The Works of Jerry Iuliano
 Ancient Numbers Revealed in Scientific Formulas  

Compiled by Joseph E. Mason

Aztec Hunab Number 378 and 82944

The Roman Measures

For obvious reasons, more measuring devices and measurable structures survive from the Roman world than from any other ancient culture.  Yet nobody has ever been able to exactly define what was intended to be the standard length of the Roman foot.  This would be the measure adopted by the Roman bureaucracy as the national reference.  (Although a vast amount of alternative standards, apart from the variable "Roman" foot, were in concurrent use both in Rome itself and throughout the Empire).  Researchers have believed the number of variations in the national standard was due to poor regard toward the maintenance of accuracy, but this is not the case.  Because the identical range of variations to which the Roman measures were subject, are detectable in the measurement systems of all other nations.  Luco Petto, a Renaissance antiquarian, argued intelligently, that although rules varied in a general sense, if any of them exactly agreed, then this would imply an intentional standard.  When subjected to this scrutiny, so many of the Roman rulers achieve such a level of correspondence that the conclusion that must be drawn is that the variations are indeed fully intentional. 

Not only are the Roman variations in their measuring devices intentional, it would seem that they are constructed to a greater degree of accuracy than are modern rules.  When purchasing modern devices across the counter, either foot rules, tape measures or metre sticks, the variations may be as much as .3%.  The ancient devices would seem to be subject to much lesser variations from their intended lengths, from .15% at a maximum.  In the examples that follow, it is difficult to assess how accurate are the reported lengths; did those who made the physical measurements use agreeable standards?  What were their criteria for the intended length, such as demarcation points, etc?  All one may do is to take the reported lengths, usually given in millimetres, and make an accurate conversion by using the metre taken as 3.2808427ft.  With so many references to compare, a statistically accurate picture will emerge. 

In the book, All Done With Mirrorsthe variety of measures are each given descriptive names as briefly described in the essay on the Greek Foot.  But for now, the values of the Roman feet, which are accepted as being 24 to 25 of the Greek feet, are here listed in their ten potential values in two rows, separated by the fraction 440 to 441, as letters of the alphabet.  The fraction between each measure across the two rows is 175-176

 a  .949122  
 b .954545  

 c .96  

 d .965487  

 e .971003  

f  .951279

g .956714

 h .962181  

i .96768

i .96768

The values of certain of the Roman feet which have survived, either as rules or as standards engraved upon monuments, are listed, and their proposed values from the table above are listed alongside to their level of accuracy.  The first values are a set of six, which were taken from well-preserved both bronze and bone rulers found in Pompeii. 

 Given values  

 closest as above  

 ratio of accuracy  

I   .965994



II   .965985



III   .965202



IV   .956201



V   .972113



VI   .971785



These eight values are taken from rules found in Switzerland, Germany, France and England. 

 Given values  

 closest as above  

 ratio of accuracy  

 VII   .959646  



VIII   .964567



  IX   .962927  



X   .967192



XI   .960630

c (x 2)


XII.   958006



XIII   .964567



The final two values are taken from standards engraved on the monument of Cossutius and the Capitol. 

 Given values  

 closest as above  

 ratio of accuracy  

XIV   .967



 XV   .965833  



 This is very conclusive of both the accuracy of the measuring devices and of the general theory concerning the conventions that govern the differences. These comparisons are random, no selection process has discarded any non-conforming values. Analysis of the measurements from buildings, as accurately examined by surveyors, yield even closer values to those predicted. For example Petrie's measurement of the Great Pyramid, later substantiated by Cole's report, gives the Roman foot of the classification "h" as above, exactly, and Petrie's measurement of the inner lintel diameter of Stonehenge yielded a foot within one part in eighteen thousand of the value "j" above, of .9732096ft. Hundreds of such comparisons leave little room for doubt as to these theoretical values fitting the facts. 

The natural log e 2.718281... is integral to the Roman foot .9732096 through the harmonic 82944:

 (82944 + (IN 97.32096))^ (1/Pi ) = 100 /e

 (82944 ^ (1/Pi ))/100 = cos 137.036000986

( 378 * 97.32089313 / 1000 ) ^ Pi  =  82944 

The Roman architect, Marcus Vitruvius, has left records of a perfectly good reason as to why there should be a ratio of 175 to 176 between the columns of the table. He stated in his description of the odometer " . . . that if the wheel of the carriage is four feet in diameter, it will have travelled 12 ½  feet in one revolution". Clearly, this means that the pi ratio that is used is 25/8 or 3.125, when multiplying by counts of four this renders integrity in the solutions -- although it is inaccurate to a rate of over 20 feet in one mile. But, if the longer, by the 175th part, module is used in the perimeter than that of the diameter, then perfect accuracy has been maintained, because it will have corrected the pi ratio to a value of 22/7 which is sufficiently accurate for virtually any calculation. Unfortunately, precious little is known of these Roman itinerary distances. Archaeologists continue to ignore this method of cultural analysis; metrology is totally neglected. Consequently, the vast majority of Roman milestones have been ripped from their carefully calculated positions and placed in lapidary collections, which renders them totally useless. Old surveys from the Eighteenth and Nineteenth Centuries, notably that undertaken by Boskovitch with the milestones along the Appian Way, although fragmentary, would indicate that the itinerary distances were calculated in terms of the mile of 5000 feet of .965487ft, which is 1471.4 metres between milestones. Vitruvius' carriage wheel diameter would then be four feet of .96ft, or 24 25ths of the English foot. This would fit the English statute mile of 5280ft rather well, making it 7/8ths of the 6000ft 10 stadia of the Greek foot of 1.0057143ft, (25 to 24 of the Roman .965487ft). Values of this classification (Root Canonical) may therfore have been universally used for long distance measurement. 

