It has long been realised that there were apparent relationships and common pedigrees within systems of metrology adopted by several early and late era civilisations of the Middle East, Near East, Mediterranean and Europe.
A drove of researchers have commented on this and have attempted to identify the original system from which a raft of latter, regional systems were derived.

Particular numbers and ratios tend to recur in grain weights, cubic capacities and length increments between cousin civilisations. The foundation numbers for each system are, on the surface, large, complicated looking values and few researchers have any inkling as to why such cumbersome numbers were initially chosen in the first instance. For the foundation numbers of any system, the ancient metrologists used numbers with many factors. This is a point not often grasped by researchers. Such numbers often appear cumbersome when expressed in decimal (base ten) form, which is generally unsuitable for them. We shall express them in terms of their factors when convenient.

To understand the numbers one must first delve into the astronomical and navigational sciences developed in antiquity and come to the realisation that the values incorporated into a length, weight or volume were for mnemonic reference to such things as the "size of the Earth" or perhaps the "cycle of the moon", etc.
Once one knows this, then the ancient standards of the Sumerians/ Babylonians, Egyptians, Hebrew/ Phoenicians, Greeks, Romans, Celts/ Norse/ Gaul's/ Iberians/ Britons and others of these people who scattered abroad to distant colonies, can be understood, restored to full integrity and shown to be of a common origin.

Over time small amounts of drift and error might well have occurred in the standards of inter-bickering nations, but the important factor was that these nations of cousin peoples had their systems fashioned on the selfsame parcel of original base numbers. The numbers were derived from an earlier, very sophisticated system found encrypted into the pyramids of the Giza Plateau.

Far from these systems developing over time and getting progressively more sophisticated, the evidence clearly suggests an international system of metrology that started out as a full, scientifically complete construct, which, if anything, was in decline by the time the Christian era dawned. With the coming of Roman Christianity the formerly advanced sciences of metrology were systematically and deliberately eradicated and, those civilisations forced to embrace Roman state Christianity, were delivered into the "dark ages" by the loss of knowledge contained within traditional metrological systems.

The original system covered all contingencies and used the full range of base numbers from 1 to 12 (or progressions of 13 in some calendar counting), including the ratios PHI & PI. By the dawn of the Christian era some civilisations in decline were seemingly using only limited portions of the overall, earlier system for their national measures, weights, volumes and area standards.

For several centuries archaeologists have attempted to reconstruct the regional standards of past civilisations by taking measurements within ruined remnant structures, measuring capacities within surviving amphora vessels, or by analysing the decipherable meanings within ancient inscriptions and texts. From this endeavour a reasonably healthy dossier of information now exists and we have a fair or close knowledge of the measurement increments, weights and volumes preferred by particular civilisations. In most instances the final, officially accepted figure, as to what constituted the national standard in use during a particular epoch, is based upon averages.
Scientists have, for example, weighed large batches of coins, such as the Roman Silver Denarius, (1/50th of a Roman pound) to arrive at an average weight for the Roman "pound".

IN QUEST OF THE ORIGINAL STANDARDS.

The main book of reference in this study will be Ancient Metrology, by Donald Lee Lenzen, published in 1989, and it comes highly recommended for those engaged in comparative analysis of ancient standards.
Mr. Lenzen devoted ten years to his study of systems of metrology used by the great civilisations and gathered clues from widely diverse sources including artefacts and ancient quotations. He also took a fully scientific approach to his work and based his final conclusions on measurement, weight and volume averages. In a few instances fully intact sets of weights, which had formerly been the official "standards" for an entire advanced civilisation or merchant assayers, have survived and can be used to indicate the standard.

This study will show that with very minute, visually undetectable and reasonable, modification to "official" length and volume "averages" or an adjustment of "a few grains" to a "weight standard" artefact, one is delivered into a stream/ progression of numerical values that relate to astronomy, navigation, etc.
The original "grain" weight found in sets of weights was based upon a wheat seed. Counts of barleycorns were also used for reference to the grain weight of the Hebrew gold Shekel, whereas carob beans became the medium, at some latter era, for "jeweller's weights" (carats) in weighing out quantities of precious gems and gold.
Grain weight, as a set ancient method for arriving at a weight standard, was derived from counted quantities of healthy wheat seeds and the original stone or metal "scale weights", used by ancient traders, merchants or official assayers were first determined by counting out exact numbers of wheat seeds. Although some Mediterranean gold coins, such as the heavy and light Hebrew Shekels were also compared to specific numbers of "barleycorns", their measured weights show implicitly that they were, first and foremost, based upon specific numbers of wheat grains…consistent with all other weight systems of the ancient Mediterranean.

LET'S TRY TO LOOK AT THIS LOGICALLY AND SET SOME PRELIMINARY GROUND RULES!

The process of unravelling the ancient Mediterranean/ European metrological standards of Weights, Volumes, Area and Length measurements is daunting, and no-one has been wholly successful in accomplishing this task thus far. In order to succeed we have to try to put ourselves into the mindset of the ancient mathematicians. We have to try to double-guess what they were trying to accomplish in choosing the difficult numbers that they deliberately incorporated into their Weights and Measures standards.

Some years ago, in conversation with a friend, Tom Brown, former director of Borderland Research Foundation, he made an incisive, but limiting observation about many modern scientists. His generalised estimation of them was that they 'were good at measuring things'. Tom's somewhat sardonic comment was suggesting that the, "what you see is what you get", clinical approach of many scientists doesn't necessarily translate into gaining a full understanding of what's going on. More lateral thinkers, using the precise, cold, clinical facts accrued by scientists, often have a better chance of making a correct, overall evaluation of the evidence. So, with a little sprinkle of lateral thinking let's assess known facts about ancient systems of metrology using the following terms of reference:

• The ancient mathematical, astronomical and navigational sciences were in a high state of development when the known systems of metrology were put in place many thousands of years ago.
  
  
• The systems of metrology that were used by individual nations of the Mediterranean Basin and Europe did not develop in isolation, but had a common pedigree or root source, from which all regional systems stemmed.
  
  
• Numerical values chosen for weights or measurements, within the systems of individual civilisations, were in perfect ratio to each other, with no arbitrary or orphan values. The system used by any one nation of the ancient Mediterranean/ European theatre was also in a perfect and easily calculable ratio to the preferred systems of neighbouring nations.
  
  
• Each nation encoded into their weights, measures, volumes and chronology standards, highly scientific information about such things as the true equatorial circumference of the earth and principles of navigation for successful intercontinental voyages. The systems encoded cyclic information related to the sun and the moon, from which accurate calendar systems were maintained.
  
  
• The measurement systems were based, first and foremost, upon the equatorial size of the Earth, reducing to smaller incremental values, in families of numbers, down to small denominations. The number families were, primarily, founded upon "6 & 7" increases working in unison or separately, an "11" series of navigational numbers, individual cubits that related to 3 closely associated readings of the size of the Earth and a PHI series of numbers for special measurements.
  
  
• Identification of the number system that the ancient mathematicians wished to encode shall be the primary quest of this study and rate as more important than the true or actual "official" weight, volume or length found in a surviving weight standard artefact, volume vessel or measuring rod. Although there will be reasonably strict adherence to the "official" measured attributes of artefacts, very miniscule (almost undetectable) variations to averages shall be deemed allowable. Ancient scientists, creating a weight standard, would count out specific numbers of wheat seeds (like 933120* to create the Sumerian/ Babylonian Talent weight…our quest shall be to find the "intended number" of seeds for each division within a weight system or the "intended volume capacity" value to be found in an amphora vessel. It will be demonstated that the "correct" numbers found in weights and volumes were highly important to navigation, the equatorial circumference of the Earth or the duration of celestial cycles. The necessity of using the "special" numbers in all trade and daily transactions kept the highly important values eternally alive and at the forefront of memory. Lenzen provides the very best averages that 10-years of intensive research could identify. This study will attempt to show how a fully integrated mathematical system lies very close to Lenzen's estimates.

* Footnote: 933120 is an excellent example of an abundant number in ancient usage, being 28 × 36 × 5.

GRAIN WEIGHT & THE INCH.

A functioning, flourishing civilisation must have a traditional "staple" food source to ensure its survival. For Eastern civilisations the staple was predominantly rice; for North and South American civilisations it was corn and for Mediterranean/ European civilisations it was wheat. The civilisations that based their survival on grain staples grew a variety of seed grasses, but wheat remained, far and away, the most important. The warlike Romans conquered the ancient Mediterranean and further afield using wheat to nourish their armies.

The weight standards for ancient Mediterranean civilisations were based on the accumulative counts of wheat grains. When a standard was being created or replaced/ restored the official assayer for the nation would design the standard around a specific number of wheat grains and count out quantities of "healthy wheat" seeds. The largest weights created, nation-by-nation, which are generally referred to as "Talents" by modern archaeologists, would be in a precise ratio to smaller weights within the selfsame family of weights.

The weight's standards for one Mediterranean/ European nation would also be in a perfect ratio to those of another and there was a general sharing of standards between civilisations, extending back for thousands of years.
This methodology, in creating a standard, is about as perfect as can be achieved…to base a system of weights on the smallest common denominator of one grain of wheat. The wheat seed is reasonably consistent in size and weight, year-by-year and crop-by-crop within traditional growing regions like the Mediterranean.

When one considers the grain weights found in the "Talents" (and reduced expressions thereof) between nations, the realisation comes that the numbers chosen by the official assayers are very cumbersome. It was the prerogative or option of the assayers to make the counts simple, based upon nice big round numbers that reduced by ½ or ¼ to the smaller weights within the standard. This was, however, never the case, which compels us to ask the question, "why does the standard contain such a difficult set of numbers?" There was, very obviously, another element for consideration encoded into the standards, but what could that be?

The same argument can be applied to ancient lengths or volumes. There was a base increment shared by the nations, which played the role of the lowest common denominator for lengths. By comparing the wheat grain number counts that occur within the "grain weights" standards we are able to see what specific numbers were important to the assayers. As it turns out, the most viable base increment of length (converting to cubic capacities) is the traditional "British standard inch".

Archaeological evidence of the last 150-years has shown that the British standard inch and foot measurements are very old and will fit the dimensions of the Great Pyramid, as well as other significant edifices, such as the Greek Parthenon, perfectly. Although the Greeks used up to four variable foot measures, ranging from 12.096, 12.15, 12.16512 or 12.6 inches, respectively, for various calculation functions, they all stem from the same inch as was carried to Britain and France by as early as 5000 BC. Volume standards of the ancient Mediterranean are based on this sized cubic inch and, without this base increment, the intended codes encrypted into a vessel are obscured and unrecognisable. Although ancient civilisations used a far wider range of measurement increments than those that survived into modern times, they are all based upon the ancient inch, which in recent eras has become known as the British Standard inch.

WHERE WAS THE ANCIENT, INTERNATIONAL BUREAU OF STANDARDS?

Figure 1: The pyramids of Giza provided standards for many nations simultaneously and commissioned representatives from satellite or distant nations could, periodically, come to Egypt to check the integrity of their national standards and have new "master sets" issued.

It is a common practice that Weights, Measures and Volumes "master sets" are always housed within temperature controlled environments. This ensures that latter made duplicate sets, based upon the master set, can be fashioned to very precise tolerances. In the King's Chamber of the Great Pyramid a blocked up vent shaft was found. Once this was cleared the dank air of many centuries dissipated quickly and the room assumed a temperature that never varied, summer or winter, night or day.

Each of the pyramids of the Giza Plateau had large stone "coffers" or boxes in them, which were erroneously classified by archaeologists as stone coffins for dead Pharaohs. The fact that there has never been any evidence of burials within the pyramids has not diminished this untenable theory and it continues to be represented as the purpose for the magnificent pyramid edifices. A far more plausible explanation for the "coffers is that they were containers for master sets of weights and volume vessels, as well as measuring rods. These were kept in perfectly controlled environments within the pyramids. Each pyramid encoded particular, unique information and the standards housed within each would have been dedicated to the linear and geometric attributes of that particular pyramid, both internally and externally. All of this activity was going on many millennia before the Dynastic period of Egypt and the pyramids are far older than they've been represented to be*.

During the course of this study there will be constant reference and comparison to the pyramids of the Giza Plateau, as everything found in the Weights, Volumes and Measurement Standards of Mediterranean nations has a pedigree back to these magnificent structures. The length increments of each nation mentioned herein are perfectly divisible into the dimensions of the pyramids, whether we're talking about Greek feet, Roman feet, Assyrian cubits, Hebrew cubits or the ancient increments of Europe. The Giza Plateau, as well as other centres around Egypt, once represented the international Bureau of Standards.

*Footnote: Were it not for the poorly executed forgeries of inscriptions by Col. Richard Howard-Vyse in 1837, the name Khufu or Cheops would never have been associated with the Great Pyramid. With time and funding running out, Col. Richard Howard-Vyse had to make a big discovery in the Great Pyramid...and it, conveniently, ended up being the name of Khufu in a cavity above the King's Chamber. Unfortunately the name was rendered "Khnem-Khuf," which we now know means, "the brother of Khufu". Parts of the inscriptions or various cartouches were written in a late era hieratic script, which did not appear in Egypt until about 2000 years after the hieroglyphic writing form contemporary to Khufu's time. Col. Richard Howard-Vyse got his funding and the chair at a British University... and we got lumbered with pyramids built far too late. The Pharaoh Khufu or Cheops is known to have excavated around the ancient Sphinx, which was buried up to it's neck in sand in his day. Geologist, John Anthony West and others have dated the Sphinx to a period well before 12000 B.C. Large vertical ruts in the Sphinx were done by water erosion and there's been no significant rainfall in the region since about 12000 BC. The Great Pyramid is thought to be contemporary with or built a little after the Sphinx, which probably served the function of providing the "reduced level" surveying line or benchmark for all of the structures of the Giza Plateau.

SETTING THE STAGE.

The purpose of this article is to demonstrate that the known lengths , volumes, weights and areas, used as "standards" by many "cousin" nations of the early Mediterranean and Europe are exact fractions and factors of values found upon the 3 main pyramids of the Giza (Gizeh) Plateau of Egypt. In the course of this study decimal numbers are used for convenience and some values will display long tails of decimals, which would have been absolutely impossible to visually mark or detect in a length or weight standard. Examples of this will include numbers such as 29.53125-days, used to describe a lunar month (708.75-hours). It must be realised that the values expressed have to be stated at the degree of precision shown, as they are, simply, a decimal form of a fraction or factor. A number like 933.12 is simply indicating 1/10000th of a foundation value of 933120 (the number of seeds of grain in a Sumerian/ Babylonian talent weight). No values can be "rounded", as they are only whole number, foundation values rendered as a smaller division of itself.

Senior lecturer and mathematician, Professor Bruce Moon of Chrischurch, New Zealand, has suggested that a section of this study be devoted to tables, showing the ancient foundation values and how they reduce by fractions and factors. Professor Moon, quite correctly, contends that the ancient mathematicians would have worked in fractions. It is quite obvious, in viewing the array of values used, that these fractions were in special number families, such as 11, 7 or 6. It is the theory of this researcher that ancient mathmaticians manipulated numbers in every conceivable way, including decimal form. They used a far more expanded set of measurements than any of our modern nations inherited and also had multiples of compass systems based upon 360, 630, 640 and 660-degrees, respectively. These systems were used in both navigation or for staying abreast of sun or moon periods, etc., within a celestial cycle.

TAMING THE BEAST

A solar year is 365.2422-days and a lunar year is 354.3643519-days. The lunar nutation cycle, where the moon goes to a position called major standstill, returns to minor standstill, then returns to major standstill again, takes 6798.36-days or 18.61329277 solar years. The Earth is 24902.44523-miles in equatorial circumference. The polar circumference is 24816.55084-miles. The cycle of the Precession of the Equinoxes takes 25776-years to complete.

So, with these horrible numbers to contend with, provided that at some stage one's sciences or generations of careful observation have produced the near values to these numbers, how do scientists turn this "beastly" set of difficult values into an ordered, integrated and functional mathematical system?

The solar year can be called 365.25-days, which is a nice rounded number equating to 8766 hours.
The lunar year can be called 354.375-days, which is 8505 hours.
If a calendar is produced that runs for 7 solar years, then that equates to 2556.75-days.
If the lunar period within that calendar runs for 7.2 years, then that equates to 2551.5-days.
If a measurement rule is produced, based upon 5.25 feet, then 487 X 5.25 = 2556.75 feet/ days.
The same measurement rule can be used for the moon and 486 X 5.25 = 2551.5 feet/ days.
If an auspicious mistletoe culling ceremony is performed on the 6th day after the calendar commences at the Winter Solstice, then the solar and lunar cycles can end on the same day 7 solar years later.
If the world is described as 12 X 12 X 12 X 12 X 1.2-miles, then that's 24883.2-miles...only 18.8 miles short.
If one wishes to navigate using an "11" series of numbers, those miles can be 5280 feet each.
If one wishes to navigate using a "6&7" series of numbers, those miles can be 5250 feet each.
A wonderful little window of opportunity arises when a straight-line diameter, using an "11" number is converted to a "6" based circle using PI @ 3.141818182. Therefore 550 X 3.141818182 = 1728, which is divisible by 360-degrees.
A wonderful little window of opportunity arises when a straight-line diameter, using a "6&7" number is converted to an "11" based circle, using PI @ 22/7. Therefore 525 X 3.142857143 = 1650, which is divisible by 660-degrees.
A wonderful little window of opportunity arises when 1/7th of a 360-degree circle (51.42857143-degrees) is multiplied by 1.75 = 90. A 630-degree compass will work very well using "7" series values.
If the cycle of the Precession of the Equinoxes is described as 25920-years, then that's 72 X 360.
If the lunar nutation cycle is described as 6804-days, then that's 19.2 lunar years, which is nicely divisible by "6&7".

And that's about it really; the rest is just fraction expressions of these major, final numbers, divided down into very small increments of time or length. The small discrepancies of time were easily corrected, periodically, by such events as observing the day of the equinox or solstice and the insertion of a few intercalary days at the end of a 7-year calendar period. The discrepancies in the "size of the Earth" standards, as opposed to the "true" size, were so small as to be negligible, especially when sailing regionally around the Mediterranean. The simple mathematical systems made navigational plotting very easy.

There was little need for much "original and highly innovative thinking", as the whole mathematical parcel had been fully thought out at some unknown, remote epoch. The "standard" numbers were universally taught, preserved and shared by all of the cousin nations of ancient Europe and the Mediterranean for millenniums. This is seen to be the case when one studies the dimensions of structures and artefacts from these regions, which date to remote epochs.

As stated, for convenience, the values shown herein are rendered in decimal form. They can however be displayed as whole numbers and fractions and this would, undoubtedly, have been the form in which they were used, calculated or spoken of. For anyone wishing to convert these numbers to fractions see: http://school.discovery.com/homeworkhelp/webmath/dec2fract.html

For converting these numbers to factors or other mathematical expressions, see the range of conversion calculators at: http://school.discovery.com/homeworkhelp/webmath/

THE PYRAMID DIMENSIONS.

The Great Pyramid had an intended or design base length of 756 feet, a face slope angle of 51.84-degrees, a flat top 44 feet square at a vertical height of 453.6 feet, a side diagonal length from the base paving slab level to the edge of the altar floor of 576 feet, a "symbolic" height (including the non existent capstone) of 480 feet, a "symbolic" diagonal side length of 611.7894615 feet (378 feet ÷ 51.84 COS). The ratio of its base length (756 feet) to its true height (453.6 feet) was 1.6666666 to 1 (the same ratio encountered between a hypotenuse and an adjacent in a 3,4,5 triangle. If its base length (756 feet) is divided by 1.25 (the ratio between the hypotenuse and opposite in a 3,4,5 triangle) the value achieved is 604.8 feet (the perimeter value of the Great Pyramid @ 756 feet per side = 3024 feet...1/2 of 6048 feet, which value represented 1-minute of arc under the Great Pyramid's Earth equatorial assignment). The dimensions given allowed the Great Pyramid's coding to be read according to a combined "6&7" series of numbers, founded upon the value 42. As will be demonstrated, the known length standards of all ancient cousin civilisations of the Mediterraean Basin will perfectly fit into these dimensions. These include: a Greek mile of 5250 feet, a stadia of 630 feet, a short stadia of 525 feet, a reed of 10.5 feet, an Assyrian Royal Cubit of 25.2 inches, A Hebrew/ Celtic Royal Cubit of 21 inches, an Egyptian Royal Cubit of 20.61818182-inches, Hebrew cubits of 17.5 & 16.8 inches, Greek feet of 12.6 inches, Roman feet of 11.666666 and 11.664 inches, etc. Areas vould be read in pyramid acres of 28800 square feet (ref. Herodotus).

The Great Pyramid had a "symbolic" length of 756.25 feet (756 & 1/4th feet). This allowed the pyramid to be read in an "11" or "11&6" series of values. It is from this calibration that the league (16500 feet), mile (5280 feet), furlong or furrowlong (660 feet), chain (66 feet), rod/ perch (16.5 feet), fathom (originally 5.5 feet...persisting as the merchant navy fathom in Britain) and link (7.92 inches), were derived. Areas could be read in British acres of 45360 square feet.

