ITS EARLIEST STAGES. 121 



intercalation. This can hardly be coasidered as an improvement in 

 the Greek calendar already described. 



The first cycle which produced any near correspondence of the 

 reckoning of the moon and the sun, was the Octaeteris, 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 365| 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 per- 

 sons and times ; probably different persons proposed different forms ot 

 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 9.9 lunations 

 is something more than 2922 days; it is more nearly 2923^; hence 

 in 16 years there was a deficiency of 3 days, with regard to the mo- 

 tions of the moon. This cycle of 16 years (Hecccedecaeteris), with 3 

 interpolated days at the end, was used, it is said, to bring the calcula- 

 tion right with regard to the moon ; but in this way the origin of the 

 year was displaced with regard to the sun. After 1 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 agree- 

 ment: and we have thus a cycle of 160 years. 21 



This cycle of 160 years, however, was calculated from the cycle of 

 16 years; and it was probably never used in civil reckoning; which 

 the others, or at least that of 8 years, appear to have been. 



The cycles of 16 and 160 years were corrections of the cycle of 8 

 years ; and were readily suggested, when the length of the solar and 

 lunar periods became known with accuracy. But a much more exact 

 cycle, independent of these, was discovered and introduced by Meton, 22 

 432 years B. c. This cycle consisted of 19 years, and is so correct and 

 convenient, that it is in use among ourselves to this day. The time 

 occupied by 19 years, and by 235 lunations, is very nearly the same; 



21 Geminus. Ideler. - 2 Ideler, Hist. Unters. p. 20S. 



