The Octon of 4 Eclipse Years

Having seen, in the last post, that three eclipse years fitted into the three-year count at Le Manio, another eclipse fact has come to light, recorded within the nearby site of Crucuno, between its dolmenA chamber made of vertical megaliths upon which a roof or ceiling slab was balanced. and rectangle. The coding of time at Crucuno was an evolution of a new metrologyThe application of units of length to problems of measurement, design, comparison or calculation. based upon 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]. in which, the right triangle of longest integer side lengths was replaced by fractions of a foot using the same two numbers as the sides would have had. This allowed the measurement of a time period to be simultaneously seen in both days and months. That this was possible can be seen at Le Manio, where it could be noticed that 32 lunar months equaled exactly 945 day-inches.

As already stated, numbers were not notated but rather, a measurement (of days) could be known by the smaller numbers of days that can perfectly divide into it. It is therefore important, when studying megalithic methods, to look at the prime factors found within time lengths since then one can see a measurement as they had to, and see how their counted monuments contain numerical oddities or coincidences; which is how they discovered or expressed their understanding of Time.

For instance, in this case, if 945 days equals 32 then the lunar month must be 29.53125 (945/32) days. The factors of 945 are 27 x 5 x 7 and so the lunar month is (27 x 5 x 7 divided by 32). For practical reasons this is best expressed by three numbers as (27 x 35)/32 and if, as at Crucuno, each month was counted as 27 feet, the number of days within one month could also be counted using rational fractions of a foot of 32/35 feet. And this latter unit is the Iberian foot commonly found in megalithic structures of the Atlantic coast of Europe, with Brittany, Le Manio and Crucuno, directly on a peninsula of that coast.

At Crucuno themegalithic appear to find another near equation between periods, namely 47 lunar months (1388 days) and four eclipse years (because, at Crucuno, a count starts (as is often the case) from a Dolmen (at an eclipse) and the count then ran in months equal to 27 feet up to the Crucuno Rectangle, within which the counting continued, in an array of 27 foot squares within the rectangle, of rows containing 4 units east-west and then two additional rows below. Note how the diagonal again marks the solsticeThe extreme points of sunrise and sunset in the year. In midwinter the sun is to the south of the celestial equator (the reverse in the southern hemisphere) and in midsummer the sun is north of that equator, which is above the geographical Equator). sun-angle. After two rows had been counted, the month count was within the 47^th month (1388 days) while four eclipse years equals 1386.5 days, one and a half days less. If days were coded as Iberian feet of 32/35 feet, then the fourth 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. will precede the 47^th lunar month by 1.36 or 4/3 such feet and this would have been accurate to about one and a half minutes and hence, for the stone age, exactly the case. The basic count could have used Iberian feet for days and the number of months counted by there being 27 feet in each month.  

We can now progress from the previous posting on the eclipse year, anomalous monthThe time taken for the Moon, in its orbit, to reach its nearest position (largest size) to the Earth equal, on average, to 27.554 days. and its π (pior π: The constant ratio of a circle's circumference to its diameter, approximately equal to 3.14159, in ancient times approximated by rational approximations such as 22/7.) relationship through the equal perimeter relationship. The fourfold nature of the diameter (of 4 anomalistic months), leads to the possibly of extending the equal perimeter square, whose perimeter is the eclipse year of 346.62 days, in the following way:

There is a Geometry lesson on this kind of procedure.

This kind of fourfold transformation of a day-inch or other counted length into the length of a circular structure hold promise when one comes to the reported finding that circular rings have a circumference that is counted according to an astronomical cycle. The advantages of a counted circle is that it becomes a continuous recurrence, within which eclipses, for example, can be anticipated over more than the Octon, since there are many differences within eclipses seen four eclipse years apart. This is largely due to the distance between the sun and moon from the earth , and because the apparent size of their discs seen from earth crucially affects what an eclipse looks like. This can be observed in the case of the moon, due to the anomalistic month of 27.554 days, while earth’s orbit causes the sun to change size during the year. The best eclipse cycle would be one in which the same type of eclipse happens when it ends as happened when it started.

One unique cycle exists that achieves just that, called the SarosThe dominant eclipse period of 223 lunar months after which a near identical lunar or solar eclipse will occur., and the next article in the series on eclipses will discuss the main way this was achieved by making the retrograde motion of the lunar nodes within the Saros period commensurate with the anomalistic month.