] [x MEMOIR EXPLANATORY OF A NEW PERPETUAL CALENDAR. 



The Golden Number, being the remainder after division by 19 of the year plus 1, the 

 excess of 10, -where the year itself is to be divided by 19, agreeably to my rule, becomes 

 an equivalent expression for the excess of 11 in the tables referred to. 



It will be perceived that the Gregorian Epacts in Table D of my Tablet, are merely 

 arranged in sets or sequences in a more orderly manner, beginning at 1 and ending at 30, than 

 they presented themselves in the course of the foregoing explanations, and that the short 

 column of four numbers, from which they are, according to their several places in the 

 series, to be deducted, namely 13, 44, 43, and 42, assumes, at the same time, greater 

 symmetry. 



The difference between those numbers and the Epact can never, in April, exceed IS, 

 hut whenever the 14th day of the Paschal Moon falls on the 18th day of that month, and 

 happens at the same time to be Sunday, Easter Sunday must be a week later, or the 25th 

 of April. It must always be at least one day after the Paschal Term, but whether it is 

 to be celebrated one or seven, or any intermediate number of days after that term, will 

 always be correctly determined, when the day of the week on which the term occurs has 

 been found by the Civil Calendar. It is obvious that the number of days to be counted 

 forwards, must be the difference between 8 and the number which indicates the day of the 

 week. 



Before the close of the past year, I had prepared, in manuscript, a specimen of the 

 Perpetual Calendar described in the foregoing pages, and had solved, by means of it. 

 numerous chronological questions, trying uniformly the correctness of my results by the 

 tables and formula; of Lord Macclesfield and Mr. Galloway, when I learned from the 

 Journal of the Franklin Institute, for November, that the next British Almanac and Com- 

 panion would contain an Article from the pen of Mr. Augustus De Morgan, of University 

 College, London, on the subject of a controversy not unlikely to arise, respecting the 

 proper day of celebrating Easter in 1845. My rules gave me, as the Tablet shows, the 

 23d of March; but being naturally desirous of testing their accuracy, in that as well as 

 other instances, by such distinguished mathematical authority, I awaited the receipt of a 

 copy of that instructive Annual, which a friend had ordered from England, and which he 

 kindly placed in my hands in the course of the winter. As it embraced, what I had anti- 

 cipated, a very learned, interesting, full, and satisfactory Essay "on the Ecclesiastical 

 Calendar," I could not but be highly gratified at finding my rules confirmed by every 

 example therein computed, and more especially by the discovery that, owing to the 

 mechanism of my Tablet, which spared me the labour of several arithmetical steps, which 

 Mr. I)c Morgan, (who proposed to himself, and has ably executed, the more difficult task 

 (if pure calculation according to Delambre's analytical formulae, and independent of all 

 tabulation,) had been compelled, under the assigned limits of his problem, to take, I was 

 enabled to attain, in much less time, by rules occupying less space, and requiring less 

 mental and manual effort, the same results with those yielded by his fifteen " short arith- 

 metical directions," given at pages 15 and 1G. It appeared to me, besides, that the risk 

 of error was considerably lessened in my process, by the operation's consisting, for the 

 most part, cither of the mere setting down, or of the addition of figures, these figures being. 



