Dominical Letter
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
her complicated system of movable and immovable feasts (see
CALENDAR, CHRISTIAN), has from an early period taken upon herself
as a special charge to regulate the measurement of time. To secure
uniformity in the observance of feasts and fasts, she 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 she 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 nundinae,
periods of eight days; and in their marble fasti, or calendars, of
which numerous specimens remain, they used the first eight letters
of the alphabet to mark the days of which each period was
composed. When the Oriental seven-day period, or week, was
introduced in the time of Augustus, the first seven letters of the
alphabet were employed in the same way to indicate the days of
this new division of time. In fact, fragmentary calendars on
marble still survive in which both a cycle of eight letters-A to
H-indicating nundinae, and a cycle of seven letters -A to G-
indicating weeks, are used side by side (see "Corpus Inscriptionum
Latinarum", 2nd ed., I, 220. -The same peculiarity occurs in the
Philocalian Calendar of A.D. 356, ibid., p. 256). This device was
imitated by the Christians, and in their calendars the days of the
year from 1 January to 31 December were marked with a continuous
recurring cycle of seven letters: A, B, C, D, E F, G. A was always
set against 1 January, 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 P 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=92s 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
D=92s. The year 1908, therefore, had a double Dominical Letter, E-
D. 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.
This, of course, is all very simple, but the advantage of tile
device lies, like that of an algebraical 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 I
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=92s, which gives the Dominical Letter for any year, or the
second Dominical Letter if it be leap year:
1.Add 1 to the given year.
2.Take the quotient found by dividing the given year by 4
(neglecting the remainder).
3.Take 16 from the centurial figures of the given year if that can
be done.
4.Take the quotient of III divided by 4 (neglecting the
remainder).
5.From the sum of I, II and IV, subtract III.
6.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
(4) 2392 - = 2389
(5) 2389 / 7 = 341, remainder 2.
Therefore, the Dominical Letter is E.
But the Dominical Letter had another very practical use in the
days before the "Ordo divini officii recitandi" was printed
annually, and when, consequently, a priest had often to determine
the "Ordo" for himself (see DIRECTORIES, CATHOLIC). As will be
shown in the articles EPACT and EASTER CONTROVERSY, Easter Sunday
may be as early as 22 March or as late as 25 April, and there are
consequently thirty-five possible days on which it may fall. It is
also evident that each Dominical Letter allows five possible dates
for Easter Sunday. Thus, in a year whose Dominical Letter is A (
i. e. when 1 January is a Sunday), Easter must be either on 26
March, 2 April, 9 April, 16 April, or 23 April, for these are all
the Sundays within the defined limits. But according as Easter
falls on one or another of these Sundays we shall get a different
calendar, and hence there are five, and only five, possible
calendars for years whose Dominical Letter is A. Similarly, there
are five possible calendars for years whose Dominical Letter is B,
five for C, and so on, thirty-five possible combinations in all.
Now, advantage was taken of this principle in the arrangement of
the old Pye or directorium which preceded our present "Ordo". The
thirty-five possible calendars were all included therein and
numbered, respectively, primum A, secundum A, tertium A, etc.;
primum B, secundum B, etc. Hence for anyone wishing to use the Pye
the first thing to determine was the Dominical Letter of the year,
and then by means of the Golden Number or the Epact, and by the
aid of a simple table, to find which of the five possible
calendars assigned to that Dominical Letter belonged to the year
in question. Such a table as that just referred to, but adapted to
the reformed calendar and in more convenient shape, will be found
at the beginning of every Breviary and Missal under the heading,
"Tabula Paschalis nova reformata".
The Dominical Letter does not seem to have been familiar to Bede
in his "De Temporum Ratione," but in its place he adopts a similar
device of seven numbers which he calls concurrentes (De Temp.
Rat., cap. liii). This was of Greek origin. The Concurrents are
numbers denoting the days of the week on which 24 March falls in
the successive years of the solar cycle, 1 standing for Sunday, 2
(feria secunda) for Monday, 3 for Tuesday, and so on. It is
sufficient here to state that the relation between the Concurrents
and the Dominical Letter is the following:
Concurrents 1 2 3 4 5 6 7
Concurrent 1 = F (Dominical Letter)
Concurrent 2 = E
Concurrent 3 = D
Concurrent 4 = C
Concurrent 5 = B
Concurrent 6 = A
Concurrent 7 = G
HERBERT THURSTON
Transcribed by Martin Wallace, O.P.
http://www.knight.org/advent
From the Catholic Encyclopedia, copyright � 1913 by the
Encyclopedia Press, Inc. Electronic version copyright � 1996 by
New Advent, Inc.
Taken from the New Advent Web Page (www.knight.org/advent).
This article is part of the Catholic Encyclopedia Project, an
effort aimed at placing the entire Catholic Encyclopedia 1913
edition on the World Wide Web. The coordinator is Kevin Knight,
editor of the New Advent Catholic Website. If you would like to
contribute to this worthwhile project, you can contact him by e-
mail at (knight.org/advent). For more information please download
the file cathen.txt/.zip.
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