Ancient lunar calculations made at Knowth

What this stone demonstrates is that the Neolithic people who constructed the mound were aware that the solar year, which is 365 days long, does not contain an equal number of synodic periods of the Moon. But it also shows they were aware of the great 19-year Lunar Cycle and studied the movements of the moon over long periods of time.

A synodic period of the Moon is marked by the return of the Moon to the same phase, and is exactly 29.531 days long. So therefore, 12 lunar months, or 'Synodic months' is exactly 354.372 days long. But this is a whole 11 days shorter than a tropical year. The Neolithic mound-builders knew this, and used the Lunar Stone to record their calculations of the numbers of synodic lunar months in tropical years.

25 synodic months is 738.275 days, which is 8 days longer than 2 tropical yrs.
37 synodic months is 1092.647 days, 3 days short of 3 tropical years.
49 synodic months is 14 days shorter than 4 tropical years.
62 synodic months is 5 days longer than 5 tropical years.

It is this value in the sequence which is represented on the lunar stone at Knowth. There are a total of 31 'waves' across the stone, surrounded by representations of the Moon – 29 of them – representing the 29 days of the synodic lunar month.

If we double the number of waves, we get 62, representing 62 synodic periods of the Moon, which, as we have already seen, is just 5 days longer than 5 tropical years.

The sequence continues until we get a very close correlation between synodic months and tropical years: 99 synodic lunar months is only 2 days longer then 8 tropical years. But even closer still is 136 synodic months, which ends about a day before 11 tropical years.

And if we add 99 synodic months to 136 synodic months we reach the "Metonic Cycle": 19 tropical years is equal to 235 synodic lunar months, or 254 tropical lunar months. A tropical lunar month is defined by the amount of time it takes the Moon to reach the same background stars again – it is equal to 27.322 days. The Metonic Cycle gets its name from a Greek called Meton who lived in Athens in the 5th century BC, and who claimed he discovered this cycle of the Moon himself based on simple observations. Based on our studies of the Lunar Stone at Knowth, we now know the "Metonic Cycle" was known about long before Meton ever existed.

CALCULATING THE YEAR

Furthermore, it is possible that this kerbstone was used to calculate the exact number of days in the tropical solar year. There are 29 moons in total, 22 crescents and seven circular moons which are really double circles, and potentially signifying an extra count. There is a folk tale still in existence from Brittany to Scotland which says that you should never count stones more than once because you will never get the same number. The numbers and arrangements at Stone Age sites were chosen so that there were several ways of counting them.

If we count the moons, to get 29, and add the second set of circular moons, we get 36. If we double 36 (and the stone already suggests doubling with the waved line - 2x31=62) we get 72, and add the solar spiral, we get 73. 5 times 73 is equal to 365, the exact number of days in the year. Every fourth year, add the solar spiral to get 366. Another 'Lunar Stone' at Knowth can also be used to calculate the exact length of the year, as well as both the siderial and synodic lunar months.

The "waved line" feature can also be seen to have supplemental counts on the left side, continuing from 31 to 32, 33 and 34.

32 synodic months is also a significant subunit of the Metonic Cycle, because when doubled it becomes 64 synodic periods which ties in with five calendar synodic periods of Saturn. 33 synodic months is one-third of the very important metonic subunit: 99 synodic periods ends just two days after eight tropical years. And 34 is one-quarter of another large Metonic subunit: 136 synodic months ending about one day before 11 tropical years.

When considering these engravings we must remember that the method of observation does not require complex equipment or machinery, and does not involve complicated mathematics. What it involves is simple observation over long periods of time. These engravings were obviously an attempt by the Neolithic astronomers to pass on their knowledge to the next generation – a quest in which they succeeded. 5,000 years on we too can get an insight into the astronomical observations of our "primitive" ancestors, and we too can watch the heavens and observe the Metonic cycle for ourselves.

Further reading on the web:

Fractions, cycles and time - a guide by Ivars Peterson.
Movement and phases of the Moon - by Mike Wilson.
The Church Lunar Calendar -based on the Metonic Cycle.

Acknowledgements:
Kind thanks to Professor George Eogan, director of excavations at Knowth, for his kind permission to access the site and take photographs.
I am also greatly indebted to Charlie Scribner, who has opened my mind to the lunar cycles with his authoritative writings and private communications.

Other pages of interest:
The Metonic Cycle - an illustrated lesson on how it works.
Another lunar stone - calculating the siderial and synodic months, and the length of the year at Knowth.
Equinox sunlight at Knowth - Sunlight in the western passage.
Inside Knowth west - 5,000-year-old megalithic engravings.