Nubes, 615–19.
Chorus of Clouds.
The Moon by us to you her greeting sends,
But bids us say that she’s an ill-used moon,
And takes it much amiss that you should still
Shuffle her days, and turn them topsy-turvy:
And that the gods (who know their feast-days well)
By your false count are sent home supperless,
And scold and storm at her for your neglect.[19]
[19] This passage is supposed by the commentators to be intended as a satire upon those who had introduced the cycle of Meton (spoken of in [Sect. 5]), which had been done at Athens a few years before “The Clouds” was acted.
The correction of this inaccuracy, however, was not pursued separately, but was combined with another object, the securing a correspondence between the lunar and solar years, the main purpose of all early cycles.
Sect. 5.—Invention of Lunisolar Years.
There are 12 complete lunations in a year; which according to the above rule (of 29½ days to a lunation) would make 354 days, leaving 12¼ days of difference between such a lunar year and a solar year. It is said that, at an early period, this was attempted to be corrected by interpolating a month of 30 days every alternate year; and Herodotus[20] relates a conversation of Solon, implying a still ruder mode of [121] intercalation. This can hardly be considered as an improvement in the Greek calendar already described.
[20] B. i. c. 15.
The first cycle which produced any near correspondence of the reckoning of the moon and the sun, was the Octaëteris, or period of 8 years: 8 years of 354 days, together with 3 months of 30 days each, making up (in 99 lunations) 2922 days; which is exactly the amount of 8 years of 365¼ days each. Hence this period would answer its purpose, so far as the above lengths of the lunar and solar cycles are exact; and it might assume various forms, according to the manner in which the three intercalary months were distributed. The customary method was to add a thirteenth month at the end of the third, fifth, and eighth year of the cycle. This period is ascribed to various persons and times; probably different persons proposed different forms of it. Dodwell places its introduction in the 59th Olympiad, or in the 6th century, b. c.: but Ideler thinks the astronomical knowledge of the Greeks of that age was too limited to allow of such a discovery.
This cycle, however, was imperfect. The duration of 99 lunations is something more than 2922 days; it is more nearly 2923½; hence in 16 years there was a deficiency of 3 days, with regard to the motions of the moon. This cycle of 16 years (Heccædecaëteris), with 3 interpolated days at the end, was used, it is said, to bring the calculation right with regard to the moon; but in this way the origin of the year was displaced with regard to the sun. After 10 revolutions of this cycle, or 160 years, the interpolated days would amount to 30, and hence the end of the lunar year would be a month in advance of the end of the solar. By terminating the lunar year at the end of the preceding month, the two years would again be brought into agreement: and we have thus a cycle of 160 years.[21]