122 THE GREEK ASTRONOMY. 



(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. 



In order that 235 months, of 30 and 29 days, may make up 6940 

 days, we must have 125 of the former, which were called full months, 

 and 110 of the latter, which were termed hollow. An artifice was 

 used in order to distribute 110 hollow months among 6940 days. It 

 will be found that there is a hollow month for each 63 days nearly. 

 Hence if we reckon 30 days to every month, but at every 63d day 

 leap over a day in the reckoning, we shall, in the 19 years, omit 110 

 days ; and this accordingly was done. Thus the 3d day of the 3d 

 month, the 6th day of the 5th month, the 9th day of the 7th, must 

 be omitted, so as to make these months " hollow." Of the 19 years, 

 seven must consist of 13 months ; and it does not appear to be known 

 according to what order these seven years were selected. Some say 

 they were the 3d, 6th, 8th, llth, 14th, 17th, and 19th; others, the 

 3d, 5th, 8th, llth, 13th, 16th, and 19th. 



The near coincidence of the solar and lunar periods in this cycle 

 of 19 years, was undoubtedly a considerable discovery at the time 

 when it was first accomplished. It is not easy to trace the way in 

 which such a discovery was made at that time ; for we do not even 

 know the manner in which men then recorded the agreement or dif- 

 ference between the calendar day and the celestial phenomenon which 

 ought to correspond to it. It is most probable that the length of the 

 month was obtained with some exactness by the observation of eclipses, 

 at considerable intervals of time from each other ; for eclipses are very 

 noticeable phenomena, and must have been very soon observed to occur 

 only at new and full moon. 23 



The exact length of a certain number of months being thus known, 

 the discovery of a cycle which should regulate the calendar with suf- 

 ficient accuracy would be a business of arithmetical skill, and would 

 depend, in part, on the existing knowledge of arithmetical methods ; 

 but in making the discovery, a natural arithmetical sagacity was prob- 

 ably more efficacious than method. It is very possible that the Cycle 

 of Melon is correct more nearly than its author was aware, and more 



23 Thucyd. vii. 50. 'H ct\fivrj it&tfaei' hi,yxave yap trava&rjvos ovca. iv. 52. Toy 

 j\iov f/cX(T/ff rt lyivtro rrepl vovprjviav. ii. 28. 'Kovurjviq. Kara ff\/jv)]v (Sxrirep Kai p6vov 

 tl tlvai ylyvccdai fivvarbv) & fjXios i^&nre USTU nioriftppiav Kai TruXtv av f7rA7/)u)0>7, y* 

 Kai aartowv TU'Si/ tieAavlvTUV. 