The Great Pyramid could be symbolically read in pure PHI values (1.6180339 to 1). In a literal sense, the Great Pyramid was built to comply to "rounded PHI" dimensions and its 756 feet length is 560 increments of 16.2-inches (16 & 1/5th inches). By symbolically viewing 1.62 inches as representing 1.6180339 inches, the dimensions were converted to PHI based proportions. Therefore: the side diagonal length from the base paving slabs to the symbolic apex, derived by 378 ÷ 51.84 COS = 611.7894615 feet, could be rendered as 378 feet X 1.6180339 (PHI) = 611.6168142 feet for a diference in the reading of only about 2 inches.

The Khafre Pyramid's intended design length is 15/16ths of that of the Great Pyramid. Therefore: 756 ÷ 16 = 47.25 feet X 15 = 708.75 feet. The Khafre Pyramid was built to code lunar cycle values and was fully a "pyramid of the moon". It differered in its face degree angle from the Great Pyramid, inasmuch as it was built to the 3,4,5 triangle principle. Half its base length is 354.375 feet (354 + 1/3rd of 8...or 1/8th of 2835 feet). The sum of 354.375-days is the duration of 1 lunar year, made up of 12 lunar months of 29.53125-days or 708.75 hours. The 3,4,5 method by which Khafre Pyramid was built used a base increment of 118.125 feet for its design formula. Half Khafre's base length was 118.125 feet X 3 (354.375 feet), its height was 118.125 feet X 4 (472.5 feet) and its diagonal face slope was 118.125 feet X 5 (590.625 feet). The Octagon of Newark, Ohio earth embankment complex in the USA was 2835 feet long, from the alcove at the front of the altar, extending at an azimuth angle of 51.84-degrees, to the outer extremity position of the end gate. The distance of 2835 feet was the perimeter value of Khafre Pyramid, or 118.125 feet X 24. The design width of the inner Avebury Henge complex of England was 1181.25 feet from the rear faces of the Station Stones at the WSW and ENE gateways at an azimuth angle of 68.04-degrees (There are 6804 days in the lunar nutation cycle...or 500 X 68.04-inches in the perimeter value of the Khafre Pyramid).

The Menkaure Pyramid is 356.4 feet per side or 1425.6 feet for the whole perimeter (259.2 fathoms). It was built to an "11" series or "6&11" series of numbers, used in navigation. Like the Great Pyramid, it was dual coded to be read in "rounded PHI" (1.62) or ""pure PHI" (1.6180339) increments and had a design face slope angle of 51.84-degrees. The Pyramid was abandonned to the creeping desert before it was fully finished in pre-Dynastic times and a later Pharaoh of the Dynastic period attempted to have the top section finished in inferior mud-brick. The slumping or rounding out of the top apex section has led to a lesser height and archaeologists assign erroneous face degree angles to the edifice accordingly. Under its pure PHI assignment, the length of the diagonal face side was meant to be 288 feet and convey the same coded relationship as "Y" Holes Circle and the Aubrey Circle at Stonehenge.

THE HEBREW LIQUID VOLUME STANDARDS.

Let's look at a fairly recent civilisation enjoying its "golden age" only 3000 years ago…the Hebrews who occupied the dangerous bridgehead to 3 continents, now referred to as Israel. There is considerable confusion and interchanging of terms related to the Hebrews, who are generally categorised under an umbrella term as Jewish or Israelites. The fact is that there were some Israelite Hebrews and one tribe within the 12 major Israelite tribes was "of the House of Judah". By about 500 B.C. most of the tribes had moved away from the region after engaging in endless wars, being conquered and enduring the rigours of captivities. Whereas the vast majority of the Israelites sought refuge in Europe amongst cousin peoples, the Tribe of Judah and a small contingent from the Tribe of Benjamin opted to remain living on that dangerous piece of real estate until 70 A.D., when the Roman's, under Titus, exiled the remnant survivors of the Jewish revolt.

We know that during the Late Hebrew golden age of about 1000-900 BC there was considerable maritime activity from the Hebrew/ Phoenician ports at Tyre, Lebanon and that "round ships" were plying thriving trade routes, one of which extended to the Great Lakes* region of North America. Large quantities of copper were being mined in North America and brought back for refinement in Israel, mostly at Enzion Geber. This shows an advanced ability to navigate to distant ports across the Atlantic.

*Footnote: "Around the northern shore of Lake Superior there are 'about 5000 ancient copper mine workings, from which an estimated 500 million pounds of copper were removed...and there is no evidence of what became of it'. This copper appears to have been shipped away from North America.

At Enzion Geber on the sea-coast of Southern Israel (approachable either from the Red Sea or from the Eastern base of the Mediterranean, where ore could be rafted over the "Reed Sea", are the remains of, 'the biggest smelting installations of the ancient East...consisting of a regular ultramodern furnace with a system of air channels, chimney flues and openings...the most interesting things were casting moulds and a vast quantity of copper slag'. Werner Keller dates this great ancient blast furnace to within the period of Solomon's reign after 1000 B.C."

The furnace system used is comparable to the modern Bessemer system (see The Lost Ten Tribes of Israel Found, by Steven M. Collins, pgs. 26-28). Similar Phoenician mining and smelting operations appear to have been carried out at Sarina Beach in Western Australia, where a ancient large mining port, mine workings and slag heaps have been located.

Let's now consider how the Hebrews were coding principles of navigation…amongst other things, into their volume capacities.

Donald L Lenzen provides substantiated reference to the fact that the Hebrews had 3 liquid volume standards, which were the Desert Standard, the Jerusalem Standard and the Sepphoris Standard. These are documented in rabbinic texts. Here are Lenzen's estimates (left), based upon exhaustive assessments related to the cubic capacities of ancient, unbroken or reconstructed Hebrew vessels. One unbroken museum example, found at Qumran, has writing on it to indicate its capacity in Hebrew Log and Seah measures. All volumes are shown in cubic inches.

The Sepphoris liquid volume measures positively code the true equatorial circumference of the Earth, according to the Parthenon platform standard of 24883.2 miles (12 X 12 X 12 X 12 X 1.2). Let's consider the numbers:

• A Cor @ 22394.88 cubic inches provides a very significant ratio to the 24883.2 mile (131383296 feet) circumference of the Earth and 22394.88 feet would be 1/ 5866.66666th of that Earth size value. The inverse of this ratio X 3 = 17600 and the 22394.88 number proves to be a concise incremental fraction of the true Earth size. A measurement of 22394.88 feet would be 12960 Egyptian Royal Cubits of 20.736 inches (1.728 feet) each. When the Great Pyramid Earth circumference standard is divided by the Cor the result is: 130636800 ÷ 22394.88 = 5833.333333. Again this is a very important numerical progression, much used in antiquity. Two times 5833.33333 is 116666.6666 and the ratio 1: 1.1666666 designated the difference between a common cubit and a Royal Cubit (eg. 18 inches X 1.166666 = 21 inches). Also, on the Great Pyramid, the perimeter value (3024 feet) ÷ 58.333333 = 51.84 (the Great Pyramid's diagonal face angle in degrees). Three times 5833.333333 = 17500. A Cor @ 22394.88 cubic inches = 12.96 cubic feet and provides a mathematical progression related to the Precession of the Equinoxes. It is important to note that the Egyptian Royal Cubit of 20.736 inches was 1.728 feet and that there are 1728 cubic inches in a cubic foot volume (12 X 12 X 12). A Cor volume @ 22394.88 cubic inches is 9/10ths of 24883.2 inches.

Footnote: Professor Bruce Moon, Senior Lecturer in Mathematics, in his assessment of the foregoing paragraph, suggests stating it in the following (less decimally defined) terms:

"The Parthenon platform standard value for the Earth's equatorial circumference was 24883.2 miles (125/10). The Great Pyramid value is 247419/11 miles (123×9×7×5/22). A little calculation shows that these figures are in the ratio 176/175.

"The Great Pyramid perimeter is 3024 ft (122×7×3) and its diagonal face angle 51.84º.
(123×3/100) Their numerical ratio is thus 175/3.
"Since the numerical value of the Cor (in cubic inches) is 125×9/100, its ratio to the Parthenon equatorial circumference of the earth (in miles) is 9:10. Expressing the circumference in feet, this ratio is 3/17600. For the Great Pyramid circumference, the ratio is thus 3/17500 (12/7000). Again, a Cor of 22394.88cu.ins =12.96cu.ft. [1cu.ft =1728(123)cu.ins] As an Egyptian Royal Cubit is 1.728(12/10)3 ft(20.736ins), 22394.88ft is thus equal to 12960cubits."

Note: a small 2, 3, or 5 in the foregoing paragraph means "to the power of".

• A Bath @ 2239.488 cubic inches is 1/10th of a Cor and works to the same mathematical progression or ratio system.
  
  
• A Hin @ 373.248 cubic inches, if representing 373.248 miles, would be 1/66.666666th of the equatorial circumference of the Earth, whereas 373.248 feet would be 216 Egyptian Royal Cubits of 20.736 inches each. A Hin @ 373.248 cubic inches = .216 cubic feet and provides a mathematical progression related to the Precession of the Equinoxes and diameter of the moon in miles.
  
  
• A Cab @ 124.416 cubic inches, if representing miles, would be 1/200th of the equatorial circumference of the Earth, whereas if representing 124.416 feet would be 1/1056000th of the Earth's circumference. There are multiples of cairn and standing stone marked lengths complying to 12441.6 feet in the Waitapu Valley of Northland, New Zealand. A value of 124.416 feet would be 1/1050000th of the Great Pyramid equatorial standard of 24741.81818 miles.
  
  
• A Log @ 31.104 cubic inches is, again, clearly coding the 24883.2 mile equatorial circumference and 31.104 X 800 = 24883.2 or 31.104 feet = 1/4200000th of the Great Pyramid navigational standard of 24741.81818 miles.

Lenzen notes that the Sepphoris standard exceeded the Jerusalem standard and attributes this fact to rabbinic writings. The ratio is 6:5.
Again, the Jerusalem standard is perfectly suited for mnemonic reference to the size of the Earth.

• If the 18662.4 cubic inch Cor were treated as linear feet, then 7000 such intervals of length would go into the Great Pyramid's assignment for the Earth size @ 24741.81818-miles and 7040 would go into the "true" equatorial circumference @ 24883.2-miles.A Cor @ 18662.4 cubic inches = 10.8 cubic feet and provides a mathematical progression related to the Precession of the Equinoxes, diameter of the moon, etc. The value of 18662.4 is 3/4ths of 24883.2.
  
  
• A Bath of 1866.24 cubic inches, if treated as linear miles would be 1/13.3333333rd of the true circumference of the Earth.
  
  
• A Hin of 311.04 cubic inches, if treated as linear miles, would be 1/80th of the true equatorial circumference @ 24883.2-miles.
  
  
• A Cab of 103.68 cubic inches (51.84 X 2) is in mnemonic reference to several ancient navigational, rotational or precessional principles. The ancient number describing the Earth's speed of rotation was 24883.2 miles ÷ 24 hours or 1036.8 MPH. If one travels a league of 16500 feet, then the circumference generated by a league diameter is 51840 feet and this value is perfectly divisible by 360-degrees. This relationship was used extensively in ancient navigational plotting. The slope angle of the Great Pyramid is 51.84-degrees.
  
  
• A Log of 25.92 cubic inches would be in deference to the Precession of the Equinoxes, enduring for 25920-years. The outer face of the Heel Stone at Stonehenge sits 259.2 feet from the centre of the site.

Again, Donald L Lenzen's estimates sit to the left and are virtually no different to a widely used mathematical progression of antiquity. This set of "corrected" numbers can be used for mnemonic recall of the size of the Earth under the "true" and Great Pyramid standards.

• The Cor @ 15552 cubic inches, if read as linear miles, would go into the 24883.2-mile circumference of the Earth 1.6 times. If read as 15552 linear feet, this length would be 1/8400th of the Great Pyramid equatorial standard of 24741.81818 miles. A volume capacity of 15552 cubic inches would be 7.2 ancient British Bushels. The distance from the centre of Newark, Ohio's Octagon earth embankment circle component to the centre of its octagonal earth embankment component is 1555.20 feet (18662.4 inches). A correct Cor cube container could have been fabricated with the inner inch dimensions of 25" X 25" X 24.8832". A Cor @ 15552 cubic inches = 9 cubic feet.
  
  
• The Bath @ 1555.20 cubic inches complies, in reduced ratio, to the codes nominated for the Cor.
  
  
• The Hin @ 259.20 cubic inches, if read as linear miles, would go into the 24883.2-mile equatorial circumference 96 times. If read as 259.2 linear feet it would be 1/504000th of the Great Pyramid equatorial standard of 24741.81818 miles. At 259.2 feet it would also be the distance from the centre of Stonehenge to the outlying face of the Heel stone or the intended diagonal face length up Silbury Hill. The full perimeter value of Menkaure Pyramid @ 356.4 feet per side was 259.2 fathoms of 5.5 feet each. The 2592 number is one of the foremost values of antiquity.
  
  
• The Cab @ 86.4 cubic inches carries very important codes in its numerical value. The Sun is 864000 miles in diameter. A distance of 86.4-miles would be 1/288th of the true circumference of the Earth or 86.4 linear feet would be 1/1512000th of the equatorial Earth circumference based upon the Great Pyramid reading of 24741.81818 miles (two sides of the Great Pyramid total 1512 feet). A formula for finding the size of the Earth by a straight reading of the Great Pyramid's dimensions is to multiply its perimeter value (3024 feet) by 43200 (½ of 86400).
  
  
• The Log @ 21.6 cubic inches codes the diameter of the moon (2160 miles) or the period of time the sun spends in each house of the zodiac (2160 years) during the 25920-year cycle of precession. A linear distance of 21.6-miles would be 1/1152nd of the size of the Earth under the 24883.2 assignment or 21.6 feet would be 1/6048000th of the Earth's circumference under the 24741.81818-mile assignment. Note, the distance of 6084 feet is 1-minute of circumference arc under the Great Pyramid navigational assignment. The Desert standard Log @ 21.6 cubic inches would be 1/100th of an ancient British Bushel.

THE HEBREW DRY VOLUME STANDARD AND THE "11" SERIES SIZE OF THE EARTH.

The Hebrew liquid volume values (superficially) relate to either the "true" size of the Earth, based upon the Parthenon platform code, or the navigational size of the Earth, which breaks down very fluidly into degrees, minutes and seconds of arc (Great Pyramid standard). The most convenient way of measuring distance upon the open sea was in leagues, miles or furlongs and this "11" series was encoded into the Hebrew Sepphoris dry volume standard.

To arrive at his estimates, Donald L Lenzen refers to the capacity of an unbroken jar located at Qumran, which was inscribed, "Two Seah and 7 Logs". The official capacity of the jar is deemed to be 2175.52 cubic inches. According to my "corrected" reckoning the capacity should yield 2178 cubic inches, so the margin of difference is 2.48 cubic inches shortfall in the artefact's measured capacity, making the vessel 99.886134 true
The correction seems reasonable, inasmuch as a Log capacity of 39.55 cubic inches will not provide any coded value that works in a mathematical progression, whereas a Log of 39.6 works in a dynamic way. We know that the Hebrews, along with their much scattered cousin peoples in surrounding countries, were working to precise ratios and coding significant, meaningful numbers into their volume vessels. Let's see what very useful information a Log of 39.6 cubic inches would provide, as 720 Logs of 39.6 cubic inches create a Homer of 28512 cubic inches.

• A Homer of 28512 cubic inches is an "11" series number (2592 X 11). Under an "11" series reading of the Great Pyramid, its base perimeter was read as 3025 feet rather than 3024 and by this means a navigational system could be created that worked to leagues, miles, furlongs, chains, rods/ perches, fathoms and links. This system was tremendously convenient, as a linear league (16500 feet) travelled converts to 51840 feet in circumference. This is then reducible to 144 feet per degree of arc, which facilitates the calculation of degree angles back to point of departure or onward to destination, despite many course changes en route. A Homer @ 28512 cubic inches = 16.5 cubic feet and provides a mathematical progression related to navigation. The rod/ perch measurement of ancient Britain was 16.5 feet and the league was 16500 feet. Both are based upon an "11" series of numbers.
  
  
• The cubic inch capacity number used for the Homer is remarkable, as it provides a window of opportunity to work in all 3 geodetic systems simultaneously, whether it be the 24883.2-mile circumference, the "11" series @ 24750-miles or the Great Pyramid standard @ 24741.81818-miles. It also allows for navigation using a Roman foot of 11.664 inches, a British foot of 12 inches, a Greek foot of 12.6 inches, a Hebrew/ Celtic common cubit of 18 inches, the "6 & 7" series Egyptian Royal Cubit of 20.61818182 inches, the "11" series Egyptian Royal Cubit of 20.625 inches, the "true" equatorial circumference Egyptian Royal Cubit of 20.736 inches, a Hebrew/ Celtic Royal Cubit of 21 inches, a rounded PHI increment of 32.4 inches (Megalithic Yard) and all increases on these values leading up to Greek Stadia, Greek miles, British Miles and Leagues.
  
  
• In navigational plotting the difficulty was in keeping accurate track of the degree angle back to point of departure and toward the destination at all times. Accurate knowledge of position relied heavily on constant mental arithmetic, on the part of the navigator, related to ship speed and angle of travel. When the navigator called for a new course change the leg just completed had to be accurately marked on the plotting chart. Each time a leg was completed a new calculation of degree angle to the destination (and port of departure) had to be made. This entailed creating a circle, based upon the length of the last leg completed, which could be broken down into accurate degrees of arc (reducible by either 320 or 360-degrees).
  
  
• The Homer value @ 2851.2 acts as a circumference number code for the 3 geodetic systems and would have been extremely helpful in teaching the overall principles of navigation or all incremental length values that could be pressed into service in ocean traversals. To accentuate the Great Pyramid navigational system (24741.81818-miles), based upon using numbers in "6 & 7" progressions, the formula was: 28512 ÷ 3.142857143 (22/7 rendition of PI) = 9072 (the length of the Great Pyramid is 9072 inches per side (756 feet X 12). This value of 9072 feet (3 circuits of the pyramid's base perimeter… 3024 feet) is also 1.5 minutes of equatorial arc under the literal Great Pyramid coding. The 9072 value, or increases thereof, is divisible by a range of known ancient increments based upon 6 & 7 progressions, used by diverse civilisations of the Mediterranean and Europe. The value 9072 feet is 5280 X 20.61818182 inches (the length of the 6 & 7 series Egyptian Royal Cubit X the British standard mile)…in other words it's a cubit-based mile. The existence of the 20.61818182 inch cubit is confirmed by dividing the base length of the Great Pyramid (756 feet...9072 inches) by 440. This equals 20.61818182 inches. The existence of this cubit is also confirmed by an Egyptian measuring rod in the collection of the Turin Museum, which has been measured to the third decimal place as 20.618 inches.
  
  
• To accentuate the symbolic Great Pyramid code, working to "11" values, the formula was: 28512 ÷ 3.141818182 = 9075. This is based upon viewing the Great Pyramid as having a perimeter of 3025 feet for readings in "11" series numbers, wherein 9075 feet is 1.5 minutes of arc for a full equatorial circumference of 24750-miles or 7920 leagues. This is the predominantly used "11" series, which provided the most simple means of doing linear calculations at sea. The "11" series straight line values used in voyages would translate to "6" based circumferences reducible by 360-degrees. The value of 9075 feet is 5280 X 20.625 inches (the length of the "11" series Egyptian Royal Cubit). Again, this is a cubit-based mile. The existence of the 20.625 inch Royal Cubit is confirmed by the careful measurements of Sir William Flinders Petrie in the King's Chamber of the Great Pyramid. Petrie concluded that the room was built according to a cubit of 20.620 inches, plus or minus .005 of an inch. The upper scale of his estimate is, therefore, 20.625 inches (see The Pyramids and Temples of Gizeh, by Sir William Flinders Petrie).
  
  
• A formula that could have been used to recall the "true" size of the Earth was: 28512 ÷ 3.125 = 9123.84. This would represent 3 symbolic circuits of the Great Pyramid under a "true" Earth equatorial circumference assignment or 1.5 minutes of arc (where 6082.56 feet = 1 minute of arc under the 24883.2-mile assignment). The value of 9123.84 feet is 5280 X 20.736 inches (the length of the "true" equatorial sized Earth's cubit)…a cubit based mile. As stated, the existence of the 20.736 inch cubit is confirmed by the paving slab widths at the base of the Great Pyramid, which comply to 20 X 1.728 feet or 34.56 feet. A 1.728 feet cubit (20.736 inches) would be 1/1750th of the perimeter value of the Great Pyramid's base (3024 feet).
  
  
• A 28512 feet value equates to a league of 16500 feet X 1.728 feet (20.736 inches)…or a cubit based league. If one travelled in straight-line values of this cubit based league, then the circumference generated from such a diameter (using PI @ 3.141818182) would be 51840 cubits. One degree of arc on such a circumference would be 248.832 feet. Remember, the ancient value for the true size of the Earth was 24883.2 miles.
  
  
• Design geometry dictates that the Great Pyramid had a base length of 756 feet and a side diagonal length of 576 feet, terminating at a flat top floor 44 feet square. The capacity volume of the Great Pyramid was, therefore, 92160000 cubic feet. If 92160000 blocks of 1 cubic foot each were placed end to end and stretched around the 24883.2-mile equator, it would take 1.4256 such batches of blocks to complete an equatorial circumference. The sum of 1.4256 is half of 2.8512.
  
