On Matters That May Be Performed ad libitum
Although throughout the world the solar calendar is known and in common use, it has nevertheless seemed fitting to preserve the custom of announcing the day according to the lunar calendar; this may indeed be done ad libitum at the liturgical reading of the Martyrology. The importance of computing the lunar day is evident from the fact that the supreme Solemnity of Easter, together with the Lent that precedes it and the Easter season that follows, depends upon the full moon of the month of April. For this reason the lunar computation is retained in this typical edition of the Martyrology, so that the special bond between the people of the Old and the New Covenant may shine forth, also in the celebration of the paschal mystery. Moreover, the lunar computation is maintained by the Eastern Churches and by very many non-Christian religions and cultures throughout the world.
In this Martyrology, arranged above the notices of the Saints, there are thirty letters — as many as the numbers of which the cycle of the moon’s epacts was composed by chronographers — which, when the appropriate computation has been made, indicate for each day of the whole year which day of the moon is to be announced. Each letter, furthermore, refers to a corresponding number set beneath it, arranged in a series of thirty or twenty-nine marks, which designates the individual days of the lunar month. The use of these series of letters and numbers, devised for finding the moon, is governed by suitable temporary tables, in which to each year there corresponds: its own golden number, which indicates the position of the current year within the lunar cycle of nineteen years used in these computations; likewise the epact — that is, the difference of eleven days that occurs between the end of the lunar year and the beginning of the solar year; and lastly the letter of the Martyrology, intimately bound to this aforesaid epact, as the appended table shows:
[The original prints here a correspondence table of the Martyrology letters and the epacts. As the worked examples below confirm, the lowercase letters a–u correspond to the epacts I–XIX (for instance d = IV, u = XIX), the capital letters continue through the higher epacts (for instance F = XXV, marked both in black and in red, and M = XXVII), and the cycle runs to epact XXX.]
All these elements necessary for the computation of the moon, for the span of time between the years 2004 and 2033, are found in the temporary table below. To announce, therefore, the day of the lunation on each day of any given year: once the golden number is known, the epact is to be taken, and then the letter corresponding to it; this letter, sought out in the equation tables of the Martyrology placed above the notices of the Saints, will show the number of the lunar day corresponding to it — namely, which day of the moon is to be announced on each day of the whole year, up to the last day of December.
Example: In the year 2005 the current golden number is 11, to which corresponds the epact XIX and the Martyrology letter “u,” which is to be sought throughout that whole year in the equation tables of the Martyrology. When these are consulted, to the first day — that is, the Kalends of January — the letter “u” will give the number 20, which is the moon to be announced; and to the second day of August — that is, the fourth day before the Nones of August — the number 26.
On the Announcement of the Moon
In those years in which the golden number 1 occurs, from the Kalends of January the moon is always to be announced as one day less than is noted in the Martyrology, until the end of that lunation.
Example: In the year 2204, in which the current golden number is 1, there corresponds the epact XXVII and the Martyrology letter “M,” which is to be sought throughout that whole year in the equation tables. When these are consulted, on the first day — that is, the Kalends of January — the letter “M” will appear to correspond to the number, or day of the lunation, 29; yet in its place 28 is to be announced as the moon. This is to be continued only as far as the second day — that is, the fourth day before the Nones of January — when the moon will be 29 (even though the number 30 is noted); whereas on the third day — that is, the third day before the Nones of January — the moon 1 will correspond as usual.
This rule, however, is set aside whenever to the said golden number 1 there corresponds the capital Martyrology letter “P,” under which the moon is always to be announced just as the number in the equation tables indicates — that is, exactly as is customary in the other years.
If any year happens to fall on the twenty-fifth epact, to which corresponds the double capital letter “F” — one marked in black, the other in red — the day of the lunation is to be determined according to whether the golden number is among the first eleven, or from 12 up to 19.
Example: In the year 2011 the golden number 17 corresponds to the epact XXV, and accordingly to the Martyrology letter “F.” On the thirteenth day — that is, the Ides of April — of that year, under the letter “F” varying moons are indicated; nevertheless, since the golden number is greater than 12 inclusive, the moon is to be announced as under the black epact, namely 10. But in the year 2303, to which the golden number 9 corresponds and likewise the epact XXV, on the same Ides of April, since the golden number is less than 11 inclusive, the day of the lunation is to be announced under the Martyrology letter “F” written in red, namely 9.
The temporary table is valid only up to the year 2199; but others may be constructed with the help of the special perpetual tables for the equation of the cycle of epacts, from which, for any number of years, once the golden number is known, the epact and the Martyrology letter corresponding to each year may be derived. Such a new table, drawn up after the manner of the following specimen, is in turn valid only until the time of the change of the cycle of epacts.
Example: From the year 2200, to which the golden number 16 corresponds, and with which the appended specimen begins, up only to the year 2299, the proposed table may be composed, in which are gathered together all the elements necessary for finding which moon is to be announced — but only within that span of time.
Table of the Martyrology Letters Corresponding to the Golden Numbers and Epacts, from the Beginning of the Year 2200 to the End of the Year 2299
[A tabular specimen follows in the original, listing the golden numbers, their epacts, and the corresponding Martyrology letters for the years 2200–2299.]
In the year 2245, therefore, to which the golden number 7 belongs, there will correspond the epact IV, and accordingly the lowercase Martyrology letter “d,” from which, as stated above, the day of the lunation for each day of that year is found.
Computing the Golden Number and the Epact
The golden number: having computed the integer part of the ratio between the year whose elements one wishes to find and 19, the golden number is obtained by subtracting from that same year — with one added — the aforesaid integer part multiplied by nineteen.
The epact: having computed the sum produced by multiplying by 11 the golden number of the year whose epact one wishes to find, the epact is obtained — from now until the year 2099 — as follows:
a) if the sum of this multiplication is greater than thirteen, by adding one to the remainder of the whole-number quotient that results from that same sum (after thirteen has been subtracted) when it is divided by thirty;
b) but if it is less than thirteen, by adding one to the sum of the aforesaid multiplication, with thirty added and thirteen subtracted (that is to say, by adding eighteen to the sum of the multiplication).
From the year 2100 to 2199, in place of the numbers thirteen and one, the numbers fourteen and two respectively are to be used.
Temporary Table of the Epacts and Martyrology Letters
[A table follows in the original with the columns: Year of the Lord, Golden Number, Epact, and Martyrology Letter.]