[ DAwsoNl SOLAR AND LUNAR CYCLES IN BOOK OF DANIEL 41 



Comparing this accuracy with our Gregorian calendar, the error 

 of the Mahonimedan calendar is little more. But, as its cycle is only 

 30 lunar years, instead of the four centuries required to complete the 

 Gregorian adjustment of intercalary days, it may be considered distinctly 

 superior. In view of the greater difficulty of obtaining lunar data 

 correctly and the modern character of the Gregorian calendar, it may 

 very well be that this lunar calendar is based on the prophetic number, 

 with an error purposely introduced for convenience. 



III. — The solar year and the lunar month. — A common measure 

 for these periods is necessary as a basis for a natural calendar, in which 

 the year and lunar month are both preserved. There are two well- 

 known cycles which serve this purpose. In the Metonic cycle, 19 solar 

 5'ears = 235 lunations; this being divided into a series of months 

 which gave a total of 6,940 days for its period. The Calippic cycle 

 made a correction on this by deducting one day in four j\Ietonic cycles, 

 or 76 years. It thus has 76 years = 940 lunations ; with a total of 

 27,750 days in that period. This cycle also corresponds more closely 

 with the anomalistic month; and it thus brings the hour of the new 

 moon at the beginning and end of the cycle, into better accord with 

 observation. The following are the actual lengths in days, which these 

 cycles have at the epoch 1900 A.D. : — 



Metonic. Solar years 19 x 365.2421961 = 6939.60173 days. 

 Lunations 235 x 29.530.58870 = 6939.68835 " 



Calippic. Solar years 76 x 365.2421961 = 27758.40690 day.s. 

 Lunations 940 x 29.53058870 = 27758.75338 " 



The advantage of the correction made by the Calippic cycle is 

 thus evident. Its accord with the solar year is nearly three times as 

 close as the Metonic cycle; and with the lunar month, five times as 

 close; as will be seen by reducing them both to any period of the same 

 length. 



In both cycles, the solar error is greater than the lunar in any 

 given period; and the most favourable comparison is therefore on the 

 lunar basis. The two best comparisons that can be obtained from these 

 cycles, are, the relation of the lunar month to the day, as given by the 

 Calippic cycle; and the relation of the solar year to the lunar month, 

 for which both cycles give the same result, as the adjustment in days 

 is then eliminated. The following comparisons, therefore, show the 

 lowest errors in these cycles. 



