, in cubit measure, which we identify as 20.625 inches. They not only were aware of its existence, they avoided its practical implementation. They did so fully aware of the confusion it would create for later students of Egypt. They were building an environment of awe. They had a peculiar method for avoiding direct acknowledgment of it. I shall show how they manipulated their edifices as a result. My illustrations include cubits, digits, inches, professional rods, and chambers.

Professional Remarks on Cubits

In 1877 Flinders Petrie published a book he called Inductive Metrology, Hargrove Saunders, London. He was 24 years old. His technical references included several from the British Museum, as well as from other geographical locations. He later referred to his work when he made comments considering the dimensions of cubits and digits, The Pyramids and Temples of Gizeh, Chapter 20, Section 141.

Since Egypt held many modern academic minds entranced, Petrie's 1877 investigations brought him to everyone's attention. He listed 28 Egyptian items, good, bad and indifferent, that showed the cubit ran from 20.42 to 20.84 inches in length, with an average of 20.64 inches. After he concluded his 1882 and 1883 physical pyramid survey he stated:

On the whole we may take 20.62 ± .01 (inches) as the original value . . .

He was now willing to specify what he believed to be the true Royal Cubit measure. I will show how he arrived at this value -- for the simple reason that he did not find it in any existing Egyptian structure or measuring rod.

Following is earlier Egyptian cubit data he classified in Inductive Metrology, page 50.





Damietta monolith . . .





Antinoe, triumphal arch




Siout, chambers




B. M. 113





Thebes, rock chambers




Antinoe, baths




B. M. 10 Alexandria





B. M. 582 (tablet) . .





Biban el Melouk, tomb IV.




Siout, chambers




Jeezeh Great Pyramid*





Bronze axe





B. M. 518





Jeezeh 8th Pyramid





B. M. 584 (tablet)





Jeezeh 5th Pyramid





Jeezeh 4th Pyramid .





Antinoe, column of Severus




Biban el Melouk, III. East




Biban el Melouk, V. East




Philae, East temple




Siout, chambers




Elephantine, Nilometer




Antaiopolis, monolith




Jeezeh 3rd Pyramid .





B. M. 525 Memphis





B. M. 42 Abydos .





B. M. 90 Greek





B.M. is British Museum (7). Jeezeh is Giza gathered from multiple sources (5). Other sources were identified in his tabular matter.

Petrie tabulated in ascending order. Clearly, we see that his cubit dimensions run continuously from 20.42 to 20.84 for a span of 0.42 inches, almost linearly through 30 mixed Dynasties. They are scattered over that range, not clustered tightly around a central value. The Egyptians deliberately added extra large range of values in different structures which appear to us as lack of Central Authority. But the almost linear scatter seems artificial, not natural. It does not follow a bell-shaped, Gaussian function, curve of random scatter. Since this runs over nearly three thousand years, from 3,000 BC to Ptolemaic times, and is so artificial in form, it means that the Egyptian people followed an unidentified intellectual force to produce such unnatural pattern through all those years.

This practice has confused generations of researches. It has led all following people to believe the Egyptians did not follow sound scientific principles. As a consequence everyone since has looked upon them as simpletons in their building and construction. Nothing could be farther from the truth. Petrie himself was not sure how to treat these discoveries. For example, if we put the Great Pyramid (Giza 1) base length at 440 cubits, which virtually everyone accepts, the cubit measure is 20.611 inches, not 20.625.

As I shall show, the value of the cubit over a period of more than 2,000 years, from Dynasty III (2700 BC) to the Thirtieth Dynasty (300 BC), from measure of monument and rods, was the same. Petrie's comment "that it slightly increased on an average by repeated copyings in course of time" is not correct. We also know that Petrie's conclusion that the result of the cubit is always within 1/50 inch of 20.63 and that of 20.62 ± .01 as the original value is correct but that his remarks about this background evidence is speculative. He just did not know how to handle it.

Petrie offered examples of the cubit lengths he discovered from his pyramid survey work. Note the scattered evidence as in the previous example.

Petrie's notes on Giza 1:

From The Pyramids and Temples of Gizeh

Cubit Length

In Inches

By the base of King's Chamber, corrected for opening of joints

20.632 ± .004

By the Queen's Chamber, if dimensions squared are in square cubits

20.61  ±   .02

By the subterranean chamber

20.65  ±   .05

By the antechamber

20.58  ±   .02

By the ascending and Queen's Chamber passage lengths

20.622 ± .002

By the base length of the Pyramid, if 440 cubits

20.611 ± .002

By the entrance passage width

20.765 ±   .01

By the gallery width

20.605 ± .032

Note Petrie's 20.611 value for the Great Pyramid if we assume 440 cubits base length. J. R. Skinner (above) in 1876 used 20.612 as his main authority.

Petrie could find no certain measure in the Second Pyramid.