  
• The Menkaure Pyramid's length @ 356.4 feet goes 80 times into 28512 feet.
  
  
• From the foregoing, the reader will be able to see that very profound geodetic principles are coded within these cubic inch capacity measures and each reduction of the Homer (Ephah, Seah, Cab & Log) contains similar navigational information, as do the numbers generated within the Hebrew liquid volumes. The initiators of these capacity standards chose the final volume numbers with tremendous care and scientific prowess…they really knew what they were doing.

Let's go and check what the Greeks were up to with their volume standards.

THE GREEKS COPIED AND USED THE EGYPTIAN VOLUME SYSTEM.

Essentially, the Greek volume system is simply the Egyptian system in reduced ratio. Lenzen mentions two "capacity marked" earthenware vessels found at the bottom of a well at the Acropolis. One was marked as a public standard Khous and bore the official "owl" stamp of Athens. The second item was an official water clock, marked as two Khous. From this and other evidence he reconstructs his estimate of the Greek volume system in the following way, as shown to the left.

• For the liquid capacity a Metretes volume, which was exactly 1/5th of an Egyptian Theban, could be fashioned from a rectangular vessel 22.68 inches X 22.68 inches X 4.536 inches. The Metretes was equivalent to 2 Egyptian Beshu. The 4.536 inches would be in homage to the 453.6 feet height of the Great Pyramid to the top of its altar floor, which height was 1.66666666 less than the Great Pyramid's length of 756 feet. The 22.68 inches is in homage to the 2268 feet for 3 sides of the Great Pyramid or the period of 2268-days, which is 1/3rd of the 6804-day lunar nutation cycle. Similarly, a rectangular vessel of 9.072 inches X 9.072 inches X 28.35 inches would measure out as a Metretes. The Great Pyramid had an inch length of 9072 and the Khafre Pyramid was 2835 feet in base perimeter. A Metretes @ 2332.8 cubic inches = 13.5 cubic feet and provides a mathematical progression related to the lunar cycle.

The Greek volumes are in a perfect ratio to the Egyptian volumes, which meant that trade between the Greeks and Egyptians was reasonably simple Let's look at the Greek volumes as they relate to the Egyptian Theban.

• 1 Theban = 5 Metretes or 60 Chous or 720 Cotyle or 2880 Oxybaphon or 4320 Cyathus.
  
  
• 1 Theban = 3.75 Medimnus or 22.5 Hecteus or 180 Choenix.
  
  
• 1 Theban = 6.75 cubic feet.
  
  
• These whole number and fraction values like 3.75 are the commonly used numbers of antiquity. This includes the divisions of numbers within the Greek system of 6, 12, 48, 144, 192, 576, 864 or 1152, which recur from continent to continent across the ancient world.
  
  
• The original Bushel in England was, undoubtedly, 2160 cubic inches (1 bucket or flat-bottomed tub with a base of 270 square inches and a height of 8 inches. The circular base would need to have been 18.5411617 inches in diameter or very close to the coded number of 58.33333 inches in circumference. This is consistent with the description given to the old English bushel measure as, "any round measure with a plain and even bottom, being 18.5 inches wide throughout and 8 inches deep". This literal description was later used to create the American bushel of 2150.42 cubic inches, which was, undoubtedly, a shortfall of some 10 cubic inches on the intended, original bushel.
  
  
• There were 5.4 "original" bushels of 2160 cubic inches to the Egyptian Theban. It seems obligatory that a volume of 2160 cubic inches (6 X 6 X 6 = 216) would have been used, as the number 2160 is one of the most important of antiquity. The sun spends 2160-years in each house of the zodiac during the 25920-years of the Precession of the Equinoxes and the moon is 2160-miles in diameter. It was very important to remember the number 2160.
  
  
• The Sumerian/ Babylonian Homer volume was 21600 cubic inches or 10 "original bushels" used in England at a later era.

THE GREEK VOLUMES AND THEIR CODES RELATED TO THE SIZE OF THE EARTH.

Thee Greek volumes, like those of the Hebrews, provide codes for remembering the size of the Earth under 3 equatorial systems.

• The Metretes (superficially) relates to the "6 & 7" equatorial assignment wherein the base perimeter of the Great Pyramid (3024 feet) represents ½ a minute of arc and 2332.8 feet would be 1/56000th of 24741.81818 miles. The length of 2332.8 feet would also be 1350 Egyptian Royal Cubits of 20.736 inches (1.728 feet). The distance of 2332.8 feet complies also to one of the 4 known Greek feet measurements (12.15 inches) and there are 2304 (1152 X 2) of these in 2332.8 feet.
  
  
• If the Metretes is treated as a circumference value for navigation, it reduces to 742.5 when divided by 3.141818182. This is an "11" series number and if read as feet of 12 inches would be 1/176000th of the Equatorial size of the Earth under the 24750-mile (7920 league) assignment. The value of 742.5 feet would also be 432 Egyptian Royal Cubits of 20.625 inches each. Note, the Great Pyramid is 432 Hebrew/ Celtic Royal Cubits of 21 inches per side (756 feet). The value of 742.5 feet would also equate to 275 rounded Megalithic Yards of 32.4 inches each or 135 fathoms. It can be seen that the Metretes was perfectly suited to use as a navigational increment for producing both linear and circumference increments, under the "11" series navigational system of straight line distances. A circumference of 1 Metretes @ 2332.8, when divided by 360-degrees, would produce a 1-degree value of 6.48. This is part of a mathematical progression leading to 29520…the number used to describe the duration of the Precession of the Equinoxes.
  
  
• The Chous @ 194.4 cubic inches, if read as feet, would be 1/672000th of the circumference of the Earth under the "6 & 7" assignment. The length of 194.4 feet would be 112.5 Egyptian Royal Cubits of 20.736-inches (1.728 feet). This measurement would also be 192 Greek feet of 12.15 inches. This value has all of the same attributes as the Metretes, in that it can be used as a navigational circumference. When divided by 3.141818182 it produces a linear value of 61.875. When 24750 miles are divided by 61.875 the result = 400.
  
  
• The Cotyle @ 16.2 cubic inches, if read as feet, would be 1/8064000th of the equatorial circumference of the Earth. The number 8604 is 8 X 1008 and the distance of 100.8 feet is 1-second of arc under the "6 & 7" Earth circumference assignment. The length of 16.2 feet would be 16 Greek feet of 12.15 inches.
  
  
• The liquid volumes of the Chous, Cotyle, Oxybaphhon and Cyathus are in convenient ratio reductions to the 2551.5-day (7.2 lunar year) cycle of the moon and would have been used, primarily, in that mnemonic function. The 2551.5-day count was the means of keeping track of the moon within the Sabbatical Calendar system, which tracked the sun for 7 solar years (2556.75-days) simultaneously to tracking the moon for 7.2 lunar years. The 5.25-day difference in the two totals is why the Druids held a Mistletoe culling ceremony on the 6th day after the winter solstice/ full moon conjunction…such that the lunisolar Sabbatical cycle would terminate on the same day 7-years later. The volume codes also worked well within the 6804-day lunar nutation cycle (18.613- solar years…major standstill to major standstill).
  
  
• The dry Medimnus volume @ 3110.4 cubic inches was the largest Greek volume and positively codes the true size of the Earth in its numerical makeup. The value 3110.4 X 8 = 24883.2 and, if this total was read as miles it would be the equatorial size of the Earth to a tolerance of 18.8 miles short of the figure we use in modern times (24902 miles).
  
  
• The Medimnus @ 3110.4, if used as a circumference, it would produce the value of 990 when divided by the PI rendition of 3.141818182. The sum of 990 feet would equate to 1.5 furlongs or 576 Egyptian Royal Cubits of 20.625 inches. This value would also be 180 fathoms of 5.5 feet each…again, perfectly suited to navigation under the "11" system. A Medimnus @ 3110.4 cubic inches = 1.8 cubic feet.
  
  
• The dry Hecteus volume @ 518.4 cubic inches related in a dynamic way to ancient navigational principles. There would be 48 increments of 518.4-miles in the 24883.2-mile circumference. Likewise, under the "6 & 7" geodetic, Earth circumference assignment of 24741.81818 miles (the Great Pyramid standard) 518.4 feet would be 1/252000th of the Earth's circumference. In navigation, a linear distance travelled of 1 ancient British league (16500 feet…25 furlongs) generates a circumference of 51840 feet, using PI @ 3.141818182. The 518.4 cubic inch Hecteus would also be for mnemonic recall of the speed of the Earth's daily rotation, which is 24883.2 miles ÷ 24 hours = 1036.8 MPH. Therefore, the Hecteus codes ½ of the Earth's rotational speed in the MPH number it provides. Under the all encompassing, integrated system of antiquity a cubic foot of water was 1728 cubic inches. If this is divided by the special, much used ratio of 1.6666666 to 1, found within 3,4,5 triangle computation, then the result is 1036.8 cubic inches...again relating to the Earth's rotational speed in MPH.
  
  
• The dry Choenix @ 64.8 cubic inches can relate to navigation and Earth circumference values under the 24883.2 and 24741.81818 assignments. It is also an incremental value associated with the Precession of the Equinoxes (25920-years…6480 years X 4).
  
  
• The merits of the Coytle and Cyathus volumes have already been touched upon.

ROMAN MEASURES OF CAPACITY AND THE EQUATORIAL SIZE OF THE EARTH.

Lenzen shows two forms of volume measurement under the Roman system, which relate to liquid and dry measures.

The Roman liquid volumes show an astonishing degree of sophistication, inasmuch as they are all simple ratio reductions on the true equatorial size of the Earth. The ancient Egyptians, Greeks, Hebrews and Britons seem to have been preoccupied in making their "volumes" comply with the size of the Earth in miles of 5280 feet. The number that ancient cousin peoples chose to represent the true equatorial size of the Earth was 24883.2-miles and they encoded this value, in various ways, from the Mediterranean Basin to New Zealand.

• The Roman liquid Amphora volume X 16.6666666 = 24883.2 (read as miles). An Amphora @ 1492.992 cubic inches = .864 cubic feet and provides a mathematical progression related to the Precession of the Equinoxes and navigation. The sun is 864000-miles in diameter.
  
  
• The Roman liquid Urna volume X 33.3333333 = 24883.2 (read as miles).
  
  
• The Roman liquid Congius volume X 133.3333333 = 24883.2 (read as miles).
  
  
• The Roman liquid Sextarius volume X 800 = 24883.2 (read as miles).

Apart from the ½ value of 24883.2 (12441.6) being encoded, in feet, on multiple occasions within the Waitapu Valley of Northland, New Zealand, it is also encoded, in reduced ratio, into the platform upon which the Greek Parthenon of Athens is built. The Parthenon length, anciently, represented 1 second of arc for the world and was measured by Penrose to be very close to 101.376 feet. Lenzen suggests 101.375 feet. Mathematical progression evidence or the logical use of numbers would suggest 101.376 feet, culminating in the 24883.2-mile value… Therefore, 101.376 feet (one second of Earth arc) X 60 = 6082.56 feet (one minute of arc) X 60 = 364953.6 feet (1-degree of arc) X 360 = 131383296 feet (divided by 5280 to render the length in miles) = 24883.2 miles. This total would be very easy to remember when using the formula, 12 X 12 X 12 X 12 X 1.2.

The coding contained within the Roman dry measure volume is even more remarkable mathematically and codes the size of the Earth under 3 systems. Despite the fact that the Parthenon platform gives a true reading of 1 second of arc for the world, this was not the preferred system for navigation around the world. The most versatile system, used universally by the cousin nations, was based upon the Great Pyramid's rendition of ½ a minute of arc under two complimentary systems. Please read: http://www.celticnz.co.nz/Waitapu_Valley/Waitapu7.htm within this website, a partial synopsis of which is.

Several formulas showed how to calculate the circumference of the Earth or 1-degree of arc, based upon the Great Pyramid's dimensions and angles.

• Divide the vertical height of the Great Pyramid by half the length of the top altar floor (453.6 ÷ 22 = 20.61818182). This numerical value is the same as dividing the base length inch value (9072 inches) by 440.
  
  
• The sexagesimal & septimal cubit (working backwards in 6 & 7 progressions from the full size of the Earth) was 20.61818182 inches long. This number was multiplied by 1200 and the result read as miles (24741.81818 ...130636800 feet). 1-degree of arc under this system was 68.727272 miles or 362880 feet.
  
  
• If we divide the full perimeter of the Great Pyramid (3024 feet...36288 inches) by the length of the altar floor atop the Great Pyramid (44 feet) then the result is 68.727272...the number that indicates 1-degree of arc in miles.

This Earth size value (24741.81818 miles works exceedingly well when doing sexagesimal calculations and our ancient Sumerian compass system (set to 360 degrees, with 60 minutes per degree and 60 seconds per minute) is fully sexagesimal.

The Great Pyramid was literally 756 feet long and complied to many increments of measurement within that length, which were based upon the numbers 6 & 7. Everything from Hebrew/ Celtic Royal Cubits of 21-inches and their "common" counterparts of 18 inches would fit snugly. Smaller fractions of the Greek Stadium and mile values fitted this length perfectly as well.

• The British had a series of measurements that were based upon the number 11. The surviving lengths into modern times were the mile (5280 feet), furlong (660 feet), chain (66 feet), rod & perch (16.5 feet), fathom (earlier known to be 5.5 feet...this size fathom was still the merchant navy fathom in England in the 19th century A. D.) and link (7.92 inches). Based upon ratio relationships between these values it becomes glaringly apparent that the ancient British league was 16500 feet (3.125-miles). Historians and experts in the study of ancient Metrology have commented in their works that an old English league was known to have been "about 3-miles".
  
  
• Although some classicist historians might hold to the view that this "11" series came into existence with the Tudor Monarchs (notably Henry VIII & Queen Elizabeth I), it is known that the 11 system is very old and measurements like the "chain" are traceable to ancient times. Author/ mathematician John Michell points out that the "Kings Girth" measurement, established by "King of all the English", Athelstan (circa 935 AD), was made up of mile (5280 feet), furlong (660 feet) and acre (66 feet chain X 660 feet furlong) increments. They were already thousands of years old when King Athelstan pressed them anew into service. King Henry VIII appears to have done little more than adjust the avoirdupois weight system slightly. He and Elizabeth I made it obligatory for merchants to use a 7000 grain pound as the English standard rather than the widely used 5400 grain Saxon pound.
  
  
• To work the "11" series on the Great Pyramid a symbolic adjustment had to be made to its length and 3 inches had to be added per side. This extra morsel was, undoubtedly, once marked into the base paving slabs, increasing the overall reading of the base perimeter from 3024 feet to 3025 feet. Now the pyramid complied to "11" series readings, as listed above. Under this length assignment (756.25 feet) it was 137.5 fathoms long.

Using the same logical sequence to produce an Earth circumference value under the "11" system we have:

• 756.25 feet ÷ 1.6666666 = 453.75 feet (the pyramid's vertical height assignment under the 11 series...this is about 9 inches greater than its true, assigned height, which was based upon a PHI progression that finished out at 453.049492 feet). 453.75 ÷ 22 (half the top altar floor length) = 20.625. Egyptian Royal Cubits often hover very close to this value in terms of their official length, which would be virtually undetectable alongside a cubit of 20.61818182. Sir William Flinders Petrie postulated on the existence of a cubit fashioned to this size.
  
  
• 20.625 X 1200 = 24750 (read as miles). This Earth circumference divided by 360-degrees = 68.75-miles per degree of arc Again the full perimeter value of the Great Pyramid under this assignment (3025 feet) when divided by the length of the top altar floor (44 feet) produces 68.75. The Earth's equatorial circumference can now be read fluidly in any of the 11 series values and equates to 7920 leagues for full equatorial circumference.
  
  
• Menkaure Pyramid provided 11 series navigational information also and when its length (356.4 feet) is divided by its slope angle (51.84-degrees) the resultant number relates to 1/10th of 1-degree of Earth circumference arc (6.875).

It was seemingly essential for ancient navigators to measure their linear progress across oceans in terms of these 11 series values, hence the league or fathom have always been nautical terms. There's a very important reason for working in 11 series, straight line distances travelled, as they create very convenient relationships with the PI ratio (where a circle's circumference is always 3.1416 times larger than its diameter). One could, equally, work fluidly in "7" series increments for navigation, like the Greek mile of 5250 feet (see http://www.celticnz.co.nz/Waitapu_Valley/Waitapu7.htm within this website).

SYRIAN LIQUID CAPACITY MEASURES.

Donald Lenzen refers to a system in place within Syria, which was based upon the legal burden that could be carried by an ass in Egypt, as well as the whole Roman Empire. This was limited to 200 Roman pounds or the cubic capacity of 20 Roman Congius of liquid. By comparative analysis of several historical references, Lenzen was able to compute the Syrian system to the following close values:

The system used in Syria is very comparable to other systems used by the Hebrews, Greeks and Romans. The Syrian Metretes is the same as the Egyptian Artaba and 1.0368 times greater than the Babylonian/ Sumerian Artaba @ 3600 cubic inches. The 1.0368 ratio is in mnemonic homage to the 1036.8 miles per hour that the Earth rotates…..24883.2 miles ÷ 24 hours = 1036.8 MPH. A Metretes @ 3732.48 cubic inches = 2.16 cubic feet and provides a mathematical progression related to the Precession of the Equinoxes. It also codes the diameter of the moon @ 2160-miles.

THE ROMAN DRY VOLUMES AND THEIR CODES RELATED TO THE SIZE OF THE EARTH.

Lenzen's scientific evaluation of the Roman dry measures is as follows:

• The true equatorial circumference of the Earth (131383296 feet) ÷ 1900800 = 69.12. This figure (read in miles) would be 1-degree of arc for the world under the 24883.2-mile (true size) assignment. An Amphora @ 1900.8 cubic inches = 1.1 cubic feet and provides a mathematical progression related to navigation using the "11" series (league, mile, furlong).
  
  
• The "11" series (league, furlong) circumference of the Earth (130680000 feet) ÷ 1900800 = 68.75 (read as miles) would be 1-degree of arc for the world under the 24750-mile assignment.
  
  
• The "6 & 7" series (yard or reed) circumference of the Earth (130636800 feet) ÷ 1900800 = 68.727272 (read as miles) would be 1-degree of arc under the sexagesimal/ septimal system.
  
  
• The true equatorial circumference of the Earth (131383296 feet) ÷ 633.6 = 207360. This figure (read as 20.736 inches) was length of the Egyptian Royal cubit, which mnemonically coded the 24883.2-mile (true size) assignment.
  
  
• The "11" series (league, furlong) circumference of the Earth (130680000 feet) ÷ 633.6 = 206250. This figure (read as 20.625 inches) was the length of the Egyptian Royal Cubit, which mnemonically coded the 24750-mile assignment.
  
  
• The "6 & 7" series (yard or reed) circumference of the Earth (130636800 feet) ÷ 633.6 = 206181.8182. This figure (read as 20.61818182 inches) was the length of the Egyptian Royal Cubit, which mnemonically coded the 24741.81818-mile assignment.
  
  
• The Choenix volume of 59.4 cubic inches is an "11" series number and relates to the "11" series Earth circumference system of 24750 miles or 130680000 feet. A 59.4 feet value would be 1/2200000th of the equatorial size of the Earth under that assignment.
  
  
• The Sextarius volume of 39.6 cubic inches, again, was aligned to the 24750-mile equatorial system and a 39.6 feet value would be 1/3300000th of the Earth's circumference under that assignment. The number of leagues (3.125-miles …16500 feet) in the "11" series circumference of the Earth is 7920 (3960 X 2).
  
  
• The Hemina volume of 19.8 cubic inches alludes again to the "11" series Earth size system and an increment of 19.8 feet would be 1/6600000th of the 24750-mile size of the Earth.
  
  
• As shown with previous national systems, these numbers also worked as circumferences for navigation. Let's discuss the merits of the Amphora @ 1900.8 in this regard…1900.8 ÷ 3.141818182 = 605. This value, in feet, would be 1/216000th of the equatorial size of the Earth under the "11" series assignment. The value of 605 feet would be 110 fathoms of 5.5 feet each.
  
  
• If an enlarged 19008 value of the Amphora volume were divided by the PI rendition 22/7 (3.142857143) then the total would equal 6048. This value, in feet, is 1-minute of equatorial arc under the Great Pyramid's "6 & 7" assignment, which represented the Earth's circumference as 24741.81818-miles. A linear increment of travel equating to 6048 feet could be read in a range of measurement values, including: Greek Samos feet of 1.008 inches (6000), Greek feet of 12.6 inches (5760) Egyptian Royal Cubits of 20.61818182 inches (3520), Egyptian Royal Cubits of 20.736 inches (3500), Hebrew/ Celtic Cubits of 21 inches (3456), rounded Megalithic Yards of 32.4 inches (2240), Hebrew reeds of 10.5 feet (576), Greek short stadia of 525 feet (11.52), Greek stadia of 630 feet (9.6).
  
  
• If the enlarged 19008 value of the Amphora were divided by the ratio 3.125, which denotes the difference in a mile (5280 feet) and league (16500 feet), then the result is 6082.56. If read in feet this would be 1 minute of arc under the ancient rendition of the "true" equatorial circumference @ 24883.2-miles. The value of 6082.56 = 3520 Egyptian Royal Cubits of 20.736 inches.

