140 THE GREEK ASTRONOMY. 



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 pre- 

 ceding month, the two years would again be 

 brought into agreement : and we have thus a cycle 

 of 160 years 21 . 



This cycle of 160 years, however, was calcu- 

 lated from the cyle of 16 years; and 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 correc- 

 tions 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 dis- 

 covered 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; (the 

 former time is less than 6940 days by 9J hours, 

 the latter, by 7J hours.) Hence, if the 19 years 

 be divided into 235 months, so as to agree with the 

 changes of the moon, at the end of that period 

 the same succession may begin again with great 

 exactness. 



31 Geminus. Ideler. " Ideler, Hist. Unters. p. 208. 



