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.
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.
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.
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.
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.
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).
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”.
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:
What really happens when Earth turns? The rotation of Earth describes periods that are measured in days. The solar year is 365.242 days long, the lunation period 29.53 days long, and so forth.
Extracted from Matrix of Creation, page 42.
Earth orbits the Sun and, from Earth, the Sun appears to move through the stars. But the stars are lost in the brightness of the daytime skies and this obscures the Sun’s progress from human view. However, through observation of the inexorable seasonal changes in the positions of the constellations, the Sun’s motion can be determined.
The sidereal day is defined by the rotation of Earth relative to the stars. But this is different from what we commonly call a day, the full title of which is a tropical day. Our day includes extra time for Earth to catch up with the Sun before another sunrise. Our clocks are synchronized to this tropical day of twenty-four hours (1,440 minutes).
The Sun circumnavigates the zodiac in 365 tropical days, within which 366 sidereal days have occurred. There is one full Earth rotation more than there are sunrises within a year. This hidden oneness within the year is recapitulated in the one-unit difference between the number of sidereal days and the number of tropical days in a practical year.
The small catch-up time in every day is about three minutes and fifty-six seconds long. This unit defines not only a sidereal day with 365 such units but also the practical year of 365 tropical days. The catchup unit is the difference between the duration of a sidereal day and that of a tropical day. It relates the Sun’s daily motion to the rotation of Earth and is a fundamental unit of Earth time (figure 3.6).
THE MOON GATHERS THE TEN THOUSAND WATERS
The sidereal day (the duration of one rotation of Earth) is a very significant cosmic unit. The Jupiter synodic period of 398.88 tropical days is within 99.993% of four hundred sidereal days long. Therefore, twenty-five Jupiter synods (365 lunar orbital periods) equal 10,000 sidereal days since four hundred times twenty-five is 10,000.
A sidereal day differs from a tropical day due to the motion of the Sun during one tropical day. The three-minute-and-fifty-six-second time difference between these two days, the aforementioned catch-up unit, is quite useful when applied as the unit to measure the length of these days. A tropical day has 366 of these units while the sidereal day has 365 of the same units. The difference between the two is one unit.
Since 365 lunar orbits equal 10,000 sidereal days, it follows that a single lunar orbit has a duration of 10000/365 sidereal days. There are 365 units in a sidereal day, and therefore 10,000 units in a lunar orbit, so this new unit of time is 1/10000 of a lunar orbit. One ten-thousandth of a lunar orbit coincidentally is three minutes and fifty-six seconds in duration. The proportions in the Jupiter cycle combine with the lunar orbit, solar year, and Earth’s rotation to generate a parallel number system involving the numbers 25, 40, 365, 366, 400, and 10,000.
This daily catch-up unit I shall a chronon. Its existence means that the rotation of Earth is synchronized with both the lunar orbit and the Jupiter synodic period using a time unit of about three minutes and fifty-six seconds.
The sidereal day of 365 chronons is the equivalent of the 365-day practical year, the chronon itself is equivalent to the sidereal day, and so on. The creation of equivalents through exact scaling enables a larger structure to be modeled within itself on a smaller scale. This is a recipe for the integration of sympathetic vibratory rhythms between the greater and the lesser structures, a planetary law of subsumption.
The exemplar of the chronon was found at Le Menec: It’s egg-shaped western cromlech has a circumference of 10,000 inches and, if inches were chronons (1/365th of the earth’s rotation), then the egg’s circumference would be the number of chronons in the lunar orbit of 10,000. Dividing 10,000 by 366 (the chronons in the tropical day) gives a lunar orbit of 27.3224 – accurate to one part in 36704! The forming circle of Le Menec’s egg geometry provided a circumpolar observatory of circumference 365 x 24 inches, which is two feet per chronon versus the chronon per inch of the egg as lunar orbit.
The quantified form of the Le Menec cromlech was therefore chosen by the builders to be a unified lunar orbital egg, with a forming circle represented the rotation of the Earth at a scaling of 1:24 between orbital and rotational time.
This design is further considered in Sacred Number and the Lords of Time, chapter 4: The Framework of Change on Earth, from the point of view of the cromlech’s purpose of providing a working model of the lunar orbit relative to the rotation of the circumpolar sky, leading to the placement of stones in rows according to the moon’s late or early rising to the East.