THE ALEXANDRIAN VOLUMES AND THE SIZE OF THE EARTH.

The city of Alexandria was established by Alexander the Great in 332 BC as a Greek centre in Egypt and grew in less than a century to be larger than Carthage. In became an international city, as well as a Mediterranean centre of commerce and shipping... with a diverse assortment of foreign residents. Alexandria passed formally into Roman jurisdiction in 80 BC, although it had been under Roman influence for 100-years before that time. It was at Alexandria that Julius Caesar had his liaisons with Cleopatra in 47 BC. Being a port city, second only to Rome in influence and standing, its weights, measures and volume standards are very important to consider.

As an aid in arriving at the Alexandrian standard for cubic capacity, Donald L Lenzen quotes an historical text, which say's, 'The Cubus was a vessel, the sides of which were formed by six equal squares having each of its sides a foot long, the solid contents of the cube was equal to the amphora' (Rhem. Fann. De Pond, & C.V. 59-62).
This rendition relates to the Roman foot of 11.664 inches.
Lenzen gives the following values for the Alexandrian measures of capacity:

To arrive at his estimate of what constituted an ancient Alexandrian Amphora volume, Lenzen relied upon the liquid weight of an Alexandrian Talent. I believe that the literal "Cubus" volume gives a far closer reading, based upon a Roman foot of 11.664 inches. This means 11.664 X 11.664 X 11.664 = 1586.874323 cubic inches. This is only a 2.87 cubic inch increase on the 1584 cubic inch figure and anyone commenting on the volume of an Amphora would, quite reasonably, speak of it as a Roman cubic foot. Whereas the 1592.5 value, proposed by Donald Lenzen, has no significance amongst the parcel of ancient, special numbers, the 1584 value is very dynamic and was much used. Let's put it through its paces to see what it can do.

• A 1584 feet value is 288 fathoms (5.5 feet), 96 rods/ perches (16.5 feet), 24 chains (66 feet), 2.4 furlongs (660 feet) and it's also 1/12th of 19008 (the value used in the Roman dry volume Amphora).
  
  
• A circumference of 1584 feet would reduce to a diameter of 504 feet, using PI @ 3.142857143 (22/7). The 504 value was much used in antiquity. Amongst other things it represented 5 seconds of equatorial arc under the Great Pyramid geodetic system. A value of 50.4-days was very useful in measuring periods of time within the lunar nutation cycle of 6804-days. The Assyrian Royal Cubit was 25.2 inches (½ of 50.4).
  
  
• A linear measurement of 1584 feet would convert to a circumference of 4976.64, which is 2880 Egyptian Royal Cubits of 20.736 inches or 8 such cubits per degree of arc.
  
  
• A circumference of 1584 feet ÷ 3.125 would produce 506.88 feet, which is 1/259200th of the Earth's circumference under the 24883.2-mile reading. The 25920 number, of course, relates to the cycle of precession, etc.
  
  
• The Urna @ 792 cubic inches codes a dynamic number, much used in the "11" series geodetic system. Under that system the Earth was considered to be 7920 Leagues in equatorial circumference. Under the "true" Earth size system the diameter of the Earth was 7920-miles (24883.2-miles ÷ 3.141818182 = 7920).
  
  
• The Congius @ 198 cubic inches, if read as 198 feet would be 1/660000th of the size of the Earth under the "11" series assignment of 24750-miles.
  
  
• The Sextarius @ 33 cubic inches, if read as 33 inches, would closely parallel a standard increment called the Vara, which has survived until modern times in Spanish speaking countries. The Indian Gaz is very close to this value also and, along with the Vara, is probably a residual "11" based measurement from the ancient parcel.

EGYPTIAN MEASUREMENTS OF VOLUME.

Lenzen speaks of 8 Egyptian vases which had their capacities recorded as 400 Hons. After measurement of all vessels the mean average was found to be 29.2 cubic inches. He describes another set of unmarked vessels achieving a mean average of 29.1 cubic inches and from that deduces an overall mean average, for all 17 vessels, of 29.15 cubic inches. His assessment of the Egyptian volume designated a Hon was then adjusted by him to 29.16 in consideration of a relationship he felt existed between 300 Hons and a close approximation to the Egyptian Royal Cubit measurement.
Again, Lenzen's estimated figures for the Egyptian volumes are shown to the left and comply perfectly to much used codes of antiquity:

An Egyptian Theban cube vessel could be fabricated, based upon lunar code numbers associated with the nutation cycle of 6804-days. The value of 3 sides of the Great Pyramid is 2268 feet and this number, in reduced ratio size, was the primary contributor to the Egyptian standard of capacity. A Theban @ 11664 cubic inches = 6.75 cubic feet and provides a mathematical progression related to the lunar cycle.

• The volume of a Theban translates to a cube vessel whose internal length, breadth and width are, essentially, 22.68 inches each. The 22.68" X 22.68" X 22.68" total would be 11666.19283 cubic inches. It is important to realise that the 11664 cubic inch Theban, or indeed the 11.664-inch long Roman foot were dual read as 11666.666666 and 11.666666 respectively. The 1.1666666 ratio is one of the most important of antiquity.
  
  
• The volume of a Beshu could be fashioned in various ways, based upon the lunar coding. A workable example would be 11.34 inches height X 11.34 inches width X 9.072 inches breadth (the Great Pyramid was 9072 inches long per side and the Station Stone's Rectangle at Stonehenge was 113.4 feet wide).
  
  
• These Egyptian volumes are in a perfect ratio to the later Greek volumes. The Egyptian Hon, for example, would be 1/80th of a Metretes.
  
  
• A cube of 22.68 inches per side is also 7 "rounded" double PHI inches of 3.24 inches or 14 "rounded" PHI inches of 1.62 standard inches.
  
  
• Calibration by "rounded" PHI system reflects the use of PHI inches, used in the Megalithic Yard measurement, first discovered by Professor Alexander Thom. Professor Thom found a recurring interval of length amidst the ancient, weatherworn Megalithic structures of Great Britain, which he dubbed the Megalithic Yard. He estimated this length to be about 82.9 centimetres (32.6378 inches). It is, in fact, a pure PHI based measurement and the formula for finding it is 20 inches X PHI (32.360678 inches) or about a quarter of an inch shorter than Thom's estimate. The Great Pyramid is, symbolically, 280 of these increments in length or literally 280 "rounded MY of 32.4 inches each. Several well-surveyed British sites can be positively demonstrated to comply to the MY measurement. It is also very prominently represented at Carnac, Brittany, France. Amongst many coded instances at Carnac it is found in the distance from the solitary hubstone of the western circle to the 2 most extreme components to the east, which lie at a distance of 1300 MY (of 32.360678 inches) and 1300 "rounded" MY (of 32.4 inches), respectively.
  
  
• If the volume of a Beshu, (1166.4 cubic inches) is divided by 22.68 (lunar code), then the result is 51.42857143 cubic inches. The degree angle complying with 1/7th of a 360-degree circle was 51.42857143-degrees. There is, therefore, a strong recurring coded degree angle component found when using these assigned cubic capacity numbers for the Theban, Beshu, Honnu and Hon volumes.
  
  
• If one divides the Beshu @ 1166.4 by 360 (as in degrees of arc) then the total is 3.24.
  
  
• If one multiplies the cubic capacity of a Theban @ 11664 cubic inches X 11200, then the result is the size of the Earth in feet, based upon the Great Pyramid perimeter of 3024 feet representing ½ a degree of Earth circumference arc. The use of 112 and 2240 became integral to the British CWT and Ton weights.
  
  
• If the ancient figure that was used to describe the duration of the lunar nutation cycle (6804 solar days) is stated in hours (163296 hours), then 11664 hours (substituted for the Theban's 11664 cubic inches) represents 1/14th of the period.
  
  
• Under the Sabbatical Calendar system the calendar ran for 7 solar years (2556.75-days) and 7.2 lunar years (2551.5-days) concurrently before commencement of another sabbatical period. The difference between 7-solar years and 7.2 lunar years is 5.25 days. Ancient Druidic priests of Gaul, who fashioned the bronze plaque "Calendar of Coligny" could calculate the two concurrently running cycles of the lunisolar calendar in increments of 5.25-days (using a ½ reed rod of 5.25 feet). Under this system there were 486 periods of 5.25-days in the 2551.5-days of 7.2 lunar years. There were also 487 periods of 5.25-days in 7-solar years. The Calendar of Coligny plaque was 4.86 feet in length…for a combined top and bottom length total of 116.64-inches.
  
  
• The value of 11664 hours is 486 solar days. The hour total in 2551.5-days (7.2 lunar years) is 61236, which is 11664 X 5.25-hours. Druidic Priests performed a "Mistletoe" cutting ceremony 5.25-days (6th day) after a Winter solstice and full moon conjunction. This meant that 2551.5-days later (7.2 lunar years) the Sabbatical calendar period would end and a new one would commence. The ending day was also 7-solar years after the Winter solstice, full moon conjunction.

From these numbers it is quite easy to detect that the Egyptians were using the Theban, Beshu, Honnu and Hon for mnemonic reference to periods of the moon within the Sabbatical calendar system. Primary numbers used for tracking lunar periods within the Sabbatical cycle were 48.6, 40.5, 32.4, 16.2, as well as 5.25.

Now that the Theban "trivia" has been dealt with, let's get into the real stuff…navigation.

EGYPTIAN NAVIGATIONAL CODES AND THE SIZE OF THE EARTH.

The most primary functions of the Theban, Beshu, Honnu and Hon were to act as "circumference codes" in navigation. They were for remembering the size of the Earth and designed to provide suitable "linear codes" for straight-line voyages that converted to sexagesimal circumferences for degree angle readings through 360-degrees.

• A Theban @ 11664 ÷ 3.141818182 = 3712.5. If this number were read as feet, then it would also equate to 2160 Egyptian Royal Cubits of 20.625 inches. An increment of 3712.5 feet would also be 1/35200th of the equatorial size of the Earth under the "11" series assignment. Under this system the Egyptian Royal Cubit value for the size of the Earth is 76032000 Royal Cubits, breaking down to 211200 Cubits for a degree of arc, 3520 for a minute of arc and 58.666666 Cubits for a second of arc. The Earth was considered to be 24750 miles in equatorial circumference under the "11" series reading.
  
  
• The 3712.5 feet value is also 675 fathoms of 5.5 feet each or 1375 rounded Megalithic Yards of 32.4 inches each. The 11664 (feet) circumference generated by these straight-line values equals 32.4 feet per degree of arc or 12 rounded Megalithic Yards.
  
  
• Although this Theban coding might only have been used as a navigational teaching system, it was possible for a navigator at sea to calculate distances travelled in accruing intervals based upon 675 fathoms or 1375 rounded Megalithic Yards. The ship might do a straight-line voyage accumulating to, say, 47 such intervals before the navigator assigned a new heading to suit the wind conditions. Once the overall distance of the leg had been marked as a straight line on the plotting chart, a circle with a diameter equivalent to the leg travelled would be centred on the end of the line, or point arrived at. Each degree of that circle would represent 12 rounded Megalithic yards… X 47.
  
  
• The Theban @ 11664 ÷ 3.142857143 (22/7) = 3711.272727 and if read as feet would = 2160 Egyptian Royal Cubits of 20.61818182 inches.
  
  
• The Theban @ 11664 ÷ 3.125 = 3732.48 and if read as feet would = 2160 Egyptian Royal Cubits of 20.736 inches.

SUMERIAN/ BABYLONIAN MEASURES OF CAPACITY

Donald L Lenzen used "weight" clues to estimate the capacities of Sumerian/ Babylonian volumes, referred to in historical literature. Using an ancient ritual text preserved in the Louvre Museum, he was able to reconstruct the sequence of various volume measures. He estimated the volume of the ancient Qa, based upon a statement related to a "Sutu of 10 Minas". The Babylonian Mina was a unit of weight and a Sutu was made up of 10 Qa, so the volume of a "liquid" Qa was, anciently, considered to be the grain weight of a Mina. This was probably a merchant "close approximation", in much the same way that a "Cubus" volume closely approximated the weight of an Alexandrian Amphora of liquid.

Obviously the civilisations that (according to historical accounts) gave us the sexagesimal system for navigation and 360-degrees in a circle were working to that number rather than 358.3216 for their Artaba volume. Lenzen's estimate for the cubic capacity of a Qa is 59.72 cubic inches, which is a marginal shortfall on 60 cubic inches. His estimate for the weight of a Babylonian Mina is based upon a count of 15102.72 grains. Whereas this number is without meaning within the ancient parcel of useful numbers, a count of 15120 grains would have tremendous significance and relate to the dimensions of the Great Pyramid, complete with its many codes.

• The 12960 number is one of the most used in antiquity and is the ½ value of 25920, the number used to describe the duration of precession in years. If 129600 cubic inches, as represented by the Archane volume, were considered as feet, then this would be a 1/1008th segment of the world under the Great Pyramid assignment of 24741.81818 feet. Alternatively, 1008 feet would be 10 seconds of Earth circumference arc, or 1000 Greek Samos feet. An Archane @ 12960 cubic inches = 7.5 cubic feet and provides a mathematical progression related to the 360-degree compass system and navigation by the Greek or Hebrew "7" system (reeds, Greek miles of 5250 feet).
  
  
• If the 129600 number were read as feet and considered as a circumference value for navigation, then the value would reduce to 2.5 leagues (41250 feet) when divided by 3.141818182. This is 24000 Egyptian Royal Cubits of 20.625 inches.
  
  
• The 129600 feet value would reduce to 24000 Egyptian Royal Cubits of 20.61818182 inches if divided by PI @ 3.142857143 (22/7). This is 1/3168th of the 24741.81818, Great Pyramid standard circumference.
  
  
• The 129600 feet value would reduce to 41472 feet if divided by 3.125, which is 24000 Egyptian Royal Cubits of 20.736 inches and 1/3168th of the 24883.2 mile "true" equatorial circumference.
  
  
• The Homer @ 21600 cubic inches codes the 2160 mile diameter of the moon and the 2160-years the sun spends living in each house of the zodiac during the precession of the equinoxes. It, of course, functions perfectly as a circumference for navigation and when divided by 3.141818182 converts to 6875. There were 68.75 miles for every degree of equatorial arc under the 24750 mile, "11" series reading. When the 21600 value is divided by 3,142857143 (22/7) the value derived is 6872.727272 and there were 68.727272 miles for each degree of arc under the Great Pyramid (24741.81818-mile) assignment. When the 21600 value is divided by 3.125, then the derived value is 6912 and there were 69.12 miles per degree of arc under the 24883.2-mile, "true" equatorial assignment.
  
  
• The Artaba at 3600 cubic inches is reasonably self-explanatory, providing a wide range of navigational options, as do the Sutu @ 600 cubic inches and Qa @ 60 cubic inches.

EACH NATION CREATED PERFECT VOLUME VESSELS BY USING THE PHI FORMULA.

Although the cousin nations made their measures either the same or in easily calculable ratios to their trading neighbors, they also required precise formulas for fashioning very individual circular jar or tub vessels for their own coded volumes of preference. The standard formula used universally appears strongly to be:

10 inches ÷ PHI (1.6180339) = 6.18034 inches.

The mathematical relationships shared in common by many civilisations intimates, very strongly, that the 6.18034 inch increment was used universally to calculate the bases for all "official standard" measuring tubs or vessels used by the cousin nations of the ancient Mediterranean Basin. For example:

• 1 Egyptian Theban tub @ 11664 cubic inches could have a circular base of 18.541 inches (3 X 6.18034") and sides 43.2 inches high. There would be 270 X 43.2 cubic inches in 11664 cubic inches The length of the Great Pyramid is 432 Hebrew/ Celtic Royal Cubits of 21-inches).
  
  
• 1 Greek Metretes vessel @ 2332.8 cubic inches (actually a liquid volume) could have a circular base diameter of 12.36068 inches (2 X 6.18034") and sides 19.44 inches high. The 19.44 number was used for lunar calculations and the Roman Pace @ 58.32 inches was 3 X 19.44 inches. There would be 120 X 19.44 cubic inches in 2332.8 cubic inches.
  
  
• The Hebrew Homer @ 28512 cubic inches could have a circular base diameter of 30.9017 (5 X 6.18034") and sides that were 38.016 inches high. The number 38.016 is a navigational use number and the Roman Amphora @ 1900.8 cubic inches was 50 X 38.016. Alternatively the Hebrew Homer @ 28512 cubic inches was 750 X 38.016 cubic inches.
  
  
• The Roman Amphora @ 1900.8 cubic inches could have a circular base diameter of 12.36068 inches (2 X 6.18034") and sides 15.84 inches high. The 15.84 number was used in navigation and there would be 120 X 15.84 cubic inches in 1900.8.
  
  
• The Babylonian Archane @ 129600 cubic inches could have a circular base diameter of 49.44272 inches (8 X 6.18034") and sides that extended above the base 67.5 inches. The number 129600 was used in navigation. The sum of 12960 years is half the cycle of the Precession of the Equinoxes. There would be 1920 X 67.5 cubic inches in 129600 cubic inches.

Any precise volume standard used by the cousin nations could be fashioned with tremendous precision as a circular vessel when the base diameter was in allotments of 6.18034 inches. The vessels could be more squat than tall or vice-versa... it didn't matter, as long as the base retained the 6.18034 inch progression in it's diameter. The same formula, in lesser ratio, could be used to fabricate tumblers, jars or everything down to small cups for use by wine, beer or mead vendors within commercial premises.

The 6.18034 number could also be pressed into service if it was necessary to lay out circular land plots of precise square footage area. For example, an Egyptian Pyramid Acre of 28800 square feet would be a circle with a diameter of 31 X 6.18034 feet. An acre of 43560 square feet (1 furlong X 1 chain) would be a circle of 38.1 X 6.18034 feet.

It seems evident that the old Scottish Ell (37 inches) was, quite simply, 6 X 6.18034 inches originally. The Scottish Ell would work very fluidly in laying out circles of desired square footage area with reasonable calculation ease. This is, undoubtedly, one of the surviving measurements carried from Egypt to France and Britain by about 5000 BC. Half a Scottish ell could be used effectively to make old English bushel barrels or tubs of 2160 cubic inches (1/10th of a Babylonian Homer).

SUMMARY TABLES, supplied by Prof. Bruce Moon.

Corrected Ancient Volume Measures in Cubic Inches for the Major Unit of Each System.

Note: a small 2, 3, 4 or 5 means "to the power of".

(Note the predominance of twelve as a factor)

Owing to the large number of common factors in these measures, there are often simple relationships between them, which we obtain by looking at their ratios and cancelling common factors. Examples are the following.

A:B 6:5; B:C 6:5; C:D 6:11; D:E 110:9; E:F 3:4; F:G 25:12; G:H 2:5; I:J 6:5; J:K 11:18; K:L 9:100

A:G 15:1; A:H 6:1; B:E 8:1; B:F 6:1; C:F 5:1; D:I 15:1; D:J 18:1; E:F 3:4; E:K 1:5; F:H 5:6;

[It is interesting to note that though the Greeks were very familiar with ratios and competent in their use, particularly in geometry, they failed to recognize that they are simply numbers - the set of "rational numbers" may all be expressed as ratios of whole numbers. There are some ratios which cannot be so expressed. The ratio of the diagonal to the side of a square (√2) is irrational (a fact which apparently horrified Pythagoras) and so is the golden ratio (1 + √5)/2....Bruce Moon].

Having assessed the volume standards of a selection of Mediterranean civilisations and seeing vivid examples of profound codes lurking in the national capacities, let's now address official "weights" standards of the cousin nations.

THE HEBREW WEIGHTS.

Lenzen provides several biblical and historical quotes related to the Hebrew coin weights system, which allow us to establish what the sought after grain weight was. In a quote by Josephus there is reference to the Hebrew Shekel being 'equal to four Athenian Drachmae'. Charles Seltman, author of, Greek Coins fixes the weight of the Drachmae @ 65.59 imperial grains, making the heavy Hebrew shekel close to 262.36 grains. The light Hebrew Shekel was set to half the grain weight of the heavy Shekel, or something in the close proximity of 131.18 grains. Apart from complying to these wheat grain weights, the coins weights were also calculated according to barleycorns, which were about .8 of the size and weight of a wheat seed. There was also use of gerah beans, which were rated as being the equivalent of 16 barleycorns. In the final analysis, however, weight standards were founded upon and resolved back to the weight of wheat, which remained the final authority.
After a comprehensive assessment of all available information, Lenzen provides the following estimates for the Hebrew heavy and light "Desert" standard.

In Ninevah archaeologists discovered a very large number, inscribed into a clay tablet, which was 195955200000000. This has become known as the Ninevah constant. It's interesting to note that the "true" equatorial circumference of the Earth (24883.2-miles), encoded into such edifices as the Parthenon of Athens, bears a relationship to the Ninevah constant. Therefore: 195955200 (abbreviated) ÷ 24883.2 = 7875, so it's apparent that there's a relationship to the grain weight of the Hebrew heavy Talent as well.

By adjusting the grain count for a shekel by less than ½ a grain, the number derived becomes highly significant and relates, simultaneously, to a "7" number series used by the Greeks and a mathematical progression that relates to the moon or Sabbatical calendar system. Let's see what this progression did under the ancient astronomical/ navigational system.

