768 



THE POPULAR SCIENCE MONTHLY. 



though they would in nineteen years fall upon the same day of the 

 month, they fell about an hour and a half earlier in the day, and this 

 in sixteen cycles, or about three hundred and twelve years, would make 

 a difference of one day. As these tables were published by ecclesiasti- 

 cal and secular authority, and could not be changed without such au- 

 thority, another method was resorted to to find the times of the moon 

 without the use of these tables. This method was called the epact, 

 which we will now proceed to consider. 



The lunar year, as we have already seen, differs from the solar year 

 by about eleven days, i. e., if a new moon occur January 1st of any 

 year, on January 1st of the next year the moon will be eleven days old, 

 on the same day of the next year twenty-two days old, the next thirty- 

 three days old, which equals a whole lunation plus three days. This 

 cycle corresponds with the lunar cycle, and is constructed as follows : 



Lunar Cycle. 



Epact. 



1 

 2 



3 

 4 

 5 

 6 

 7 

 8 

 9 

 10 





 11 

 22 



3 

 14 

 25 



6 

 17 

 28 



9 



Lunar Cycle. 



11 



12 



13 



14 



15 



le 



17 



18 



19 



Epact. Paschal Limits. 



20 



1 



12 



23 



4 



15 



2G 



7 



18 



March 24 



April 1 2 



April 1 



March 21 



April 9 



March 29 



April 17 



" 6 



March 26 



From this table the astronomical moons not only for Easter but for 

 the whole year can be found without variation of more than a day for 

 about three hundred and twelve years, at the end of which time the new 

 moon will fall one day earlier, when a new set of epacts must be made, 

 the first of which will be 1 instead of 0, and the succeeding ones will 

 be changed correspondingly. To find the age of the moon for any day 

 of the year, we add to the epact the date of the month, and one for every 

 month from March inclusive, the epact for a year being eleven days, 

 or a day a month nearly. This sum, casting out thirty if required, 

 will give the age of the moon at the given day : e. g., suppose it be 

 required to find the moon's age on Chi'istmas-day of the year 1868. 

 We find, by the method already explained, that 1868 was the seventh 

 year of the lunar cycle, whose epact in the table we found to be 6, to 

 which adding 25 and 10 gives 41 ; from this deduct one lunation (29 

 days) = 12 days for the moon's age on that day. The epacts are 

 calculated to show the moon's age on March 1st in any year of the 

 cycle. 



The rule for finding the Sunday letter of any year, as given in the 

 "Book of Common Prayer," is constructed upon this principle : The 

 dominical letter of the year of Christ, according to N. S., would have 