Giza II

Cubit Length

In Inches

Tenth Course Level

20.82   ± .01

First Course Height

20.76   ±  .03

Passage Widths

20.72   ±  .01

Great Chamber

20.640 ± .005

Lower Chamber

20.573 ± .017

Petrie found the measure highly variable in the Third Pyramid.

Giza III

Cubit Length

In Inches


20.768 ± .015

Granite Course Heights

20.162 ± .017

First Chamber

20.65   ±  .10

Second Chamber

20.70   ± .05

Granite Chamber

20.74   ± .2

Arranging the examples geographically, Petrie states that the cubit used was as follows :—

Great Pyramid at Gizeh Khufu

20.620 ± .005

Second pyramid at Gizeh Khafra

20.64   ±  .03

Granite temple at Gizeh Khafra

20.68   ±  .02

Third Pyramid at Gizeh Menkaura

20.71   ±  .02

Third Pyramid parabolas walls Menkaura

20.69   ±  .02

Great Pyramid of Dahshur ?

20.58   ±  .02

Pyramid at Sakkara Pepi

20.51   ±  .02

Fourth to sixth dynasty, mean of all

20.63   ±  .02

Note by Petrie: 1. On the facade of one of the tombs at Beni Hassan there is a scratch left by the workman at every cubit length. The cubit there is a long variety, of 20.7 to 20.8 inches.

Piazzi Smyth (Our Inheritance in the Great Pyramid - 1877) always used a cubit length of 20.7 inches.

We can see from these multiple examples that there was a loose range of cubit dimensions in the pyramids, and in any one structure, from 20.1 to 20.84 inches per cubit. Petrie found that the mean of all his samples was 20.63. (He stated +/- .02 because of his statistical uncertainty.) These number did, indeed, include 20.625 inches as an average. If we had many more examples we would expect the "mean" to show an even tighter centering to 20.625. Importantly, the individual numbers did NOT sit on 20.625 inches.

We know from the work on Giza I that the architects could hold extremely tight control on their work. The displacement from true north of the Giza I case was measured by Petrie as -3'20", -3'57", -3'41", and -3'54" on the four sides. The greatest difference in angle among these was 37 seconds. This means that over 770 feet the Great Pyramid was built to a nearly perfect square. G. J. Oaten of Melbourne, Australia, who digitized Petrie's book, stated: After his extensive triangulation on the Giza plateau Petrie was somewhat taken back by what he uncovered and said of the Great Pyramid . . . a triumph of skill. Its errors, both in length and in angles, could be covered by placing one's thumb on them."

One cannot obtain such great accuracy if one cannot measure with equal accuracy. I conclude that lack of measurement control was not an accident of time and that other, human elements, altered the results we find today. The evidence is not what we would find in a natural system.

We would believe that Giza I, the most magnificent structure ever built, would be held to a certain statement of dimensions. We know from the excruciating work done by Petrie that it should show exact dimensions -- 440 cubits per side. As Petrie hoped when he circumnavigated the entire structure. Petrie was impressed. So are we. But the dimensions did not show 440 cubits, they showed something less. If the dimensions were 440 cubits the cubit had to be 20.611 inches, not 20.625. Giza I was short by 9075 - 9068.8 or 6.2 inches per side.

Can anyone familiar with the exact facts of the structure believe the architect did not know he was building to something less than the ideal? Consider the exact figures he used when he wanted to. He had to know. Then why?

It was at this point that I began to realize that the ancient Egyptians, and all those who followed, refused to build, or to imitate with statuary, dimensions that would be an exact duplicate of 20.625 inches. They were not scared of that value; they were in awe of it.

A most interesting fact is that the earliest Egyptian stone monuments (circa 3,000 BC) used the same variable cubit lengths as later monuments, in spite of the great design contrast displayed among contemporary structures.

Earlier I showed that H. G. Woods compared to then known rod and building lengths. He cited:

The Turin cubit is 20.611 inches. (This is Giza I cubit used by the Egyptian builders.)
The Louvre cubit is 20.591
The Nilometer cubit (Wilkinson) is 20.625
The Gizeh cubit (Petrie) is 20.632±.01 " (This is the King's chamber dimension cited by Petrie.)

Woods was not careful in his citations. For example, the Turin Museum rods run thus:

Turin Museum


Supplement #8391


Catalog #6349


        Surface B


        Surface C


        Surface D


Catalog #6348


Supplement #8647


Catalog #6347


Obviously there is no 20.611 unless Woods did not keep accuracy and meant Catalog #6347.

