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A common year has a dominical letter, which is simply the dominical letter of its first Sunday. For example 2003 has 5 January as its first Sunday so has Dominical letter E. In Leap Year s, the leap day has no dominical letter. This ensures that each date has the same dominical letter every year, but causes the days of the weeks of the dominical letters to change within a leap year. Hence leap years have two dominical letters: the first for January and February and the second for March to December. The second dominical letter is the dominical letter of the first Sunday of October (which is the same as for January in a common year). The year 2004 has Dominical letters DC. Examples include: The dominical letter of a year determines the days of week in its calendar:
HISTORY A device adopted from the Romans by the old chronologers to aid them in finding the day of the week corresponding to any given date, and indirectly to facilitate the adjustment of the "Proprium de Tempore" to the "Proprium Sanctorum" when constructing the ecclesiastical calendar for any year. The Church, on account of its complicated system of movable and immovable feasts (see Christian Calendar ), has from an early period taken upon itself as a special charge to regulate the measurement of time. To secure uniformity in the observance of feasts and fasts, it began, even in the patristic age, to supply a ''computus'', or system of reckoning, by which the relation of the solar and lunar years might be accommodated and the celebration of Easter determined. Naturally it adopted the astronomical methods then available, and these methods and the methodology belonging to them, having become traditional, are perpetuated in a measure to this day, even the reform of the calendar, in the prolegomena to the Breviary and Missal. The Romans were accustomed to divide the year into ''nundinæ'', periods of eight days; and in their ''marble , B against 2 January , C against 3 January , and so on. Thus F fell to 6 January , G to 7 January ; A again recurred on 8 January , and also, consequently, on 15 January , 22 January , and 29 January . Continuing in this way, 30 January was marked with a B, 31 January with a C, and 1 February with a D. Supposing this to be carried on through all the days of an ordinary year (i. e. not a leap year), it will be found that a D corresponds to 1 March , G to 1 April , B to 1 May , E to 1 June , G to 1 July , C to 1 August , F to 1 September , A to 1 October , D to 1 November , and F to 1 December — a result which Durandus recalled by the following distich: :Alta Domat Dominus, Gratis Beat Equa Gerentes :Contemnit Fictos, Augebit Dona Fideli. Now, as a moment's reflection shows, if 1 January is a Sunday, all the days marked by A will also be Sundays; If 1 January is a Saturday, Sunday will fall on 2 January which is a B, and all the other days marked B will be Sundays; if 1 January is a Monday, then Sunday will not come until 7 January , a G, and all the days marked G will be Sundays. This being explained, the Dominical Letter of any year is defined to be that letter of the cycle A, B, C, D, E, F, G, which corresponds to the day upon which the first Sunday (and every subsequent Sunday) falls. It is plain, however, that when a leap year occurs, a complication is introduced. February has then twenty-nine days. Traditionally, the Anglican and civil calendars added this extra day to the end of the month, while the Catholic ecclesiastical calendar counted 24 February twice. But in either case, 1 March is then one day later in the week than 1 February , or, in other words, for the rest of the year the Sundays come a day earlier than they would in a common year. This is expressed by saying that a leap year has two Dominical Letters, the second being the letter which precedes that with which the year started. For example, 1 January 1907 , was a Tuesday; the first Sunday fell on 6 January , or an F. F was, therefore, the Dominical Letter for 1907. The first of January, 1908, was a Wednesday, the first Sunday fell on 5 January , and E was the Dominical Letter, but as 1908 was a leap year, its Sundays after February came a day sooner than in a normal year and were Ds. The year 1908, therefore, had a double Dominical Letter, ED. In 1909, 1 January was a Friday and the Dominical Letter was C. In 1910 and 1911, 1 January fell respectively on Saturday and Sunday and the Dominical Letters are B and A. CALCULATION This, of course, is all very simple, but the advantage of tile device lies, like that of an Algebraic Expression , in its being a mere symbol adaptable to any year. By constructing a table of letters and days of the year, A always being set against 1 January , we can at once see the relation between the days of the week and the day of any month, if only we know the Dominical Letter. This may always be found by the following rule of De Morgan's, which gives the Dominical Letter for any year, or the second Dominical Letter if it be leap year: #Add 1 to the given year. #Take the quotient found by dividing the given year by 4 (neglecting the remainder). #Take 16 from the centurial figures of the given year if that can be done. #Take the quotient of III divided by 4 (neglecting the remainder). #From the sum of I, II and IV, subtract III. #Find the remainder of V divided by 7: this is the number of the Dominical Letter, supposing A, B, C, D, E, F, G to be equivalent respectively to 6, 5, 4, 3, 2, 1, 0. For example, to find the Dominical Letter of the year 1913: :(Steps 1, 2, & 4) 1914 + 478 + 0 = 2392 :(3) 19 - 16 = 3 :(5) 2392 - 3 = 2389 :(6) 2389 / 7 = 341, remainder 2. Therefore, the Dominical Letter is E. COMPLETE TABLES Table of dominical letters for years For years outside the range of this table, use the fact that the dominical letters repeat exactly every 400 years. , , , , , |
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