EASTER. 



EASTER. 



742 



the one already given, which is that of our own time, from which we 

 shall be able to make the shifts apparent, and to connect them with 

 the above-mentioned necessary corrections. Tables of this form were 

 not given by Clavius himself, but were published in England, we 

 believe by Lord Macclesfield, at the time of the discussions preceding 

 the alteration of the style in 1752. 



In the first column are the days of the month, from March 21 to 

 April 25, and Easter may fall on any one of these days except the first. 

 In the second column are the dominical letters, explained in DOMINICAL 

 LETTER, and which can be found by the table there given. In leap- 

 year, take the second letter of the year in finding Easter. Then follow 

 certain columns, each of which has a heading to show to what years it 

 belongs. Thus, the column headed 1700-1899 belongs to all years 

 from 1 700 to 1899, both inclusive. These columns contain the nineteen 

 golden numbers variously dispersed. Every year has its golden number 

 found thus : add 1 to the year and divide by 19 ; the remainder, or 19, 

 if there be no remainder, is the golden number. 



Take the first of these columns, namely, 1583-1699. Opposite to 

 April 8 is written the number 15. This means that, from 1583 to 

 1699, whenever the golden number is 15, the fourteenth day of the 

 calendar moon is the 8th of April. And so in like manner throughout 

 theae columns each golden number is written opposite the day which 

 is the fourteenth of the calendar moon when that golden number 

 occurs. Thus from 2600 to 2899, the fourteenth of the paschal 

 (calendar) moon is always on the 2nd of April whenever the golden 

 number is 16. 



Let us now suppose the first column constructed. It is contrived, 

 an before noticed, so as to make the calendar full moons follow the real 

 ones. To keep this up, whatever alterations must be made in a cycle 

 adapted to the real moon, the same must be made for the calendar 

 moon. As far as 1699 no alteration is requisite, for Clavius does not 

 make the first alteration on account of the incorrectness of the cycle 

 till 1800, and the year 1600 is leap-year in the Gregorian calendar as 

 well as in the old one. The reader must remember that the cycle of 

 19 years is one in which every fourth year is leap-year. As soon as 

 1700 comes, we have a fourth year which is not leap-year, so that the 

 day which would have been called February 29 is called March 1, and 

 so on. Each golden number then is written one place lower from 1700 

 to 1899 ; though it would better have represented the reason of the 

 change if each day of the month had been written one place highr. 

 The same thing takes place at 1800; but here Claviua puts the moon 

 back a day, or makes his calendar moon a day older, to correct the 

 accumulated error of the cycle. But the previous step makes the 

 calend&t moon, at any given day, a nominal day younger than it would 

 otherwise have been. These two changes destroy each other's effect in 

 1800, and the cycle continues unaltered till 1899. At 1900 the first 

 change is repeated ; but 2000 i leap-year in the new calendar, and 

 therefore no change is then requisite. And again, though 2100 is not 



leap-year, yet as 300 years have elapsed, the correction for the fault of 

 the cycle is introduced at the same time with that for the abandoned 

 leap-year, and the two destroy each other's effects, as before. This 

 column then is good till 2199. The next column is now easily explained : 

 but in the next one to that, or 2400-2499, we begin with a year in 

 which the correction for the cycle is to be made without being de- 

 stroyed by that arising from abandoning leap-year. That is, the moon, 

 on any given day, ia to be a day older than it would otherwise have 

 been. The numbers must then each be put back a day, which is seen 

 to be done. In this manner, if it be remembered that, beginning at 

 1800, seven following corrections of the cycle are made at the end of 

 periods of 300 years each, and then one at the end of 400 years the 

 reader would be able to construct farther cycles for himself, if it were 

 not for one peculiarity which we now notice. 



At the bottom of the columns it will be seen that there are in one 

 or two [ihci's numbers which do not rise cr fall with the rest. This 

 was a sacrifice of uniformity to the desire of preserving one charac- 

 teristic of the old calendar, namely, that the fourteenth of the calendar 

 moon never fell on the same day of the same month at any two epochs 

 which were within nineteen years of each other. This would have 

 happened sometimes, owing to the corrections above described : and 

 Clavius took a very simple method of avoiding it, which is explained in 

 the article already cited. The effect of his method is to produce the 

 slight departure from uniformity of alteration above noted. 



It will thus be seen that in the calendar which is now in use, one, 

 two, or even three days of error have not (provided the moon was 

 made too young, not too old) been thought of so much consequence as 

 either ease of calculation, or attention to existing notions upon the 

 subject. Of this we entirely approve, and agree with Clavius in 

 asserting that any rule which is fixed would be better than diversity of 



To find Easter by the preceding table, first find the golden number, 

 and then the dominical letter. [DOMINICAL LETTER.] Take the proper 

 column, and find out the day opposite to which the golden number 

 stands. Go on from that day to the next f Mowing day which has the 

 dominical letter opposite to it : that day is Easter Sunday. For 

 example, take 1847. Add one, and divide by 19 ; the remainder is 5, 

 the golden number. The dominical letter found in the article cited is 

 C. In the column 1700-1899, we find 5 opposite to March 30, which 

 is the fourteenth of the calendar moon. The next C is opposite April 4, 

 which is Easter Sunday. 



Again, to find Easter in 2384. Divide 2385 by 19, and the remainder 

 is 10, the golden number. The dominical letter (the second) is G. 

 In the column 2300-2399 the 10 is opposite to April 7, and the next G 

 is opposite to April 8, which is Easter Sunday. 



The dominical letter may be found by a short calculation as 

 follows : 



I. Add one to the given year. 



II. Take the quotient of the given year, divided by four, neglecting 

 the remainder. 



III. Take 16 from the centurial figures of the given year, if it can 

 be done. 



IV. Divide III. by 4, neglecting the remainder. 



V. From the sum of I., II., and IV., subtract III. 



VI. The remainder of V., after division by 7, is the number under 

 dominical letter in 



G F E D C B A 

 0123456 



But if the year be leap-year, it is the second dominical letter which 

 i thus found. 



As instances, take 1847 and 2384, as above given. 



I. 1848 2385 



II. 461 596 



III. 2 7 



IV. 1 

 V. 2307 2975 



VI. 4 (C) (0) 



The above is for new style ; for old style proceed as follows : To the 

 number of the year add its quotient when divided by 4, and 4 : the 

 remainder, after division by 7, is to bo used as the VI. of the preceding 

 rule. Thus for 1683, we have 



1583 

 395 



7)1982 



283 Rem. 1. Dominical Letter F 



The cycle for Easter-day, old style, is given at the beginning. 



The sole authority on the subject of the Gregorian Calendar is, of 

 course, Clavius, the authorised contriver of it, or at least the person 

 to whom the other delegates of the Roman see (if indeed any of them 

 took any share in the execution of the plan) intrusted the explanation 

 of it. In his work already mentioned, he has given all the results for 

 every year from 1600 to 5000 : he thinks his rule will be correct 



