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.
A 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.