The Nilometer reading of 20.625 by Woods is a borrowing from John Gardner Wilkinson:

A Second Series of the Manners and Customs of the Ancient Egyptians V1 (1841), Kessinger Publishing, LLC (September 10, 2010)
(Including Their Religion, Agriculture, Etc., Derived From A Comparison Of The Paintings, Sculptures, And Monuments Still Existing, With The Accounts Of Ancient Authors. In Two Volumes)

This is what Wilkinson had to say:

The careless manner in which the graduation of the scales of the Nilometer at Elephantine has been made by the Egyptians, renders the precise length of its cubit difficult to determine; but as I have carefully measured all of them, and have been guided by their general length as well as by the averages of the whole, I am disposed to think my measurement as near the truth as possible; and judging from the close approximation of different wooden cubits, whose average M. Jomard estimates at 523.506 millimetres, we may conclude that they were all intended to represent the same measures, strongly arguing against the supposition of different cubits having been in use, one of 21 and others of 28 and 32 digits; and indeed, if at any time the Egyptians employed a cubit of a different length, consisting of 24 digits, it is not probable that it was used in their Nilometers, for architectural purposes, or for measuring land.

Wilkinson clearly struggles with the length of the cubit. As he says it renders the precise length of its cubit difficult to determine. But then he goes on to say that he thinks his measurements as near to the truth as possible. In other words, if measurements do not show a consistency he will force them to be consistent. He falls back on the values given by Jomard.

Edme François Jomard (1777–September 22, 1862) was a French cartographer, engineer, and archaeologist. He edited the Description de L'Égypte and was a member of the Institut d'Egypt established by Napoleon. In his writings he gave more honest examples of the Egyptian cubit:













Jomard gave the last value, 20.748, as the correct Nilometer reading. Wilkinson did not like that value.

From this history we cannot accept the article by Woods as accurate. Not only must we contend with variable cubit lengths but also the wishes of the experts.

In his 1877 book Petrie shows the Nilometer length as 20.79 inches. He may have borrowed it from Jomard, who gives 20.748.

All in all, we must be in deep distrust of the experts on measurement of actual structures and measuring rods.

The evidence suggests the Egyptians felt perfectly free to play around with their construction measurements as long as they avoided, but respected, the central design of a cubit of 20.625 inches.

They seemed spooked by the 20.625 dimension. They avoided erecting monuments exactly on that dimension. This phenomenon is displayed in both building dimensions, and in their measuring rods.

The Historical Record on Egyptian Digits

The digit, from about a dozen examples deduced from monuments, I had concluded to be .727 ± .001; here, from three clear and certain examples of it, the conclusion is .727 ± .002 for its length in the fourth dynasty, practically identical with the mean value before found. (Flinders Petrie Pyramids and Temples of Gizeh, Section 141.)

But compare this statement with the evidence he presented.

From Petrie's Inductive Metrology, page 53.






B. M. 777





B. M. 857





4M4/5ehallet monolith





B. M. 23





B. M. 800





B. M. 854





Siout Chambers





B. M. (Pirinet)





B. M. 62





B. M. 469





Jeezeh sarcophagus





Jeezeh 7th Pyramid





B. M. 70b





B. M. 826 Thebes





B. M. 27





B. M. 512





B. M. 153 Thebes





B. M. (16 + 52) Karnak





Most of his examples are from the British Museum.

We see the pattern of digits is similar to the pattern of cubits. They are scattered and not clustered around one central value.

When we take Petrie's value of 0.727 for the spacing between marks on the cubit and multiply it times 28 marks we obtain 20.356. Obviously this does not give us a cubit length of 20.625 inches.

Petrie meandered in his thoughts over this problem, Section 141.

As I have already pointed out the cubit and digit have no integral relation one to the other; the connection of 28 digits with the cubit being certainly inexact, and merely adopted to avoid fractions. Now these earliest values of the cubit and digit entirely bear out this view; 28 of these digits of .727 is but 20.36 ± .06, in place of the actual cubit 20.62 ± .01. Is there then any simple connection between the digit and cubit? Considering how in the Great Pyramid, the earliest monument in which the cubit is yet found, so much of the design appears to be based on a relation of the squares of linear quantities to one another, or on diagonals of squares, it will not be impossible to entertain the theory of the cubit and digit being reciprocally connected by diagonals. A square cubit has a diagonal of 40 digits, or 20 digits squared has a diagonal of one cubit; thus a square cubit is the double of a square of 20 digits, so that halves of areas can be readily stated. This relation is true to well within the small uncertainties of our knowledge of the standards; the diagonal of a square cubit of 20.62 being 40 digits of .729, and the actual mean digit being .727 ± .002. This is certainly the only simple connection that can be traced between the cubit and digit; and if this be rejected, we must fall back on the supposition of two independent and incommensurable units.

Petrie was following his predecessors in attempt to explain why the digit had no direct integral relation with the cubit. The diagonals of the squares was a childish approach to this problem. Neither was the Great Pyramid the earliest monument in which the cubit was found. Some other reason had to exist why the two were so badly incommensurate with each other. When we design measuring sticks or tapes we make the subdivisions suitable one to the other. Why did the ancient Egyptians not follow that natural practice?

For the same reason they did not permit an actual structure measurement unit be equal to 20.625 inches.

If we were to rigidly define the spacing between marks on a cubit we would force acknowledgment of the length of the cubit. Thus we would bring the entire system back to acknowledgment of a standard, and that standard would be 20.625 inches per cubit. Since the ancient Egyptians would not accept open admission of that value they were forced to a "floating" expression of the distance between digits. That is what the evidence shows.

