116 MEMOIR EXPLANATORY OF A NEW PERPETUAL CALENDAR. 



some new adjustment. But, pursuing, without regard to future reforms of either Calendar, 

 the plan I have just described as far as the 87th centurial figures, and comparing, at 

 every step, the results derived from my General Rule, when applying the successive equa- 

 tions so obtained, with the Epacls set down in the extended Tables, I found them to be in 

 exact correspondence with each other, line by line, and letter by letter, throughout the cir- 

 cuit, from little a to capital P. In fact, the equations in Column C are identical with the 

 figures, which stand in the first column of Table II. (Encyclop. Brit., Art. " Calendar,") 

 under the Golden Number 1, and immediately by the side of the 30 letters running up the 

 column from D to C. Delambre pronounces the Epact-letters useless; I trust, therefore, 

 that for discarding them, in company with the Dominical, from my Tablet, I shall not 

 incur the reproach of being hostile to Letters in general. 



The Gregorian Annual Epact being thus accessible, with very little more trouble than 

 the ordinary process of finding the Golden Number, (since three, out of the four lines of 

 figures to be added together, require no computation, but merely to be set down on paper 

 in the order stated,) it remains for me to elucidate my mode of deducing from the Epact 

 the Paschal Term, or the 14th day of the Paschal Moon, (most commonly, but improperly 

 called " The Paschal Full-Moon,") on which Easter Sunday depends. 



The Paschal Moon is that whose 14th day, counting the new moon as the first, never 

 falls earlier than the 21st of March, nor later than the 18th of April, reckoning the 

 calendar lunations of those months respectively, to contain 30 and 29 days; for Easter, 

 according to the usage of the western churches of the Roman empire, sanctioned by the 

 Council of Nice, must be celebrated on a Sunday, which Sunday must follow the 14th day 

 of the Paschal Moon, so that whenever the Paschal 14th, or Term fell on Sunday, Easter 

 could not arrive until the next Sunday. If the Term fell on Saturday, Easter came one- 

 day after that Saturday, viz., on the next day; consequently the interval between the Pas- 

 chal Term and Easter might be 7 days, but could never be less than one day: and since the 

 Term could not happen before the Calendar- Vernal Equinox, (which, whatever might be 

 the astronomical fact, was, by the Church, invariably fixed on the 21st of March,) Easter 

 Sunday, it is clear, must have its place between the 22d of March and the 25th of April, 

 both days inclusive. 



Now supposing the 14th day of the Paschal Moon to coincide with the Calendar 

 Equinox, that moon must have been new, or in its first day on the 8th of March, (for 21 

 less 13, is 8,) and the preceding moon must have been 23 days old on the 1st of March, 

 just a week earlier, (for 8 less 7, equals 1.) That is to say, the moon on the 1st day of 

 March, must have been of exactly the same age as it was on the 1st of January; the in- 

 terval between those days in common years, being two lunations, (one of 30, the other of 

 29 days,) or 59 days in all. The Epacts belonging to January and March are, of course, 

 identical, as they arc seen to be in every Epact Almanac: and it is manifest that when 

 the Calendar-Moon's age on the first day of the year, exceeds 23 days, (in which case the 

 new moon of March would happen before the 8th, and its 14th day, consequently, before 

 the Equinox,) the Paschal New Moon will be in April, and when 23 or less, will happen in 

 March. 



