Further Details
The Metonic cycle is related to two less accurate subcycles:
- 8 years = 99 lunations (an Octaeteris) to within 1.5 days, i.e. an error of one day in 5 years; and
- 11 years = 136 lunations within 1.5 days, i.e. an error of one day in 7.3 years.
By combining appropriate numbers of 11-year and 19-year periods, it is possible to generate ever more accurate cycles. For example simple arithmetic shows that:
- 687 tropical years = 250921.39 days
- 8497 lunations = 250921.41 days
giving an error of only about half an hour in 687 years (2.5 seconds a year), although this is subject to secular variation in the length of the tropical year and the lunation.
Meton of Athens approximated the cycle to a whole number (6940) of days, obtained by 125 long months of 30 days and 110 short months of 29 days. In the following century Callippus developed the Callippic cycle of four 19-year periods for a 76-year cycle with a mean year of exactly 365.25 days.
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