MEMOIR EXPLANATORY OF A .NEW PERPETUAL CALENDAR. 117 



If, then, the Paschal Term occurs on the 21st of .March, the Animal Epact is 23 

 if on the 22d M it is 22 



if on the 23d " it is 21 



and so on, up . . . to the 31st " and down to the Epact 13, 



the day of the month rising by one, as regularly as the Epact descends by one, so that 

 their sum is always the same, ..... viz. I I. 

 and the Paschal Term in March must, of course, be that number less the Epact. 

 Advancing with the Day of the Month to the 1st of April, we descend to the Epact 12 



to the 2d " to 11 



to the 3d " to 10 



and so on, up . . . to the 12th " and down to the Epact 1, 



the sum being always 13, 



anil the Paschal Term in that part of April which precedes the 13th, is 13 less the Epact. 

 Arriving, in like maimer. at the 13th of April, we have the Epact 0, or 30 



at the Mill " 29 



at the 15th " 28 



i nd so on, up . . .to the 18th " and down to the Epact 25, 



the sum being always 43, 



and the Paschal Term for the rest of April is 43 (or 30 + 13) less the Epact; subject, 

 however, to two exceptions in the case of the clouhk Epacis (25'-26, and 25-24.)* 



The Gregorian Calendar of Epacts (sec Table III., Encyclop. Brit., Art. " Calendar,") 

 has been so constructed, that the Epact 25 belongs, whenever the Golden Number exceeds 

 11, to the same day with the Epact 26, and is then marked with an accent, to distinguish it. 

 Now since 13, less 26, gives the 17th day of April as the proper Paschal Term or limit : ■-'.". 

 in order to produce the same result, must be subtracted from 42. 



B) a like contrivance, the Epact 25 (not accented) belongs, when the Golden Number 

 does not exceed 11, to the same daj with the Epact 21; and since 43, less -'."», \ iclds the 

 15th of April as the proper Paschal Term or Limit; 21, in order to produce the same 

 result, must likewise be subtracted from . . . 12. 



In this manner both the exceptions arc readily provided for, with a single diminuend ' 12. 



This artifice, employed in the construction of the Tabic of Gregorian Epacts, l>\ making the age < » I the 

 moon to differ, occasionally, a day more from the truth, than it would otherwise have done, preserves between 

 the Old and New Calendars, a certain conventional resemblance, which consists in the non-repetition o! 

 annual epact within the same lunar cycle. For the reason of this arbitrary mode of writing Ihi nd ol 



varying, consequently, the Paschal Term, I must refer to regular treatises on the subject, remarking onrj 

 this device of Clavius, to which I have adjusted the operation of my own. does bj no means prevent, in i 



/. ter Sunday from falling, repeatedly, in tl cycle of 19 years, ri omelimes 



thrice, on the same day of the month. In the la^-t lunar cycle, for instance, ending with 1843, tin N'ew : 



t occurred thrice on the 3d day of April, and in duplicate four limes, on othei days ol ihi month. In ihe 

 present cycle, ending in lftiiv!, like duplicate Easters, on certain d mth, will hi i nmr-. In the 



course of the very first cycle of the refo imilar co ' place thn N 



md would have done 90 seven limi Style, il th Juli m mode ol reckoning had i;" 1 i • n ■ 

 VOL. \. — 30 



