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 (within which almost identical eclipses re-occur) 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, 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).

This triangle, symbolic of 37, often appear in pairs within stone L8 with 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 *** and forms an intermediate hypotenuse within the 5-12-13 triangle equal to 12.368 months, the solar year. Three solar years then appears to have been seen as composed of 12+12+13 which is exactly how Arab and medieval astronomers came to organise their intercalary months within the Callippic cycle of 4 Metonic periods (= 4 x19 years equalling 76 solar years).

The Saros period appears to have been indicated on stone L9, below these triangles, using 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 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 18 years to be seen as six periods of 37 lunar months, equal to 222, plus one lunar month.This enabled a pre-arithmetic culture to approach prime number 223 from a another large unit, repeated six times.

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