MliMOIli EXPLANATORY OK A M'.W PERPET1 \l I \ll\!.\i;. 



I 2 1 



Take any Gregorian annual Epact 

 below 13 from . . . 13, 



Si:: i 

 & from 13 + 31 — II. 



23 from 13 + 30 = 43; 

 C24i 

 1 .V > from 13 



Bui take 



w$ 



13 + 29=42. 



I To obtain the 

 \Paschal 'Term 



in April 



in March 



in April 



in April 



Take any Julian annual Epact 

 below 5 from .... 5, 



s ? J 



between < & > from 5 + 31 = 30, 

 above 15 from 5+30= 15; 

 Bid take 29 from ."> + 29 = 34. 



memory niiu-ht be technically aided by adverting to the fact, that 31, :><>. and 29 day?, 

 arc the length of Civil months in all Leap Year--, as well as that of artificial Lunations in 

 the existing Church Calendar; and that the 13th and 5th were the days of the month on 

 which the Ides and Nones, in every month but four, of the old Roman Calendar began. 



It is of more importance, however, to state, that, having procured, in April last, through 

 the politeness of Professor E.Otis Kendall, from the Library of the High School of Phila- 

 delphia, the use of Delambre's History of Modern Astronomy, I have, since then, calcu- 

 lated, according to my Tablet, every example given in Book I., "on the reformation of the 

 Calendar." ( including the extreme cases put by Delambre, to illustrate his principle-, in the 

 controversy with Ciccolini, about the relative merits of their respective formula'.) and that 

 I have found my results not only to correspond uniformly with those which are there 

 computed, but to be reached much more expeditiously also, than by the processes there 

 employed. 



I have, moreover, been prompted by curiosity, as well as by caution, to extend my 

 secular corrections as far as Delambre had pursued his, in the Connoissance des Terns, 

 for l v 17, ami to carry down, accordingly, with the mechanism of the asterisks, ray 

 equations in Columns A and C, to the 500th century. I compared, as I proceeded, a few 

 -. at various epochs, and many, near the termination of my task, with the answers 

 contained in his beautiful "Table Pascale," at page (3, Book I. (Astron. Moderne,] wh< re 

 the Gregorian Eastera are obtained by inspection after the Dominical Letter and Epact 

 are known; and I had the pleasure to find, in every instance, the results still identical. 



Without doubting for a moment, or presuming to call in question, the correctness of 

 ih'' principles on which that Paschal Table has been constructed. I feel it, nevertheless, 

 incumbent on me to remark, that, from the text of Delambre, at page 24, it would appear 

 that Clavius's Great Table, which is almost universally consulted as a standard, diners 

 from Delambre's .-mall one, by including, among the years in which Easter happens on 

 the 22d of March, the year :! s t;o. According to Delambre's formula' and Paschal Table, 

 Dominical Letter being <•. and the Epact 24,) it will fall on the 22d of April; 

 irding to Gauss's formula, (M being 2 and \ being 5,) on the same daj ; by the tables 

 of Lord Macclesfield and Mr. Galloway, (the Golden Number being !. and the Dominical 

 Letter (.. on the same day; and, finally, b\ Mr. De Morgan's Rules, and l>\ mj own, on 

 the i-. on the 22d of Vpril. \\ ith such a preponderance of concurn nt 



timony in favour of the conclusion at which I arrive, I cannot but suppose thai ' ' .■ ius 

 v.— ni 



