The Quantification of Eclipse Cycles

Following on from the last post:
Given the many sub-cycles found in the Moon’s behavior, and the angle of its orbit to the EclipticThe path of the Sun through the sky along which eclipses of sun and moon can occur, traditionally divided into the 365¼ parts of the solar year, each part then a DAY in angle rather than time., one would expect the eclipse phenomenon to be erratic or random but in fact eclipses repeat quite reliably over relatively fixed periods that were quantified symbolically by megalithic astronomy, within monuments and by the “sacred” numbers and geometries which encapsulate eclipse cycles, as with many other cycles.

An eclipse cycle repeats, to greater or lesser degree of accuracy, over an integer number of days or months. And because of a lack of conventional arithmetic or notation like our own in the megalithic, the practical representation of a cycle would be a raw count of days or months, using uniform measures, which could then be interpreted by them using (a) the rational fractions of whole unit metrologyThe application of units of length to problems of measurement, design, comparison or calculation., (b) the factorization of a measured length by counting within using measuring rods or (c) using right-triangles or half-rectangles, which naturally present trigonometrical ratios; to compare different time cycles.

The Eclipse Year

The solar yearFrom Earth: the time in which the sun moves once around the Zodiac, now known to be caused by the orbital period of the Earth around the Sun. (365.242 days) is longer than the lunar year of 12 lunar months (354.367 days) and we know that these, when counted in day-inches, gave the megalithic their yard of 32.625 (32 and 5/8) inches and that, by counting months in megalithic yards over one year, the English footThe standard prehistoric foot (of 12 inches) representing a unity from which all other foot measures came to be formed, as rational fractions of the foot, a fact hidden within our historical metrology [Neal, 2000]. (of 12 inches) was instead the excess over a single lunar year of the solar year, of 12.368 lunar months. 0.368 in our notation is 7/19 and the megalithic yardAny unit of length 2.7-2.73 feet long, after Alexander Thom discovered 2.72 ft and 2.722 ft as units within the geometry within the megalithic monuments of Britain and Brittany. is close to 19/7 feet so that counting in months cancels the fraction to leave one foot.

But when long counts were made, the observed eclipses all occurred at an average distance from each other of 173 1/3 days and the latter could be “counted” to give a new type of year, the eclipse yearthe time taken (346.62 days) for the sun to again sit on the same lunar node, which is when an eclipse can happen. of 346 and 2/3 day-inches. These “eclipse seasons” are the periods in a given year where either, most commonly, the moon is eclipsed by the Earth or, less commonly, the sun is eclipsed by the Moon. And the only places where any two tilted circles (such as the ecliptic and lunar orbit) touch, about a common centre (the earth), are always diametrically opposite. These points are called the lunar nodes.

Naked eye observation can easily infer, over longer periods of time, that these two invisible points are moving backwards upon the ecliptic and that eclipses occur within a pattern of these equal periods of 173.31 and hence also of twice that within an eclipse year of 346 .62 days. There were two eclipse periods within the other years because there were two crossing points of the sun’s path (ecliptic) and moon’s path (the lunar orbit).

The megalithic could easily handle small rational fractions of a day, such as 346 plus 2/3 days (or 346.666). And over three years, as with the three year count found at the Le Manio Quadrilateral, this could be read as 1038 +2 or 1040 day-inches. This appears marked in the southern curb of the Quadrilateral, as in the silhouette below.

If the “counting line” of 1040 day-inches were divided into three and each third further divided by 2, the pattern of the eclipse seasons could be shown upon the count. And once an actual eclipse was shown within a day-inch count, the count could be conducted indefinitely into the future and past to estimate the locations in time of past and future eclipse seasons. Another interesting numerical fact is that 346.62 is the square of the nodal cycle of 18.618 years, meaning that the nodes move (retrograde) on the ecliptic by one day in angle in 18.618 days* – but we must leave that 18.618 curiosity to a later post.

*a period usefully called the Node Day

The main takeaways from this are:

That the anatomy of eclipses within time could and was quantified by the megalithic astronomers as another set of cycles, namely the eclipse seasons, eclipse year and the nodal cycle.

That the megalithic could quantify the eclipse cycles through counting time, and arrive at rational number values, either in months or days, represents an unexpected transformation made possible by the especially quantifiable relationships of time still found in our skies.

For more on this read Sacred Geometry: Language of the Angels and Sacred Number and the Lords of Time.

The next article will examine evidence, at Crucuno (near Le Manio), for the counting for the Eclipse Cycle of 4 eclipse years, which is just less than 47 lunar months.