• The Hebrews, like the Greeks, showed a preference toward working in a "7" series of numbers and had a Royal Cubit of 21-inches. Within this standard they worked in reeds of 10.5 feet or ½ reeds of 5.25 feet on up to short stadia of 525 feet ...then larger Greek stadia of 630 feet onward to Greek miles of 5250 feet. They also worked in a range of other numerical standards. The distance of 7875 feet, suggested by the Talent grain count, would be 1.5 Greek miles, 750 reeds and 4500 Hebrew/ Celtic Royal Cubits. There would be 3.141818182 (PI value used in navigation) increments of 7875 miles (of 5280 feet) in the Great Pyramid geodetic assignment, which represented the equatorial circumference as 24741.81818-miles.
  
  
• If the 7875 feet length were treated as a linear distance for use in navigation, then this would convert to 24750 feet (1.5 leagues…4500 fathoms) of circumference using the PI rendition of 3.142857143 (22/7). The 24750 figure is, of course, the "11" series assignment for the equatorial circumference This would mean that every degree of circumference arc would be 68.75 feet (12.5 fathoms). The circumference value of 24750 feet would also equal 14400 Egyptian Royal Cubits of 20.625 inches, which would reduce to 40 cubits per degree of arc.
  
  
• The Mina @ 13125.0 grains codes a very important ratio and mathematical progression (1.3125), which contains the significant periods of the moon, as well as principles of navigation. These numbers include: 5.25 (used in the Hebrew and Greek measurement systems and also as a period in days (5.25-days) within the lunisolar Sabbatical Calendar); 118.125 (used as a day count to describe 4-lunar months); 354.375 (a lunar year in days); 472.5 (the height in feet of the Khafre Pyramid and, in days, the duration of 16 lunar months); 590.625 (the length in feet up the face of the Khafre Pyramid and, in days, 20 lunar months), 708.75 (the length, in feet, of the Khafre Pyramid and, in days, 2 lunar years), etc. As a ratio 1.3125 is multifunctional and is usable in converting measurements from, say, 4 feet to 5.25 feet (½ reed).
  
  
• The Shekel @ 262.5 grains is similar in its attributes to the Mina @ 13125.0. It was an important number used in tracking the period of the moon within the lunar nutation cycle of 6804-days or within the 2551.5-day (7.2 lunar years) lunar period of the Sabbatical calendar.
  
  
• Under a tradition that survived into mediaeval times in Europe, 75 Roman miles represented 1-degree of arc for the world. As will be shown as we proceed, this tradition relates to a "7" series of numbers, within which the 13125 value is centrally important.

Lenzen states that, 'The Hebrews, like the Babylonians, had two weight standards, one double the weight of the other'. He then provides substantiating ancient quotations or modern scientific assessments in support of his contention. The light Desert Talent is, therefore, simply ½ the value of the heavy Desert Talent. There was, yet, another variation within the system called the Jerusalem standard, which was also divided into "heavy & light" categories. The creation of the Jerusalem standard is said to have occurred around the time of building of the Second Temple, wherein the older Shekel weight was increased by a fifth part. Here's Lenzen's estimate (left) of the heavy Jerusalem standard grain weight.

By adjusting the Shekel weight by one third of a grain, the Hebrew Jerusalem standard springs into life and has great significance. The numbers generated by this grain count are very useful and were fully embraced by the Greeks. A Talent of 945000 grains would contain the following navigational attributes:

• If a length of 94500 feet (150 Greek stadia of 630 feet each or 1.8 Greek miles of 5250 feet each) were converted to a circumference, then the result would be (using the 22/7 PI rendition of 3.142857143) 297000 feet. This is 18 leagues or 825 feet (150 fathoms) per degree of arc. A convenient increment for use at sea for linear distances would be stadia or Greek miles, providing easy calculation of degree angles back to point of departure or onward to destination.
  
  
• The Mina @ 15750 grains, if read as feet, would equal 1500 Hebrew reeds. This is the measurement increment referred to in the Bible verse of Ezekial 40: 5, which is described as, 'six cubits long by the cubit and an hand breadth'. Based upon the era when the scriptural account was written, Lenzen refers to an early era Hebrew cubit of an estimated 16.84 inches. He also considered the Hebrew handbreadth to have been an estimated 4.21 inches, making the cubit referred to in Ezekial as 21.05 inches. Six such cubits would equal a reed of 126.3 inches or 10.525 feet. Whereas a number 10.525 is without meaning and works in no useful mathematical progression, the value 10.5 feet is dynamic and works very fluidly in the known national measurement or weights systems based upon "7". A small cubit of 16.8 inches would be equally dynamic, as would a "handbreadth" of 4.2 inches.
  
  
• The Shekel @ 315 grains, if read as feet, would comply with the length found on the inner rim of the Sarsen Circle at Stonehenge (½ Stadium). The original circuit was made slightly elliptical to carry different length and breadth codes, but when based upon PHI reductions of the Aubrey Circle (288 feet diameter) and "Y" Holes Circle (178 feet) the Sarsen Circle is seen, mathematically, to equate to 110 feet for its outer diameter. The reduction formula between the circles of Stonehenge is 288 feet ÷ 1.6180339 (PHI) = 178 ("Y" Holes) ÷ 1.6180339 = 110 (Sarsen Circle outer diameter). This diameter is reduced to 100 feet for the inner diameter in consideration of the 5 feet widths of the lintels, creating a circumference that is dual read as PI and 315 feet simultaneously. The Brasen Sea structure, fabricated by the Widow's Son, Hiram of Tyre, for the Temple of Solomon was, undoubtedly, made to the 21-inch cubit standard. Given the Brasen Sea's described dimensions, it would have been 630 inches (5 reeds) in circumference.

By an adjustment of less than a quarter of a grain on the Shekel weight, estimated by Donald L Lenzen, it makes sense and works fluidly as a dynamic mathematical progression.

• The Jerusalem Talent @ 472500 grains is coding a very special lunar number found in the vertical height of the Khafre Pyramid. Khafre's external dimensions are dedicated to the cycle of the moon and it's vertical height is 472.5 feet. If this period was read as days it would represent 16 lunar months of 29.53125 days each (synodic). The Khafre Pyramid also codes the geometric principle of the 3,4,5 triangle. As will be demonstrated, the 4725 value occurs frequently in the weights standards of several civilisations. If the Jerusalem light Talent were read as 4725 feet (450 reeds) and used as a linear measurement for navigation, then it would convert to a circumference of 14850 feet (2700 fathoms) using the PI rendition 3.142857143 (22/7). This is 2.5 rods/ perches of 16.5 feet per degree of arc. The "4725" set of numbers was very popular for use in various Mediterranean weights systems.
  
  
• If the Jerusalem Talent value @ 472500 were read as a circumference of 4725 feet, 1-degree of arc would be 13.125 feet (reminiscent of the 131.25 grains found in the Hebrew light Shekel, Desert standard).
  
  
• The 7875 grains that constitute the weight of the Jerusalem light Mina is reminiscent of the Hebrew heavy Talent, Desert standard.
  
  
• The 157.5 grain weight of the Jerusalem Shekel identifies a very important number, used in a mathematical progression. The progression provides a series of values that refer to the lunar cycle and navigation. It's of interest to note that archaeologist William Flinders Petrie measured the Grand Gallery within the Great Pyramid to be 1883.6 inches or 156.96666 feet (essentially 157 feet). It would appear that the original architects wished to encode 157.08 feet for mnemonic reference to the numbers representing the ½ value of PI @ (3.1416). A small extension to the length runs to just inside the alcove at the top end of the Grand Gallery, undoubtedly coding 157.5 feet. Alternatively, a small reduction of the length runs to the face of the step at the top end of the gallery @ 1815.5 inches or 151.2916 feet. This would have been intended to represent 151.2 feet (a geodetic code under the Great Pyramid's navigational system). Two base sides of the Great Pyramid equate to 1512 feet…or ¼ of a minute of Earth circumference arc.

THE GREEK WEIGHTS.

Donald L Lenzen quotes ancient historians or modern scholars, where they make reference to (or comparisons between) the Hebrew and Greek coin weights. He also quotes author, Charles Seltman who contends that a Greek Drachma of about 65.59 imperial grains weight was used in Athens, Euboea, Samos, Corinth and Cyene. There was a relationship between the Hebrew and Greek systems, with certain weight denominations, like the Greek Didrachma, being the same as the Hebrew Desert standard, light Shekel.

The Greeks displayed a preference toward working in "7" values and had a mile of 5250 feet. This was 30 feet shorter than the so-called British Mile, which worked to an "11" series of numbers. The Greeks also had a Stadium measurement of 630 feet. This was the "7" equivalent to the furlong @ 660 feet and, again, was 30 feet shorter than the furlong.

• The Greek Attic Talent @ 393750 grains, if read as feet, would represent 75 Greek Miles or 625 stadia. This value, converted to a circumference, using 3.142857143 (22/7), would be 1237500 feet or 75 leagues of 16500 feet each. A degree of arc within this circumference would be 625 fathoms of 5.5 feet each. Essentially, the 373750 coding is for teaching principles of navigation, using a "7" set of numbers in straight line voyages, converting to a circumference from which degree angles can be conveniently read.
  
  
• The Greek Attic Mina @ 6562.5 grains, if read as feet, would be 1.25 Greek miles of 5250 feet each. This is a very convenient navigational increment and was probably used at sea. It would also represent 125 short stadia of 525 feet each. This value, 6562.5 feet would convert to a circumference of 20625 feet (247500 inches) or 12000 Egyptian Royal Cubits of 20.625 inches (using the PI rendition of 3.142857143). One degree of arc under this system would be 687.5 inches (one degree of arc under the "11" series geodetic system was 68.75 miles) or 33.33333 cubits per degree. A tail of .3333333 is simply indicative of 1/3rd and every 3 degrees of this circumference would be 100 Egyptian Royal Cubits.
  
  
• The attributes of the Didrachma @ 131.25 grains has already been discussed in relation to the Hebrew Desert standard, light Shekel. The Greek Drachma @ 65.625 grains is the ½ value of the Didrachma.

By adjusting Lenzen's estimated grain weight of the Didrachma by about a ¼ of a grain of wheat, the entire system comes pulsing back to life. This "Commercial" system is in homage to the moon and provides a series of numbers for tracking the movements of the moon within the solar year, lunar year or lunar nutation cycle of 18.613-years.

• The Commercial Talent @ 590625 grains is accentuating a length value found on the Khafre Pyramid. The diagonal length, up the face, from the base to the apex of Khafre was set by a 3,4,5 triangle formula to be 590.625 feet. This value, divided by two, is 295.3125 feet and there are 29.53125-days in a lunar month (to a tolerance of about 57 seconds excess). This form of lunar coding was very popular, with several of the cousin nations using a 4725 number (or increases/ decreases) as a value in their weights systems. The vertical height of 472.5 feet was the design height of Khafre Pyramid and is 29.53125 feet X 16. The Hebrews made their light Desert Talent 472500 grains or .8 of the Greek commercial Talent. The 590625 & 4725 number combinations were used in other forms of Greek and Roman weights, such as their systems for weighing out quantities of gold. Half the base length of Khafre Pyramid was 354.375 feet and, in days, this was the length of a lunar year.
  
  
• Unsurprisingly the dynamic lunar number 590625 found in the grain weight of the Greek talent converts to a navigational number when multiplied by the PI rendition 3.142857143 (22/7). The total derived is 1856250 and this value, in feet, would be 112.5 leagues of 16500 feet each. It's interesting to note that 11.25 degrees is 1/32nd of 360 degrees. The value of 1856250 feet would be 1/70.4th of the circumference of the Earth under the "11" series geodetic system, which tailored the equatorial circumference of the Earth to 24750-miles.
  
  
• The Commercial Mina @ 9843.75 grains would be used for mnemonic reference to the 9.84375-days in 1/3rd of a lunar month. These very difficult and highly scientific numbers, once found, had to be remembered forevermore or precise calculations related to the moon's annual cycle could not be done. The lunar cycle needed to be included within the lunisolar Sabbatical Calendar or the 18.613-year lunar nutation cycle (set anciently to 6804-days). With the loss of the numbers would begin the decline and eventual loss of the concept of civilisation and optimised, functioning society. The numbers were kept in constant remembrance within the weight grain counts or cubic inch capacities of the Amphora vessels.
  
  
• The Commercial Didrachma grain weight @ 196.875 grains (based upon the lunar cycle mathematical progression), became the foundation number for the Egyptian, Roman and Greek "Beqa", gold dust weighing standard.
  
  
• The Commercial Drachma grain weight @ 98.4375 grains, again, amongst other things like navigation, provides mnemonic reference to 9.84375-days or 1/3rd of a lunar month. The numbers themselves are very versatile and profound, with many facets, functions and interrelationships to other national systems. There was an expansive, multi-disciplined science to be found within these grain weight mathematical codes or their cubic capacity counterparts.

ROMAN GOLD STANDARD WEIGHTS.

The Roman Gold standard is based upon a Talent that is the same grain weight as the Babylonian gold standard. This is how Lenzen assesses the Roman system (left box):

Again, the dimensions of the Great Pyramid, Khafre Pyramid and the Greek Stadium measurement are present within these grain weight numbers.

• The Roman Talent @ 378000 grains is in homage to ½ the side length of the Great Pyramid at 378 feet. This was also the diameter of Stonehenge (NW to SE).
  
  
• The Mina @ 6300 grains is again in homage to a measurement from the Great Pyramid, each side of which is 63 feet X 12. The distance of 63 feet is also 6 reeds of 10.5 feet each. A distance of 630 feet was marked into the running track at Olympia and is the true Greek Stadium measurement, although measures like 525 feet have sometimes been called a Stadium. The inner rim circumference of Stonehenge's Sarsen Circle was, in one intended reading of its coding, ½ a Stadium @ 315 feet [the Sarsen circle was built to be slightly elliptical and a coded reading of one cross-diameter was 100 feet to 100.8 feet. From this, readings of 314.16 feet (PI coding), 315 feet (Stadia coding) or 100.8 feet diameter (1-second of Earth circumference arc coding under the Great Pyramid equatorial circumference of the Earth assignment) were included in the readings]. The Stadium was very important to measuring the size of the Earth under the Egyptian sexagesimal system wherein there were 576 stadia per degree of arc. The upward, diagonal face length of the Great Pyramid from its base to the flat floor altar atop the pyramid was 576 feet.
  
  
• The Libra of 4725 grains is, once again, in homage to the vertical height of the Khafre Pyramid @ 472.5 feet. Khafre Pyramid dimensions occur in the weights standards of several Mediterranean civilisations, with the number 4725 being, arguably, the most popular choice upon which to found a grain weight. The Libra, in an abbreviated form of its "spelling" became the (lb) pound of England, although it was only .675 the weight of the pound restored by Henry VIII.
• The value of the Roman Uncia is 2 Egyptian Beqa (a gold weight standard value used in the Nubian goldfields and adopted by several civilisations). The Greeks also used the Beqa, which they called a Tridrachm @ 196.875 grains. The Roman Beqa, of equal grain weight to the Tridrachm or Egyptian Beqa, was called a Semuncia.

Figure 2: These Egyptian "Beqa" weights are all marked to indicate that they were used for weighing quantities of gold dust, as each bears the "gold" insignia. This, seemingly, complete set was found at Khartoum.

THE ROMAN LIBRA OF WEIGHT AND THE PONDO OF ACCOUNT.

The Babylonians had 2 kinds of Talent weights, one of which featured in everyday transactions and another that was reserved exclusively for payments to the Royal treasury. The ordinary Talent was 60 Mina and the Royal Talent was 61.666666 Mina (61& 2/3rds).
The Romans appear to have had a similar system in place to do with their Libra, wherein there was an ordinary Libra of weight (4725 grains) and a slightly heavier Libra of account called the Pondo (4921.875 grains).

Donald L Lenzen, after combing a myriad of ancient references, concludes that the values for the Libra of weight and the Libra of account or Pondo were based upon 96 & 100 silver Denarius coins respectively to achieve the following grain values:

The Roman's show a surprising degree of sophistication in their choice of coded values, which this researcher finds astonishing, considering their track record of violence and pigheaded brutality. Prejudices aside, they're to be congratulated for the coding they managed to encrypt into the grain weight of a Pondo.

• The Libra of weight is clearly in homage to the 472.5 feet height of the Khafre Pyramid, which is a strong lunar code. The sum of 4725 grains is 160 X 29.53125 (the number of days in a lunar month).
  
  
• The Pondo of account is a lunar code also and pays homage to the lunar month and lunar year. The lunar month is 29.53125-days (according to the ancient system which was correct to within 57 seconds per lunar month). One-sixth part of a lunar month would be 4.921875-days. This period would also be 1/72nd of a lunar year.

To estimate the grain values of the Roman Silver Denarius coin and Libra weights, Lenzen lists the accrued "averages" arrived at after 3323 Roman coins, of varied eras, were officially weighed. The averages showed a Denarius of 49.27 grains and a Libra of 4730.70 grains.
He later includes an additional refined "average" based upon weighing 2456 Brass Sestertius coins, bringing the total of all coins weighed to 5779. From this he deduces that the Roman Libra weight, as found in surviving coinage, averages 4720.15 grains. This is a marginal shortfall of only 4.85 grains from the 4725 grains weight proposed by this researcher as the true value of the Roman Libra.
It's fair to deduce that the surviving coins, weighed by modern scientists, were somewhat worn by the time they had been used in multiple ancient transactions or had jostled together for years in ancient merchant's kisum money & stone weights pouches. It is therefore reasonable to look at a slight increase on the averages found by modern scientists, in order to reach the intended grain weight of the assayers and coin fabricators of old.

THE ROMAN SILVER STANDARD.

Donald L Lenzen concluded that the early Alexandrian Libra of Account became the Silver standard, still used in Florence, Italy in 1340 AD. This same standard was adopted by King Edward III to facilitate English wool exportation to Italy. The system was:

This system is somewhat more simple than the sophisticated standards in the possession of the Hebrews, Greeks, Assyrians, Babylonians or Egyptians. Other of the Roman standards used much more complex numbers also. The system is, however, capable of producing some navigational information, especially in terms of the Libra weight. This version, found in Florence in 1340 A.D., is probably only a shadow of its former self.

• If the 5250 grains of the Libra were read as feet, then the length would be a Greek mile. This distance X 3.142857143 (22/7) would produce a circumference of 16500 feet or 1 league. Although full knowledge of the ancient British league was lost, it was known to have been about 3-miles. In ratio with other lengths, such as the furlong, it would have been 3.125 miles. By the 19th century in England, many old measurements were obscured or distorted. A navy fathom, for example was, by that time, 6 feet (2 yards), whereas a merchant navy fathom was still the old 5.5 feet ("11" series).

The above system was, more or less, what Edward III introduced to England in 1340 AD and what persisted until Henry VIII modified it slightly almost 250-years later.

ALEXANDRIAN WEIGHT STANDARD.

Lenzen provides this estimation of the weight system used at Alexandria, an international centre of commerce from 320 BC.

The Alexandrian system is sophisticated and introduces dynamic values from the ancient parcel of special navigational numbers.

• The Alexandrian Talent @ 403200 grains, if read as feet, would be 640 Greek stadia of 630 feet each or 76.8 Greek miles of 5250 feet each. The 76.8 mathematical progression leads to numbers such as 2304 and each face of the Great Pyramid was 230400 square feet or 8 Egyptian acres.
  
  
• If the 403200 grains of the Alexandrian Talent were considered as feet, then such a length would be 1/324th of the circumference of the Earth under the Great Pyramid equatorial assignment of 24741.81818-miles. The 324 value is highly important and was representative of "rounded" PHI measurement. The Megalithic Yard of Britain was based upon 20-inches X 1.6180339 (PHI) = 32.360678-inches. Because PHI increments were difficult to work with a rounded value of 32.4 inches was also used in standard measurements. The Great Pyramid's perimeter value @ 3024 feet is 1120 increments of 32.4 inches. The 112 value became important to the British weights system as a CWT of 112 lb.
  
  
• If the 403200 feet were converted to a circumference for navigation, using the PI rendition of 3.142857143 (22/7), the result would be 1267200 feet or 76.8 leagues of 16500 feet. This circumference would also be 240 miles of 5280 feet and 1-degree of arc would be 640 fathoms of 5.5 feet. As stated, the 5.5 feet fathom persisted as the English merchant navy fathom until well into the 19th century AD.
  
  
• The Alexandrian Mina @ 6720 grains, if considered as feet, would be 640 Hebrew reeds of 10.5 feet, 3840 Hebrew/ Celtic Royal Cubits of 21-inches, 4480 Hebrew/ Celtic common cubits of 18-inches, 6400 Greek feet of 12.6 inches and 4800 old Hebrew cubits of 16.8 feet. Another form of cubit was a Hebrew one of 17.5 inches and there would be 4608 such cubits in 6720 feet. The Assyrian cubit of 25.2 inches was 2 Greek feet and there would be 3200 Assyrian cubits in 6720 feet. The sum of 6720 feet is 1.28 Greek miles. A length of 67.2 feet would go into the base perimeter of the Great Pyramid @ 3024 feet a total of 45 times.
  
