MEMOIR EXPLANATORY OF A NEW PERPETUAL CALENDAR. 113 



The solar equation belonging to any Gregorian century beyond the limits of the Tablet 

 might be found, by numbering from to 28, the equations in Column A, opposite to the 

 centurial figures lvin^ between 28 and 56. Tor, since the secular corrections recur in 

 like order, at every succeeding period of four times seven centuries, tlutt equation to which 

 the Remainder, on dividing the given centurial figures by 28, stood attached, would be the 

 Equation required, which may likewise be obtained without the use of tables, by a short 

 rule given hereafter, near the close of the memoir. 



I proceed to explain, as briefly as possible, the construction of the Ecclesiastical side of 

 the Calendar, and the means I adopted, soon after the civil side had been completed, of 

 connecting them with each other, thus making two of the monthly numbers in Table B, 

 namely :! and 6, still representing March and April, contribute towards shortening the 

 calculations respecting Easter; and causing also a single additional Column, C, to serve as 

 a convenient substitute for an extended table of thirty lines of Epacts, indexed with as 

 many alphabetical letters, great and small, and consisting of nineteen numbers in each 

 line. 



Aided by .Mr. Galloway's article, before referred to, and by one of Lord Macclesfield's, 

 published in the Philosophical Transactions of 1750, (No. 494, page 117,) I found the 

 task less difficult than I had anticipated. They describe the ingenious, but involved and 

 intricate mode of expressing, in the Church Calendar, successive differences between Solar 

 and Lunar years, by mean-; of Epacts or Increments. These Epacts arc so derived from 

 the Golden Numbers, (that is, from the order in which the years stand in the Metonic cycle 

 of 10 years.) as to indicate the age, at the beginning of each year, of an imaginary moon, 

 whose artificial phases, though approaching, seldom correspond with, but arc generally 

 a day or two in advance of, the mean movements of the true moon. They state that, 

 supposing the Epact of the year 1 to be 11, (that is, the difference between the common 

 Solar year of 365 day- and the Lunar year of 351 days,) the Epact of each following 

 year of the first cycle of 19 is obtained, by adding 11 to that of the former year, and by 

 rejecting • :". as often a- tin- sum exceeds 30; but that at the 20th, 39th, 58th, 77th, ice, 

 years, viz., at the beginnings of each succeeding cycle, 12 is to be added to the epact of 

 the last year of each preceding cycle, and continued augmentations of 11, and rejections 

 of 30. are to take place as before. Hence I inferred that the Golden Numbers, as Rc?n<mi- 

 </'/•- on division by 19 of the year plus 1, might be dispensed with, and their place in 

 computation be conveniently supplied, by adding to 11 times the year, the I9tfa part oi 

 the year, used a- a quotient, or whole Vumber; taking care only that, when the Julian yeai 

 happens to be a multiple of 19, one less than the 19th part shall be added. This eaB} 

 formula yielded me. without a failure, the constantly recurring 19 Epacts that mark the 

 ancient calendar, beginning with 11 and ending their round with 2D; and the Genera] 

 Rule at the bead of my Tablet, as there modified, is precisely an equivalent for it. hut 

 provides, at the same time, a practical advantage in the arrangement of the figures. Tin 

 omission of fractions advances by 1, in the order prescribed, each successive set or cycle 

 o| EpactB, while the exception Stated, guards effectually against the intercalation of I 

 taking place at any earlier date than the proper cycle; just as, in the Civil Calendar, I less 

 than one- lth part of the year i- added m .human and February of leap years. The reason 

 vol. x.— 29 



