The information below (without diagrams and using the rational logic of our functional mathematics: of equating things, dividing or multiplying both sides, transfering across the equation using reciprocation, and so on) leads to a verbose and quite hard to understand how the unit of length in day-inches for 4 eclipse years (EY) is the same length as one quarter of a day count for the the moon's nodal period of 6800 days (18.618 years), if then counted in megalithic inches (MI = 0.815") of which there are 40 in a (Carnac) megalithic yard (CMY) and 100 MI in a megalithic rod (MR = 2.5 CMY). An article is in preparation demonstrates how much easier was the megalithic approach to understanding this strange equation, found at Le Menec's western cromlech, where the radius of the forming circle is 17 MR = 4 EY = 1386.48 day-inches = 1700 day-MI.

A Follow up to this Article now exists, called Origin of the Megalithic Inch ... using megalithic numerate thinking

first published on MatrixOfCreation.co.uk, Monday, 30 April 2012 12:57

At Le Menec, the western cromlech's radius of 17 megalithic rods = 42.5 megalithic yards was first found to equal four eclipse years in day-inch counting but then seen to contain the same number of megalithic inches (1700) as would be generated by counting one quarter of the moon's nodal period of 18.6 years (6800 days). (See Sacred Number and the Lords of Time page 98-99 or PDF: The Meaning of Le Menec)

The number of these two types of inch, found within seventeen megalithic rods, cannot without a reason correspond to the number of days in (a) four eclipse years (a length of time significant as being the Octon eclipse cycle) and (b) one quarter of the moon's nodal period. Two such unlikely correspondences occurring within the same unit length (effectively multiplying each individual unlikeliness) forming a probability lower than either taken individually.

There is therefore likely to be a systematic reason for why this singular length should simultaneously represent the key day counts for eclipse year and the related nodal cycle that regulates eclipses.

The nodal cycle can be expressed as equal to 19.618 eclipse years and 19.618 eclipse years, divided by four eclipse years, is the ratio 4.9045, which ratio is six times a megalithic inch of 0.8174 inches. This numerical value for the megalithic inch is therefore 19.618 eclipse years divided by 24 eclipse years, and the latter period is six times 17 megalithic rods or 255 megalithic yards. This would make a megalithic yard equal to 24 eclipse years of day-inch counting divided by 255  or 32.623 day-inches, as found at Carnac.

The three main types of year, solar, lunar and eclipse, are therefore commensurate, dividing into each other in a rational fashion, involving whole numbers. 

This megalithic yard was derived at Le Manio’s Quadrilateral (PDF) from a day-inch count enabling three lunar years to be subtracted from three solar years, to make a megalithic yard then defined as,

megalithic yard = 3 times (Solar Year minus the Lunar Year)

or 3*(365.25 - 354.375) = 261/8 =32.625 day-inches

Since, as above, 24 eclipse years as a day count equals 255 MY then,

The eclipse year, EY = 255/24 x 3*(SY - LY) = 30 * 17/16 * (SY - LY)

and (SY - LY) = 87/8 = 10.875 days

Therefore, EY = 30 * 17/16 * 87/8 day-inches    (relationship A)

the solar, lunar, eclipse years being abbreviated as SY, LY, EY 

This can be expressed as, the eclipse year is thirty times the ratio of the squares of the solar and lunar years times the excess of the solar year over the lunar year.

Meanwhile, the moon's nodal period of 19.618 eclipse years is 6800 days long  = 17 ×4 ×100 days. Le Menec's western cromlech has a radius of 17 megalithic rods which equal 17 x 100 megalithic inches, where a megalithic inch (M-inch) is 1/40th of a megalithic yard, 1/100th of a megalithic rod. This length at Le Menec is therefore a quarter count for one lunar nodal period, counting one day per megalithic inch so that 

an eclipse year (EY) in megalithic inches equals  
(17 * 4 * 100)/ 19.618
 megalithic-inches   (relationship B) 
which is that same length as 
30 * 17/16 * 87/8 day-inches   (relationship A)

therefore,

 (17 * 4 * 100)/ 19.618  megalithic-inches = 30 * 17/16 * 87/8 day-inches

The number of eclipse years in the nodal cycle is therefore numerically produced when 19.618 is taken to one side as,

 400/30 * 17/16 * 8/87 = 19.616585

This demonstrates the identity within the parallel usage of inches to count four eclipse years and megalithic inches to count one quarter of a nodal cycle as the same length of seventeen megalithic rods found as the radius of Le Menec’s western cromlech.

A Follow up to this Article now exists, called Origin of the Megalithic Inch, using megalithic numerate thinking.