Coincidence with English Inches

Earlier I several times mentioned the coincidence between rod length intervals and integral English inches. This coincidence depends on the length of a royal cubit of 20.625 inches and division into seven palms to give an interval of 2.946 inches, a palm difference of 0.054 (1.36 mm) from 3.0 inches. This was a consequence of the length of the royal cubit being close to 21 inches. Following is an illustration of nine rods from the Italian Turin Museum and Petrie's London Museum. Two of these are "short" rods. (A "short" rod is one palm shorter than a regular length.)


Turin #1

Turin #2

Petrie #6

Petrie #8

Turin D

Petrie #1

Petrie #9

Petrie #10

Petrie #11

Rod Length










Palm Length










These "short" rods should not be confused with a regular rod with six palms (long palms). Such a palm is ideally 3.438 inches in length, a difference of 0.062 (1.57 mm) from 3.5 inches. Thus the 3.0 inch and the 3.5 inch palms are both within 1.6 mm of the ideal English measure. One can see the proximity in the graphical plot of palm lengths above.

This proximity causes one to wonder if the ancient Egyptians somehow were trying to avoid the English measure, just as they avoided the cubit of 20.625 inches. One becomes more suspicious when all measuring rods, and palm lengths, were so scattered. Did the Egyptians intentionally create rods and palms that were intentionally amiss of an ideal standard, so that no two seemed to agree with one another? Were they afraid of creating a standard? A graphical plot of the differences around 20.625 cubit length shows an apparent random distribution. No causative assignment to the differences is evident except manufacturing carelessness (or manufacturing intent). Evolutionary drift over time in any one direction is not indicated, since this "manufacturing sloppiness" seems to follow all social eras.

As I shall show, this apparent purpose of avoidance of the true cubit goes back into time with the first stone monuments of the Third Dynasty. Again, the Egyptians were avoiding that magical number.

The Architect Kha Rods

I shall now consider the cubit rods of Kha, architect to Amenhotep II, 7th Pharaoh of Egypt's 18th Dynasty, circa 1400 BC. We have two rods from the same source.

Read more:

Specimen #1: Turin Museum Supplement # 8391. Folding wood rod, hinged in the center, from the funerary chamber of the architect Kha, found in its original leather case. No hieroglyphic dedication. A typical cross-sectional shape of five surfaces with a bevel face. One scale inscribed on three sides -- B top, bevel face, and front. This was truly a working-man's rule.

My thanks to Marcella Trapani of the Turin Museum for the information about the leather case.

Rod Length = 20.81 inches -- Palm mean length = 2.973 inches -- Digit mean length = 0.737 inches.

Hinge spacing = 0.014 inches.

Marked off in palms with the right-most palm divided into one-half palm first and then 2 digits from the end. The left-most section has palms 6 and 7 combined into one length.

This working rod length exceeds the royal cubit of 20.625 by 0.185 inches (4.7 mm).

This is probably the best example of a working rod, but the lack of inscribed digit subdivisions would make it impossible to use in fine measurements.

As one can readily see, the rod was an extra long "cubit."

A question naturally arises: did this extra-long cubit dictate the "working" length of all cubits supervised by Kha? Was this his method for avoiding a true cubit of 20.625 inches?

If he was the Pharaoh's supreme supervisor for all construction projects, and if this was his working cubit, then all projects came under this length supervision.

Compare this cubit length with an ideal rod of 20.625 inches.

I shall now illustrate with the famous bronze Royal Cubit rod from Kha in the Turin Museum #8647.

The left photograph shows the cubit rule covered in gold leaf - it was a personal gift from Amenhotep II. Kha's scribal pallets and a writing tablet are beyond the cubit rule on the right. The folding cubit rod is on the left partially outside the photograph. The right photograph shows an instrument of unknown use. Someone has speculated that it was used as a protractor. A section of the folding rod protrudes from the right.

Hieroglyphic inscriptions cover the two ends and four sides of the gold-covered rod. The front contains the measurement scale. The division of the digits into subdivisions, starting with 2 and progressing to 16, is from the left end, not the right as usually found.  (Was Kha left handed?) Digit 12 is divided into 14 subdivisions instead of 13. The following digits pick up correctly. The digits were inscribed to 15. Digit 16 is divided into two parts, top to bottom. Thereafter 3 palms were not subdivided; the total length would make 28 digits. The total length of 20.632 inches exceeded the Royal Cubit length by 0.007 inches, hardly discernible in a practical sense. (.737/16 = 0.046 inches spacing between lines on the finest division.) This rod meets the ideal Egyptian digit length of 0.737, and the ideal palm length of 2.946 -- within ability to measure. We might say this rod is within the ideal boundaries --  but not quite.

Why would a gift from one's king contain a mistake in scales on the face of the cubit? Was the man who created the rod that sloppy? Remember, Kha was the king's architect. He probably was the best the king could find.

