Ancient Weights,

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  • 7/29/2019 Ancient Weights,



    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.


    1 Archane128995.793 cubic inches, equals:6 Homer @ 21599.298 cubic inches, or36 Artaba.. @ 3583.216 cubic inches, or216 Sutu @ 597.202 cubic inches, or2160 Qa. @ 59.720 cubic inches.


    1 Archane 129600 cubic inches, equals:6 Homer @ 21600 cubic inches, or36 Artaba.. @ 3600 cubic inches, or216 Sutu @ 600 cubic inches, or2160 Qa. @ 60 cubic inches.

    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 value of 25920, thenumber 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 orHebrew "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 by3.141818182. 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 Pyramidstandard 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" equatorialcircumference.

  • 7/29/2019 Ancient Weights,


    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 milesper 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.



    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 circularjar 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-


    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 innavigation and there would be 120 X 15.84 cubic inches in 1900.8.

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    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


    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. Thevessels 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


    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".


    A Sepphoris liquid. Cor 22394.88 125 9/100

    B Jerusalem liquid Cor 18662.4 124 9/10

    C Desert liquid Cor 15552 124 3/4

    D Sepphoris Dry Homer 28512 122 1811

    E Greek liquid Metretes 2332.8 12234/5F Greek dry Medimnus 3110.4 1239/5

    G Roman liquid Amphora 1492.992 125 6/1000

    H Syrian liquid Metretes 3732.48 12418/100

    I Roman dry Amphora 1900.8 12311/10

    J Alexandrian Amphora 1584 12211

    K Egyptian Theban 11664 12234

    L Babylonian Archane 129600 123523

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    (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


    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