  
• If the 6720 feet was converted to a circumference using the PI rendition 3.142857143 (22/7), then the resultant circumference would be 21120 feet, which is 1.28 Leagues or 4 miles of 5280 feet. There is ample evidence to suggest that circles were divided by 360-degrees, 320-degrees and, in the case of values based upon "7", the division of a circle could be 630-degrees (like the Brasen Sea). If the 21120 feet circle was divided by 320, then the result would be 66-feet. North and South American civilisations seemed to prefer circles dividing by 1/8th segments. One 360th of the 21120 feet circumference is 58.666666 feet.
  
  
• The Libra @ 5040 grains, if considered as feet, would be 480 Hebrew reeds or 4800 Greek feet, etc. The Roman foot is considered to be, officially, 11.664 inches and, certainly, that exact number is of extreme importance in terms of volumes and grain weights. In actual measurements, however, it would have been used as the important ratio value 11.6666 inches. (11 & 2/3rds inches) The length of 5040 feet would then be 5184 Roman feet of 11.66666 inches. The slope angle up the side of the Great Pyramid was 51.84-degrees.
  
  
• The Uncia of 420 grains codes one of the most used numbers of antiquity, which was the basis of the Great Pyramid's "6&7" coding (6 X 7 = 42). Length increments like the Greek mile or Stadium were divisible by 42… (5250 ÷ 42 = 125 or 630 ÷ 42 = 15)…and as all geriatric fans of "Hitchhikers Guide to the Galaxy" know, 42 is the secret of the universe.

THE EGYPTIAN WEIGHTS STANDARD.

Figure 3: The 8 stone weights shown are "Beqa weights", which were formerly used in the Nubian gold fields and inscribed with the "Nub" sign (the hieroglyph for gold). Donald L. Lenzen states that, 'The Beqa was multiplied decimally up to 2000 units and divided binarily down to 1/16th shekel'.

The 8 stone weights shown are accompanied by signs, which indicate that they represent 1/3, ½, 1, 1½, 2, 3, 6 & 10 Beqa.
Lenzen compares the weight values of four official, carefully marked, Egyptian stone weights to arrive at his average for a Beqa @ 196.65 grains. The stones, all notably inscribed with the names of a king or governor, range from the eras of 2250 BC to 1450 BC. Donald Lenzen's estimate is shown at the left.

The Roman Attic Talent was exactly the same as the Egyptian Talent and the same holds true for the Beqa Shekel weight utilised in both regions.

SO WHAT WAS THE BEQA CODING?

The Beqa went on to be adopted by both the Greeks and the Romans and the numbers generated by it are related to the lunar cycle, as found encoded into the dimensions of the Khafre Pyramid. Let's look first of all at how the Greeks and Romans used the Beqa. Again, Donald L. Lenzen's averages are found in the boxes to the left:

To understand the entire Beqa system and exact ratio variations to it adopted by Mediterranean civilisations, one must understand the coded dimensions of the Khafre Pyramid.

• The length of the Khafre Pyramid is 15/16ths of the Great Pyramid's length or 708.75 feet. The formula for finding its true intended length is, therefore, 756 ÷ 16 = 47.25 feet X 15 = 708.75 feet.
  
  
• The Khafre Pyramid was built to demonstrate 3,4,5 triangulation and lunar cycle codes simultaneously. Therefore half its base length (354.375 feet) represents the "adjacent", as well as the lunar year of 354.375-days. The height of the Khafre Pyramid was intended to be the "opposite" and achieve 472.5 feet (16 lunar months of 29.53125-days each = 472.5-days). The side face of the Khafre Pyramid was intended to be the "hypotenuse" and achieve 590.625 feet (20 lunar months of 29.53125-days = 590.625-days). The base increment for 3,4,5 calculation on the Khafre Pyramid was 118.125 feet, representing 118.125-days or 4 lunar months.
  
  
• The base perimeter of the Khafre Pyramid is 2835 feet or 340200 inches. The lunar nutation cycle was anciently calibrated to endure for 6804-days and that cycle was coded around Khafre's base in 5 inch increments. One long cubit measuring rod found in Egypt is officially recorded to be 25 inches in length and 1360.8 of them would represent a perimeter circuit of Khafre. Also, 1360.8-days is 1/5th of the lunar nutation cycle. Alternatively, a Sumerian/ Babylonian double cubit of 25.2 inches would fit Khafre's perimeter perfectly (1350 units…or 2700 units for their foot of 12.6 inches).
  
  
• In the above picture of Beqa stone weights (Figure 3), if the 4th weight from the top left represents 1½ Beqa then its grain value is 295.3125. The lunar month was anciently configured to endure for 29.53125-days.
  
  
• Similarly, the white alabaster weight (bottom right of the above picture), if representative of 3 Beqa, would be 590.625 grains. This is indicating the base to apex diagonal side length of the Khafre Pyramid (590.625 feet) or 20 lunar months if the number is used to describe the passage of days.
  
  
• The same "hypotenuse" number batch is found in the Greek talent of 590625 grains (corrected). The vertical height value of the Khafre Pyramid (472.5 feet) is alluded to in the Roman libra of 4725 grains.
  
  
• The Khafre Pyramid numbers were distributed internationally and featured on the Calendar of Coligny artefact of France, at Stonehenge, prominently between the central small mounds of the Octagon of Newark Ohio and within the ancient Crosshouse of Miringa Te Kakara in New Zealand.

THE SUMERIAN-BABYLONIAN WEIGHT STANDARD.

Figure 4: Some stone "Duck Weights". This design, showing a duck with its head turned to lie along the length of its body, was a popular style of weight used in the ancient Assyrian-Babylonian region.

The British Museum has in its collection a black basalt weight (exhibit 91005) made by King Nebuchadrezzar II. Its inscription certifies that it was a copy of a weight belonging to Sumerian King Shulgi (2095 - 2048 B.C).
The weight is inscribed, 'one mina true weight' and its officially published weight is 15100 grains
Donald Lenzen states that, 'This is the usual heavy or double mina. The single or light mina would weigh 7550 grains'.

Here are Lenzen's published results (left column), based on the Nebuchadrezzar II black basalt standard. In 606 B.C Nebuchadrezzar II restored the ancient Sumerian weights system used 1500-years prior to his reign.

The Nebuchadrezzar II black basalt weight was intended to convey 15120 grains, as this is a very important Great Pyramid number. The Talent, Mina & Shekel, in double or single guises, were configured for mnemonic reference to the following:

• The "double standard" Talent was 90720 grains. The Great Pyramid is 9072 inches in length per side (756 feet). The distance of 9072 feet is 1.5 minutes of equatorial arc for the Earth, based upon a Great Pyramid navigational standard, which fixed the Earth size to 24741.81818-miles. Under this system one circuit of the Great Pyramid's perimeter (3024 feet) represented ½ a minute of arc.
  
  
• One "double standard" Mina was 1512 grains and two sides of the Great Pyramid are 1512 feet.
  
  
• A "double standard" Shekel was 252 grains and 1/3rd of a side length of the Great Pyramid is 252 feet (24-reeds).
  
  
• The "single standard" Talent was 45360 grains and the height of the Great Pyramid to the top surface of its flat floor altar was 453.6 feet under its sexagesimal assignment. A principle of 3,4,5 triangulation was used to arrive at this height, wherein one side of a 3,4,5 triangle is always 1.6666666 less than the hypotenuse. The 756 feet base length of the Great Pyramid, if called a hypotenuse value, would produce an "opposite" of 453.6 feet. This height value on the Great Pyramid is arguably its most important feature, as it is the basis of a "Royal Cubit" formula for the size of the Earth and how to grid reference the Earth for accurate navigation.
  
  
• The "single standard" Mina was 7560 grains. The side length of the Great Pyramid is 756 feet.
  
  
• The "single standard" Shekel was 126 grains and 126 feet (12 reeds) is 1/6th of the Great Pyramid's length. The ancient reed length, much used in lunisolar calendar calculations, was 126 inches.

The detectable error in the black basalt weight made by Nebachadrezzar II and based upon King Shulgi's earlier weight from 1500-years earlier, was only 20 grains less than these values. This error is .0457 of an ounce making it .998677248 true. Again, it must be realised that there will be small discrepancies in the final weight achieved, depending upon the actual weight of the grain seeds. The important thing to concentrate on was the actual number of grains counted out to make the weight, for it is that number which holds the key to the science being encoded. The final weights found in a duck weight artefact will be very close to the sought after number, but will rarely be totally exact.

THE SUMERIAN-BABYLONIAN ROYAL STANDARD.

Lenzen goes on to state, 'The Sumerian-Babylonian talent contained 60 mina, however, according to ancient Sumerian text there was also a talent of 61.666666 mina' (61 & 2/3rds) (Wengler in Deimel Orentalia 5, p. 48, Metrologia, p.99.)

Lenzen bases his final conclusion of the Royal Talent's intended weight on the average weight of 3 artefacts, which are:

• A grey basalt duck weight (British Museum exhibit 104,724) inscribed, "Two talents, correct weight". The artefact weighs 133.5 lbs.
  
  
• A green syenite duck weight dating to 770 BC and found at the Palace of Eriba-Marduk (British Museum exhibit 91433) inscribed, "30 true Mina". The artefact weighs 33.203 lbs
  
  
• A black basalt duck in the Istanbul Museum, inscribed "Dungi King of Ur, two Minas of correct weight". It is said to weigh 15494 grains, which would translate to 2.2134 lb

Under this system the green syenite duck weight was intended to be 1/4th the weight of the grey basalt duck, double talent weight and the black basalt duck weight was 1/60th of the grey basalt, double talent weight. The lightest value, the black basalt weight, was also intended to be 1/15th of the green syenite duck weight.

This slightly heavier standard was for payments to the royal treasury and some weights of this type bear the inscription, "of the King".
Here's a "corrected" rendition when interpreting the grey basalt double talent as 133.302875 lb (or about .49 of an oz lighter than its official weight). The boxes to the left are, again, based upon Lenzen's overall averages in assessing weights during 10-years of analysis.

Donald . L. Lenzen's overall average estimate for the Royal double Mina is only ¼ of a grain less than 259.20 grains for the Heavy Shekel. This puts the Mina at 15552 grains, identifying a very important value in the ancient astronomical/ navigational parcel of numbers…for some of the following reasons:

• A 3,4,5 triangle with a hypotenuse of 25920 (the number used to describe the duration of the Precession of the Equinoxes in years) would have an adjacent of 15552.
  
  
• Under the Great Pyramid navigational system, where the world was considered to have a circumference of 24741.81818-miles (130636800 feet), the sum of 15552 feet represented 1/8400th part.
  
  
• At the "Octagon" earth mound complex of Newark, Ohio the distance between the centre of the circle component to the centre of the octagonal component is 1555.2 feet.
  
  
• The number 1555.2 is made up of progressions of numbers related to the Precession of the Equinoxes and at least two of the azimuth angles of the 8 embankments of Newark, Ohio's Octagon are parts of that progression (38.88 and 64.8-degrees respectively).
  
  
• The essential element is that the grain values of the Royal set are based upon 129.6 grains and relate to the Precession of the Equinoxes.
  
  
• When one compares the difference in grain values between the common double mina and the larger Royal Double Mina, it amounts to 43.2 grains. When this is allowed to accumulate upward to the level of the common double talent as opposed to the Royal Double Talent, then the difference is 25920 grains…and precession endures for 25920-years.

By allowing the system to be read (symbolically/ literally) as either 15555.55555 grains or 15552 grains for each 60 double Mina allotment during a transaction, merchants trading in combined sexagesimal/ septimal systems would be able to calculate volumes easily and encounter no significant, detectable error in quantities based upon weight.
The true system would, of course, be based solidly on one set numerical choice and the true pyramid numbers are derived from utilising the 15552 grains to represent 60 Double Mina.

The ancient Sumerian text stating that there was a slightly heavier Talent of 61.66666 (61 & 2/3rds) regular Mina's is very nearly correct to a tolerance of 11.6756 grains per Mina increase. Merchants would have, most certainly, viewed this Royal Talent as "rounding out" to 61 & 2/3rds normal Mina's. The primary goal of the astronomer/ mathematicians was to have a Talent of exactly 933120 grains. The sum of 933120 feet would be 1/140th of the Great Pyramid's equatorial circumference assignment of 24741.81818 miles.

The Hebrews had a volume called a Lethech which was based upon a cube, with each side complying to their 21-inch Cubit. The sought after value of this coding was 9331.2 cubic inches or 5 baths of 1866.24 cubic inches each. To achieve the goal exactly the Cubit would have had to be 21.053. Two sides could have been 21 inches, with the third set at 21.12 inches (code related to the mile of 5280) to get the relationship closer.

THE BABYLONIAN GOLD STANDARD.

Donald L. Lenzen gives us this quote: 'For weighing gold an important alteration was made. The shekel of 125.856 grains was retained, but a new mina of 50, instead of 60 shekels, was introduced'.
Here is Lenzen's estimate (left column) of what the gold standard would have been:

The Great Pyramid is 756 feet long and half its length is 378 feet. The defining width of Stonehenge is 378 feet and the site will fit comfortably into a circle (NW to SE) of that diameter, with a small over-shoot NE & SW, where the containment ring is set to 384 feet (deliberately slightly elliptical site).

• The gold standard of the Babylonians introduces a series of numbers embraced and adopted by the latter Greeks, who configured their Stadium measurement to 630 feet. This length is found at Olympia in the clearly marked distance of the running track. The start and finish lines are cut into solid rock and Lenzen states that the distance measured between cuts is 192.28 metres (630.84 feet).
  
  
• The so-called Greek Stadium is also found at Stonehenge as a half value within the Sarsen Circle, where the inner rim sweep was intended to convey 315 feet.
  
  
• The Brasen Sea structure of the Temple of Solomon had a rim circumference of 30 Royal Hebrew Cubits of 21 inches each, culminating into a value of 630 inches or 5 reeds (of 126 inches each).
  
  
• A side of the Great Pyramid at 756 feet would be 12 increments of 63 feet.
  
  
• The 63 series of numbers related to the reed measurement and was highly important to calculations within the Sabbatical calendar system or the 6804-day lunar nutation cycle (see The Calendar of Coligny article within this website). From a wide body of clues and giving logical consideration to a mathematical progression based upon "63" (7 X 9) it's evident that the Greek Stadium was intended to be 630 feet.

The Sumerian/ Babylonian double talent was 129.6 pounds (½ of 259.2 lbs), which codes the number for precession. Both the remnant British weight standard and the Sumerian/ Babylonian standard stem from the dimensions of the Great Pyramid.

The Sumerian/ Babylonian Royal Double Talent was based upon 933120 grains (6 series of numbers), which equates to 133.3028571 British standard lbs. The grey basalt "Double Royal Talent" duck artefact from Mesopotamia is said to weigh 133.5 lb (total error is 3.154 ounces excess…making it .9985233 true).

THE ASSYRIAN WEIGHTS.

With the adjustment of the Syrian light Shekel of less than ¼ of a grain of wheat, the entire mathematical progression pulsates back into life and all of the numbers make perfect sense. It can be readily seen that these are numbers shared by several other civilisations for their weights standards and the use of these numbers will translate fluidly into accurate, safe navigation at sea or into tracking the cycle of the moon.
Lenzen quotes William Ridgeway and Soutzo, wherein they write, 'The Roman Centupodium was equal to and derived from the Assyrian Talent. The Romans obtained their own pound by dividing the Assyrian Talent into one hundred parts instead of sixty'.
This preoccupation, between nations, of divvying up the original parcel of highly scientific numbers into preferred or convenient allotments, was a widespread practice. Even though one nation didn't necessarily duplicate the exact system of a neighbouring nation, all were drawing from the same wellspring of original numbers and not creating non-aligned orphan values. Each nation religiously and rigorously adhered to a policy of using particular numbers that were, at least, a simple ratio variation on the numbers used by all other cousin nations. This policy facilitated trade and the exchange of currencies or volumes of goods, as well as assured that the "special knowledge" was used conspicuously on a daily basis and kept at the forefront of memory. The heavy Assyrian Talent and the heavy Hebrew Talent were exactly the same grain weight value.

SUMMARY TABLES, supplied by Prof. Bruce Moon.

Corrected Ancient Weights in Grains for the Major Unit of Each System.

Note: a small 2, 3, 4, 5, 6 or 8 means "to the power of".

Notes: * For each of these cases, there is a corresponding 'Light' Standard whose talent is half the weight of the heavy talent.
§ This is the abundant number mentioned earlier.

a The Egyptian Gold and Greek Attic talents have the same values as the Hebrew Desert Light.
b The Assyrian Heavy and Light talents have the same values as the Hebrew Desert ones.
c The Greek Tridrachm talent is the same.
d The Babylonian Gold talent is the same.

Examples of relationships between these values are:

N:O 5:6; O:P 8:5; P:Q 25:16; Q:R 80:1; R:S 24:25; Q:T 10:9; T:U 25:24; U:V 4:9; V:W 35:36 [Bruce Moon].

SO HOW DOES ALL OF THIS COMPARE TO THE BRITISH WEIGHT'S STANDARD?

The modern British Weights system is historically traceable to Henry VIII in 1527. The standard "Tower" or "old Saxon" pound of 5400 grains was discarded during the reign of Henry VIII and the Troy pound of 7200 grains was instituted in its place. This new standard was later reduced to the 7000 grain pound, which persisted into modern times. The 7000 grain pound standard that Henry VIII finally settled on was, whether he realised it or not, the ancient Egyptian Sep weight. Henry VIII did little more than revamp the 1340 AD avoirdupois system of Edward III, which was based upon a late era Roman trade Mina of 16 Uncia (@ 437.5 grains each. It's most unfortunate that Henry VIII eliminated the Saxon pound of 5400 grains.

Few people seem to realise that the entirety of the ancient Egyptian weights, measures, volume and area standards migrated to Germany/ France/ Spain/ Portugal/ British Isles/ Scandinavia from the Middle East/ Near East as early as 5000 BC and were continuously used, venerated and reasonably preserved. Whereas creeping aridity, abandonment of a homeland and latter influxes of nomadic foreigners, migrating up from Africa or elsewhere, changed the former ethnic/ cultural balance of the Middle East and Near East over several millenniums, the situation in Western Europe, amidst cousin peoples, changed very little for a long period. Regional European priests maintained their former homeland standards via early era artefacts, carried with their forebears to Europe.... or within enduring standing stone monuments erected by the new migrants upon arrival. The foremost great library of the Egyptian homeland mathematical codes survives at Carnac in Brittany, France. It's evident that the late era Druids preserved ancient knowledge and were totally conversant with the old sciences well into Roman times. Most of the in-depth knowledge seems to have been "bludgeoned to death" and systematically eradicated during the Roman occupations and latter Roman Christian eras. Catholic churches were built over thousands of former standing stone circle sites to smother and obliterate the scientific knowledge they mathematically encoded.

The "bloody-minded" people of the British Isles always maintained that there was something sacred about their measurement standard and that they must preserve it at all cost. Groups, who at late eras fell under the labels of Celts, Gaul's, Iberians, Britons, Angles, Saxons, Jutes, Picts or many other names, maintained the same vigilant stance as best they could, even throughout the oppressive years of cruel Christian domination. The measurement standards of Europe have a 6000 to 7000-year old pedigree within the European theatre and were, to a large part, rigidly maintained for accuracy in several regions, including France, up until fairly recent centuries. Although some of the original weights, measures and volumes were preserved much was lost under the relentless preoccupation of the Roman church to eradicate all things Pagan.

It is beyond the scope of this article to do so, but the many, varied, old and traditional units of weight, measurement and volume used throughout Europe need to be closely scrutinised and compared to ancient Mediterranean standards.

The biggest blunder Henry VIII made was in eliminating the Saxon pound of 5400 grains, for the number 54 was the numerical key to unlocking dynamic ratio and mathematical progression codes residing in all the standards of each ancient Mediterranean nation. Henry VIII, in his ignorance, severed this delicate last link to the scientific knowledge that had guided a multitude of civilisations for many thousands of years. In doing so he most certainly (if only inadvertently) earned his title of "Defender of the Faith" (Fidei Defenso), bestowed upon him by Pope Leo X of Rome in 1521, as a reward for attacking Lutheran ideas. Perhaps Henry's religious fervour and abhorrence for the heresies of Saxony, at the time, induced him to ban old Saxon units, which had been used in England for 1000-years…and were fully a part of the old Pagan knowledge.

It would almost seem that Henry VIII, being a Catholic King at the time, did not solicit expert advice from individuals associated with the old merchant and trade guilds when he remodelled England's weight standard. The old English guilds retained vestiges of profound knowledge relative to the former systems. Most of the early "Pagan" scientific knowledge had been "driven underground" due to foreign occupation, domination and religious persecution. Many of the more traditional systems of Weights, Measures and Volumes found in ancient England, Ireland, Scotland & Wales can be shown to be "ratio" compatible with each other… or to more geographically distant standards found throughout the Mediterranean Basin. The oldest guilds, which were, more often than not, aligned to secret societies, had been responsible for encoding unauthorised "Pagan" geometries and mathematical principles into the great cathedrals of Europe, under the supposedly watchful, but patently ignorant eyes of their mediaeval Catholic overseers.

THE MODERN BRITISH WEIGHTS SYSTEM IS SIMILAR TO THE EGYPTIAN KITE, DEBEN & SEP.

