HOW TO PREDICT EASTER. 



22. Let it be remembered that the astronomical year consists of 

 365 days, 5 hours, 48 minutes, and 48 seconds, and that a lunar 

 month varies in length from about 29| days to 29| days, its 

 average length being exactly 29 days, 12 hours, 44 minutes, and 

 3 seconds. 



It will appear from these numbers that 19 astronomical years 

 consist of about 



D. H. M. S. 



6939 14 27 12, 

 while 235 average lunar months consist of about 



D. H. M. S. 



6939 16 31 45. 



It appears, therefore, that 235 average lunar months exceed 

 19 astronomical years by only 2 hours, 4 minutes, and 33 seconds. 



It follows from this, that if the course of time be resolved into 

 a succession of periods, or cycles, of 19 astronomical years, the 

 same phases of the moon which are presented in any year of one 

 cycle will be reproduced in the corresponding year of the next 

 cycle, on the same days, but 2 hours, 4 minutes, and 33 seconds 

 later. If, therefore, the dates of the phases, those of the new 

 moons for example, in each successive year of any one such cycle 

 be ascertained, either by immediate observation or by calculation, 

 their dates in the successive years of the next cycle will be on the 

 same days, but 2 hours, 4 minutes, and 33 seconds later. 



If, therefore, time were counted by astronomical years, and if 

 the period of the lunar changes were always equal to the average 

 lunar month, the days of new moons of any one cycle of 19 years 

 being ascertained, the days of the new moons of every succeeding, 

 and of every preceding cycle, would be known. 



23. But time is not counted by astronomical years, and the 

 period of the lunar phases is not always the same, and therefore 

 this reproduction of the series of lunar phases, or corresponding 

 days, will not take place. 



Unlike the astronomical year, the civil year is not constantly of 

 the same length. It consists, as has been already explained, some- 

 times of 365, and sometimes of 366 days. Neither is a cycle of 19 

 successive civil years always of the same length. Such a cycle 

 contains sometimes only five, and sometimes four, leap years, and 

 consists, therefore, sometimes of 6940, and sometimes of 6939 days. 

 It, therefore, sometimes exceeds a cycle of 19 astronomical years by 

 nearly a quarter of a day, and sometimes falls short of such a cycle 

 by more than three-quarters of a day. If four successive cycles 

 of 19 civil years be taken, three of them will exceed one astro- 

 nomical year by something less than a quarter of a day, and the 

 fourth will fall short of an astronomical year by something more 



13 