Compare the two rods: 20.81 inches with 20.632.

The gold covered bronze rod is nearly perfect in length. Perhaps the 0.007 extra length is due to the gold leaf that covers the rod. If so we would have an example of a perfect cubit. Then the Egyptians of 1400 BC knew and respected that length.

But if we take the hinged rod it is extra long, on a working man's rule. Did Kha not realize that he had two rods with different lengths? Or did he accept one as a memento to perfection, while he accepted the other as a working measure. Did he know that he had to work to that imperfection as an acceptance of a way of avoiding an imperfect length in the over-control in measure? How else would we explain the difference from the perfect rod to the imperfect one? Except we throw Kha and his society back into the conundrum of primitive practices.

The Egyptians knew what they were doing, and did it with willingness. Kha preserved the gift from his King as a token of the perfection they avoided in practical application.

Three Turin rods were first discussed in detail by Richard Lepsius in 1865: the wooden Amenemipt rod, the green-black basalt rod, and the Kha bronze rod. Die Alt-Aegyptische Elle, R. Lepsius, Berlin, 1865.

The attempt by Lepsius to derive a standard rod from these New Kingdom rods greatly influenced generations of Egyptologists. As he stated:

"Yet it cannot be doubted that the ancients were able to make accurate measurements and possessed precise yardsticks, which could not be changed arbitrarily; it is curious that not a single one of these has yet been discovered. The question now is whether the subdivisions in the preserved specimens allow us to reconstitute this exact standard."

But this remark is not correct. We know, if we assume the bronze rod was covered with gold leaf, that the bronze rod should have been cut to the exact length of 20.625 inches.

Otherwise the assessment by Lepsius has not been seriously altered in the past 150 years. We are still uncertain of the design of exact practical working rods. The evidence speaks to manufacture of rods that seemingly were arbitrary in their lengths. In other words, Royal Administrations did not define Measurement Standards to any identified rules. The concern of Lepsius was further expressed in his struggle to find a reason for division of the standard cubit into 7 parts, and why there were "great" and "small" cubits. He asked:

"It is also obvious how improbable it would be that one would have used a shorter cubit alongside the 'royal one' at the same time and in the same place, the difference between these construction cubits being the width of a palm..."

"Whence the unnatural and impractical partition, (into 7 parts), which allows for only one integral subdivision of the cubit without fractions of a palm? . . . The assumption that the great or royal cubit, not just the small one, would have been divided into only six palms seems so much more probable to me."

Lepsius could understand why there would be six and seven palms in a cubit, but not why there would be a short cubit.

An attempt to show evolution of cubit rods is hampered by the great differences among extant examples, lack of examples from early Egyptian history or the predynastic period, and lack of long-term continuity that we can reliably follow. My emphasis here is on the conceptual logic behind the odd cubit designs. The contrast between the working rod of Kha and the so-called ornamental rods is a dramatic illustration of how confused our understanding has been. The prominent position of the ornamental, seemingly followed by most researchers, may be due to their exciting nature and consequent preservation, while working rods were mundane without attributes of note, and hence not preserved. We today might quickly forget an ordinary tape measure while a gold pocket watch would garner much care.

The data is so scant that we cannot form firm conclusions. We cannot help but be led to the fact that something is misunderstood in the historical record. If cubits had such meandering lengths one could not place within them digits or palms with fixed standards. We can understand why Petrie was so confused by the evidence.

The Giza I Chambers

The Queen's Chamber has dimensions of 205.68 mean inches along the east wall and 206.02 on the west wall. This is a nominal dimension of 10 cubits -- but a little short.

Because the King's Chamber has garnered so much attention by later observers, and because it seems to have been built as an example of cubit definition, I shall give it attention here.

Petrie noted that the "whole chamber is shaken larger." He examined the amount of change at the second course. He then said that "these quantities must be deducted from the measures, it order to get the true original lengths of the chamber."

He based this on his assessment of an earthquake disruption that took place in the chamber.

(Someone had hand dubbed plaster several places in the chamber. Petrie felt that this action had been done while the chamber was under construction, not by later visitors from the modern era.)

Petrie goes on to remark that "we have the following values for the original lengths of the chamber."







Petrie Top






Divide by 20.625






Divide by 10 and 20












Petrie Mean






Divide by 20.625






Divide by 10 and 20












Petrie Base






Divide by 20.625






Divide by 10 and 20






By "mean" Petrie did not intend an average between top and base, but some other position up the side walls, perhaps the second course. We can see the enlargement of the chamber from top to bottom.

He reported the angular displacement of the walls with respect to one another, to show how the entire chamber was rotated around some displacement axis. This was slightest at the top and largest at the base, from one minute at the top to nearly five minutes at the bottom.