According to the Encyclopaedia Britannica (15th Edition) article devoted to ancient Weights and Measures, some 3400 weights have been recovered from archaeological digs in Egypt/ Nubia. Although there are many combinations of weights in various progressions of numbers, the basic unit appears to be a "Kite", equating to .16 British Standard ounces. One hundred "Kite" make one "Deben", equivalent to a modern era British Standard ounce and 10 Deben make one Sep, which equals 1 British Standard pound.

Ancient Egyptian weights have been found that are in allotments of Kites ranging from 1 to 6.6. This is how the basic Sep/ Pound system would look in terms of "grains":

It's very important to realise that this English system is a very late innovation that is only 475 years old. Whereas the system introduced by Henry VIII (and firmly set into law by Elizabeth I) has a direct pedigree to more ancient systems, it lacks the fluidity of, say, an Egyptian or Greek system, which clearly coded such things as the equatorial size of the Earth through the full range of lesser divisions.
This "walking wounded", English weights system is altogether too symmetrical and rounded in its numbers @ 7000 grains per pound to provide any truly dynamic navigational coding, which shows that almost a thousand years under Roman Catholicism had taken a heavy toll on the developed sciences of Britain from the pre-Roman epochs. The simple, 7000-grain pound was little more than a "halfway house" between dynamic ancient science and modern, sterile decimalisation. It was directly related to and a variation on the Avoirdupois system instituted by Edward III in 1340 AD for standardised trade with Italy. Thankfully, the ancient inch and foot were still intact in England....bloodied but unbowed.

THE FRENCH.

A more rational and traditional weights system was introduced into France in 789AD based upon expert consultation that had occurred between Charlemagne, King of the Franks and the Caliph Harun-Al-Rashid of Bagdad. Charlemagne introduced the ancient Babylonian system, based upon the Arabic gold Dinar. Here is Lenzen's assessment of what Charlemagne's system was:

Charlemagne assigned Frankish names to these divisions, calling his largest weight a "Pile". The heavy and light systems of Charlemagne are based upon the dimensional numbers occurring on the Great Pyramid and, with those numbers, came dynamic navigational codes.

• Charlemagne's Talent was 907200 grains, and the Great Pyramid was intended to convey 9072 inches of length. A distance of 9072 feet would be 1.5-minutes of equatorial arc under the "6&7" geodetic assignment found encoded into the literal dimensions of the Great Pyramid.
  
  
• The Mina @ 15120 grains is mnemonic reference to 1512 feet, which was the value of two sides of the Great Pyramid.
  
  
• The Shekel @ 252 grains, if considered to be 252 feet, would be 1/3rd of the length of the Great Pyramid and the value of 25.2-inches became the Assyrian cubit.
  
  
• A light Talent of 453600 grains was in mnemonic reference to the vertical height of the Great Pyramid to the top of its flat altar floor (it never had a full apex top). The 453.6 feet height is extremely important to the Great Pyramid for providing mnemonic reference to the size of the Earth and 1-degree of circumference arc. This height is geometrically determined by a rule that in a 3,4,5 triangle the "adjacent" is 1.66666666 less than the "hypotenuse". The base length of the Great Pyramid (756 feet) ÷ 1.66666666 = 453.6 feet.
  
  
• The Mina @ 7560 grains is for recall of the Great Pyramid's length @ 756 feet.
  
  
• The Shekel @ 126 grains is for recall of 1/4th the length of the Great Pyramid and this value influenced the Greek foot at 12.6-inches or the Hebrew reed @ 126-inches.

This exceptional lineup of values, issuing forth from Caliph Harun-Al-Rashid of Bagdad, is unsurprising as the Caliph was very well informed about the old codes. Since the capture of Alexandria in 640 A.D., the Arabs had been translating into Arabic as many rare manuscripts as they could obtain. They ransacked monasteries for rare copies of Euclid, Galen, Plato, Aristotle and the Hindu sages. Translators of the rare manuscripts were paid in gold by the weight of each manuscript. While Europe, under the yoke of the church, was plunged into the Dark Ages, the Arabs were becoming increasingly enlightened and their scholarship soon eclipsed the "bludgeoned to death" sciences of the west.

In 1350 King John of France decided to revise the system by making another "Pile" that was 1/25th the size of that instituted some 560-years earlier by Charlemagne. Here are Lenzen's values for King John's weights, based upon the full official set kept at the Conservatoire National Des Arts et Metiers in Paris.

The last entry (.8203125) in the above list relates to the fact that the French, under King John and future monarchs, used barleycorns to determine grain weight and these are about .82 the weight of a wheat grain. It's apparent that earlier civilisations based everything, first and foremost, on wheat weight, then made reference/ comparisons to the relative weights of other grains or beans after that.
Because King John configured his system on that of Charlemagne, whose system, in its turn, was founded on the ancient Babylonian/ Sumerian system, it works well for navigation or astronomical calculations. It's doubtful that King John ever really knew the significance of the numbers he had in his possession, but at least he knew he had something significant that needed to be preserved. He, unlike so many others, was wise enough to know that he shouldn't throw the baby out with the bath water. This system survived until 1790, when it was replaced by the metric system. Let's put King John's system through its paces and show "nos amis en France" the treasure they had in their possession, until it was supplanted by metric measurements.

• King John's Pile @ 189000 grains, if read as 189 feet would code 1/4th of a side of the Great Pyramid. The number was used copiously in ancient astronomy and navigation. The duration of 189-days would be 1/36th of the lunar nutation cycle, set to 6804-days. There would be 13.5 periods of 189-days in the 2551.5-days representing 7.2-lunar years. The lunisolar Sabbatical Calendar ran for 7 solar years (2556.75-days) and 7.2 lunar years concurrently. The difference in the periods was 5.25 days and the entire 2556.75-day solar period or the 2551.5-day lunar period were totally divisible by 5.25. (487 & 486 respectively). This is why the Druids had a mistletoe culling ceremony 5.25-days (6th day) after the winter solstice/ full moon conjunction and used a half reed measuring rod of 5.25 feet. Whereas an increment of 189 feet will divide into the base perimeter of the Great Pyramid 16 times (3024 feet), it will divide into the base perimeter of the Khafre Pyramid 15 times (2835 feet).
  
  
• As a navigational number, 189 is equally dynamic. If the 189000 grains of King John's Pile were read as linear feet, they would equate to 36 Greek miles of 5250 feet each. The same distance would be 300 Greek stadia of 630 feet each or 180000 Greek feet of 12.6 inches. The same distance would be 110000 Egyptian Royal Cubits of 20.61818182 inches each, 108000 Hebrew/ Celtic Royal Cubits of 21-inches each, 70000 rounded Megalithic Yards of 32.4 inches each and even 135000 ancient Hebrew cubits of 16.8 inches each. 189000 feet would be 1/691.2nd of the Great Pyramid's coding for the circumference of the Earth. Under the "true" circumference of 24883.2-miles one degree of arc is 69.12-miles.
  
  
• If the 189000 grains were read as linear feet and converted to a circumference using the PI rendition of 3.142857143 (22/7), then the result would be 594000 feet or 36 leagues of 16500 feet each. This circumference would also be 112.5 miles or 900 furlongs.
  
  
• If 189000 feet were treated as a circumference, then it would reduce to 35000 Egyptian Royal Cubits of 20.625 inches each when divided by the PI rendition of 3.141818182. If 189000 feet were divided by 3.142857143 (22/7) then the result would equate to 35000 Egyptian Royal Cubits of 20.61818182 inches each. If 189000 feet were divided by 3.125 then the result would be, dually, 60480 feet and 35000 Egyptian Royal Cubits of 20.736 inches. Under the Great Pyramid's geodetic coding one minute of arc for the equatorial circumference was 6048 feet.
  
  
• King John's Livre @ 7560 grains is coding the length of the Great Pyramid @ 756 feet. All of the above principles related to navigation or the lunar cycle can be applied, by use of this number.
  
  
• King John's Marc @ 3780 grains is coding ½ the length of the Great Pyramid @ 378 feet. The same length is the defining diameter of Stonehenge.
  
  
• King John's Ounce @ 472.5 grains is coding the 472.5 feet height of the Khafre Pyramid or 16 lunar months @ 29.53125-days each (472.5-days). The navigational principles and lunar tracking methods can be facilitated by use of this number. It is also directly related to Roman and Hebrew weight's systems, which used the same numerical combination.

King John's system, like that of Charlemagne before him, is dynamic because it's fully founded on the most ancient numbers. The age-old numbers most certainly persisted in France (Gaul) during the Druidic era and are clearly encoded into the Calendar of Coligny artefact, which was, at some epoch, brutally smashed to pieces (probably in the Roman Christian era). Thankfully enough of the pieces survived to make decoding possible (see The calendar of Coligny within this website).

In comparison to King John's system, the English system, instituted by Henry VIII, is pretty lack-lustre. It preserves basic principles and that's the main thing. All of its numerical components, like 2240, 112, 16, 14 or even 437.5 will divide fluidly into the base perimeter measurements of the Great Pyramid (3024 feet) in a meaningful way. The 3024 feet ÷ 437.5 (grains per ounce) = 6.912 and there were 69.12-miles in one degree of arc under the ancient "true" equatorial reading of 24883.2-miles. There's a glimmer or spark of life in the English system yet, but it's more dead than alive.
With solid, investigative probes to find the older traditional weights mentioned in British folklore, or those extractible from artefacts, understandings of more sophisticated ancient systems would resurface.

HEBREW LENGTHS.

Here is Lenzen's assessment on the left:

This (above) is part of the old standard and seems to have been used in the building of the first Temple.

The Siloam inscription in King Hezekiah's water aqueduct, while confirming the existence of the 21-inch cubit, also identifies another Hebrew cubit of 17.5 inches. This would make perfect sense, inasmuch as a 17.5 inch increment would go into a base side of the Great Pyramid (756 feet…9072 inches) a total of 518.4 times. The Great Pyramid and the other pyramids of the Giza Plateau provided the "standard" that all of the cousin nations, in various ratio divisions, were using for their national standards.

The 518.4 number is coding the 51.84-degree angle of the Great Pyramid's side, the 5184 square reeds its base occupies, the 5184-years in 1/5th of the Precession of the Equinoxes, the 518.4 miles per hour (X 2) that the Earth rotates at daily and the 51.84 Pyramid acres (28800 sq. feet) of the four faces and base of the Great Pyramid. The 1.75 inch increment also divides perfectly into the built in dimensions of the Khafre Pyramid, divulging important coded information in every case, which related to the lunar cycle. The base length of Khafre was 486 such increments and the means of tracking the 2551.5-days (7.2 lunar years) of the moon within the Sabbatical Calendar system was in 486 periods of 5.25-days. The Hebrews would also have used a measurement of 17.6 inches to cater to "11" series lengths, and their 21-inch Royal Cubit would naturally convert to an 18-inch common cubit, using the standard ratio of 1.16666666 to 1.

It's important to realise that everyone was using everyone else's measurements and the Hebrew system would have included all of the "11" series divisions (fathoms, etc.) as well as each of the Egyptian Royal Cubits (for mnemonic reference to the size of the Earth). The Hebrews also seemed to have a particular liking to the "7" series of numbers (like their Greek conquerors) and the Greek Stadium (630 feet), Greek short stadia (525 feet) a Hebrew stadia of (700 feet) and Greek mile (5250 feet) were used by them. They also had many other units, including a Parasang of 4 Greek miles or 21000 feet. There were also several small units in use, some of which were introduced by Babylonian conquerors.

THE GREEK LENGTHS.

Lenzen identifies a series of complex values, which he relates back to a Greek foot of 12.164 inches. There were, in fact, four types of Greek feet, three of which were very close in value. Let's list Donald Lenzen's estimate and then attempt to show what the Greek scientists were trying to accomplish and remember by this choice of increments. The first analysis will be based upon measurements undertaken on the Parthenon in 1846 by Penrose, wherein the base platform complies to 1-second of arc for the equatorial size of the Earth.

This "new Greek foot" calibration is based upon the size of the Earth and is a variation on the most common or normal Greek measurement system that used a foot of 12.6 inches. This calibration is highly scientific.

The Parthenon platform, upon which the edifice stands, was carefully measured by Francis C Penrose in 1846. Lenzen, in commenting on Penrose's findings, gives a value of 12.165 inches for the new Greek foot, based upon the Parthenon complying to 100 such feet in width. This is 1.01375 British feet and if the value were adjusted by a mere .00001 of an inch, then the Greek foot would be in a perfect ratio to the "true" size of the Earth and 100 such feet would be 1 second of arc. Therefore we have:

1.01376 feet (12.16512-inches) X 100 = 101376 feet (1-second of equatorial arc) X 60 = 6082.56 feet (1-minute of equatorial arc) X 60 = 364953.6 feet (1-degree of equatorial arc) X 360 = 131383296 feet = 24883.2- miles (the true size of the Earth under the old calibration). This is 12 X 12 X 12 X 12 X 1.2.

In the above list, the Stadia is 600 "New Greek feet" whereas the Amma is 60, the Orgyia is 6, the Cubit is 1.5, the Pygon is 1.2, the Hand is .3 and the Digit is .06 respectively. This system is exclusively for mnemonic reference to the "true" size of the Earth.

Let's look at another two systems that relate to the Greek foot of 12.15 inches and the Samos foot of 12.096-inches respectively. There should, theoretically, be yet another Greek foot of 12.1-inches.

The Greek foot of 12.15 inches was used as a calculation increment for tracking the progress of the moon during the 2551.5-day period (7.2 lunar years) of the lunisolar Sabbatical calendar system. The Sabbatical calendar system was based upon 7-solar years (2556.75-days) and the difference between the sun and moon periods, within the calendar count, was 5.25-days. A mistletoe culling ceremony on the sixth day after the full moon/ winter solstice conjunction put the 2-periods in synchronisation for the next 7-years. Lunar major standstill/ winter solstice provided the primary reference day. The 12.15- inch Greek foot was also for following the progress of the moon during this 18.613-year (used as 6804-days anciently) lunar nutation cycle. There would be 56 periods of 121.5-days in the 6804-day cycle, which would go a long way toward explaining the 56 posts on the Aubrey Circle at Stonehenge. Lenzen states that there is general acceptance that the Roman measurements were 24/25ths of the Greek measures. This appears to be sustainable in consideration of the Roman foot at 11.664 inches and a Greek foot at 12.15 inches.

The Samos foot of 12.096 inches was dedicated to the Great Pyramid's equatorial circumference code for the size of the Earth. The Samos foot works in exactly the same way as the foot found by Penrose at the Parthenon and 100 such Samos feet equal 1 second of arc under the Great Pyramid's equatorial assignment. Incidentally, this distance (100.8 feet) is the measured distance between two opposing lintel faces or megaliths across the Sarsen Circle at Stonehenge (1-second of Earth circumference arc). The Sarsen Circle was made slightly elliptical to accommodate 90-degrees opposed codes.

These variable Greek feet measures were the equivalent, in Greece, to the Egyptian Royal Cubits in Egypt and contain all of the same information in reduced ratio. These rulers functioned more as calculators.

The main Greek measurements for distances were a "7" series composed of 12.6 inches (Greek foot), 2.52 feet (Assyrian Cubit), 10.5 feet (Reed) 525 feet (short Stadium), 630 feet (Stadium) and 5250 feet (Greek Mile). The Greeks, like the Hebrews, had a seeming preference to working in "7" values, but would have used the entire range of measurements, including the increments based upon PHI (1.6180339).

THE ROMAN MEASUREMENTS.

The Roman foot was found to be 11.664 inches by John Greaves, professor of geometry, who in 1639 went to Rome specifically to ascertain the length of an ancient Roman foot. Greaves located a monument of Roman architect, Stalius Asper and measured bas relief instruments used by him in the first century A. D. Greaves concluded, after careful investigation, that the Roman foot, 'contained 1944 such parts as the English foot contains 2000'. This means a Roman foot of 11.664 inches.

Donald L Lenzen provides the following estimate (left) of what the Roman length measurements were:

It is very apparent that this Roman system is a duplication of the Greek "lunar" system that used a foot of 12.15 inches, in Greece, as the calculating increment. There is a direct ratio relationship between the Roman foot (at an enlarged value) and the Greek foot…eg. 11664 ÷ 12.15 = 960. The Egyptian Theban volume was 11664 cubic inches.

We can ascertain from this that the Romans were using all of the Greek measures, if in reduced ratio, and had the same line-up of "feet" to serve various types of navigational and cyclic calculation functions.
The numerical value of 11.664 was highly important to several Mediterranean civilisations and represented a definitive number in their cubic capacity and grain weight systems. For practical measurements of length, however, it's apparent that the Romans used a foot of 11.66666 inches, as, when multiplied by 3, this resolves to 35-inches, then 70, 105, 140, etc. This is a convenient "7" series increment to work with and, despite the long tail of decimals in this display, is simply 11 & 2/3rds inches.

By their having an increment of 11.66666 inches it is also evident that the Romans measured decimally with a ruler of 10-inches. Throughout the Mediterranean a special ratio of 1 to 1.1666666 was applied to standard measurements and Royal Cubits would reduce to common cubit status by application of this ratio. In a general sense, the 1 to 1.1666666 ratio would elevate a "6" series number to a "7" series number, thus a Celtic common cubit @ 18-inches X 1.166666 = 21-inches…the length of the Hebrew/ Celtic Royal Cubit.

The above representation of what the Romans had and used by way of length measurements is only a very small part of what they possessed. We can say with reasonable certainty that "everyone used everything that everyone else had"…until the latter eras when civilisations went into decline and the "special knowledge" began to be lost.

There is reason to believe that the Romans and others used a ratio/ progression of 1.3125 for convenient mnemonic recall of the size of the Earth. This numerical combination occurs in the Hebrew Desert Heavy standard for weights, with a Mina of 13125.0 grains. As stated, the rational and functional Roman foot for measuring overland distances would have been the simple 11.66666 inch foot (11 & 2/3rds inches), which was a "7" series measurement, totally compatible with the Hebrew and Greek measurements. For example, there would have been 5400 of these Roman feet (11.666666-inches) in a Greek mile of 5250 feet (5000 Greek feet of 12.6-inches). Likewise, there would have been 720 of these Roman feet in a Hebrew Stadium of 700 feet (400 Hebrew Royal Cubits of 21 inches each).

One of the concepts of ancient metrology, which survived into mediaeval times, was that 75 Roman miles represented 1-degree of arc for the world, although scholars of the time had, seemingly, no lingering knowledge of the actual, former length of a Roman foot.

If we multiply a foot of 11.66666 inches X 5000 we get a Roman mile of 58333.3333-inches. If 75 such Roman miles represent 1-degree of arc for the world, then that equates to 4375000-inches or 364583.33333 British feet of 12-inches each. This value, multiplied by 360 = 131250000 British feet or 135000000 Roman feet. This is also 12500000 Hebrew Reeds of 10.5 feet each or 125000000 Greek feet of 12.6-inches each. Essentially, this very plausible coded representation for the size of the Earth is a purely "7" series way of calibrating the equatorial circumference. The sum of 131250000 feet equals 24857.955455 British miles, 27000 Roman miles or 25000 Greek miles. This same circumference was probably 5000 Egyptian Atur of 26250 British feet each.

It is noteworthy that the 4375 numerical combination found in the inch value of 75 Roman miles (1-degree of equatorial arc) has been traditionally preserved in the grain weight systems of European countries and 437.5 grains is the British Standard ounce. It was also the weight of a trade Uncia adopted by King Edward III in 1340 A.D., based upon the Roman Silver standard Mina.

THE EGYPTIAN MEASUREMENTS.

The Egyptians used a great many measurements, but Donald L Lenzen's list homes in on, primarily, the Royal Cubit and its subdivisions. In truth, there were 3 major Royal Cubits in use, as well as, potentially, several more. The most important function of the Royal Cubits was for mnemonically coding the equatorial size of the Earth under 3 marginally different assignments. Let's look at these:

Each of these Royal Cubit measurements and their subdivisions relate directly to the size of the Earth. The simple formula to find the equatorial circumference under each assignment is to multiply the value of the "Royal Cubits" (shown above) by 1200 and read the result as miles. The "6&7" series Royal Cubit represented the literal length of Great Pyramid @ 756 feet and 440 such cubits equal 756 feet. This cubit gives an equatorial circumference of 24741.81818-miles wherein the 3024 feet perimeter of the pyramid represents ½ a minute of arc. Sea voyaging under this system would have measured distances in Hebrew Parasangs of 21000 feet, Greek Miles of 5250 feet, Hebrew Stadia of 700 feet, Greek Stadia of 630 feet, Short Greek Stadia of 525 feet, Reeds of 10.5 feet, Assyrian Cubits of 25.2 inches, Hebrew/ Celtic Royal Cubits of 21-inches, "Cubits of a Man" of 16.8 feet and Greek feet of 12.6 inches.

The "11" series Royal Cubit gives an equatorial circumference for the Earth as 24750-miles. Again the Royal Cubit in the list is multiplied by 1200 and the resultant total read as miles. This cubit was for traversing the oceans according to an "11" series of numbers and distances travelled were read as Leagues (16500 feet), Miles (5280 feet), Furlongs (660 feet), Chains (66 feet), Rods/ Perches (16.5 feet), Fathoms (5.5 feet) and Links (7.92 inches). To code this system the Great Pyramid had to be, symbolically, viewed as 3-inches longer per side, or 756.25 feet, for a full perimeter of 3025 feet (½ a minute of arc).

