Metrology can seem quite arbitrary in its choice of aggregate measures, that is as to how a given foot measure is divided up into subunits or multiplied into a common range of greater lengths, defined for a given foot or MODULE*.
The idea of a foot module comes from the NEED to create a set of measures NUMERICALLY interrelated to each other, around a foot length equal to one english foot.
It was John Neal who discovered that ALL the modules of Ancient Metrology (discovered in many lands so as to form Historical Metrology) were linked together in small number ratios (i.e. significant but rational differences in length), these rational differences ONLY employing just prime numbers 2, 3, 5, 7, 11, though often being microvaried within each module by larger number ratios such as 441/440 and 176/175 (smaller rational differences) that appear to have had special uses such as providing versions of PI (so as to retain whole numbers between any radius/diameter and the circumference of the circle it defines.)
Therefore, although there were many modules or types of foot in ancient near eastern metrology, each module had exactly the same set of larger aggregates, subdivisions and smaller microvariations. Examples are
- AGGREGATES: Cubits of 3/2 ft, Steps of 5/2 (2.5 ft), Yards of 3 ft, Fathoms of 5 ft, Chains of 22 ft, Furlongs of 600 or 660 ft, Miles of 5000 ft
- SUBDIVISIONS: Digit, Inch (thumb), Palm,
- MICROVARIATIONS: 441/440 =(), 176/175 = (), their sum of 126/125 (= 1.008 ft), their complex product 3168/3125 (= 1.01376 ft), 225/224
It appears that these toolkits of modular lengths were generated using rescaling of certain standard aggregates and microvariations, probably using right triangles to reproportion between modules and microvariations within modules. Please see Appendix Two of Sacred Number and the Origins of Civilization for an idea of how this pattern formed our historical measures.
The Inch and Megalithic Inch
The Le Manio Quadrilateral shows that astronomers in the 5th millennium BCE counted astronomical time using inches, whose length was exactly that preserved in the English foot and one twelfth of the foot. Since the English foot came to be the UNITARY MEASURE = ONE within ancient metrology, one should note that twelve subdivisions are not normal for the ancient feet of modules other than the Greek/English module. Most feet were subdivided by 16 units, so that a Cubit of 3/2 feet would be seen as containing 16 / 2 = 8 x 3 = 24 digits. A digit is therefore smaller by 12/16 or ~0.75, a sort of finger width rather than a thumb width.
As my brother and I have shown, the Quadrilateral displays the differential day-inch count length of three solar and three lunar years, this being the origin of the Carnac Megalithic Yard (CMY) of 32.625 day-inches ( = 261 / 8) or 2.71875 ft. According to Neal's ancient metrology, Thom's unit of Megalithic YARD ( of three feet) should really be called Megalithic STEP (of 2.5 feet), that is Thom did not know enough about historical metrology to correctly name the unit he had deduced as operational within megalithic monuments.
When Thom then went on to find a unit one 40th of a megalithic yard, within the megalithic "art" of spirals, cup marks and cup and ring marks, he called this unit (= 0.815 inches) the megalithic inch, when in fact it is a megalithic digit. This may all seem pedantic, yet when seen to be a digit with 16 in a foot (of 1.0875 ft) and 40 in a CMY then something crucial about the use of megalithic inches comes to the fore.
Carnac's famous Alignments begin to the west with the hamlet Le Menec, nestled within a massive stone circle called the Western Cromlech. Thom surveyed this cromlech as being a Type 1 Egg shape with a forming circle of 42.5 CMY which is more simply seen as 17 megalithic rods, or more properly, seventeen megalithic fathoms.
Thom's survey of Le Menec's western cromlech showing an Egg shape
based upon a forming circle (red) of radius 17 megalithic rods = 1386.48 ft
This length has two parallel uses for megalithic astronomy.
- In INCHES this length equals the day-inch count of four eclipse years (EY = 346.62 days), a periodicity which functions as an eclipse cycle called the Octon, similar in length to 47 lunar months.
- In MEGALITHIC INCHES this length equals 1700 day-inches, one quarter of the 6800 days in 18.618 years, the time between lunar standstills.
It seems bizarre that seventeen rods based upon the CMY (differential length between three solar and three lunar years) should then yield, in one length, the length of the two main cycles defining eclipses and the movement of the moon's nodes, if the two types of inch are employed. However, one can see how this might have been discovered using the pre-arithmetical methods of the megalithic astronomers.
As I mentioned in a previous context of Arbor Low, megalithic astronomers could multiply and divide using right triangular ratios, a method I call Triangular Proximation, since the two longest sides must be close to each other so as to appear within the same triangle. In this case one can assume that the astronomers were aware of the Octon eclipse cycle of 4 eclipse years (= 1386.48 day-inches ~ 47 lunar months) and the length of the nodal cycle as 6800 day-inches. One quarter of 6800 days is 1700 day-inches which is then proximate to 1386.48 day-inches of the Octon. A Triangle formed with these two lengths will manifest the ratio numerically equal to the megalithic inch, i.e. 0.8156" based upon the Carnac MY of 32.625":
The utility of the megalithic inch is demonstrably the cause of the seemingly bizarre equation of two time period counts within the same overall dimension but then counted using two different measures, the original day-inch and the subsequent day-megalithic inch, directly available by bringing a 1700 day-inch count into a proximate right triangle. The inches in the hypotenuse, if brought down vertically onto the base, will naturally define the megalithic inch, 1700 of which now subdivide the base length of the triangle.
One sees also how the megalithic yard is really a step of 2.5 feet each with 16 megalithic inches but actually revealed to be (as they are metrologically) megalithic digits, with 40 digits within the megalithic "yard" and 100 in the megalithic step, hence 1700 in 17 megalithic "rods", which are actually megalithic fathoms. The MODULE is then (as Neal has it) a microvaried Sumerian foot (12/11 feet) or, more accurately, a microvaried Saxon foot of 1.0875 feet. But that is a later way of thinking only developed later in the Ancient Near East, when arithmetic could be used instead of metrology's natural language of geometry.