Petrie tells us he used the base of the walls, not the mean or top, to calculate his value for the cubit. Petrie gives 20.632 +/- .004, using only the base measurements. Summing the four base lengths and dividing by 4 (82.525 / 4) we obtain 20.631. Apparently he took the sum of the four sides at the base and divided by four to obtain an average. The error he reports must come from calculation of his measurement error to give him 20.628 to 20.636. Thus we see that his values could be very nearly the ideal of 20.625 and must come from the enlargement he observed.

His measurement resolution is in hundredth of an inch over 400 inches. Pretty good I will say.

Using 10 cubits for the E and W walls, and 20 cubits for the N and S walls these average overall to

Average sum of all walls at all levels yields 82.471 / 4 = 20.617

Using 20.625 the error is 20.616, over all, almost identical to the 10/20 result.

In fact, the values obtained by averaging all measurements including higher on the walls actually yields lower cubit numbers. I do not understand how Petrie could have rationalized these smaller numbers into the "whole chamber is shaken larger."

The south and west numbers suggest that the chamber actually collapsed in on itself during earthquake activity, but the value is very small. (The number is 0.008 cubits, average.)

His choice for base measurement was strictly personal based on his intuition of the past history of the chamber. He may have gleaned it from the condition of the northern and eastern end, which led him to believe an enlargement had taken place.

We see that whether we use a divisor of 10/20 or 20.625 the results are very nearly or exactly the same. This is because the chamber was held so nearly to 10 by 20 cubits.

If we return to the widespread dispersion of the cubit shown in the tables above we see how well the builders held the King's chamber to the ideal of 20.625 inches, perhaps modified by earthquake activity.

As I stated, if the builders were in awe of the 20.625 dimension, why did they include it in the Giza I chambers? They did not include it in the over all length of the Giza I pyramid. Many other places show where they purposely avoided it. What made the interior of the pyramid different?

For a very simple reason: They did not include it IN the chamber; they included it in the ABSENCE of that value. They were not creating that dimension; they were creating the absence of that dimension. The King's chamber was a hollow reflection of the 20.625 dimension. When Petrie used his measurement sticks in the King's chamber he was pressing outward against a solid substance, not inward against that solidity.

The Egyptians would avoid 20.625 inches in a structures outward appearance, but not in a hollow representing that dimension. This shows us something about the mentality of the Egyptian society.

To make a more complete account I offer the following. Petrie reported the absolute levels of the King's chamber in inches with respect to the pyramid exterior pavement:

This permits calculation of the diagonals of the King's chamber.  Because of the erratic floor levels, differing by two inches, some uncertainty exists in arriving at the intent of the architect in sizing the height. Calculating the differences:

we can arrive at a number that makes mathematical sense. If we use 11.18 cubits, midway in these values, we find that the diagonal measure across a short end of the chamber from floor to ceiling is 15 cubits. We also find that a diagonal across the entire chamber from a floor corner to an opposite ceiling corner is 25 cubits. (152 + 202 = 252)

There is certainly no magic in these numbers and would have been included only because the architect did not want to waste space. He chose a convenient height to provide reaffirmation of his mathematical knowledge.

A Theoretical Ideal Cubit

Take the value of a rod of 20.626 inches.

Divide by 28 to obtain a digit length of 0.7366 inches.

Divide by 7 to obtain a palm length of 2.946 inches.

Divide by 6 to obtain a long palm length of 3.438 inches.

Compare with the tabulations from Petrie, Kha's Gold rod, and others given above.

Clearly we see no obvious reason why the digits, palms, and length should not be fixed with one another.

Lepsius in 1856 put it plainly: it is curious that not a single one of these has yet been discovered. For more than 150 years that consensus has not changed.

As Petrie in 1883 put it: As I have already pointed out the cubit and digit have no integral relation one to the other.

Petrie then tries to find a relationship in the squares of diagonals, and continues with This is certainly the only simple connection that can be traced between the cubit and digit; and if this be rejected, we must fall back on the supposition of two independent and incommensurable units.

Anyone in this civilized world who has used measuring sticks knows that the divisions are directly and tightly related to the total length: everyone. Why did the ancient Egyptians void a rule that is so natural?

They were forced to these strange manipulations by the simple fact that they did not want to admit the open acknowledgment of that mysterious and magical length we know as 20.626.

Otherwise why would they build the greatest building in the world, with such tight control, tighter than any building since, and give it 20.611 inches per cubit instead of 20.626?

Lepsius then wanted to know why those ancient Egyptians would devise a short cubit of 17+ inches. "It is also obvious how improbable it would be that one would have used a shorter cubit alongside the 'royal one' at the same time and in the same place, the difference between these construction cubits being the width of a palm . . ."

The difference was an exact palm, 20.626 inches - 2.9466 inches = 17.6794 inches.

For a simple and practical reason: When they were building an edifice they did not need to bother themselves with the length of a regular cubit of 20.626 inches. All the builders had to do to avoid 20.626 was multiply 6/7.

As Lepsius said: "The assumption that the great or royal cubit, not just the small one, would have been divided into only six palms seems so much more probable to me."

