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stands against Sunday, or the Lord's-day, in Latin Dies Dominica, is called the Dominical Letter, and serves to denote that day, as the other letters do the other days of the week.
The Dominical Letter is different every year. As the common year consists of 365 days, that is, fiftytwo weeks, and one day, it is evident the year must begin and end on the same day of the week, and therefore the next year will begin on the day, following. This occasions the first Sunday in January to fall every year a day sooner than it did the year before, and consequently to be denoted by a different letter.
In biflextile or leap-year, consisting of 366 days, there are fifty-two weeks, and two days over ; that if the leap-year begins on a Sunday, it will end on a Monday, and the next year begin on a Tuefday, and consequently the Dominical Letter wilt be removed two places backwards, that is, if it be A at the beginning of the leap-year, it will be F the year following. By this means, every fourth year being bissextile, the order of the Dominical Letters is interrupted, and the series does not return to its first state till ander four times seven, or twenty-eight years. This period of time is the cycle of which we are now discoursing.
The Dominical Letters are not the same in the Gregorian, as in the Julian calendar. By the reformation of the calendar under Pope Gregory, the order of the Dominical Letters was disturbed ; for the year 1582, which at the beginning had G for its Dominical Letter, came to have C in October, by the retrenchment of ten days after the 4th of that month. And thus the Dominical Letter of the ancient Julian calendar is four places before that of the Gregorian, the letter A in the former answering to D in the latter.
In order to find the year of the folar cycle for any year of Christ, proceed thus: Add 9 to the given year, and divide the sum by 28; the remainder will fhew the year of the cycle, and the quotient the number of cycles fince the birth of Christ. If there be no remainder, the gifunt year is the 28th or last year of the cycle. The reason of the addition of 9 is, because the ninth year of the solar cycle was past, when the first year of the Christian computation began.
The cycle of indietion is a circle or revolution of fifteen years, which when expired begins anew, and goes round again without intermission. This cycle bas no relation to the celestial motions, but was made use of by the Roinans to make known the time of paying certain taxes, or for other civil
purposes. purposes. The popes have dated their bulls by the year of the indi&tion ever fince the time of Charlemagné.
'The commencement of this cycle being fixed to the 3d year before Christ, add 3 to the given year, divide the sum by 15, and the remainder will fhewt the year of indiation for any given year of Christ. If nothing remains, it is the 15th or last year of the cycle.
OF THE GOLDEN NUMBER, AND THE EPACTS, The prime or folder number 'is a revolution of
mineteen years, and is that particular number which thews the year of the lunar cycle for any given year. So that to find the year of the funar cycle is to find the golden number. These numbers are called golden, because, being of excellent use, they were expressed in ancient calendars by figures of gold.; :"...
In the first year of our Saviour's nativity, the golden number was 2.; therefore add ito any given year of Christ, divide the sum by 19, and the re
mainder is the golden number for that year. If nothing remains then 19. is the golden number. Thus, for instance, divide 1801 by 19, the remainder will be 15, the golden number for 1800,
This number is used in the calendar to Thew the changes of the moon, and thereby to determine. the time of Easter, and other moveable feasts.
Epacts are, as the word implies, added ' numbers; that is, a number of days added to the lunar year, to make it equal to the folar year. The solar year has 365 days, and almost 6 hours; and the lunar year 354 days, and upwards of 8 hours. The dif, ference is the pact. Now, as this difference is not much short of 11 days, it was made the epact of the first year of the lunar cycle.
To find the iepact ; multiply the golden mumbes by 7. II, from that product fubtract 11, divide the remainder by 30, and the remainder of the divisioni is the epact. For example ; I would know the epact for the year 1800, of which the golden number is 15. This multiplied by 11 produces 165, from which 11 being subtracted, there remains 154; and this when divided by 30, has a remainder of 4, the epaet required.
If after the operation nothing remains, then 30 is the cpact!
CHAP CHAP. LX.
HOW TO FIND THE Moon's 'AGE, AND THE
for March o in common years, and, in leapyears, for April 2, for May 3, for June 4, for July 5; for August 6, for September 8, for October 8, for November 10, for December 10, for January o, for February 2.
Having added to the epact the number for the month, according to the foregoing rule, add thereto the day of the month for which the moon's age is required. The sum of these three, if less than 30, is the moon's age ; if more than 30, take 30 from it, and the remainder is the age of the moon.
The moon's age, subtracted from the day of the change, leaves the day of full moon. When nothing remains, that day of the month is the day of change.
How old is the moon on the 20th of May 1800 ? In order to resolve this question, add to the epact, already found to be 4, the number for May, which is 3, and 20, the day mentioned in the question, the sun will be 27 days, the answer required.