Dominical Letter (Lat. dominica, the Lord's), the letter used in the calendar to denote Sunday for a given year. The council of Nice (325) established the rule that Easter Sunday should be the first Sunday after the full moon which happens upon or next after March 21. For the purpose of determining when Easter falls, and for other similar problems concerning the day of the week and the day of the year, it was early found convenient to place the first seven letters of the alphabet in succession against the days of the months, putting A to Jan. 1, and repeating the seven letters as often as necessary until Dec. 31. The letter which falls against the first Sunday in January will fall against every Sunday in the year, and this is the dominical letter for that year, unless it be leap year; and then, as Feb. 29 as well as March 1 is marked D, the dominical letter for the last ten months of the year will be the preceding letter of the alphabet. Finding the dominical letter will enable one to find what day of the week a given date in the year is.
But the dominical letter, being known for any one year, can be found for any other, by simply remembering that an ordinary year is 52 weeks and 1 day, a leap year 52 weeks and 2 days, so that the dominical letter will go backward from G toward A, one letter for a common year and two for a leap year. This gives rise to an arithmetical rule which may be thus expressed : To the number of the year add one quarter of itself, neglecting fractions, and divide the sum by 7; then for the 19th century subtract the remainder from 8, or, if it is 0, from 1, and the new remainder will indicate the place of the dominical letter in the alphabet; for the 18th century subtract from 7; for the 17th century, and back to 15S2, the year in which the Gregorian calendar went into operation, subtract from 6, or if the remainder is 6, from 13; for dates previous to 1582 subtract from 3, or if the remainder is 3 or more, from 10. But the dominical letter thus obtained for a leap year belongs to the time after Feb. 29, and for the preceding two months the dominical letter was the succeeding letter in the alphabet. This new remainder is also the date of the first Sunday in January for that year.
The same date in February will fall on Wednesday; in March, on Wednesday; in April, on Saturday, etc.; as may be seen from the fact that the first days of the 12 months have annexed to them in the calendar the initials of the words: At Dover Dwell George Brown, Esquire, Good Christopher Finch, And David Friar. For example, the day of the week on which New York was incorporated, June 12, 1665, is thus found: (1665 + 416) 7=297, with a remainder of 2; and, it being the 17th century, 6 - 2=4, which shows the dominical letter for that year to have been D. Then, as June begins with E, June 1, 1665, was Monday, and the 12th was Friday. President Barnard of Columbia college gives the following rule for finding the dominical letter: Give to the letters A, C, E, G, in which order the dominical letters return with the leap year centurial in every succession of four centurial years, the numerical values which correspond to their places in the alphabet, 1, 3, 5, 7; find in this series the number corresponding to the given century, and call this the centurial; multiply the twenties of the incomplete century by 3, and call the product the vigesimal; multiply the fours in the excess of twenties by 2, and call the product the qua-ternial; multiply the final remainder by 6, and call the product the residual.
If the sum of the numbers thus obtained is 7 or less, it is the numerical value of the dominical letter; if it is greater than 7, subtract 7 as often as may be necessary to reduce it to 7 or below, and the final result is the dominical letter.