Mediaeval scholars who studied ancient metrology knew by tradition that there were 75 Roman miles in one degree of latitude. However, they had no method of identifying which value of the Roman foot gave the correct solution, and no longer did they have the technical ability to accurately measure the degree, which is around 69 statute miles in length. At the three longest values of the original table, marked e, i and j, the degrees are exactly seventy five 5000ft Roman feet miles at the latitude of 10°, the latitude of 38° and that of the average degree at 51°.


Close inspection of Harleston's plans of the city, whereupon all distances are notated in hunabs, reveals that there is little doubt that this was a vitally important measurement in the overall plan. Canonical modules repeatedly occur; numbers such as 144, 288, 216 720 etc., but the number which occurs most frequently is a distance of 378 hunabs and it did not escape Harleston's notice that this was a geodetic value. It is very accurately the 100,000th part of the mean perimeter of the earth. However, where there are fractured or irrational numbers in the significant distances which he noted, almost invariably these become integral and rational in terms of directly related measures, such as the Greek, Roman, Mycenaean and particularly the vara, which is the Megalithic Yard. Unfortunately, Harleston never connected his standard unit to those of other ancient systems, he continued to view the value as exclusively an American contrivance and invariably expressed it in metres. 

  378 +288 = 666  
A link to the Roman foot... 97.32096... through the Aztec Hunab
number 378 can also be demonstrated through the harmonic 82944:

 ( 378 * 97.32089313 / 1000 ) ^ pi = 82944  

 ( 288 ^ ( 2/Pi  )) * 1000 = 378 * 97.32089313  

The fine structure constant...aem... can now be shown as a derivative of the Hunab number..378

  378 * 97.32089313 / 100000 = cos 137.036000986 = cos 1/aem  

                                                       J. Iuliano

As well as his masterly interpretation of the architect's numerical design through the measures, he went much further in explaining practical reasons for this layout of temples and pyramids. He noted that from the vantage point of the pyramid summits, a range of celestial bearings, extreme moon and sun declinations and certain stellar alignments were indicated by prominent foresights. In reverse, the pyramids could also be used as foresights to these phenomena from distant locations, these outlying observation points were clearly indicated by carved stones at the precise positions which he was able to predict, and in addition, were distanced in regular numbers of his standard unit.

These findings alone could have prompted serious archaeological investigation and eventual recognition of his valuable work. After all, these were observations of a similar nature to those noted by a host of other investigators in relation to ancient monuments throughout the world. But Harleston went much further. He noted ratios relating to phi, e, the speed of light and distance ratios to the planets, including those invisible to the naked eye in the architectural layout of Teotihuacan, and much more. His overall conclusions infer that the builders had as great, or a greater, grasp of the laws of physics than does modern man. And however that may be, it was far too great a concept to be rationally debated, and as a consequence the Society of Americanists continues to ignore all of his claims. Even the well founded ones, such as the identification of the standard unit. Harleston is endowed in courage and vision; it is such a pity he went public with too much. 

Aspects of what has been covered concerning Central American metrology are more detailed in All Done With Mirrors, including how the modules of construction and their classification values may be decoded from the simple ratios of the pyramid dimensions. 

(Sent via e-mail October 3, 2004)


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Note from Joseph E. Mason:

The number 82944 is 288 squared. For more information about these and other similar numbers and their connections to ancient numbering systems, see the links on the index page.

The fine-structure constant is said to be the "coupling constant" or measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e.g., electron, muon) and light (photons) interact. Some say it represents the probability that an electron will emit or absorb a photon.

electron = .510998902 mev / (c ^ 2 )
Me = electron mass = 9.1093826 * ( 10 ^ - 11 ) grams
Re = electron radius = 2.817940285 * ( 10 ^ - 7 ) meters
K = coulumbs constant = 8.987551705 * ( 10 ^ 9 )
Gn = gravitational constant in newtons = 6.6742 * ( 10 ^ - 11 ) k^3/m/s
c = speed of light = 299792458 meters/seconds
h = Planck's constant = 6.62606891 * ( 10 ^ - 34 ) Joules
E = permittivity of space = 8.854187818 * ( 10 ^ - 12 ) Fm<

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This page was originally uploaded October 4, 2004

This page was last updated April 23, 2005

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