Gavrinis R8: Diagram of the Saros-Metonic Cycle

The Saros cycle is made up of 19 eclipse years of 364.62 days whilst the Metonic cycle is made up of 19 solar years of 365.2422 days. This unusually small number of years, NINETEEN, arises because of a close coupling of most of the major parameters of the Earth-Sun-Moon system which acts as a discrete system, a system also commensurate with Jupiter, Saturn, Uranus and Venus. It is this type of coherent cyclicity which lies at the centre of what the megalithic were able to achieve through day-inch or similar counting of visible time periods and comparing of counts using geometric means. [see my books, especially Sacred Number and the Lords of Time, for a fuller discussion].

It would have been relatively easy for megaithic astronomy to notice that eclipses occur in slots separated by eclipse seasons of 173.3 days and also to see that the difference between lunar and solar years resolves over the 19 year of the Metonic so that lunar orbits, lunar months, the starry sky and the rotation of the earth provide a close repetition of alignments over 19 solar years which equal 235 lunar months and 254 lunar orbits. The Saros period is 223 lunar months long and is therefore one lunar year of 12 months short of the Metonic of 235 lunar months.

The situation in the last year of the Metonic is therefore identical but (symmetrically) in-reverse to the first year, on a continuous but discrete basis [that is, providing you start counting on an eclipse]. The Saros then ends12 months before the Metonic so that the Saros is 18 solar years long plus, quite closely, the 10.8 day difference between the lunar and solar years. This phenomenon is clearly presented on Gavrinis’ stone R8, in the middle “register”, such engraved art at Gavrinis dividing their stone pallettes into different elements of a related summary of astronomical phenomena seen through the tools of a megalithic science involving counting, alignment, geometry, and metrology.

Central section of Gavrinis stone R8 clearly shows the Saros and Metonic Cycles as ending between 18 and 19 years less the difference between the lunar and solar years

 In the figure above, the right shows the four-square geometry whose diagonal is the length of the solar year relative to the length of the base (=4) as being the length of the lunar year of 12 lunar months. The difference in length of these two years is shown “centre stage” and is accurately 10.8 inches long, numerically representing the difference in terms of day-inch counting. The curvilinear lines around the vertical are emblematic of counting as fundamental to this type of art. The diagonal actually shown here is continued into the representation of a series of solar years, here numbered so that, in the 19th year, something new happens: the year rises up but is bent leftwards in what is one of the most distinctive patterns in Gavrinis’ art.

We know, as stated above, that the Metonic is 19 years long and that the Saros is a year less, plus the 10.8 day difference between lunar and solar years, so that the 10.8 day-inches is shown centrally above on R8 both refers to the initial four-square relating the solar and lunar year, by the excess then found over 18 years, of 10.8 day-inches.

This is a very compact and intuitive diagramming language which communicates, without words but with an implicit familarity of day-inch counting, an inter-related cyclicity of crucial importance discoverable using this megalithic science. Similar components are to be found on other stones and astronomy appears to be the purpose of this notational art, designed to educate and explain important facts, within an oral megalithic culture.

What stone L9 might teach us

image of stone L9, left of corridor of Gavrinis Cairn,
4Km east of Carnac complex. [image: neolithiqueblog]

This article was first published in 2012.

One test of validity for any interpretation of a megalithic monument, as an astronomically inspired work, is whether the act of interpretation has revealed something true but unknown about astronomical time periods. The Gavrinis stone L9, now digitally scanned, indicates a way of counting the 18 year Saros period using triangular counters  founded on the three solar year relationship of just over 37 lunar months, a major subject (around 4000 BC) of the Le Manio Quadrilateral, 4 Km west of Gavrinis. The Saros period is a whole number, 223, of lunar months because the moon must be in the same phase (full or new) as the earlier eclipse for an eclipse to be possible. 

On the roof with Anthony Blake (left) on the DuVersity Albion Tour, in August 2004.

Handling the Saros Period

223 is a prime number not divisible by any lower number of lunar months, such as 12 in the lunar year. 18 lunar years equates to 216 lunar months, requiring seven further months to reach the Saros condition where not only is the lunar phase the same but also, the sun is sitting upon the same lunar node, after 19 eclipse years of 346.62 days.

However, astronomers at Carnac already had a number of 37 lunar months (just less than three solar years) in their minds and, it appears, they could apply this as a length 37 units long, as if each unit was a lunar month. We also know that the unit they used for counting lunar months was originally 29.53 inches (3/4 metre) or later, the megalithic yard. Visualising a rope of length 37 megalithic yards, the length can be multiplied by repeating the rope end-to-end. After six lengths, 222 or 6*37 lunar months were represented, one lunar month less than the 223 lunar months which define the Saros period.

