The Metonic Period is the 19 year anniversary of the Moon which dominates the repetition of cyclic astronomical aspects in the sky. We know that the megalithic identified this period and others of similar length (the Saros and Nodal periods), because interrelated units of measure, especially the megalithic yard and royal cubit, can be found within monuments which recorded these periods as counted lengths.
How the Metonic Works
There is only numerical way to arrive at a system in which there is an anniversary between the sun, the moon and the stars over 19 years (as in the Metonic period), involving having a lunar orbital period (around the earth) which divides into the same period, in this case exactly 254 times.

 254 lunar orbits of (on average) 27.32166 days equals 6939.7 days
 19 solar years of 365.2422 days equals 6939.6 days and
 235 lunar months of 29.53059 days equals 6939.7 days
If the moon returns to the position of the sun after 19 years then the phase of the moon will be the same so that there will be 254 minus 19 equal to 235 lunar months in the Metonic observatory and it is in the nature of orbits which become commensurate with each other (as discrete, wholenumber gravitational systems), to fall into such resonant relationships rather than chaotic ones.
Signature Ratios within the Metonic
Since the solar year, lunar orbit and month are synchronous, the excess of the solar over lunar year will form a near rational (i.e. integer) fraction of months or orbits, in that case an excess of 7/19 (0.368) lunar months.

 The lunar orbit is 27.32166 days
 The lunar month is 29.53059 days
Similarly, the excess of the lunar month over the lunar orbit become the rational and fractional ratio found between their frequencies within the 19 year Saros cycle, that is 254/235; which has the fractional part, reciprocated of 1/0.08085 = 12.368 which is then N for the N:N+1 triangle describing the orbit relative to the month, of the moon.
However, the lunar orbit is also found to be 10,000 time periods long, the unit of time being the excess of the solar over the sidereal day***, which in Matrix of Creation I called the chronon after the god of time.

 *** The sidereal day is relative to the stars and it is the time for the earth to rotate once whilst the solar day is that time plus the time taken for a location upon the earth to catch up with the sun's motion within the solar year, this due to the earth's orbit around the sun.
Once the earth's rotation and lunar orbit came to be set to this chronon ratio of one solar excess to ten thousand solar excesses per orbit, the orbit of the moon can be visualised as containing 10,000 chrononinches as a length (the circumference of the Le Menec western cromlech near Carnac town in Brittany) and this actual length of 10,000 inches can be divided by the number of orbits in the Metonic so as to create the 39.37 inch metre standard (its legal ratio in the U.S.A [Berriman 1953, p21]) which is 10,000/254 inches.

 We will later look at how three quarters of this length of 39.37 inches equals 29.528 inches, one part in 9742 of the lunar month's average duration of 29.53059 days, a relationship seen very clearly at Le Manio's Quadrilateral [HEATH & HEATH, 2010 & HEATH 2014] marking a count of three solar years and three lunar years, and their difference of one megalithic yard of 261/8 dayinches.
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