1 14 MEMOIR EXPLANATORY OF A NEW PERPETUAL CALENDAR. 



is the same also, for omitting the fractions occurring between multiples of 19, in the 

 Church Calendar, as those occurring between multiples of 1, in the Civil. 



With a view to demonstrate, without a large array of figures, the consistency of my 

 Rule with well-established tabular modes of finding the Epact, I refer to the extended 

 Table of Epacts in the Encyclopedia Britannica, (article "Calendar," page 12,) where, in 

 line c, beginning with 11, will be found all the Julian Epacts, under a Golden Number, how- 

 ever, always one behind, or one less than, that which was originally assigned to the year. 

 A. D. 1 was, in the old Calendar, always regarded as year 2, of the cycle of 19. This 

 relation between the Golden Numbers and the Epacts was changed at the reformation, 

 when the line D, beginning with 1, was selected for the Gregorian Epacts between the 



years 1582 and 1G99, inclusive, and the Epacts 1, 12, 23, 4, die. 



were made to correspond with the Golden Numbers .... 1, 2, 3, 4, die. 



The Julian Epact for 1582, found by my Rule, and confirmed by the elaborate chrono- 

 logical Table contained in "The Art of Verifying Dates," a work of great learning and 

 acknowledged authority, is 25, the same that is presented in the line c, of the extended 

 Table of Epacts, under the Golden Number 5, (that of the Julian year being 6.) De- 

 scending ten places in that column, on account of the ten days suppressed at the reform, 



or, what comes to the same thing, deducting from the Julian Epact of 25 



the number of days suppressed, or 10 



we reach, or obtain . 15 

 But the advance of one Golden Number in the line D is equivalent to the addition of 11 



and thus causes the Gregorian Epact for 1582 to be 26; 



for 1583, to be 7; for 1584 to be 18; and so on; that is to say, makes it always greater 

 by 1 than the Julian, until 1700, unless the years be multiples of 19, in which case the 

 Julian Epact, as the Exception provides, will become always 29, and the Gregorian will 

 be 1. The 15, in the transition from one style to the other, is not an Epact of the year 

 in either, but a connecting link between the two. The Gregorian Epact, at that epoch, is 

 in reality greater by a unit than the Julian; and the Julian Equation, standing at the 

 head of Column C in my Tablet, being for ever, the proper starting-point for the Gre- 

 gorian Equations is 1, which number accordingly stands at the right hand of the centurial 

 figures 15 and 1G. 



The succeeding Lunisolar equations, 0, 29, 28, die, were reached in the following manner. 

 Lord Macclesfield's directions for determining " in what years the Epacts should either 

 l)e extraordinarily augmented or diminished, and the Golden Numbers should either be 

 set backwards or forwards in the Calendar," according to the divisibility of the even hun- 

 dreds by 3 or by 1, separately, or by both 3 and 4, or by neither, led me to the expedient, 

 similar to the one I had already adopted in regard to the secular equations in the Civil 

 Calendar, of marking with an asterisk, in strict obedience to the Gregorian law, every 

 centurial figure at which, in successive periods of 25 centuries, (beginning at 1800, 4300. 

 G800, &c.,) the Epact is to be increased by a unit. This correction occurs at the end of 

 every 300 years, 7 times in succession, and then once at the end of 400 years, making 8 

 corrections in the course of 2500 years. 



