Cycle a certain number of years in civil and ecclesiastical chronology. The Lunar Cycle (cyclus lune, or decemnnovalis) embraces nineteen years, after the expiration of which the days of the new and full moon generally fall again upon the same day of the month. The Greek astronomer Meton is the inventor of this cycle. Anatolius, bishop of Laodicea, in Syria, toward the close of the third century, first used it for calculating Easter (q.v.). When the Council of Nice terminated the Easter controversy, and established uniformity in the celebration of Easter, the bishops of Alexandria were commissioned to calculate annually the time of Easter, and to communicate it to the other metropolitans. At first the bishops of Alexandria used astronomical calculations, but subsequently they again adopted the lunar cycle, and by means of it calculated Easter for a number of cycles in advance. Thus the patriarch Theophilus of Alexandria prepared an Easter cycle for 480 years, or 22 lunar-cycles, beginning with the year 380. This cycle was, however; not well received in the Western churches, and patriarch Cyril consequently reduced it to 95 years, or five lunar cycles. This new Easter cycle extended from 437 to 531. When it approached its termination, Dionysius Exiguus (q.v.), in 525, proposed a new Easter cycle, which embraced 16 lunar cycles, or 304 (Julian) years. The defects of this cycle resulted from the inaccuracy of the Julian year, and were not remedied until the introduction of the Gregorian calendar. Nearly connected with the lunar cycle is the Golden Number (q.v.), which indicates what place a given year occupies in the lunar cycle. The Cycle of the Sun (or of the dominical letter) embraces 28 years, after the expiration of which the Sundays, and consequently also the days of the week, fall again upon the same days of the month. In Christian chronology it 'became early customary to use the first seven letters of the alphabet for designating the seven days of the week. A was always used for the 1st of January, and the letter upon which fell the first Sunday of the year was called the Dominical Letter, which, in ordinary years, designated every Sunday of the year. But in every fourth year the 25th of February was intercalated, and as it had the same letter as the 24th of February, the intercalary year had two dominical letters, one applying from Jan. 1 to Feb. 24, and the second from Feb. 25 to the close of the year. As an ordinary year consists of 52 weeks and 1 day, the dominical letter of the new year is generally the one preceding the dominical letter of the year past; and if all years were ordinary years of 365 days, the same dominical letter would revert every seventh year. As there is, however, a change of one day every fourth year by the intercalation of one day, and the consequent advance of the dominical letter, it takes four times seven, or 28 years, before the cycle is completed, and the same series of dominical letters recommences. Another slight disturbance is, however, produced by the omission of the intercalary day three times in every 400 years (thus, in the years 1700, 1800, 1900).
To find the dominical letter of a particular year, it is first necessary to find the place of the year in the cycle of the sun. As, according to the chronology of Dionysius, Christ is said to have been born in the ninth year of the cycle of the sun, the place of a particular year in the cycle of the sun is found by adding 9 to the given year, and dividing the whole by 28; the remainder indicating the place of the year in the cycle. For instance, to find the dominical letter for the year 1868, we add 9 and divide by 28; [thus, (1868+9)/28 = 1877/28] which leaves a remainder of 1. The year 1868, therefore, is the first of the cycle of the sun for the present century (the omission of the intercalary day in the year 1800, as stated above, interrupting the regular order of the cycle). The cycle of the dominical letter is as follows:
Year Dom. L. 1st ED 2ND C 3RD B 4TH A 5TH GF 6TH D 7TH E 8TH C 9TH BA 10TH G 11TH F 12TH E 13TH DC 14TH B 15TH A 16TH G 17TH FE 18TH D 19TH E 20TH B 21ST AG 22ND F 23RD E 24TH D 25TH CB 26TH A
27 G 28TH F The intercalary year 1868, as the first of a new cycle, has therefore the two dominical letters e d, e from Jan. 1 to Feb. 24, and d from Feb. 25 to Dec. 31. After thus ascertaining the dominical letter of the year, it is easy to find what days of every month are Sundays. For that purpose the initial letters of the several words in the following two hexameters are used:
Astra Dabit Dominus Gratisque Beabit Egenos Gratia Christicolae Feret Aurea Dona Fideli.
The initial letters of the words of these two verses are the letters designating the first days of every month. A being the 1st of January, and E being the dominical letter of the year 1868 from Jan. 1 to Feb. 24, the Sundays of 1868 are the 5th, 12th, 19th, and 26th of January. The initial D of the second word shows that the first dominical letter (E) of February falls on the 2d of February. For March and the following months, the dominical letter of the year: 1868 is D; consequently, the first Sundays of the following months are, March 1, April 5, May 3, June 7, July 5, August 2, September 6, October 4, November 1, and December 6., Finally, in order to ascertain upon which day of the month and the week full and new moons occur, the Epacts are used. —Wetzer und Welte, Kirchen-Lex. 2:960. SEE EPACTS; SEE CHRONOLOGY, CHRISTIAN.