Lepsius was part way there. Unfortunately, in spite of his tremendous technical contribution to our understanding of Egypt, Petrie was not; he went off into mathematical meandering.

The English Inch

We began this paper with the fact that we could not understand the Egyptian construction design elements unless we first admitted the English inch. The sexagesimal 20.626 theoretical divisions of a circle were identical to the English 20.626 inches in one Egyptian Royal Cubit. That Egyptian cubit had to be created at the same time as the theoretical divisions of the circle -- both of which admitted the underlying English inch. In other words the Egyptian standards of measure had to originate at the beginning of our civilized time keeping, prior to Sumerian or Babylonian or older Mesopotamian culture.

We also established that the Egyptian culture shied away from open acknowledgment of that cubit length. This habit seemed to follow the Egyptian culture for more than two millennia. Not until the reasons were lost in the habits of the following people, i.e. Ptolemaic Egypt circa 300 BC. By that time all of western culture got lost in the mud of metrology. From that point we began to invent ways to recover the lost recognition -- a confused cultural practice that we never fully came to grips with.

Until we invented the metric system, which was a poor and inadequate substitute. Simply because it was a piece meal replacement for a former integrated civilized system that combined length and weight and volume and time.

Many people in the modern world, from the past few centuries, clung to the inch as the solution to the Egyptian pyramid puzzle. But not the regular inch - something they called the Pyramid Inch. They must have had an unconscious recognition or intuitive feel for the secret that lies behind the ancient Egyptian experience. But this belief in the Pyramid Inch is now denied wholesale by the modern scholarly world.

http://www.touregypt.net/featurestories/pyramidinch.htm The Pyramid Inch and Charles Piazzi Smyth in Egypt, by Jimmy Dunn.

This following text is borrowed from http://en.wikipedia.org/wiki/Pyramid_inch.

The first suggestion that the builders of the Great Pyramid of Giza used units of measure related to modern measures is attributed to Oxford astronomy professor John Greaves (1602–1652), who journeyed to Egypt in 1638 to make measurements of the pyramid. His findings were published in his Pyramidographia and under his name in an anonymous tract.[1] More than a century later, Greaves' measurements and additional measurements made by French engineers during Napoleon's expedition in Egypt, were studied by John Taylor (1781–1864). Taylor claimed that the measurements indicated that the ancients had used a unit of measure about 1/1000 greater than a modern British inch.[2] This was the origin of the "pyramid inch". Taylor regarded the "pyramid inch" to be 1/25 of the "sacred cubit" whose existence had earlier been postulated by Isaac Newton.[3] The principal argument was that the total length of the four sides of the pyramid would be 36524 (100 times the number of days in a year) if measured in pyramid inches. Taylor and his followers, who included the Astronomer Royal of Scotland Charles Piazzi Smyth (1819–1900),[4] also found numerous apparent coincidences between the measurements of the pyramids and the geometry of the earth and the solar system. They concluded that the British system of measures was derived from a far more ancient, if not divine, system. During the 19th and early 20th centuries, this theory played a significant role in the debates over whether Britain and the United States should adopt the metric system[5].

The theory of Taylor and Smyth gained many eminent supporters and detractors during the following decades, but by the end of the 19th century it had lost most of its mainstream scientific support. The greatest blow to the theory was dealt by the great Egyptologist Flinders Petrie (1853–1942), whose father was a believer. When Petrie went to Egypt in 1880 to perform new measurements, he found that the pyramid was several feet smaller than previously believed, including the missing capstone. This so undermined the theory that Petrie rejected it, writing "there is no authentic example, that will bear examination, of the use or existence of any such measure as a ‘Pyramid inch,’ or of a cubit of 25.025 British inches."[6]

The value of 1.00106 British inches is calculated as 1/500,000,000 of the Earth's polar diameter. The pyramid inch now appears to have no significant scientific support. No direct evidence for it has ever been found, so pyramidologists argue from an increasing list of alleged numerical coincidences.

1. J. Greaves [probably not the real author], The origin and antiquity of our English weights and measures discover'd: by their near agreement with such standards that are now found in one of the Egyptian pyramids: together with the explanation of divers lines therein heretofore measur'd (London: Printed for G. Sawbridge, 1706).
2. John Taylor, The Great Pyramid, Why Was It Built? and Who Built It? (London, 1859).
3. However Newton's value for this cubit was somewhat shorter; see Peter Tomkins, Secrets of the Great Pyramid (London: Allen Lane, 1971), p. 30–31.
4. C. Piazzi Smyth, Our inheritance in the Great Pyramid, with photograph, map, and plates (London, 1864).
5. E. M. Reisenauer, "The Battle of the Standards": Great Pyramid Metrology and British Identity, 1859-1890, The Historian 65, no. 4 (Summer 2003): 931–978; E. F. Cox, "The International Institute: First organized opposition to the metric system" Ohio History v. 68: PP. 54–83 [1].
6. W. M. Flinders Petrie, The Pyramids and Temples of Gizeh (London, 1883), p189 [2].

