40 



RUYAL SOCIETY OF CANADA 



The C3'Cle itself gives a constant value for the lunar year, inde- 

 pendently of the epoch. We have therefore, the following error as 

 the limit, at the other extreme of the period of this cycle: — 



Lunar year. Epoch 600 B.C. = 3&4. 3671564 

 " cycle value = 354.36706:^5 



Error per century. 

 0.00958 day. 



Error of one day in ; 

 10,440 years. 



Mahommedan Calendar. — This calendar falls properly under this 

 head, as it is purely lunar ; and it would almost seem that its originators 

 must have known the lunar cycle above explained. If it was devised 

 by the Persians, this is by no means impossible; as, from their point 

 of view, Daniel was one of their own statesmen, and they must have 

 been acquainted with his writings. The Wise Men of the East were 

 prepared for the advent of the Messiah by his predictions. We make 

 this suggestion to account for the high accuracy of this calendar, and 

 because its basis can be deduced from this cycle by the process following, 

 if we assume the cycle to be known. 



The cycle is 2,530 lunar years = 893,005 days. The number 2,530 

 is higlily divisible, which is characteristic of prophetic numbers; but 

 the number 893,005 has no factor but five. But by deducting one 

 day, or admitting an error of a day in the 3,520 lunar years, the num- 

 ber becomes divisible by 12 and 7, and this period can be reduced to a 

 cycle of thirty years, thus: — 



893004 



30 lunar years = 



12 X 7 



= 10,631 days; 



and consequently one hinar year = 354U dsiys. Each year of 354 

 days can therefore be divided into months of 29 and 30 days, which 

 alternate evenly; and during the cycle of 30 lunar years, 11 intercalary 

 days are required. This is precisely the adjustment we find in the 

 Mahommedan calendar. The error in this calendar, at the epoch 1900, 

 is as follows: — 



Lunar year, at Epoch 1900 = 354.3670644 

 From Calendar cycle, 354^ = 354.3666066 



Error per 

 century. 



0.04100 day. 



Error of 

 one day in ; 



2439 years. 



The error is thus one day in 2,514 lunar years, at this epoch; and it 

 was the near coincidence of this period with the number 2,520, which 

 iirst drew my attention to the cycle above described. 



