COMMON THINGS THE ALMANACK. 



than three-quarters of a day. The total length of the four 

 successive cycles of 19 civil years will be as nearly as possible 

 equal to four cycles of 19 astronomical years. 



Thus it is evident that the civil year, though variable in length, 

 oscillates alternately on one side and the other of the astronomical 

 year ; and, in like manner, the cycle of 19 civil years, which 

 is also variable by one day, oscillates at each side of the cycle 

 of 19 astronomical years. The civil year and the civil cycle 

 are alternately overtaking and overtaken by the astronomical 

 year and cycle, and their average lengths are respectively equal 

 in the long run to the average length of the latter. 



In like manner, the lunar month is subject to a certain limited 

 variation, so that the phases of the real moon are alternately over- 

 taking and overtaken by those of the average moon. 



24. Now let us imagine a fictitious moon to move round the 

 heavens in the path of the real moon, but with such a motion 

 that its periodical phases shall take place in exact accordance with 

 the civil years, and with the cycles of 19 civil years, in the 

 same manner as the phases of the real moon recur in the succession 

 of astronomical years, and in the cycles of 19 astronomical years. 

 Such a fictitious moon is then the ecclesiastical moon, and is the 

 moon whose phases are predicted in the calendar. 



It will be evident from all that has been explained, that this 

 ecclesiastical moon will alternately pursue, overtake, and outstrip 

 the real moon, and be pursued, overtaken, and outstripped by it; 

 that they will thus make together their successive revolutions of 

 the heavens, and that they will never part company, nor either 

 outstrip or fall behind the other beyond a certain distance, which 

 is limited by the extent of the departure of the civil from the 

 astronomical year, and by that of the real from the average lunar 

 month. 



25. For the purposes of the calendar, therefore, the course of 

 time is supposed to consist of a succession of cycles of 19 civil 

 years, and it has been agreed that each such cycle shall com- 

 mence with a year the first day of which shall be the last day 

 of the moon's age, or, what is the same, the day on which the age 

 of the succeeding moon is 0. 



The number which marks the place of any year in the cycle to 

 which it belongs is called the GOLDEN NUMBER of the year. Thus 

 when we say that the Golden Number of the year 1855 is 13, we 

 mean that the year 1855 is the 13th year of the cycle to which it 

 belongs, and it may be thence inferred that the first year of the 

 cycle was 1843. 



26. The age of the ecclesiastical moon on the first day of the 

 first year of the cycle being known, its age upon the first day of 