We should examine these remarks. If we take modern satellite measurements and do elementary calculations upon them we can quickly see where the above assessment holds true and where it is in error.

For example, Pertrie's measurement of 9068.8 inches per side X 4 on the Great Pyramid = 36275.2. This is less than 36524, 100 times the number of days in a year, by 248.8, certainly a significant amount. We would not accept this pure guess work as a reasonable element in any metrological system. Then the above writer uses it to illustrate how the ruminations of Greaves, Newton, Taylor, and Smyth, were in error.

But he slips into a quick sidestep to support his argument. If we take the supposition that the ancients had used a unit of measure about 1/1000 greater than a modern British inch they would have arrived correctly at the earth's polar diameter. See in the Table below that 250,265,313 divided by 1.0010613 yields exactly 250,000,000. Refer to his statement above that "The value of 1.00106 British inches is calculated as 1/500,000,000 of the Earth's polar diameter."

He used the Polar Radius from the scientific measure listed in #4 the Table below. If he had slid his eye across the Table to Equatorial Radius Of Curvature he would have found 0.997704, and this would have given him less than 250,000,000 parts in the radius calculation. More importantly, the Equatorial Radius Of Curvature is the one more familiar to someone living near the equator.

Refer to http://wiki.gis.com/wiki/index.php/Longitude

        (The radii of curvature are equal at the poles where they are about 64 km greater than the north-south equatorial radius of curvature because the polar radius is 21 km less than the equatorial radius.)

That is how we arrived at the "Pyramid Inch." It was strictly a fanciful creation, depending on how we interpret the measurements and because it was so close to the reality of a perfect circle.

If Greaves, Taylor, and Smyth misunderstood their physics they conditioned generations to error.

The above writer then wrought the opposite error. How unfortunate.

We can tabulate the several connections to the Earth circumferential length and Earth radial length.

1. Take the defined radial distance and divide by the theoretical relationship between the Egyptian system and the Greek system, 20.626/1.7, and we get 12.133, the Greek foot.

See #8 in the Table below.

2.a The planet equatorial distance of 1,577,753,259 English inches divided by 250,000,000 = 6.311013, or 2 Pi (6.28318531) within 0.0278277.

2.b The planet polar distance of 1,575,109,406 English inches divided by 250,000,000 = 6.3004377, or 2 Pi within 0.0172524.

or inverted

2.c The planet polar distance of 1,575,109,406 English inches divided by Pi (6.28318531) = 501,372,895.7 divided by two = 250,686,447.9.

3. From the Parthenon range of measures of 1213.69 to the defined Nautical Mile of 1215.22 inches we can compare equatorial and polar circumferences divided by the sexagesimal values:

4. If we take the various radii divided by 250,000,000 we obtain 0.997704 to 1.0044289, #4 in the Table below.

All of this groping around was to make us familiar with the metrological problem that we face -- the English Inch.

We cannot come to grips with this problem unless we start at the beginning -- where it starts. Clearly it starts at the beginning of metrological time, at the beginning of civilized time.

But then our genii (or genius) put it into a framework that forced us to recognize his hand -- at the beginning of civilized time keeping.

That civilized time keeping began with a coordination of structural elements that included the English Inch, the Egyptian Royal Cubit, and the sexagesimal circle. We found the last in the structures of 500 BC, when the Greeks resorted to methods that remembered the sexagesimal component.

You will find remarks scattered here and there about a Divine Hand introducing itself into our civilized language. That was the hand that came down to us through the long spread of time --thousands of years.

All of these memories had to be placed in the script of metrology at the beginning of civilized time. Not only sexagesimal definition of the circle, which we all admit, but also the Egyptian Royal Cubit and the English Inch. When Petrie wrote his Pyramid book in 1883 he could not then commit himself to the Egyptian Royal Cubit prior to the first dynasties. He still considered Egypt as an evolutionary phenomena. But the Egyptian Royal Cubit has to go back in time -- way back in time. Now we know that the English Inch also had to go back in time -- way back. Regardless of the route it followed, down through Anglo-Saxon ages, it was held constant by all those people. Otherwise we would not retain the metrology record preserved through all those ages.

But an even more important phenomenon attaches itself to this long hidden record: that it should be recovered only now at the end of our age.

Yes, this is the memory of a Divine Influence that we lost long, long ago.

God is bringing himself back into relationship with man. He lived here 2,000 years ago. And died in a stupendous price that we would remember.

Only now are we recovering the metrological memory. But we must pay an equal stupendous price.

Ernest Moyer






















Radius Of



Radius Of




































#3 Divided


250 million





(2 Pi)


(2 Pi)




#3 Divided

by Circum.

Sec of Arc




(100 GF)

(Greek Feet)


(100 GF)




#3 Divided

by Radial

Sec of Arc



(100 GF)


(100 GF)


(100 GF)



(100 GF)


(100 GF)




#3 Divided

by 20.62 in.

Royal Cubit










20.62 Divided

by #6 X 0.01