The "true" Earth circumference Royal Cubit is the most accurate and gives an equatorial measurement of 24883.2-miles, which is only 18.8-miles less than the value we use today. The formula, again, is 20.736 X 1200 = 24883.2 (read as miles). The Schoenus measurement of Egypt is known to be 1200 Royal Cubits, but which one of the cubits it represents is not specified. Whichever one it is in the choice of three, it will carry a code for the size of the Earth in miles, substituting Royal Cubits for miles.

There were also other Royal Cubits, like one coding the lunar cycles. It would have had a length of 20.671875 inches. Another Royal Cubit, based upon reading the length of the Great Pyramid as 280 Megalithic Yards of 32.360678-inches (20-inches X 1.6180339…PHI), would have been 20.59315873 inches in length.

Common cubits were 1.1666666 less in length than their Royal counterparts.

Beyond this, the dimensions of the Great Pyramid, Khafre and Menkaure Pyramids show that all of the lengths used by all of the satellite nations around Egypt could be utilised as incremental values. The national standards and measurements of preference were all founded on the same original parcel of special numbers, whether ranging from a variety of small Digits, to the giant Atur length used in Egypt and, undoubtedly, representing 5 Greek miles or 26250 feet.

Greek Historian Herodotus, who visited Egypt in the 5th century B.C., made several statements about the pyramids, one of which was that the Great Pyramid had a length of 800 feet. We know that its length was 756 British standard feet, 777.6 Roman feet and 720 Greek feet, using the most common measurement increments of those nations. These were, however, only a small selection of measurement rod values, amidst a very sizable collection, that could be pressed into service.

Depending on the measurement rod that was used, certain categories of calculation could be made, including those that related specifically to the moon. If the Great Pyramid's base length is divided into 800 parts, then this means an increment of 11.34 inches. This is a very dynamic lunar number (11.34) and the width of the Sarsen Circle at Stonehenge (45-degrees azimuth to 225-degrees azimuth) was sometimes read (symbolically at least) as 113.4-feet*. This outer face width of the Sarsen Circle (on this azimuth line) was closely regulated by the positions of the Station stones.

*The Station Stones rectangle appears to have been intended to code a length of 264 feet (1/20th of a mile) and a width of 113.4 feet (strong lunar code). The Sarsen Circle Lintel faces from 225-degrees azimuth to 45-degrees azimuth fell slightly short of this diameter by, seemingly, (an intended) 3.4 feet. Despite the dilapidated condition of the Sarsens toward 225-degrees azimuth, which tends to negate the possibility of precisely reading the original architectural design intention, an external face to external face coded diameter of 110-feet appears to have been incorporated. Any such diameter would also have included "symbolic" readings, using near values of significance (for mnemonic, multicoded, versatility). The component positions of Stonehenge were multifunctional repositories of profound science, the values of which were encoded by distances and azimuth angles.

Three sides of the Great Pyramid (2268 feet) equate to 1134 feet X 2. Use of the 11.34-inch value turned the Great Pyramid into a lunar calculator, which could monitor the 2551.5-days in 7.2 lunar years (225 periods) or the 6804-day lunar nutation cycle (600 periods). The 2551.5-day count for the moon was done in conjunction with the 2556.75-day solar count within the lunisolar Sabbatical Calendar system, adopted by cousin peoples from Egypt to Europe. The 11.34-inch value also worked on the Khafre Pyramid (708.75 feet...15/16ths of the size of the Great Pyramid). There would be 750 such "lunar feet" of 11.34-inches in 708.75 feet.

Another ancient Greek statement placed the length of the Great Pyramid as 500 cubits, which would mean an increment in use of 18.144-inches. Such an increment would be very useful in doing equatorial circumference calculations.

Herodotus has been severely criticised by pyramidologists/ Egyptologists for his several "uninformed/ misinformed" statements relating to the pyramids. He said, amongst other things, that 'the surface area of each face was equal to the square of the height'. He also said that 'the surface area of each face was 8-Egyptian acres'. For making these observations, Herodotus has been severely derided by pyramidologists, who can't make his statements work...but as it turns out he was totally correct.

• The length along the base of the Great Pyramid is 756 feet; the diagonal length up a face side runs for 576 feet to a flat floor at the top which is, or once was, 44 feet long (a bit of a jumbled mess now). This configuration gives a surface area, per face, of 230400 square feet, which means an ancient Egyptian Pyramid Acre (according to Herodotus) was 28800 square feet.
  
  
• Although the Great Pyramid has a flat floor on top (and always has) it can still be symbolically read as having a height complying to the point where lines running up each diagonal face would intersect. This position would be 27 feet in the air above the flat floor altar atop the pyramid. This is what Herodotus was talking about in the design geometry. Therefore, with 230400 square feet representing the square footage value of each face, the square root of this should be the height. Inasmuch as 480 X 480 = 230400, the design height (if it was a complete pyramid with an apex) would be 480 feet of vertical height...which is true (to a tolerance of about 8 inches shortfall...it's closer to 481 feet in trigonometric calculation, based upon a true face angle of 51.84-degrees).

THE SUMERIAN/ BABYLONIAN LINEAR MEASUREMENTS.

The only indications that exist as to what constituted the Sumerian/ Babylonian linear measurement standard are clues in texts or measurements within remnant structures. To date no examples of Mesopotamian cubit rods have been recovered, but an accumulation of archaeological clues puts the "double cubit" to around 25.2 inches and the "foot" to 12.60 inches.
These measures were divided up into 60th and 30th parts respectively. The ancient foot of 12.6 inches (a twelfth of a reed) was used by the Greeks, Arabians, Persians and Assyrians.

Lenzen's averaged assessment (left hand box), based on many archaeological or historical sources, is the following:

The true base measurements of the Great Pyramid (756 feet per side) comply admirably with these "corrected" measurements and the pyramid would be 1440 Sumerian/ Babylonian double-cubits in perimeter value. This is the same number that was used on the court altar of the Temple of Solomon if its assignment was in "common" Hebrew cubits of 18 inches each.

• Six PHI reductions of the PHI assigned base length of the Great Pyramid (280 Megalithic Yards of 32.360678 inches each) resolve to a length of 42 feet or 504 inches. This was one of the calibrations built into the flat floor altar atop the Great Pyramid (overall length per side = 44 feet).
  
  
• The height of the Great Pyramid to the flat surface of its altar floor (453.6 feet under its sexagesimal assignment) was 216 Sumerian/ Babylonian double-cubits. The 216 number relates to the 2160 miles of the Moon's diameter or the 2160-years that the Sun remains in one House of the Zodiac during the Precession of the Equinoxes.
  
  
• The numbers, 504, 252, 84 & 42 are divisible by 6 & 7 simultaneously and are values within one of the most prominent and useful mathematical progressions of antiquity. These numbers featured strongly in navigation and the lunisolar Sabbatical calendar calculations...try them out and while you're at it test all of the national standards in a similar vein!

ARRIVING AT A RATIONAL CONCLUSION.

There are a drove of theories about what the pyramids were built for or what the state of scientific advancement was amidst satellite nations, in the environs of Egypt, during various ancient epochs. Most of the officially published scientific concepts portray Mediterranean nations subsisting at a rudimentary mathematical and scientific level of accomplishment, which advanced, despite frequent setbacks, over about five millennia to present levels of scientific achievement. The school of thought that predominates is isolationist driven, classicist historical interpretation. The classicist historians will tell us that systems of metrology developed as separate entities between nations and were, generally, only shared after a conquest and the imposition of the conqueror's official standards. Jewish scholars, for example, accept that many of the traditional Hebrew or Israelite standards were imposed after the Babylonian conquest.

The classicist historians have detected no generally apparent ratio relationship between one standard or another and are unable to proffer any explanation as to why such cumbersome numbers were chosen for "grain weights standards". They have not been able to detect any significance in the cubic capacities of vessels, simply because they conclude that there was no base increment like the "inch" which was standard to all or most of the nations of the Mediterranean. A thorough analysis of the sought after "grain weight" values (seed counts) in many national standards, coupled with lengths of surviving measuring rods, should have been sufficient for them to detect the most fundamental base increment used in "marked standard" volume vessels.

So, the Classicist Historians would have us believe that:

• Because of their ignorance of mathematical fundamentals, the architects of ancient Weights, Volumes, Lengths and Area standards simply chose difficult, arbitrary values when, in the course of designing a grain weight standard, they could have chosen convenient, rounded values that were easy to divide up.
  
  
• That there was no fluid and easily calculable ratio relationship existing between one nation's standard and that of another to facilitate trade, the measuring out of quantities of goods or the exchange of national currencies in gold, silver and other precious metals.
  
  
• That the nations got ("officially") to within ½ a seed of wheat weight, in potentially dynamic numerical counts of grains, but still had no knowledge of the potentialities contained within the numbers arrived at and how they could be applied to the size of the Earth, navigation, an accurate lunisolar calendar system, the 18.613-year lunar nutation cycle, etc. Apparently it's just a coincidence that they got so close to numbers that indicated a vast scientific knowledge, but they never used the numbers or knew what they had in their possession.

In consideration of the vast number of different "Mina" weights, "Amphora" volumes or "Cubit" lengths, all working in fluid ratio relationships with each other within national and international standards, the modern "official" historical interpretation is, clearly, unsustainable. On a statistical basis alone, the chances of many nations fashioning their standards to the highly scientific, interactive ratio relationships mentioned in this study, yet not understanding the science it all supported, is almost beyond calculation. The only rational conclusion that can be drawn is that ancient civilisations of the Mediterranean Basin were using a multifaceted but integrated metrological system, originally founded upon very advanced scientific understanding and achievement. The zenith epoch of that achievement is unknown, but the principles that came from it remain resident, as coded values, within and upon the pyramids of the Giza Plateau. The edifices of the plateau functioned to provide the essential mathematical elements of a comprehensive system of metrology, as well as being a Bureau of Standards for an internationally dispersed community of cousin nations.

METRICKSTERS?

In June of 1792 a project was commenced that would have major social, commercial and industrial repercussions for the two centuries that followed. Learned astronomer savants, Jean Baptiste-Joseph Delambre and François-André Méchain commenced a project to measure a curved segment of the Earth's surface in order to create a whole new measurement system. The idea was to mathematically calculate the distance from the North Pole to the equator on a meridian line that ran through Paris. Delambre worked from the north of France, beginning his survey at Dunkerque, while Méchain worked from the South, commencing his survey in Barcelona, Spain. After 7 difficult years and many privations, including imprisonment in Spain for Méchain and a very real risk of losing his wise head on the guillotine for Delambre, the two met in Carcassonne to compare notes, returning to Paris together as heroes of the day.
Sometime later, after a thorough analysis of the field notes, a platinum bar was fabricated that became the new metre, representing a ten millionth of the distance from the pole to the equator. Unfortunately it was .02mm short of the mark, which in accruing values represented a major discrepancy.

Blame for this faux pas is laid on Méchain, who supposedly didn't add his field note sums up correctly. Delambre is also held "coupable", for realising there was a mistake, but deciding to let it go unreported to the general public.
Well, that's the story we get anyway, but did these savants really make a mistake or was the outcome deliberate and contrived?

Both Delambre and Méchain were professional and much respected scientists, living in Catholic France, where ancient guild networks abounded. It was more common than not for individuals of their rank in society to rub shoulders with (or be affiliated with) the secret societies and Masonic orders. These ancient guilds had a longstanding tradition of preserving geometries and measurements from pre-Christian times and secretly encoding those principles into the great cathedrals or public buildings of Europe. Even new cities of the time, like Washington D.C., were being laid out in accordance with Masonic geometric principles, gratis of the founding fathers of the United States.

The litre is the cubic capacity of 10cm X 10cm X 10cm and this weight of water represents 1 kilogram. It just so happens, quite by chance, that one ounce in the imperial British system (437.5 grains) = 28.35 grams in the metric system. This also equates to 28350 milligrams. The selfsame value, rendered as 2835 feet, was the intended perimeter value for a full circuit around Khafre Pyramid's base. It appears obvious that the gram is related to the 437.5 grains of the British ounce of 10 Egyptian Deben. This grain count had an affiliation to the system instituted by Charlemagne. King John and Edward III, who reigned virtually contemporaneously, introduced systems that accommodated the 437.5-grain ounce admirably. King John's Pile was intended to convey 432 ounces (4320 Deben) or 27 latter English pounds of 7000 grains. There appear to have been 4375000 inches in 1-degree of equatorial arc, under a special "7" system shared by the Romans, Greeks, Hebrews and Egyptians.

The sum of 28.35 metric grams is simply the Roman trade standard Uncia adopted by Edward III in 1340 A. D…based upon a late surviving "Silver standard" Mina of 7000 grains. It seems a little uncanny and a bit too convenient that 1 ounce = 28.35 grams...a significant, old world lunar number.

• Khafre Pyramid was Egypt's Pyramid of the moon and all of its outer dimensions are related to the lunar cycle (or the 3,4,5 triangle). The base of Khafre is 15/16ths the base length of the Great Pyramid or 708.75 feet per side. Half the base length of Khafre is 354.375 feet and, under the ancient calibration, this figure represented the duration of a lunar year in days to an excess amount of almost 12-minutes. Four sides of Khafre Pyramid = 2835 feet.
  
  
• An abundance of maritime activity at the equator had, by the time of the French Revolution, allowed scientists of the time to calculate the equatorial circumference with a reasonable degree of accuracy. The old guilds, undoubtedly, knew the ancient Mediterranean figure of 24883.2-miles, which, in feet, equals 12 X 12 X 12 X 12 X 1.2 or 131383296 feet. Inasmuch as the preservation of age-old, suppressed and illegal Pagan knowledge was the "raison d'etre" behind the guilds, the activities of Delambre and Méchain would have been closely monitored by the secret societies of France.
  
  
• Physicists of the time would have concluded that the equatorial circumference was greater than the polar circumference, simply due to the speed of rotation of the Earth, causing an equatorial bulge effect by the spin's centrifugal force. This would mean the Earth was an oblate spheroid. The degree of difference between equatorial and polar circumference would have been the subject of theory, calculation and speculation.
  
  
• If one were desirous to choose an easy out, after rigours and setbacks in the field, combined with the knowledge that the field notes had areas of major discrepancy in them, then there was always a tempting solution to consider. Méchain, especially, had some big errors to contend with in his field notes…and the guillotine made short work of many bourgeois, "surplus to requirements" savants, during the heady days of the revolution. Also, one could not abrogate or bypass ones commitments and sworn obligations to the influential guilds, which were in no mood to have their founding principles rendered passé. It would appear that they set the requirements for what the metre would be and got it as close as their knowledge would allow to ancient Roman measurements. What the guilds intended, it would seem, was 3.28125-feet or 39.375-inches for the metre. This would have been in compliance with the scant and incomplete knowledge they now had of what constituted the former Roman foot. The guilds appear to have assumed that the 11.664-inch foot was the basis of the Roman standard, when, in fact, the Romans only used that value in volume measures or lunar cycle calculations. The foot they used in calculating the equatorial circumference of the Earth or in overland marching was 11.6666666-inches in length. Their equatorial circumference value was based upon 75-Roman miles per degree of arc. Their mile was 5000 Roman feet and, using the 11.666666-inch navigational foot, this equated to 25000 Greek miles @ 5250-feet each or 131250000 British feet (135000000 Roman feet) for a circumnavigation of the globe. Inasmuch as the creators of the metre were quartering the globe, they seemingly wanted to divide the Roman figure by 4. That means: 131250000 British feet ÷ 4 = 32812500 feet. But the metre was supposed to be one ten millionth of this quarter sementation or 3.28125 feet. Instead, the guild authorities, if they were orchestrating the outcome, appear to have used the 11.664-inch Roman foot and calculated the circumference as 131220000 British feet ÷ 4 = 32805000... divided by ten million = 3.2805 feet. We know that the metre calculated by Delambre and Méchain fell short by something in the vicinity of .2 of a milimetre. This discrepancy was adjusted out later and the metre has gone through several subsequent minor increases since 1799. The original metre looks to have been modelled on the ancient Roman equatorial system, with only minor drift off the original values....probably based upon flawed assumptions as to what constituted the original Roman overland foot.
  
• In an extended commentary in one of Méchain's log books, Delambre wrote: "I deposit these notes here to justify my choice of which version of Méchain's data to publish. Because I have not told the public what it does not need to know, I have suppressed all those details which might diminish its confidence in such an important mission."
  
• Another possibility for fudging the results arises when one considers the age-old formula for calculating the 24883.2-miles of equatorial circumference (12 X 12 X 12 X 12 X 1.2-miles) and then deducts a coded "28.35"-miles from that as a highly recognisable value representing an incorrect but conveniently coded difference between equatorial and polar circumference. The result would be 24854.85-miles. This divided by 4 to represent the distance between the pole and the equator = 6213.7125 miles or 32808402 feet. A ten millionth part of that would render an incremental value of 3.2808402 feet or 39.3700824 inches…et voila!…nous avons notre mètre, or an expression that is breathtakingly close. The modern metre varies from country to country, but my conversion calculator expresses it as 3.2808398 feet or 39.3700776 inches…hmmm very, very close … food for thought…Un peu de méchanceté peut-être Méchain?

I've recently read disparaging commentary, directed at the British Imperial system of metrology, issuing forth from "champions" of metrication who state such things as, 'Units of length based on body parts cannot be relied on to be accurate'...which made me think of an old quote...

'Who is this that darkeneth counsel by words without knowledge...Where wast thou when I laid the foundations of the earth? declare if thou hast understanding. Who hath laid the measures thereof, if thou knowest, or who hath stretched the line upon it? Whereupon are the foundations thereof fastened or who laid the cornerstone thereof? (Job 38: 2-6).

The ancient universal metrological science, of which the British Imperial Standard is a "walking wounded" remnant survivor, was based upon the true size of the Earth, the precise cycles of the sun & moon (producing the best lunisolar calendar system the world has ever known) and incremental values that worked wonderfully with PI for successful world navigation. The system was so advanced mathematically that it "tamed for use" the difficult PHI formula and applied it in many building applications. This old standard was a brilliant, precise and all encompassing, scientific construct that addressed every arising calculation need confronted by ancient civilisations. The system is as relevant today as it was in antiquity and has never been superceded by anything superior to it. It is at the very foundation of civilisation itself. The world's religions, long before they became corrupted by dogma and power mongery, had a pedigree back to (and were formerly based upon) this incredible parcel of knowledge.

The metrication incentive could be described along the lines of a wimpish, little boy sent forth to do a strong man's job! It is to metrology what Esperanto is to languages…It doesn't make the grade and, in an overall sense, simply wastes everyone's precious time in a naïve pursuit, which was prematurely initiated in an era lacking the essential scientific capability to achieve a reasonable result.

The metric system is an incomplete entity or orphan and could not have subsisted by itself in antiquity. The ancient civilisations used the whole range of numbers, from 1 to 13 and increases thereof. They needed progressions in 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, as well as PI, PHI and a multitude of fractions. The metric system, most certainly, existed in antiquity, alongside all of the other number systems. The full family of numbers was capable of addressing all contingencies and demands of science and ancient industry.
Ancient societies would have viewed it as sheer madness to discard over 90% of the complete system in order to work with only one of the number categories. Using the full system, in individual families of numerical progressions, was the only way of monitoring, calculating and remembering the difficult astronomical cycles or principles of navigation. The Egyptians counted in base 10 and so did everyone else amongst the cousin peoples…but they used "6, 7, & 11" numerical families, etc., (in base 10), as well.

The metric system was instituted, primarily for the convenience of bankers and bean counters. It's a nightmare for engineers and anyone else who has to work to refined tolerances. Carpenters can get by with it, as they generally work to visual tolerances that are within the capabilities of metric rulers. Trying to fashion chronology systems on a metric basis is nigh on impossible. We do, however, need the convenience of a metric system, within a wider metrological system, for some limited, decimalised functions.

It would have been more rational to simply base a system on traditional measurements increments like the inch and foot, then decimalise them. This approach has been used since time immemorial, wherein various trades have segmented up a standard ruler into divisions that suited that trade…half, quarter, eighth, sixteenth for some…third, sixth, twelfth, twenty-fourth for others…or fifth, tenth, fiftieth, one-hundredth for yet others...not to forget the "7" progressions as well. By such a simple method, everyone got on with the job and had constantly on hand the convenient increments, in fully reducible fractions, needed in their particular problem solving or fabrication functions. The whole metrication incentive has been, overall amidst the trades, a nightmare. It's a perfect example of what happens when accountants take over the world …SNAFU.

A full restoration of the ancient and highly sophisticated Mediterranean/ universal metrological system, with all of its appendages, is obligatory. Even if we move away into other realms of metrology, we still owe it to history to restore and preserve our heritage. It would be utterly sacrilegious to "kill off" the system that was at the heart of civilisation for millennia as the central ingredient in the advancement of great empires. The old scientific standard must be reinvestigated fully, reconstructed and restored to a position of prominence if we are ever to understand what has truly gone on history. To lose our grasp on the old, commonly shared metrological systems is to lose the most significant key to unlocking the scientific concepts held in universal reverence by the great empires of recorded history.

18th of November 2002. ©