Figure 1 The near-integer Anniversary of Lunar Months over Three Years

This six-fold use of the number 37 appears to be used within the graphic design of Gavrinis stone L9 (see figure 2), as the triangular shape which has an apex angle of 14 degrees and which refers to the triangle formed at Le Manio between day-inch counts over three solar and three lunar years. It appears that this triangular shape was used to refer to the counting of solar years relative to a stone age lunar calendar (see 2nd register of stone R8) but it could also have the numerical meaning of 37 because three solar years contained 37 whole lunar months just as a single solar year contains 12 whole lunar months (the lunar year).

I believe this triangle, already symbolic of 37, appears in pairs within stone L9, as a single counter showing two axe heads, their points adjacent so that they have one side also adjacent. The two triangles are found to be held accurately within the apex angle of another triangle, known to be in use at Carnac, the triangle with side lengths 5-12-13, with apex angle 22.6 degrees. These pairs would then effect the notion of addition so that each is valued at 37 + 37 = 74 lunar months.

Figure 2. The use of two three-year triangles, made to fit within the 5-12-13 triangle to form a single counter worth 74 lunar months. (MegalithicScience.org eventually became this website)

All of the three pairs have this same apex angle, of the 5-12-13 triangle, chosen perhaps because 12+12+13 = 37 whilst the 14 degree triangle was known to be rationally held within it when the 12 side is seen as the lunar year of 12 months. The third side is then 3 lunar months long (¼ lunar year) forming an intermediate hypotenuse within a 5-12-13 triangle, which is equal to the 12.368 months of the solar year. Robin Heath first identified the smaller triangle when studying the properties of the 5 by 12 rectangle of Stonehenge’s Station Rectangle, arguably made up of two 5-12-13 triangles joined by their 13 sides. Three solar years then seems to have become associated with the pattern 12+12+13 (= 37) by the historical period, since Arab and medieval astronomers came to organize their intercalary months within the Callippic cycle of 4 Metonic periods (= 4 x 19 years equaling 76 solar years).

Figure 3. The quantification of the Saros as 18 solar years and 11 days equal to 223 lunar months. The language of days and years at Gavrinis might well have been the primary perception of light and dark periods.

The Saros period of 223 lunar months then also appears indicated on stone L9, below these triangles, within the main feature of this stone, a near-square Quadrilateral having one right angle. It has a rounded top, containing a wavy engraved design emanating from a central vertical, not unlike a menhir. The waves proceed upwards but then narrow to a vestigial extent after the 18th, which would be one way to symbolise the Saros period as 18 years and eleven days in duration. A different graphical allusion was used on stone R8, again showing lines as years but giving the 19th year as a shortened “hockey stick”.

Conclusions

In Gavrinis stone L9, a “primitive” numerical and phenomenological symbolism appears to have expressed a useful computational fact: that the Saros period was one lunar month more than six periods of 37 lunar months. These three periods of 37 months were shown as blade shapes, each symbolising three solar years, but shown as pairs within three 5-12-13 triangles above a quadrilateral shape indicating 18 wavy lines plus a smallest period, this symbolising the 11 days over 18 years of the Saros Period, defined by 223 lunar months. This allowed the Saros to be seen as six periods of 37 lunar months, equal to 222, plus one lunar month. Once the count reached 222, attention to the end of the next lunar month would be key. This enabled a pre-arithmetic culture to approach prime number 223 from another large prime (37) which was nearly expressed by 3 solar years, then repeated six times yo become 222 lunar months. This same counting regime appears to have been employed elsewhere:

  1. Astronomical Rock Art at Stoupe Brow, Fylingdales.
  2. Eleven Questions on Sacred Numbers.
  3. Counting lunar eclipses using the Phaistos Disk.

Many thanks to Laurent Lescop of Nantes University Architecture Dept,
for providing the scan on which this work is based.

The Roof Axe as Circumpolar Device

This article explores the use of axe motifs within a form of carved schematic art unique to the megalithic monuments near Carnac, southern Brittany, France. First published in February 2014.

A diagram found on the underside of the capstone of a chambered dolmen called Kercado (see figure 1) appears to hold metrological and astronomical meanings. Classified as a type of AXE, local axe motifs are said to have three distinct forms (a) triangular blades, (b) hafted axes and (c) the Mane Ruthual type [Twohig, 1981[1]]. 

Figure 1 Well preserved sculpted-stone axe-head motif in Kercado dolmen

Types b and c are often found in the singular on the undersides to roof slabs and in the case of form (b), the hafted axe, I have attributed its display below the roof slab of Table des Marchands at Locmariaquer (inset right) as being used to represent the north pole between 5000 and 4000 BC, at a time when there was no star near to the pole itself. The abstract point of the north pole, the rotational axis of the earth, is shown as a loop attached to the base of the axe haft, whilst the axe head then represented a chosen circumpolar star, as this rotates counter-clockwise in the northern sky, at the fixed distance of the haft from the pole itself. Note how compatible this idea of an axe ploughing the northern skies is to our own circumpolar constellation, The Plough. Note also that the eastern horizon moves through the equatorial stars at the same angular rate as the marker star moves around the north pole.

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