Capturing Sidereal Time
We can now complete our treatment of Carnac’s astronomical monuments by returning to Le Menec where the challenge was to measure time accurately in units less than a single day. This is done today at every astronomical observatory using a clock that keeps pace with the stars rather than the sun.
The 24 hours of a sidereal clock, roughly four minutes short of a normal day, are actually tracking the rotation of the Earth since Earth rotation is what makes all the stars move. Even the sun during the day moves through the sky because the Earth moves. Therefore, in all sidereal astronomy, the Earth is actually the prime mover. The geometry of a circumpolar observatory can reveal not only which particular circumpolar star was used to build the observatory but also the relatively short period of time in which the observatory was designed. Each bright circumpolar star is recognizable by its unique elongation on the horizon in azimuth and its correspondingly unique and representative circumpolar orbital radius in azimuth. …
The knowledge that was discovered due to the Le Menec observatory is awe inspiring when the perimeter of the egg shape is taken into account. It is close to 10,000 inches, the number of units of sidereal time the moon takes to orbit the Earth. The egg was enlarged in order to quantify the orbit of the moon as follows: every 82 days (three lunar orbits) the moon appears over the same part of the ecliptic. Dividing the ecliptic into sidereal days we arrive at 366 units of time per solar day.*
*These units are each the time required for an observer on the surface of the Earth to catch up with a sun that has moved within the last 24 hours, on the ecliptic, a time difference of just less than four minutes.
82 days times 366 divided by the three lunar orbits gives the moon’s sidereal orbit as 122 times 82 day-inches. Instead of dividing 82 by three as we might today to find the moon’s orbit, the pre-arithmetic of metrology enabled the solar day (of 366 units) to be divided into three lengths of 122. If a rope 122 inches long is then used 82 times (a whole number), to lay out a longer length, a length of 10,004 inches results. If 10,004 is divided by 366 units per day then the moon’s orbit emerges as 82/3 or 27⅓ days.
If a moon marker is placed upon the Le Menec perimeter and moved 122 inches per day, the perimeter becomes a simulator of the moon. … Knowing the moon’s position on the western cromlech’s model of ecliptic and knowing which parts of the ecliptic are currently rising from the circumpolar stars enabled the astronomers to measure the moon’s ecliptic latitude.
Hence the phenomena related to the retrograde motion of the lunar orbit’s nodal period could be studied and its 6800 day length.
In 2009 I returned to Plouharnel, again for the Solstice Festival, and undertook my own research both before and after the four day event. Howard Crowhurst had undertaken a great deal of theodolite and tape work at a well known site called Le Manio. This collection of surviving monuments forms an exceptionally rich group of astronomical alignments which together carry enormous ritual significance in that these sites hold information about human conception, the gestation period and ritual use of geometry and metrology. Howard understands the site to the point where his three hour workshop covered much of this material, and the implications of it were clearly understood by non-specialists. Those readers who have the chance to attend the Festival, and who speak either English or French, should regard this experience as a megalithic ‘must’. Howard is an exceptionally good communicator of what are often seen as difficult areas of megalithic research, and he is astonishingly good at passing these ideas on to his audience with a great deal of clarity, enthusiasm and humour. It was during Howard’s seminar/workshop that he invited me to set up his theodolite within the Le Manio Quadrilateral, a curious site near the 6.5 metre high ‘Giant of Le Manio’. This done, I noticed something I had been searching for for twenty years. Read on…!
It is 10 years since my brother and I surveyed this remarkable monument which demonstrates what megalithic astronomy was capable of around 4000 BC, near Carnac. The Quadrilateral is the earliest clear demonstration of day-inch counting of the solar year, and lunar year of 12 lunar months, both over three years. The lunar count was 1063.125 day-inches long and the solar 1095.75 day-inches, leaving a difference of 32.625 day-inches. This length was probably the origin of a number of later megalithic yards, which had different uses.
This series is about how the megalithic, which had no written numbers or arithmetic, could process numbers, counted as “lengths of days”, using geometries and factorization.
The last lesson showed how right triangles are at home within circles, having a diameter equal to their longest side whereupon their right angle sits upon the circumference. The two shorter sides sit upon either end of the diameter (Fig. 1a). Another approach (Fig. 1b) is to make the next longest side a radius, so creating a smaller circle in which some of the longest side is outside the circle. This arrangement forces the third side to be tangent to the radius of the new circle because of the right angle between the shorter sides. The scale of the circle is obviously larger in the second case.
Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius.