Many thanks to Rodolphe Audette, who authorized me to publish on this site the French translation (Rodolphe's translation) of the bull Inter gravissimas and Clavius's six canons on calculating the date of Easter. To read the Latin texts and other original documents, visit Rodolphe Audette's site (archived version).
Inter Gravissimas
Gregory, bishop, servant of the servants of God, for perpetual remembrance.
Among the weightiest duties of our pastoral ministry, one of the greatest is to bring to completion, with God's help, what was entrusted to the Holy See by the holy Council of Trent.
1. As the conciliar fathers were also devoting their attention to final deliberations on the breviary, but were stopped by lack of time, they wisely resolved to refer the whole matter to the authority and judgement of the Roman pontiff.
2. Now the breviary has two principal parts: the first contains the prayers and hymns to be recited on feast days and ordinary days; the second concerns the yearly cycle of Easter and the other movable feasts, regulated by the course of the Sun and Moon.
3. As to reform of the first part, Pius V, our predecessor of happy memory, carried it out and put it into force.
4. Reform of the second part, which first requires restoration of the calendar, has often and long been attempted by our Roman-pontiff predecessors; yet it could not be brought to completion, because the various calendar-reform plans proposed by astronomers, besides involving immense and almost inextricable difficulties that have always accompanied such reform, were not lasting and, above all, did not preserve the Church's ancient rites intact, which in this matter was our first concern.
5. While we ourselves, therefore, relying on the authority God has entrusted to us despite our unworthiness, were engaged in these reflections, our dear son Antonio Lilio, professor of science and medicine, brought us a book lately written by his brother Luigi. In it, Luigi showed that by means of an entirely new epact cycle he had devised, one that on the one hand used his own very precise rules for the Golden Number and on the other adapted to any length of the solar year, all defects of the calendar could be corrected in a coherent way that would endure to the end of the ages, so that it would no longer seem liable to future variation. This new project for restoring the calendar, summarized in a small book, we sent some years ago to Christian princes and major universities, so that this work, which concerns everyone, might be carried out after consulting everyone. As those recipients expressed their agreement, as we greatly desired, we then, strengthened by that consensus, summoned to the Holy City highly competent men, long previously chosen from the chief countries of Christendom, to reform the calendar. After devoting much time and care to this laborious work, and discussing among themselves cycles gathered from many sources, ancient and modern, which they had carefully examined, they chose, upon reflection and in agreement with learned men who had written on the matter, this epact cycle above all others, even adding elements which, after mature examination, appeared indispensable for producing a perfect calendar.
6. Examination shows that three points must be settled together in order to restore Easter celebration according to the rules laid down by the Roman pontiffs of old, especially Pius I and Victor I, and by the fathers of the councils, notably those of the great ecumenical Council of Nicaea: first, the precise date of the vernal equinox; next, the exact date of the moon's fourteenth day, when it reaches that age on the equinox itself or immediately after; finally, the first Sunday following that same fourteenth day of the moon. We have therefore taken care not only that the vernal equinox be returned to its former date, from which it has already moved by about ten days since Nicaea, and that the fourteenth day of the paschal moon be restored to its proper place, from which it is now distant by four days and more, but also that a methodical and rational system be established to prevent the equinox and that fourteenth lunar day from shifting again in future from their proper positions.
7. Therefore, so that the vernal equinox, fixed by the fathers of Nicaea on the twelfth of the calends of April, may be restored to that date, we prescribe and order that in October of the year 1582 the ten days running from the third of the nones to the eve of the ides inclusive be removed; and that the day following the fourth of the nones, on which Saint Francis is traditionally celebrated, be called the ides of October; and that on that day be celebrated the feast of the holy martyrs Denis, Rusticus and Eleutherius, together with the commemoration of Saint Mark, pope and confessor, and of the holy martyrs Sergius, Bacchus, Marcellus and Apuleius; that the next day, the seventeenth of the calends of November, the feast of Saint Callixtus, pope and martyr, be celebrated; that on the sixteenth of the calends of November the office and mass of the eighteenth Sunday after Pentecost be recited, the dominical letter passing from G to C; and finally that on the fifteenth of the calends of November the feast of Saint Luke the Evangelist take place, after which the other feast days shall follow in the manner set out in the calendar.
8. But so that this suppression of ten days causes no prejudice to anyone required to make monthly or yearly payments, judges, in any dispute arising from it, shall account for that suppression by postponing the due date of any payment by ten days.
9. Next, so that the equinox may no longer drift in future from the twelfth of the calends of April, we decree that a leap day shall be intercalated every four years according to custom, except in centurial years. Those years, although always leap years until now, and although we wish year 1600 still to be leap, shall not all be leap years thereafter; rather, in each period of four hundred years, each of the first three centurial years shall pass without leap day, and the fourth shall be leap, so that years 1700, 1800 and 1900 shall not be leap years, while in year 2000 a leap day shall be intercalated according to custom, February counting 29 days; and this same order of omissions and intercalations of leap days in each four-hundred-year period shall be observed forever.
10. Moreover, so that the fourteenth day of the paschal moon be determined precisely, and the moon's age be presented accurately to the faithful according to the ancient Church practice of reading it daily in the martyrology, we order that once the Golden Number is removed from the calendar, it be replaced by the epact cycle, which, thanks to the very precise rules stated above for the Golden Number, ensures that the new moon and the fourteenth day of the paschal moon are always correctly located. This can be clearly seen in the explanation of our calendar, where paschal tables are also provided in keeping with the Church's ancient customs and enabling the date of the most holy day of Easter to be found more reliably and more easily.
11. Finally, since on the one hand the ten days removed from October 1582 (which must now be called the year of the reform), and on the other hand each of the three days that shall no longer be intercalated in each four-hundred-year period, make it necessary to interrupt the 28-year cycle of dominical letters used to this day in the Roman Church, we will that it be replaced by that same 28-year cycle as adapted by that same Lilio to the leap-day rule for centurial years and to every length of the solar year, so that the dominical letter may forever be determined as easily as before by means of the solar cycle, as explained in the corresponding canon.
12. Therefore, in accordance with what traditionally belongs to the office of the supreme pontiff, we approve by these presents the calendar now reformed and perfected through God's infinite benevolence toward His Church, and we have ordered it to be printed in Rome together with the martyrology and then published.
13. But so that both reMayn intact and free from faults and errors throughout the world, we forbid all printers established in territories subject, directly or indirectly, to our jurisdiction and that of the Holy Roman Church, to dare or presume to print or publish, without our authorization, the calendar or martyrology, jointly or separately, or to profit from them in any way, under penalty of loss of contracts and a fine of one hundred gold ducats payable ipso facto to the Apostolic Chamber. As for other printers, wherever they may dwell on earth, we impose the same prohibition on pain of latæ sententiæ excommunication and other penalties at our discretion.
14. We therefore suppress and wholly abolish the old calendar, and we will that all patriarchs, primates, archbishops, bishops, abbots and other leaders of churches put into force, for the recitation of the divine office and celebration of feasts, each in his own church, monastery, convent, order, army or diocese, the new calendar, to which the martyrology has been adapted, and that they use only this one, both themselves and all other priests and clerics, secular and regular, of both sexes, as well as soldiers and all Christians. Use of this calendar shall begin after suppression of the ten days of October 1582. For those, however, living in regions too remote to receive this letter in time, it shall be permitted to make this change in October of the immediately following year, namely 1583, or in the year after that, as soon as this letter reaches them, in the manner indicated above and more fully explained in the calendar of the reform year.
15. Moreover, by the authority entrusted to us by God, we exhort and beseech our most beloved son in Jesus Christ, Rudolph, illustrious King of the Romans-elect Emperor, as well as the other kings and princes, and likewise the republics, and we commend to them, since they have strongly urged us to complete this admirable work and, above all, to preserve harmony among Christian nations in the celebration of feasts, that they themselves adopt our calendar and ensure that all their subjects adopt it reverently and conform to it scrupulously.
16. Since, however, it would be difficult to send this letter to every country of Christendom, we order that it be made public and posted at the doors of the basilica of the Prince of the Apostles and of the Apostolic Chancery, as well as at the entrance to the Campo dei Fiori; and that among all peoples and in all lands, the same full credit be given to copies of this letter, even printed ones, accompanied by copies of the aforementioned calendar and martyrology, signed by a public notary and authenticated by the seal of a church dignitary, as would be given by all to the posted original letter.
17. Therefore let it be forbidden to all, without exception, to violate this act of our prescription, ordinance, decree, will, approval, prohibition, suppression, abolition, exhortation and prayer, or to oppose it with rash audacity. Should anyone nonetheless presume to do so, let him know that he shall incur the wrath of the Almighty and of His blessed apostles Peter and Paul.
Given at Tusculum, on the sixth of the calends of March, in the year 1581 of the Incarnation, the tenth of our pontificate.
Canons of the Perpetual Gregorian Calendar
Canon 1
The 19-Year Golden Number Cycle
The nineteen-year Golden Number cycle is the sequence of positions from 1 to 19 across 19 years, and after that sequence, its return to 1.
Example: in 1577, the position in the 19-year cycle, also called the Golden Number, is 1. In the following year, 1578, that position is 2, and so on in subsequent years, increasing by one each year up to 19, which occurs in 1595, after which the Golden Number returns to 1, so that it is 1 in 1596, then 2 in 1597, etc. This Golden Number cycle is 19 years long because after a period of 19 solar years, new moons return to the same calendar dates, though not with absolute precision, but rather a fraction of a day earlier, as explained by computists and in the liber novæ rationis restituendi calendarii Romani.
A Golden Number year ends at the end of December, and at the beginning of January of the following year a new Golden Number year begins, at the same time as civil years, which also always end in December and begin in January. Thus in 1582, the year of the 19-year cycle, also called the Golden Number, is 6 and ends at the same time as that civil year, namely in December; in January a new civil year begins, namely 1583, and in that same January a new Golden Number year also begins, namely 7. And so it will continue for subsequent years until number 19 is reached, after which one returns to 1, and so on forever.
Until now, the Roman Church has used this 19-year cycle inscribed in the calendar to determine conjunctions of Sun and Moon, and also, indeed above all, to determine the date of Easter and the other movable feasts, because the ancients believed that new moons returned to exactly the same dates and hours every 19 years. That is not correct, since new moons return to those same positions after slightly less than 19 solar years, as we said above. It follows that today new moons are shifted by more than four days from the dates indicated by the Golden Number in the old Roman calendar; and because of this, Easter is often celebrated later than the twenty-first day of the moon, despite the precepts of the ancients. Thus the Golden Number has become wholly useless for indicating new moons and movable feasts, and will become ever more useless in future, both because of the ten days to be removed from October 1582 and because of the three leap days to be omitted every four hundred years, unless one establishes thirty arrangements, that is, drafts thirty calendars among which one would always select whichever best fits a given period. And everyone can see what problems and difficulties this would create for all, especially for ecclesiastics.
To avoid these difficulties, the Golden Number in the calendar has been replaced by an epact cycle based on thirty epactal numbers, which in reality is nothing other than the nineteen-year Golden Number cycle adjusted as if the Golden Number were inscribed in 30 different calendars, as noted above and clearly explained in the liber novæ rationis restituendi calendarii Romani. In future we shall use the Golden Number not really to find new moons and movable feasts, as has been done until now in the Church, but only to find the epact of a given year, which in turn will indicate new moons and movable feasts, as we shall show in another canon. Consequently, it reMayns absolutely necessary to determine the Golden Number of any year, even though it is removed from the calendar and no longer serves directly to find new moons and movable feasts.
Therefore, in order to find the Golden Number of any given year, we have constructed the following Golden Number table, whose use is perpetual and begins in 1582, the year of reform.
---------------------------------------------------------------------- | VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX I II III IV V | ----------------------------------------------------------------------
Tabella cycli aurei numeri initium sumens ab anno correctionis 1582.
Golden Number cycle table, starting from 1582, year of reform.
Here is how to find the Golden Number using this table for any year after 1582. Assign the first number in the table, namely VI, to year 1582; the second, VII, to the following year, 1583; and so on indefinitely up to the year whose Golden Number you seek, returning to the beginning of the table whenever you reach its end. The cell corresponding to the year in question then gives the required Golden Number.
But since it would be very tedious to run through many years in this table and return several times to its beginning before reaching the year whose Golden Number is sought, especially when that year is far from 1582, we have built this other table, by which one can easily find the Golden Number of any year, whether before or after 1582. Here is how:
------------------------------------------- | Anni | Aureus | | Anni | Aureus | | Domini | numerus| | Domini | numerus| | | adde 1 | | | adde 1 | |-------------------------------------------| | Year | Nombre | | Year | Nombre | | | d'or | | | d'or | | | add. 1 | | | add. 1 | |-------------------------------------------| | 1 | 1 | | 300 | 15 | | 2 | 2 | | 400 | 1 | | 3 | 3 | | 500 | 6 | | 4 | 4 | | 600 | 11 | |-------------------------------------------| | 5 | 5 | | 700 | 16 | | 6 | 6 | | 800 | 2 | | 7 | 7 | | 900 | 7 | | 8 | 8 | | 1000 | 12 | |-------------------------------------------| | 9 | 9 | | 2000 | 5 | | 10 | 10 | | 3000 | 17 | | 20 | 1 | | 4000 | 10 | | 30 | 11 | | 5000 | 3 | |-------------------------------------------| | 40 | 2 | | 6000 | 15 | | 50 | 12 | | 7000 | 8 | | 60 | 3 | | 8000 | 1 | | 70 | 13 | | 9000 | 13 | |-------------------------------------------| | 80 | 4 | | 10000 | 6 | | 90 | 14 | | 20000 | 12 | | 100 | 5 | | 30000 | 18 | | 200 | 10 | | 40000 | 5 | ------------------------------------------- ------------------------------------------- | 50000 | 11 | | 7000000 | 1 | | 60000 | 17 | | 8000000 | 12 | | 70000 | 4 | | 9000000 | 4 | | 80000 | 10 | | 10000000 | 15 | |-------------------------------------------| | 90000 | 16 | | 20000000 | 11 | |100000 | 3 | | 30000000 | 7 | |200000 | 6 | | 40000000 | 3 | |300000 | 9 | | 50000000 | 18 | |-------------------------------------------| |400000 | 12 | | 60000000 | 14 | |500000 | 15 | | 70000000 | 10 | |600000 | 18 | | 80000000 | 6 | |700000 | 2 | | 90000000 | 2 | |-------------------------------------------| |800000 | 5 | |100000000 | 17 | |900000 | 8 | |200000000 | 15 | |1000000 | 11 | |300000000 | 13 | |2000000 | 3 | |400000000 | 11 | |-------------------------------------------| |3000000 | 14 | |500000000 | 9 | |4000000 | 6 | |600000000 | 7 | |5000000 | 17 | |700000000 | 5 | |6000000 | 9 | |800000000 | 3 | -------------------------------------------
General table for finding the Golden Number.
Look up the year in question in the table under Year. If it is present, the number to its right, after adding 1 as indicated at the top of the table, is the required Golden Number. If the year is not in the table, take the immediately lower year that is present, together with its Golden Number; then take the reMayning years from the same table, likewise with their corresponding Golden Numbers, and add them to the previously found Golden Number, subtracting 19 whenever possible. Then add 1. In this way, one obtains the Golden Number for the year in question. If the reMayning number of years is not found in the table either, again take the immediately lower year with its Golden Number, add it to the previously found value, and subtract 19 whenever possible. Continue this process until all reMayning years have been accounted for in the table. Finally, add 1 to the last Golden Number obtained from those table values, after subtracting 19 when possible, as stated above. Thus one reaches the Golden Number of the year sought. And if, after adding 1, the total is 19, so that subtracting 19 leaves zero, then the Golden Number is 19.
Let us illustrate with examples. Suppose we seek the Golden Number of year 700. Since this year is in the table and has Golden Number 16, adding 1 gives Golden Number 17 for year 700. Next, let us find the Golden Number of year 1583. Since that year is not in the table, take year 1000, the immediately lower one, with its Golden Number 12. Then take the reMayning years, namely 583; as these are not in the table either, take again the immediately lower year, 500, with its Golden Number 6, and add it to the previously found 12, giving 18. Then handle the reMayning 83 years; as they are not in the table, take year 80, immediately lower, with Golden Number 4. Added to the previously obtained 18, this gives 22, which leaves 3 after subtracting 19. Finally, take the reMayning 3 years from the table and their Golden Number 3; adding that to the retained 3 gives 6, and adding 1 as prescribed at the top of the table gives Golden Number 7 for year 1583. Finally, let us find the Golden Number of 1595. First take Golden Number 12 for year 1000 and add Golden Number 6 for year 500, obtaining 18. Then add Golden Number 14 for year 90, obtaining 32; subtract 19 to get 13; add Golden Number 5 for year 5 to get 18. Adding 1 then gives Golden Number 19 for 1595.
We always add 1 to the last obtained value because Christ was born in the second year of this Golden Number cycle, and therefore the Golden Number was 2 in the first year of the Christian era, 3 in the second, and so on.
Construction of this table is extremely simple. For the first ten years, the first ten Golden Numbers correspond directly. Then, since from year 10 onward the table progresses in steps of 10 years, and year 10 corresponds to Golden Number 10, the Golden Number increases by 10 every 10 years. One therefore doubles Golden Number 10 of year 10 and subtracts 19 from the sum (20) to obtain Golden Number 1 for year 20. To this Golden Number 1, add 10 again to obtain Golden Number 11 for year 30. Continue in this way, adding 10 every 10 years up to 100, subtracting 19 each time possible, to obtain the next Golden Number. Then, since after year 100 the table progresses by hundreds and year 100 corresponds to Golden Number 5, one doubles this 5 to obtain Golden Number 10 for year 200, because from 100 to 100 years the Golden Number increases by 5. Then add that 5 again to obtain Golden Number 15 for year 300; and likewise for each following hundred up to 1000, always add 5 to the previous Golden Number, subtracting 19 when possible, to obtain the next one. The table can thus be extended as far as desired by observing the year-step by which it progresses and the Golden Number corresponding to the start year of that progression. For example, from year 1000 to year 10000, one always adds 12 to the previous Golden Number, then subtracts 19 where possible, because this progression starts at year 1000 and advances by 1000 up to 10000, and because year 1000 corresponds to Golden Number 12.
Without this table, the Golden Number of any year can also be found very easily using arithmetic principles: add 1 to the year in question and divide the sum by 19. The reMaynder of that division is the Golden Number of the year. (Ignore the quotient; it merely indicates how many full revolutions of the Golden Number cycle have occurred from the birth of Christ to the year in question.) If the reMaynder is zero, the Golden Number is 19. For example, to find the Golden Number of 1584, add 1 and divide 1585 by 19. The reMaynder is 8, so the Golden Number of 1584 is 8. If one must find the Golden Number of 1595, add 1 to obtain 1596; division by 19 leaves reMaynder zero, so the Golden Number is 19. Likewise, adding 1 to year 1600 gives 1601; division by 19 leaves reMaynder 5, which is the Golden Number of year 1600. And so on.
Canon 2
Epacts and New Moons
The epact is nothing other than the number of days by which the common solar year of 365 days exceeds the common lunar year of 354 days. Thus the epact of the first year is 11, because this is the number of days by which the common solar year exceeds the common lunar year, and therefore in the following year the new moons arrive 11 days earlier than in the first year. The epact of the second year is therefore 22, since this new solar year again exceeds the lunar year by 11 days, which, added to the first year's 11, total 22; consequently, after this year, new moons occur 22 days earlier than in the first year. The epact of the third year is 3, because adding 11 days again to epact 22 gives 33, and subtracting 30 (an embolismic lunation) leaves 3, and so on. Epacts therefore progress by repeated addition of 11 days, always subtracting 30 when possible. But when one reaches the epact corresponding to Golden Number 19, namely 29, one adds 12, so that after subtracting 30 from 41, one returns to 11, the starting epact. This is done so that the last embolismic lunation during Golden Number year 19 is only 29 days. Indeed, if it were 30 days like the other six embolismic lunations, new moons would not return, after 19 solar years, to the same dates, but would instead shift toward month-end and recur one day later than 19 years earlier. More on this can be found in the liber novæ rationis restituendi calendarii Romani. There are therefore 19 epacts, as many as Golden Numbers, and before calendar reform they corresponded to those Golden Numbers as shown in this table:
---------------------------------------------------------------------- |Aurei numeri (Golden Number) 1 2 3 4 5 6 7 8 9 | |Epactæ (epact) XI XXII III XIV XXV VI XVII XXVIII IX | ---------------------------------------------------------------------- | 10 11 12 13 14 15 16 17 18 19 | | XX I XII XXIII IV XV XXVI VII XVIII XXIX | ---------------------------------------------------
Epact / Golden Number correspondence table before calendar reform.
But because the 19-year Golden Number cycle is imperfect, since as stated above new moons do not return at exactly the same moments after 19 years, the 19-epact cycle is also imperfect. For this reason, we corrected it so that in future, instead of the Golden Number and the 19 epacts above, 30 epactal numbers from 1 to 30 are used, though the last epact, i.e. the thirtieth, is designated not by a number but by the symbol *, because no epact can equal 30. According to different periods, 19 of these 30 epacts correspond to the 19 Golden Numbers, according to the rules of solar and lunar equation; and these 19 epacts progress as before by increments of 11, always adding 12 to the epact corresponding to Golden Number 19 in order to obtain the next epact, namely that corresponding to Golden Number 1, according to the logic described above. This is demonstrated by the following three tables: the first gives Golden Numbers and corresponding epacts from reform year 1582 (after suppression of 10 days) up to but excluding 1700, from which the second table comes into force. The third table is used from 1900 onward, and so on table after table as shown later. All this is explained more fully in the liber novæ rationis restituendi calendarii Romani. Although epacts are ordinarily changed in March, here they are necessarily changed at the beginning of the year, at the same time as the Golden Numbers they replace.
------------------------------------------------------------------------ |Aurei numeri (Golden Number) 6 7 8 9 10 11 12 13 14 | |Epactæ (epact) XXVI VII XVIII XXIX X XXI II XIII XXIV | ------------------------------------------------------------------------ | 15 16 17 18 19 1 2 3 4 5 | | V XVI XXVII VIII XIX I XII XXIII IV XV | -----------------------------------------------------
Epact / Golden Number correspondence table, from the ides of October 1582 (year of reform), after suppression of 10 days, up to but excluding 1700.
----------------------------------------------------------------------- |Aurei numeri (Golden Number) 10 11 12 13 14 15 16 17 18 | |Epactæ (epact) IX XX I XII XXIII IV XV XXVI VII | ----------------------------------------------------------------------- | 19 1 2 3 4 5 6 7 8 9 | | XVIII * XI XXII III XIV XXV VI XVII XXVIII | -----------------------------------------------------
Epact / Golden Number correspondence table, from 1700 to 1900 exclusively.
----------------------------------------------------------------------- |Aurei numeri (Golden Number) 1 2 3 4 5 6 7 8 9 | |Epactæ (epact) XXIX X XXI II XIII XXIV V XVI XXVII | ----------------------------------------------------------------------- | 10 11 12 13 14 15 16 17 18 19 | | VIII XIX * XI XXII III XIV 25 VI XVII | ----------------------------------------------------
Epact / Golden Number correspondence table, from 1900 to 2200 exclusively.
Each of these tables starts with the Golden Number of the year in which it comes into force; and although different epacts correspond to Golden Numbers across these tables, a time will nevertheless come when the same Golden Numbers will again correspond to the same epacts as before calendar reform.
Therefore, to find the epact of any year, one must look up that year's Golden Number in the top row of the table corresponding to the period to which the year belongs. Under that Golden Number, in the lower row, one finds the required epact, or the symbol *. Days marked with that epact or with * in the calendar are new moons. The Golden Number may be found either by the method described in the previous canon, or directly from the epact table for the relevant period by assigning that table's first Golden Number to its starting year, the second to the next year, and so forth. In the same way, the epact can be found without using the Golden Number by assigning the first epact to the table's starting year, the second epact to the following year, and so on.
Examples. In 1582, the reform year, the Golden Number is 6, the first value of the first table, namely the one in force from the ides of October 1582 after suppression of ten days. The epact is therefore XXVI, shown beneath Golden Number 6, and new moons occur on 27 October, 26 November and 25 December. Likewise in 1583, after reform, the Golden Number is 7, under which in the same table epact VII appears, indicating the new moons throughout that year, for example 24 January, 22 February, 24 March, etc. In 1710, the Golden Number is 1, under which, in the epact row of the second table associated with that year, one finds the symbol *, which indicates new moons throughout that year, for example 1 and 31 January, 1 and 31 March (there is in fact no new moon in February then, since * does not appear there), 29 April, etc. Finally, in 1916, the Golden Number is 17, under which, in the epact row of the third table associated with that year, one finds epact 25, written not in Roman numerals like other epacts, but in ordinary numerals. Thus in 1916 there is a new moon wherever the calendar shows epact 25 in ordinary numerals, such as 6 January, 4 February, 6 March, 4 April, etc. Whenever epact 25 corresponds to a Golden Number greater than 11, as with the eight numbers from 12 to 19, one uses epact 25 in ordinary numerals; but when that same epact 25 corresponds to Golden Numbers below 12, namely 1 through 11 inclusive, one uses epact XXV in Roman numerals. This occurs only with epact 25, never with others. In this way lunar years align more precisely with solar years. For this reason there are six places in the calendar where two epacts, XXV and XXIV, are associated with the same date, so that lunations alternate as six periods of thirty days and six of twenty-nine. This is explained at length in the liber novæ rationis restituendi calendarii Romani.
If, as distributed in the calendar, these epacts sometimes indicate new moons slightly later than ideal, this should not be surprising, for they were arranged so after mature reflection. Since no lunar cycle can match astronomical calculation perfectly and instead indicates new moons sometimes too early, sometimes too late, care was taken in distributing this thirty-epact cycle in the calendar so that new moons indicated by epacts should sometimes come late rather than early, to avoid celebrating the holy day of Easter on the moon's fourteenth day with the Quartodeciman heretics, or even before it. Besides, for Easter celebration it is preferable to consider the moon's fourteenth day (the full moon) rather than the new moon. It matters little if, occasionally and rather rarely, Easter is celebrated later than the moon's twenty-first day because a new moon was assigned too late a date. That is a lesser evil than celebrating before the moon's fourteenth day, or worse, in the previous month, which would be wholly absurd. More on this appears in the liber novæ rationis restituendi calendarii Romani, where all these matters are explained in detail.
To show where the three tables above come from and how others can be produced, we add below the perpetual table of the epact cycle and the equation table of that cycle, from which the epact of any year can be found indefinitely. The construction rules for both the perpetual epact-cycle table and its equation table cannot be described in just a few words. Moreover, the alphabetic letters found there are taken from the extended epact-cycle table. We therefore deliberately refer readers to the liber novæ rationis restituendi calendarii Romani for the full description of these rules, where that extended table appears.
-------------------------------------------------- | P l C c p F f s M i A | | * XI XXII III XIV XXV-25 VI XVII XXVIII IX XX | -------------------------------------------------- | a m D d q G g t N k | | I XII XXIII IV XV XXVI VII XVIII XXIX X | ---------------------------------------------- | B b n E e r H h u | | XXI II XIII XXIV V XVI XXVII VIII XIX | ------------------------------------------
Perpetual table of the epact cycle.
----------------------------------------------- | Anni Domini | Anni Domini | Anni Domini | |-----------------------------------------------| | Year | Year | Year | |-----------------------------------------------| | N 1 | A 2200 | q 3600 leap | | P 320 leap | u 2300 | p 3700 | | P 500 leap | A 2400 leap | n 3800 | | a 800 leap | u 2500 | n 3900 | | b 1100 leap | t 2600 | n 4000 leap | |-----------------------------------------------| | c 1400 leap | t 2700 | m 4100 | |detractis X d. | t 2800 biss.| l 4200 | |10 days removed| | | | D 1582 | s 2900 | l 4300 | | D 1600 leap | s 3000 | l 4400 leap | | C 1700 | r 3100 | k 4500 | |-----------------------------------------------| | C 1800 | r 3200 leap | k 4600 | | B 1900 | r 3300 | i 4700 | | B 2000 leap | q 3400 | i 4800 leap | | B 2100 | p 3500 | i 4900 | -----------------------------------------------
Equation table of the perpetual epact cycle.
Here is how to use these tables. First, in the equation table, find the year whose epact is sought, or if it is absent, the immediately lower year, and note the lowercase or uppercase letter to its left. Then determine that year's Golden Number as well. Next, in the epact-cycle table, find the cell containing the same letter. Starting from that cell inclusively, count three cells to the left; assign Golden Number 1 to that reached cell, Golden Number 2 to the next cell on the right, and so on up to the Golden Number of the year in question, returning to the start of the table if one reaches the end, and counting as a single cell the one of uppercase letter F under which epacts XXV and 25 appear in different numerals. Once this is done correctly, the epact of the year in question is immediately found in the cell corresponding to that year's Golden Number. Note carefully, however, that if the Golden Number is greater than 11 (as with 12 through 19) and falls on the letter F cell containing the two epacts XXV-25, one must take epact 25; one takes the other, i.e. XXV, if in that same cell falls one of the eleven Golden Numbers from 1 to 11, since these are all below 12.
Let us illustrate with examples. In year 1582, after reform, uppercase letter D corresponds in the equation table, and its Golden Number is 6. If we now assign Golden Number 1, in the perpetual epact-cycle table, to the cell of lowercase letter a (the third to the left from uppercase D), and Golden Number 2 to the next cell on the right, and so on, then Golden Number 6 of year 1582 falls in the cell of epact XXVI, which indicates in the calendar the new moons from the ides of October of that year onward. In 1583, however, once reform is in force, the Golden Number is 7 and the corresponding equation-table letter is still uppercase D. Since that year is not in the table, one must take the immediately lower year, 1582, corresponding to uppercase D. Thus, assigning Golden Number 1 to the lowercase a cell (third left from uppercase D), Golden Number 2 to the next cell on the right, and so on, Golden Number 7 of year 1583 falls on epact VII, indicating that year's new moons. Likewise, for year 4218, whose Golden Number is 1, the equation-table letter is l; assigning Golden Number 1 in the epact table to cell u (third to the left), one finds epact XIX for that year. For year 1710, uppercase C appears in the equation table and the Golden Number is again 1. If Golden Number 1 is assigned to the first cell of the epact table, namely uppercase P (third to the left from uppercase C), the epact is * for that year. Next, for year 1912, uppercase B appears in the equation table and its Golden Number is 13. Therefore, assigning Golden Number 1 in the perpetual epact table to uppercase N (third to the left from uppercase B), then Golden Number 2 to the next cell on the right, and so on, looping to the table start, Golden Number 13 falls on the second cell; the epact is XI. Again, for year 1715, uppercase C appears in the equation table and its Golden Number is 6. Assigning Golden Number 1 in the epact table to uppercase P (third from uppercase C), and Golden Number 2 to the next right cell, etc., Golden Number 6 falls on letter F, under which the two epacts XXV-25 are written differently. Since Golden Number 6 is less than 12, one takes the first, i.e. XXV, for year 1715. Finally, for year 1916, uppercase B appears in the equation table and its Golden Number is 17. Therefore, assigning Golden Number 1 in the epact table to cell N (third from B), and Golden Number 2 to the next cell rightward, and so on with wraparound, Golden Number 17 again reaches cell F, under which the two epacts XXV-25 appear. Since Golden Number 17 is above 11, one takes the second epact, i.e. 25, for year 1916. In this way, the epact of any year can be found indefinitely.
It follows that anyone can easily construct, if desired, a table like the three above, giving epacts associated with a specific range of years. Example: the third table is used up to, but excluding, year 2200. If one wanted another table beginning in 2200, one would first find the epact of year 2200 by the method already described. Indeed, if one lists the 19 Golden Numbers in order, beginning with the one for year 2200, writes below it the epact found for that same year, and then writes beneath the other Golden Numbers the subsequent epacts, each formed by repeatedly adding 11 to the previous epact (except that one adds 12, not 11, to form the epact following Golden Number 19 when 19 is not the table's last one), one obtains an epact table used from 2200 through 2299, since a different letter, namely u, corresponds to year 2300 in the equation table, and a new table must then be constructed. Example: in year 2200, the equation-table letter is uppercase A, and its Golden Number is 16. Assigning Golden Number 1 in the perpetual epact table to uppercase M (third from uppercase A), Golden Number 2 to the next cell on the right, etc., Golden Number 16 of year 2200 falls on lowercase n, under which epact XIII appears for that year. Therefore, if one begins with Golden Number 16 and epact XIII, the epact / Golden Number correspondence table is:
----------------------------------------------------------------------- |Aurei numeri (Golden Number) 16 17 18 19 1 2 3 4 5 | |Epactæ (epact) XIII XXIV V XVI XXVIII IX XX I XII | ----------------------------------------------------------------------- | 6 7 8 9 10 11 12 13 14 15 | | XXIII IV XV XXVI VII XVIII XXIX X XXI II | ---------------------------------------------------
Epact / Golden Number correspondence table, from 2200 to 2300 exclusively.
But these same epacts can be derived more easily from the perpetual epact-cycle table. Assign Golden Number 1 to uppercase M, Golden Number 2 to the next cell on the right (where letter i appears), Golden Number 3 to the next cell on the right (uppercase A), then Golden Number 4 to the next cell rightward (lowercase a), and so forth. One then writes beneath the Golden Numbers of that particular table the same epacts that correspond to those Golden Numbers in the perpetual epact-cycle table, as seen in the example. In this way one readily understands how the three particular epact tables above were constructed. Other methods, including simpler ones, for finding the epact of any year are given in the book explaining the new Roman calendar.
Canon 3
The Solar Cycle, or 28-Year Cycle of Dominical Letters
The solar cycle, or cycle of dominical letters, is the sequence of positions from 1 to 28 over 28 years, and after that sequence its return to 1. Each year of this cycle takes its position in January, in the same way as the 19-year Golden Number cycle. This 28-year cycle comes from multiplying 7 by 4, because there are seven days in the week and therefore seven dominical letters, and because one extra day is intercalated every four years, which interrupts the order of the seven letters since that year receives two dominical letters. One can therefore determine the dominical letter of any year indefinitely by means of this cycle, as we shall show at the end of the next canon.
To find the solar cycle of any year, we have constructed the following table, whose use is perpetual and begins in 1582, the year of the reform. Here is how to find the solar cycle using this table for any year from 1582 onward.
-------------------------------------------------------------------------- |23 24 25 26 27 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22| --------------------------------------------------------------------------
Solar cycle table, starting from 1582, year of reform.
Assign the first number in the table, namely 23, to year 1582; the second, 24, to the next year, 1583; and so on indefinitely until the year whose solar cycle you seek, returning to the beginning of the table each time you reach its end. The cell corresponding to the year in question gives the required solar cycle.
But because it is very tedious to run through a large number of years in this table, often returning to its beginning before reaching a given year, especially when that year is far from 1582, we have constructed this other table by which the solar cycle of any year, before or after 1582, can be found easily. Here is how.
Look up the year in question in the table under Year. If it is present, the number to its right is the required solar cycle, after adding 9 as indicated at the top of the table and subtracting 28 if possible. If the year is not in the table, take the immediately lower year that is present, together with its corresponding solar cycle. Then take the reMayning years from the same table, together with their corresponding solar cycles, and add them to the previously found solar cycle, subtracting 28 whenever possible. Finally, add 9. That sum, after again subtracting 28 if possible, is the required solar cycle. If the number of reMayning years is still not found in the table, again take the immediately lower year, add its corresponding solar cycle to the previously found one, and subtract 28 whenever possible. Continue this process with the years still reMayning until all are found in the table. At the end, add 9 to the final solar cycle obtained from the table values, then subtract 28 from the accumulated sum if possible. In this way you arrive at the solar cycle of the year in question. If, after adding 9, the sum is 28, so that subtracting 28 leaves zero, the solar cycle is 28.
------------------------------------------- | Anni | Cyclus | | Anni | Cyclus | | Domini | solaris| | Domini | solaris| | | adde 9 | | | adde 9 | |-------------------------------------------| | Year | Cycle | | Year | Cycle | | | solaire| | | solaire| | | add. 9 | | | add. 9 | |-------------------------------------------| | 1 | 1 | | 300 | 20 | | 2 | 2 | | 400 | 8 | | 3 | 3 | | 500 | 24 | | 4 | 4 | | 600 | 12 | |-------------------------------------------| | 5 | 5 | | 700 | 0 | | 6 | 6 | | 800 | 16 | | 7 | 7 | | 900 | 4 | | 8 | 8 | | 1000 | 20 | |-------------------------------------------| | 9 | 9 | | 2000 | 12 | | 10 | 10 | | 3000 | 4 | | 20 | 20 | | 4000 | 24 | | 30 | 2 | | 5000 | 16 | |-------------------------------------------| | 40 | 12 | | 6000 | 8 | | 50 | 22 | | 7000 | 0 | | 60 | 4 | | 8000 | 20 | | 70 | 14 | | 9000 | 12 | |-------------------------------------------| | 80 | 24 | | 10000 | 4 | | 90 | 6 | | 20000 | 8 | | 100 | 16 | | 30000 | 12 | | 200 | 4 | | 40000 | 16 | ------------------------------------------- ------------------------------------------- | Anni | Cyclus | | Anni | Cyclus | | Domini | solaris| | Domini | solaris| | | adde 9 | | | adde 9 | |-------------------------------------------| | Year | Cycle | | Year | Cycle | | | solaire| | | solaire| | | add. 9 | | | add. 9 | |-------------------------------------------| | 50000 | 20 | | 7000000 | 0 | | 60000 | 24 | | 8000000 | 8 | | 70000 | 0 | | 9000000 | 16 | | 80000 | 4 | | 10000000 | 24 | |-------------------------------------------| | 90000 | 8 | | 20000000 | 20 | | 100000 | 12 | | 30000000 | 16 | | 200000 | 24 | | 40000000 | 12 | | 300000 | 8 | | 50000000 | 8 | |-------------------------------------------| | 400000 | 20 | | 60000000 | 4 | | 500000 | 4 | | 70000000 | 0 | | 600000 | 16 | | 80000000 | 24 | | 700000 | 0 | | 90000000 | 20 | |-------------------------------------------| | 800000 | 12 | |100000000 | 16 | | 900000 | 24 | |200000000 | 4 | | 1000000 | 8 | |300000000 | 20 | | 2000000 | 16 | |400000000 | 8 | |-------------------------------------------| | 3000000 | 24 | |500000000 | 24 | | 4000000 | 4 | |600000000 | 12 | | 5000000 | 12 | |700000000 | 0 | | 6000000 | 20 | |800000000 | 16 | -------------------------------------------
General table for finding the solar cycle.
Here are examples. Suppose we seek the solar cycle of year 1000. Since that year appears in the table with solar cycle 20, adding 9 gives 29, and subtracting 28 leaves 1 as the solar cycle of year 1000. Now let us find the solar cycle of year 1582. Since that year does not appear in the table, take the immediately lower year, 1000, with its solar cycle 20. Then take the reMayning years, namely 582. As 582 is not in the table either, again take the immediately lower year, 500, with solar cycle 24, and add it to the previously found solar cycle 20, giving 44; subtracting 28 leaves 16. Then take the reMayning 82 years; as 82 is not in the table either, take the immediately lower year, 80, with solar cycle 24. Adding that to the already obtained 16 gives 40, from which 12 reMayns after subtracting 28. Finally, take the reMayning 2 years in the table with their corresponding solar cycle 2; adding this to the most recently obtained 12 gives 14. Adding 9 as indicated at the top of the table gives solar cycle 23 for year 1582. Finally, let us find the solar cycle of year 7075. First take solar cycle 0 for year 7000 and add it to solar cycle 14 for year 70, which gives 14.
Then add solar cycle 5 for year 5 to this 14, giving 19. Finally add 9, giving solar cycle 28 for 7075.
One always adds 9 to the final sum because Christ was born in the tenth year of this solar cycle; therefore the solar cycle was 10 in the first year of the Christian era, 11 in the second, and so on.
The construction of this table is exactly the same as for the Golden Number lookup table, except that here one subtracts 28 instead of 19. Therefore, it can easily be extended as far as desired.
Even without this table, the solar cycle of any year can be found very easily using arithmetic, as follows: add 9 to the year and divide the sum by 28. The reMaynder is the solar cycle of that year. (Ignore the quotient; it only indicates the number of complete revolutions of the solar cycle from Christ's birth to the year in question.) If the reMaynder is zero, the solar cycle is 28. For example, if I seek the solar cycle of 1582, I add 9 and divide 1591 by 28. The reMaynder is 23, so the solar cycle of 1582 is 23. If I wish to find the solar cycle of 1587, I add 9, obtaining 1596, divide by 28, and the reMaynder is zero. The solar cycle of 1587 is therefore 28. And so on.
Canon 4
The Dominical Letter
Because of the ten days removed from October 1582, and also because of the three leap days to be omitted every four hundred years as prescribed in the liber novæ rationis restituendi calendarii Romani and in the bull of Pope Gregory XIII on calendar reform, it was necessary to interrupt the 28-year dominical-letter cycle used until now in the Roman Church. We therefore provide the following dominical-letter table, to be used from the ides of October 1582, year of reform (after suppression of ten days), up to but excluding 1700.
------------------------------------------------------- |c|b|A|f|e|d|c|A|g|f|e|c|b|A|g|e|d|c|b|g|f|e|d|b|A|g|f|d| | |g| |b| |d| |f| |A| |c| |e| | -------------------------------------------------------
Dominical-letter table, from the ides of October 1582, year of reform (after suppression of 10 days), up to but excluding 1700.
Here is how to use this table. Assign letter c in the first cell to year 1582, the year of reform, after the ides of October (following suppression of ten days); then assign letter b in the second cell to the following year, 1583; letters A, g in the third cell to year 1584; and continue assigning the reMayning cells in order to subsequent years, up to the year in question, returning to the start of the table whenever you reach its end. The cell on which that year falls, provided the year is before 1700, gives its dominical letter. If the cell contains one letter, the year is common; if it contains two, the year is leap. In leap years, the upper letter indicates Sundays from the beginning of the year up to the feast of Saint Matthias the Apostle, and the lower letter indicates Sundays from that feast to year-end. Example: suppose we seek the dominical letter of year 1587. Count from 1582, assigned to the first letter c, up to 1587, assigning each year to one cell (counting paired upper/lower letters as one single cell). Year 1587 falls on letter d, which is in the sixth position in the table. The dominical letter is therefore d for the whole year, and the year is common because we found a single letter. Now seek the dominical letter of 1616. Count from year 1582 as described, up to year 1616, returning to the beginning once the table ends, and you will reach the two letters c, b in the seventh position. That year is therefore leap because a double letter was found; the upper letter c indicates Sundays from the year's start to Saint Matthias, and the lower one b indicates Sundays for the rest of the year.
But to simplify counting for years close to 1700 and avoid returning too often to the start of the table, prepare the following year table as follows: add 28 to year 1582, where the dominical-letter table begins, then add 28 again to that sum, and so on, as long as the sum reMayns below 1700 so as not to exceed the table's range.
------------------------------ | 1582 1610 1638 1666 1694 | ------------------------------
Starting years for the dominical-letter table.
So if the year whose dominical letter is sought appears in this table, the first letter of the dominical-letter table is that year's dominical letter. If not, take from the year table the immediately lower year, then count from that year in the dominical-letter table, starting at the first cell, up to the year in question. This counting leads to the dominical letter without ever needing to return to the table's beginning. For example, in 1638, which appears in the year table, the dominical letter is c, the first one in the dominical-letter table. By contrast, 1647 does not appear in the year table, so we begin counting in the dominical-letter table from 1638, the immediately lower year, up to 1647, assigning 1638 to the first cell, 1639 to the second, and so on. Year 1647 thus falls on the tenth cell, the one with letter f, which is the third after a double letter, and that is its dominical letter.
After year 1699, at whose end use of the previous dominical-letter table ceases, the following dominical-letter table comes into force. Its use begins in 1700 and is perpetual when used with the accompanying equation table, as follows:
---------------------------------------------------------- |I| |II| |III| | |----------------------------------------------------------| |d|b|A|g| f|d|c|b| A |f|e|d|c|A|g|f|e|c|b|A|g|e|d|c|b|g|f|e| |c| | e| | g | |b| |d| |f| |A| | ----------------------------------------------------------
Perpetual dominical-letter table, from year 1700 onward, if three leap years are omitted every four hundred years.
--------------------------------------------------- | | Annus| | Annus| | Annus| | Annus| | |Domini| |Domini| |Domini| |Domini| |-----|------|-----|------|-----|------|-----|------| | | Year| | Year| | Year| | Year| |-----|------|-----|------|-----|------|-----|------| | I | 1700 | I | 5700 | I | 9700 | I |13700 | | II | 1800 | II | 5800 | II | 9800 | II |13800 | | III | 1900 | III | 5900 | III | 9900 | III |13900 | |---------------------------------------------------| | I | 2100 | I | 6100 | I |10100 | I |14100 | | II | 2200 | II | 6200 | II |10200 | II |14200 | | III | 2300 | III | 6300 | III |10300 | III |14300 | |---------------------------------------------------| | I | 2500 | I | 6500 | I |10500 | I |14500 | | II | 2600 | II | 6600 | II |10600 | II |14600 | | III | 2700 | III | 6700 | III |10700 | III |14700 | |---------------------------------------------------| | I | 2900 | I | 6900 | I |10900 | I |14900 | | II | 3000 | II | 7000 | II |11000 | II |15000 | | III | 3100 | III | 7100 | III |11100 | III |15100 | |---------------------------------------------------| | I | 3300 | I | 7300 | I |11300 | I |15300 | | II | 3400 | II | 7400 | II |11400 | II |15400 | | III | 3500 | III | 7500 | III |11500 | III |15500 | |---------------------------------------------------| | I | 3700 | I | 7700 | I |11700 | I |15700 | | II | 3800 | II | 7800 | II |11800 | II |15800 | | III | 3900 | III | 7900 | III |11900 | III |15900 | |---------------------------------------------------| | I | 4100 | I | 8100 | I |12100 | I |16100 | | II | 4200 | II | 8200 | II |12200 | II |16200 | | III | 4300 | III | 8300 | III |12300 | III |16300 | |---------------------------------------------------| | I | 4500 | I | 8500 | I |12500 | I |16500 | | II | 4600 | II | 8600 | II |12600 | II |16600 | | III | 4700 | III | 8700 | III |12700 | III |16700 | |---------------------------------------------------| | I | 4900 | I | 8900 | I |12900 | I |16900 | | II | 5000 | II | 9000 | II |13000 | II |17000 | | III | 5100 | III | 9100 | III |13100 | III |17100 | |---------------------------------------------------| | I | 5300 | I | 9300 | I |13300 | I |17300 | | II | 5400 | II | 9400 | II |13400 | II |17400 | | III | 5500 | III | 9500 | III |13500 | III |17500 | ---------------------------------------------------
Equation table for the perpetual dominical-letter table, from year 1700 onward.
To find the dominical letter of a year not earlier than 1700, look in the equation table for the number written in old Roman numerals to the left of that year or (if it is absent) of the immediately lower year, then find that numeral in the perpetual dominical-letter table. Assign to the cell corresponding to that Roman numeral the year taken from the equation table, then assign the following year to the next cell, and so on up to the year in question, returning to the beginning of the table if needed. You will reach the cell of the dominical letter sought. If the letter is single, the year is common; if double, the year is leap, except for those centurial years in which the intercalary day is omitted, namely all and only those mentioned in the equation table. Since those years are common, only the lower of the two letters found is used, ignoring the upper one, which served for the previous year. In centurial leap years, namely all those not listed in the equation table, both letters found are used, as in all leap years.
Example. In year 1710, the equation table gives Roman numeral I because that year is not listed, so one must select the immediately lower year, 1700, which corresponds to numeral I. If, starting from 1700 found in the table, one counts cell by cell up to 1710 in the perpetual dominical-letter table, beginning with the first cell above which numeral I appears in the equation table, one finds dominical letter e, second after a double letter; therefore 1710 is a common year, second after a leap year. Likewise, Roman numeral III corresponds to year 1912 in the equation table. Counting cell by cell in the dominical-letter table from 1900 found in the equation table up to 1912, using as starting point the ninth cell (because Roman numeral III appears above it), we find the two dominical letters g, f, and that year is leap. Next, year 1800 corresponds in the equation table to Roman numeral II, which in the dominical-letter table corresponds to letters f, e; only the lower letter e applies to that whole year because it is a common year and the upper letter f served for the previous year, 1799. Finally, for year 3600, the equation table gives Roman numeral III beside 3500, the immediately lower year. If one counts cells from 3500 in the dominical-letter table, using the ninth cell (the one corresponding to numeral III) as starting point, one finds letters b, A, both of which are used because centurial year 3600 is leap, since it does not appear in the equation table.
To simplify counting, one again uses the procedure described above. Prepare a year table that progresses by repeatedly adding 28 to the year found in the equation table: thus, in the previous example, from year 3500 to 3528 and so on, as long as the sum reMayns below 3700. From year 3700 onward, one must indeed use another Roman numeral in the dominical-letter table, as shown in the equation table. Once that year table is prepared, we immediately know from which year to begin counting in the dominical-letter table. Returning to the previous example, we begin counting under Roman numeral III from 3584, which in the year table is the immediately lower year relative to 3600; this will again land in the cell of the two letters b, A.
------------------------------------------------ | 3500 3528 3556 3584 3612 3640 3668 3696 | ------------------------------------------------
Moreover, this same table can be adapted to any centurial year in the equation table by replacing 3500 with any other centurial year. For all centurial years associated with numerals I and II, counting starts from that centurial year itself, and also from 28, 56 or 84 years later. For centurial years associated with numeral III, one counts from that centurial year itself and also from 28, 56 or 84 years later, as well as from 12, 40, 68 or 96 years after the next centurial year. For example, in the previous table, counting must start from year 3500 itself, which is associated with numeral III in the equation table, then from 28, 56 or 84 years later, and also from 12, 40, 68 or 96 years after 3600, the centurial year immediately following 3500.
The equation table is very easy to construct. It progresses from centurial year to centurial year, but only for those that are common, since centurial leap years are omitted, because the order of dominical letters is interrupted in the former but not in the latter. That is why, after three centurial years, one is always omitted because it is leap. Then, as can be seen, Roman numerals I, II and III return in the same order.
It is therefore easy for anyone to extract from our perpetual table a specific table adapted to their own period. Indeed, if one builds a 28-letter dominical table beginning at the cell of the Roman numeral that corresponds, in the equation table, to a given centurial year, one obtains a table applicable from that centurial year up to but excluding the next centurial year that appears in the equation table; provided that of the two first letters corresponding to the centurial year from which use of the table begins, only the lower letter is taken, ignoring the upper one. This is how the following table was built, which applies from 1800 to the end of 1899, so that in 1800 the dominical letter is e, i.e. the lower letter of f, e. In the following year, 1801, the dominical letter is d, and so forth.
------------------------------------------------------- |f|d|c|b|A|f|e|d|c|A|g|f|e|c|b|A|g|e|d|c|b|g|f|e|d|b|A|g| |e| |g| |b| |d| |f| |A| |c| | -------------------------------------------------------
Dominical-letter table, from 1800 to 1900 exclusively.
We can also find easily and permanently the dominical letter of any year, whether before or after the reform year, by means of the old solar cycle, or 28-year dominical-letter cycle, used by the Church up to this day. Here is how that cycle works, with the help of an equation table that progresses from centurial year to centurial year, so that one in every four of those years is leap and in that case the corresponding Roman numeral is repeated.
-------------------------------------------------------------- |V| |VII| |II| |IV| |VI| |I| |III| | |--------------------------------------------------------------| |g|e|d|c| b |g|f|e| d|b|A|g| f|d|c|b| A|f|e|d|c|A|g|f| e |c|b|A| |f| | A | | c| | e| | g| |b| | d | | --------------------------------------------------------------
Solar cycle, or ancient perpetual 28-year cycle of dominical letters.
------------------------------------------------------------ | | Annus | | | Annus | | | Annus | | | Domini | | | Domini | | | Domini | |------------------| |------------------| |------------------| | | Year | | | Year | | | Year | |------------------| |------------------| |------------------| | V | 1 | | VI | 3100 | | VI | 5000 | | V | 1582 | | VI | 3200 biss| | VII | 5100 | |detractis X diebus| | VII | 3300 | | VII | 5200 biss| | I | 1582 | | I | 3400 | | I | 5300 | | I | 1600 biss| | II | 3500 | | II | 5400 | |------------------| |------------------| |------------------| | II | 1700 | | II | 3600 biss| | III | 5500 | | III | 1800 | | III | 3700 | | III | 5600 biss| | IV | 1900 | | IV | 3800 | | IV | 5700 | | IV | 2000 biss| | V | 3900 | | V | 5800 | | V | 2100 | | V | 4000 biss| | VI | 5900 | |------------------| |------------------| |------------------| | VI | 2200 | | VI | 4100 | | VI | 6000 biss| | VII | 2300 | | VII | 4200 | | VII | 6100 | | VII | 2400 biss| | I | 4300 | | I | 6200 | | I | 2500 | | I | 4400 biss| | II | 6300 | | II | 2600 | | II | 4500 | | II | 6400 biss| |------------------| |------------------| |------------------| | III | 2700 | | III | 4600 | | III | 6500 | | III | 2800 biss| | IV | 4700 | | IV | 6600 | | IV | 2900 | | IV | 4800 biss| | V | 6700 | | V | 3000 | | V | 4900 | | V | 6800 biss| ------------------------------------------------------------
Equation table of the old solar cycle.
To find the dominical letter of a given year, check in the equation table which Roman numeral appears to the left of that year, or, if it does not appear there, to the left of the immediately lower year, and find that numeral in the solar-cycle table. From there, counting to the right, and returning to the beginning of the table if needed, as many dominical-letter cells as the solar-cycle number of the year in question (determined according to Canon 3), you will land on the cell of the desired dominical letter. If it is single, the year is common; if double, the year is leap, except for centurial years in which the intercalary day is omitted, namely all and only those not accompanied by the mark (biss) in the equation table. Since those years are common, only the lower letter of the two found is used, omitting the upper letter, because that one served as dominical letter for the previous year. For centurial leap years, namely all those marked (biss), both letters are used as in other leap years.
Examples. In year 1699, the equation table gives Roman numeral I, located next to the immediately lower year 1600. Since the solar cycle of 1699 is 28, count twenty-eight dominical-letter cells starting from the one under numeral I, up to letter d, which is that year's dominical letter, third after a double letter. Next, year 1700 corresponds in the equation table to Roman numeral II, and its solar cycle is 1. Therefore, of the two letters d, c in the first dominical-letter cell under numeral II, the lower letter is the dominical letter for that year, because it is a common year and the upper letter d served for the preceding year 1699, as just shown. Finally, year 2000 corresponds in the equation table to Roman numeral IV, and the solar cycle of that year is 21. Counting twenty-one dominical-letter cells from the one of numeral IV gives the two letters b, A, both of which are used that year because it is leap. But the first method is simpler because it does not require the solar cycle.
Canon 5
Indiction
Indiction is the sequence of positions from 1 to 15 over 15 years and, after that sequence, its return to 1. Each year of this cycle takes its position in January in pontifical bulls, in the same way as described for the 19-year Golden Number cycle. Since indiction is often used in official writings and public inscriptions, the indiction of any year can be found easily by means of the following table, whose use is perpetual and begins in 1582, year of reform.
--------------------------------------------------- | 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 | ---------------------------------------------------
Indiction table, starting from 1582, year of reform.
Assign the first number in the table, namely 10, to year 1582, the second (11) to the following year 1583, and so on up to the year in question, returning to the start of the table whenever its end is reached. The year then falls on the required indiction.
But since it is tedious to run through a large number of years in this table and return to its beginning several times before finding the indiction of a given year, especially when that year is far from 1582, we built this other table by which the indiction of any year, before or after 1582, can be found with little effort.
--------------------------------------------- | Anni | |Indictio| | Anni | |Indictio| | Domini | | adde 3 | | Domini | | adde 3 | |---------------------------------------------| | Year | |Indict. | | Year | |Indict. | | | | add. 3 | | | | add. 3 | |---------------------------------------------| | 1 | | 1 | | 300 | | 0 | | 2 | | 2 | | 400 | | 10 | | 3 | | 3 | | 500 | | 5 | | 4 | | 4 | | 600 | | 0 | |---------------------------------------------| | 5 | | 5 | | 700 | | 10 | | 6 | | 6 | | 800 | | 5 | | 7 | | 7 | | 900 | | 0 | | 8 | | 8 | | 1000 | | 10 | |---------------------------------------------| | 9 | | 9 | | 2000 | | 5 | | 10 | | 10 | | 3000 | | 0 | | 20 | | 5 | | 4000 | | 10 | | 30 | | 0 | | 5000 | | 5 | |---------------------------------------------| | 40 | | 10 | | 6000 | | 0 | | 50 | | 5 | | 7000 | | 10 | | 60 | | 0 | | 8000 | | 5 | | 70 | | 10 | | 9000 | | 0 | |---------------------------------------------| | 80 | | 5 | | 10000 | | 10 | | 90 | | 0 | | 20000 | | 5 | | 100 | | 10 | | 30000 | | 0 | | 200 | | 5 | | 40000 | | 10 | --------------------------------------------- --------------------------------------------- | Anni | |Indictio| | Anni | |Indictio| | Domini | | adde 3 | | Domini | | adde 3 | |---------------------------------------------| | Year | |Indict. | | Year | |Indict. | | | | add. 3 | | | | add. 3 | |---------------------------------------------| | 50000 | | 5 | | 7000000 | | 10 | | 60000 | | 0 | | 8000000 | | 5 | | 70000 | | 10 | | 9000000 | | 0 | | 80000 | | 5 | |10000000 | | 10 | |---------------------------------------------| | 90000 | | 0 | |20000000 | | 5 | | 100000 | | 10 | |30000000 | | 0 | | 200000 | | 5 | |40000000 | | 10 | | 300000 | | 0 | |50000000 | | 5 | |---------------------------------------------| | 400000 | | 10 | |60000000 | | 0 | | 500000 | | 5 | |70000000 | | 10 | | 600000 | | 0 | |80000000 | | 5 | | 700000 | | 10 | |90000000 | | 0 | |---------------------------------------------| | 800000 | | 5 | |100000000| | 10 | | 900000 | | 0 | |200000000| | 5 | | 1000000 | | 10 | |300000000| | 0 | | 2000000 | | 5 | |400000000| | 10 | |---------------------------------------------| | 3000000 | | 0 | |500000000| | 5 | | 4000000 | | 10 | |600000000| | 0 | | 5000000 | | 5 | |700000000| | 10 | | 6000000 | | 0 | |800000000| | 5 | ---------------------------------------------
General table for finding indiction.
Find the year in this table or, if absent, the immediately lower year, and then the reMayning years, listing the indictions shown to the right of those years. When all these indictions have been added in the way described in the canons on the Golden Number and the solar cycle, and 3 is added at the end while subtracting 15 whenever possible, one obtains the required indiction. If the final sum after adding 3 equals 15, so that subtracting 15 leaves zero, the indiction is 15. Let us illustrate with one or two examples. For year 2000, the table gives indiction 5; adding 3 yields indiction 8 for 2000. Likewise, to find the indiction of 1582, take the immediately lower year 1000 with indiction 10. Then, for the reMayning 582 years, take immediately lower year 500 with indiction 5; adding this to the previous indiction 10 gives 15, from which nothing reMayns after subtracting 15. For the reMayning 82 years, take year 80 with indiction 5; adding this to the retained indiction 0 gives 5, and adding indiction 2 for the final 2 years gives 7. Adding 3 at the end gives indiction 10 for year 1582. Finally, to find the indiction of year 3040: add indiction 0 for immediately lower year 3000 to indiction 10 for the reMayning 40 years; this gives 10, and adding 3 gives indiction 13 for year 3040.
One always adds 3 to the final result because Christ was born in the fourth year of the indiction cycle; therefore the indiction was 4 in the first year of the Christian era, 5 in the second, and so on.
This table is constructed in the same way as those for the Golden Number and the solar cycle, except that here one always subtracts 15 whenever possible, rather than 19 or 28.
Even without this table, the indiction of any year is very easy to find by arithmetic, as follows: add 3 to the year and divide the sum by 15. The reMaynder is the required indiction. (Ignore the quotient; it only indicates the number of complete revolutions of the indiction cycle between Christ's birth and the year in question.) Thus for year 1582, I add 3 to obtain 1585, then divide by 15. The reMaynder is 10, which is the indiction of 1582. Likewise for 1587, I add 3 to obtain 1590 and divide by 15. The reMaynder is zero, so the indiction is 15.
Canon 6
Movable Feasts
According to the decree of the holy Council of Nicaea, Easter, on which the other movable feasts depend, must be celebrated on the Sunday immediately following the fourteenth day of the first month (the Hebrews call first month the lunar month whose fourteenth day coincides with the vernal equinox, i.e. 21 March, or follows it most closely). So if one determines the epact of any year according to Canon 2, then looks for that epact in the calendar between 8 March inclusive and 5 April inclusive (the fourteenth day of the moon for that epact then coincides with the vernal equinox, namely 21 March, or follows it most closely), and counts 14 days downward starting from that date inclusive, the first Sunday following that fourteenth day of the moon (so as not to celebrate with the Jews, should the fourteenth day of the moon fall on a Sunday) will be Easter Day.
Example. In 1583, after the reform, the epact is VII and the dominical letter is b. I therefore look for epact VII in the calendar between 8 March and 5 April inclusive and find it on the line for 24 March; from there I count 14 days downward to reach the fourteenth day of the moon, which falls on 6 April, after which dominical letter b appears for the first time on the line for 10 April. Easter is therefore celebrated on 10 April in 1583. Next, in 1585, the epact is XXIX and the dominical letter is f. Between 8 March and 5 April inclusive, epact XXIX is found on the line for 1 April. Counting 14 days downward from 1 April gives the fourteenth day of the moon on 14 April, which is a Sunday because that date has dominical letter f. To avoid celebrating with the Jews, who celebrate Passover on the fourteenth day of the moon, one takes the next dominical letter f, namely the one on the line for 21 April. Easter is therefore celebrated on 21 April that year. Likewise in 1592, the epact is XVI and the dominical letter is double, e, d, since it is a leap year. Counting 14 days from epact XVI, found between 8 March and 5 April inclusive on the line for 15 March, the fourteenth day of the moon falls on 28 March. And since the dominical letter then in force is the second one, d, which appears after 28 March (that is, after the fourteenth day of the moon) on the line for 29 March, Easter is celebrated on 29 March that year.
Indeed, if one counts six Sundays backward from Easter in the calendar, one reaches the first Sunday of Lent, and the first preceding Wednesday is the first day of Lent, namely Ash Wednesday; immediately before it is Quinquagesima Sunday, and before that comes Sexagesima Sunday, itself preceded by Septuagesima Sunday. Conversely, if one counts five Sundays after Easter in the calendar, Rogation Days occur immediately after that fifth Sunday, and the following Thursday is Ascension Day. The seventh Sunday after Easter is Pentecost, followed on the next Sunday by Trinity, and then on the following Thursday by Corpus Christi. Thus, since Easter in 1592 is celebrated on 29 March, Quadragesima is celebrated on 16 February, with e as dominical letter; Ash Wednesday falls on 12 February and Septuagesima on 26 January. Rogations are celebrated on 4 May, Ascension on 7 May, Pentecost on 17 May, Trinity on 24 May, and finally Corpus Christi on 28 May. The number of Sundays between Pentecost and Advent is determined as follows: count four Sundays before Christmas; the fourth Sunday before Christmas is indeed the first Sunday of Advent. Therefore, if one counts all Sundays after Pentecost up to but excluding the first Sunday of Advent, one obtains the number of Sundays between Pentecost and Advent. We will indicate shortly how to find that number.
We also constructed the following two Paschal tables, one old and one new, to help determine movable feasts. Here is how to find these feasts using the old table: look for the year's epact in the second column, then in the following column (the dominical letters) look for the first occurrence of the dominical letter in force that lies below that epact; therefore, if the dominical letter appears on the same line as the epact, take the next occurrence of that same dominical letter below it. The line of that dominical letter indeed gives all movable feasts. See the following examples: in 1583, the epact is VII and the dominical letter is b. If one takes in the old table the first dominical letter b lying below epact VII, one finds on that line Septuagesima on 6 February, Ash Wednesday on 23 February, Easter on 10 April, Ascension on 19 May, Pentecost on 29 May and Corpus Christi on 9 June; there will be 25 Sundays between Pentecost and Advent, Advent will begin on 27 November, and so on. Likewise, in 1585, the epact is XXIX and the dominical letter is f, which appears right next to epact XXIX. Therefore one must take the next f, on whose line one finds Septuagesima on 17 February, Ash Wednesday on 6 March, Easter on 21 April, etc.
Here is how to find movable feasts using the new Paschal table. Look for the year's epact in the cell of the dominical letter in force. One then immediately obtains all movable feasts. For example, for year 1585, from the cell of dominical letter f, and on the line of epact XXIX, one obtains Septuagesima on 17 February, Ash Wednesday on 6 March, Easter on 21 April, etc.
However, whether one uses the old Paschal table or the new one, all movable feasts in leap years must be determined using the second dominical letter, namely the one that comes into force after the feast of Saint Matthias the Apostle. One must not think either of the two dominical letters may be used indifferently to determine these feasts. Consequently, one day must be added to the dates of Septuagesima and Ash Wednesday when they fall in January or February. This is because before Saint Matthias, the first dominical letter is in force and it follows the second in the calendar; and after Saint Matthias, in February, although the second letter is then in force, the intercalary day must still be added in this case, so that 24 February becomes 25, 25 becomes 26, and so on. But if Ash Wednesday falls in March, nothing is added, because the second letter is then in force and the day numbers are already correct, given that the intercalary day was added in February. This is so true that if one did not use the second letter, one would not correctly determine Septuagesima in a leap year when the epact is XXIV or XXV and the dominical letters are d, c, as seen in the second and third examples, years 4088 and 3784. For example, in 2096, a leap year, the epact is V and the dominical letters are A, g. If movable feasts are sought using the second letter g, one finds Septuagesima on 11 February and Ash Wednesday on 28 February. But if one day is added, Septuagesima falls on 12 February, which is a Sunday, and Ash Wednesday on 29 February, which is a Wednesday. Easter and other movable feasts, however, reMayn on the dates shown in the table. Likewise in 4088, leap year, the epact is XXIV and the dominical letters are d, c. If one seeks movable feasts using the second letter c, one finds Septuagesima on 21 February; adding 1 gives 22 February, which is a Sunday. Ash Wednesday falls on 10 March, so nothing is added.
Finally, in 3784, also a leap year, the epact is XXV and the dominical letters are d, c. Again, using the second letter c, one finds Septuagesima on 21 February, that is, after adding 1, on the 22nd. But if in the last two examples one had used the first letter d instead, one would be mistaken, since with epacts XXIV and XXV letter d indicates Septuagesima on 15 February, which is incorrect. Indeed, the second letter c places Easter on 25 April. Therefore Septuagesima must be celebrated on 22 February, as is easily seen by counting Sundays backward from Easter to Septuagesima.
Advent always begins on the Sunday nearest to the feast of Saint Andrew the Apostle, that is, between 27 November and 3 December inclusive; therefore the dominical letter in force seen between 27 November and 3 December inclusive indicates the first Sunday of Advent. For example, if the dominical letter is g, the first Sunday of Advent falls on 2 December because that is where g appears in the calendar.
Very briefly on the number of Sundays between Pentecost and Advent: count the Sundays after Easter up to and including Saint George's feast, which is on 23 April. Then add 24 to this number, and you obtain the number of Sundays between Pentecost and Advent. For example, when Easter is celebrated on 26 March, there are then four Sundays up to and including Saint George's feast, which then falls on a Sunday; there will therefore be 28 Sundays between Pentecost and Advent. Likewise, when Easter falls on 3 April, there are then 2 Sundays up to and including Saint George's feast; there will therefore be 26 Sundays between Pentecost and Advent. If there is no Sunday after Easter up to that feast inclusive, or if Easter itself falls on that day, there will be 24 Sundays between Pentecost and Advent. Finally, if Easter is after Saint George's feast, there will be only 23 Sundays between Pentecost and Advent. Ex his omnibus facile intelligi potest, qua ratione utraque tabula paschalis composita sit. From all this, it is easy to understand how the two general Paschal tables were constructed.
These are preceded by a particular table of several years beside which all movable feasts can be found immediately; that table was built using the Paschal tables themselves, by means of which an unlimited number of other specific tables can be built for any years.
Moreover, in the first Paschal table, i.e. the old reformed table, we placed the Golden Numbers before the epacts at exactly the positions they occupied before calendar reform and by which movable feasts were then found. We did this so that anyone may recover the date of Easter and other movable feasts from the Council of Nicaea up to reform year 1582 whenever desired or needed. Movable feasts are found directly using these Golden Numbers exactly as with epacts. Suppose, for example, we wish to find the dates on which these feasts were celebrated in 1450. That year, the Golden Number was 7 and the dominical letter was d. Taking Golden Number 7 on the left and the first d below it, one finds on that line that Septuagesima was celebrated on 1 February, Ash Wednesday on 18 February, Easter on 5 April, Ascension on 14 May, Pentecost on 24 May, Corpus Christi on 4 June, that there were 26 Sundays after Pentecost, and finally that the first Sunday of Advent fell on 29 November, and so on.
Tabula Paschalis Antiqua Reformata
------------------------------------------------------------------- |Au|Cyclus|Lit.|Domi.|Dies |Dies |Dies |Dies |Corpus|Dom.|Prima| | | | |Sep- |Cine- |Paschæ |Ascen-|Pente-|Chris-|post|Domin| |N |epac- |do- |tuag.|rum | |sionis|costes|ti |Pent|Adven| |u |tarum |mi- |----------------------------------------------------| |m.| |nic.|Ian. |Febr. |Martii |April.| Maii | Maii | | | |-------------------------------------------------------------------| |16|xxiii | | | | | | | | | | | 5|xxii | d | 18 | 4 | 22 | 30 | 10 | 21 | 28 |29 N.| | |xxi | e | 19 | 5 | 23 |1 Maii| 11 | 22 | 28 |30 | |13|xx | f | 20 | 6 | 24 | 2 | 12 | 23 | 28 | 1 D.| |-------------------------------------------------------------------| | 2|xix | g | 21 | 7 | 25 | 3 | 13 | 24 | 28 | 2 | | |xviii | A | 22 | 8 | 26 | 4 | 14 | 25 | 28 | 3 | |10|xvii | b | 23 | 9 | 27 | 5 | 15 | 26 | 27 |27 N.| | |xvi | c | 24 | 10 | 28 | 6 | 16 | 27 | 27 |28 | |-------------------------------------------------------------------| |18|xv | d | 25 | 11 | 29 | 7 | 17 | 28 | 27 |29 | | 7|xiv | e | 26 | 12 | 30 | 8 | 18 | 29 | 27 |30 | | |xiii | f | 27 | 13 | 31 | 9 | 19 | 30 | 27 | 1 D.| |15|xii | g | 28 | 14 |1 Apri.| 10 | 20 | 31 | 27 | 2 | |-------------------------------------------------------------------| | 4|xi | A | 29 | 15 | 2 | 11 | 21 |1 Iun.| 27 | 3 | | |x | b | 30 | 16 | 3 | 12 | 22 | 2 | 26 |27 N.| |12|ix | c | 31 | 17 | 4 | 13 | 23 | 3 | 26 |28 | | 1|viii | d |1 Feb| 18 | 5 | 14 | 24 | 4 | 26 |29 | |-------------------------------------------------------------------| | |vii | e | 2 | 19 | 6 | 15 | 25 | 5 | 26 |30 | | 9|vi | f | 3 | 20 | 7 | 16 | 26 | 6 | 26 | 1 D.| | |v | g | 4 | 21 | 8 | 17 | 27 | 7 | 26 |2 | |17|iv | A | 5 | 22 | 9 | 18 | 28 | 8 | 26 |3 | |-------------------------------------------------------------------| | 6|iii | b | 6 | 23 | 10 | 19 | 29 | 9 | 25 |27 N.| | |ii | c | 7 | 24 | 11 | 20 | 30 | 10 | 25 |28 | |14|i | d | 8 | 25 | 12 | 21 | 31 | 11 | 25 |29 | | 3|* | e | 9 | 26 | 13 | 22 |1 Iun.| 12 | 25 |30 | |-------------------------------------------------------------------| | |xxix | f | 10 | 27 | 14 | 23 | 2 | 13 | 25 | 1 D.| |11|xxviii| g | 11 | 28 | 15 | 24 | 3 | 14 | 25 | 2 | | |xxvii | A | 12 |1 Mart| 16 | 25 | 4 | 15 | 25 | 3 | |19|xxvi | b | 13 | 2 | 17 | 26 | 5 | 16 | 24 |27 N.| |-------------------------------------------------------------------| | 8|xxiv | c | 14 | 3 | 18 | 27 | 6 | 17 | 24 |28 | | | | d | 15 | 4 | 19 | 28 | 7 | 18 | 24 |29 | | | | e | 16 | 5 | 20 | 29 | 8 | 19 | 24 |30 | | | | f | 17 | 6 | 21 | 30 | 9 | 20 | 24 | 1 D.| |-------------------------------------------------------------------| | | | g | 18 | 7 | 22 | 31 | 10 | 21 | 24 | 2 | | | | A | 19 | 8 | 23 |1 Iun.| 11 | 22 | 24 | 3 | | | | b | 20 | 9 | 24 | 2 | 12 | 23 | 23 |27 N.| | | | c | 21 | 10 | 25 | 3 | 13 | 24 | 23 |28 | -------------------------------------------------------------------
Tabula Paschalis Nova Reformata
------------------------------------------------------------------------- |L| |Dom. |Septua-|Dies |Pascha|Roga- |Ascen-| |i| Cyclus Epactarum |int. |gesima |Cine-| |tiones|sio | |t| |Epiph| |rum | | | | |D| |& Sep| | | | | | |------------------------------------------------------------------|------| | |xxiii | 1 |18 Ian.| 4 F.|22 Mar|27 Apr|30 Apr| | |xxii xxi xx xix xviii xvii xvi| 2 |25 Ian.|11 F.|29 Mar| 4 Mai| 7 Mai| |D|xv xiv xiii xii xi x ix | 3 | 1 Feb.|18 F.| 5 Apr|11 Mai|14 Mai| | |viii vii vi v iv iii ii | 4 | 8 Feb.|25 F.|12 Apr|18 Mai|21 Mai| | |i * xxix xxviii xxvii xxvi | 5 |15 Feb.| 4 M.|19 Apr|25 Mai|28 Mai| | | 25 xxv xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii | 1 |19 Ian.| 5 F.|23 Mar|28 Apr| 1 Mai| | |xxi xx xix xviii xvii xvi xv | 2 |26 Ian.|12 F.|30 Mar| 5 Mai| 8 Mai| |E|xiv xiii xii xi x ix viii | 3 | 2 Feb.|19 F.| 6 Apr|12 Mai|15 Mai| | |vii vi v iv iii ii i | 4 | 9 Feb.|26 F.|13 Apr|19 Mai|22 Mai| | |* xxix xviii xvii xvi 25 xxv | 5 |16 Feb.| 5 M.|20 Apr|26 Mai|29 Mai| | | xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii xxi | 1 |20 Ian.| 6 F.|24 Mar|29 Apr| 2 Mai| | |xx xix xviii xvii xvi xv xiv | 2 |27 Ian.|13 F.|31 Mar| 6 Mai| 9 Mai| |F|xiii xii xi x ix viii vii | 3 | 3 Feb.|20 F.| 7 Apr|13 Mai|16 Mai| | |vi v iv iii ii i * | 4 |10 Feb.|27 F.|14 Apr|20 Mai|23 Mai| | |xxix xxviii xxvii xxvi 25 xxv | 5 |17 Feb.| 6 M.|21 Apr|27 Mai|30 Mai| | | xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx | 2 |21 Ian.| 7 F.|25 Mar|30 Apr| 3 Mai| | |xix xviii xvii xvi xv xiv xiii| 3 |28 Ian.|14 F.| 1 Apr| 7 Mai|10 Mai| |G|xii xi x ix viii vii vi | 4 | 4 Feb.|21 F.| 8 Apr|14 Mai|17 Mai| | |v iv iii ii i * xxix | 5 |11 Feb.|28 F.|15 Apr|21 Mai|24 Mai| | |xxviii xxvii xxvi 25 xxv xxiv | 6 |18 Feb.| 7 M.|22 Apr|28 Mai|31 Mai| |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix | 2 |22 Ian.| 8 F.|26 Mar| 1 Mai| 4 Mai| | |xviii xvii xvi xv xiv xiii xii| 3 |29 Ian.|15 F.| 2 Apr| 8 Mai|11 Mai| |A|xi x ix viii vii vi v | 4 | 5 Feb.|22 F.| 9 Apr|15 Mai|18 Mai| | |iv iii ii i * xxix xxviii | 5 |12 Feb.| 1 M.|16 Apr|22 Mai|25 Mai| | |xxvii xxvi 25 xxv xxiv | 6 |19 Feb.| 8 M.|23 Apr|29 Mai| 1 Iun| |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix xviii | 2 |23 Ian.| 9 F.|27 Mar| 2 Mai| 5 Mai| | |xvii xvi xv xiv xiii xii xi | 3 |30 Ian.|16 F.| 3 Apr| 9 Mai|12 Mai| |B|x ix viii vii vi v iv | 4 | 6 Feb.|23 F.|10 Apr|16 Mai|19 Mai| | |iii ii i * xxix xxviii xxvii | 5 |13 Feb.| 2 M.|17 Apr|23 Mai|26 Mai| | |xxvi 25 xxv xxiv | 6 |20 Feb.| 9 M.|24 Apr|30 Mai| 2 Iun| |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix xviii | 2 |24 Ian.|10 F.|28 Mar| 3 Mai| 6 Mai| | | xvii | | | | | | | | |xvi xv xiv xiii xii xi x | 3 |31 Ian.|17 F.| 4 Apr|10 Mai|13 Mai| |C|ix viii vii vi v iv iii | 4 | 7 Feb.|24 F.|11 Apr|17 Mai|20 Mai| | |ii 1 * xxix xxviii xxvii xxvi | 5 |14 Feb.| 3 M.|18 Apr|24 Mai|27 Mai| | | 25 | | | | | | | | |xxv xxiv | 6 |21 Feb.|10 M.|25 Apr|31 Mai| 3 Iun| -------------------------------------------------------------------------
Tabula Paschalis Nova Reformata (continued)
------------------------------------------------------------------------- |L| |Pen- |Trini- |Corp.|Dom. |Dom. |Prima | |i| |tecos|tas |Chris|inter |inter |Domin.| |t| Cyclus Epactarum |tes | |ti |Pent.&|Pent. |Adven-| | | | | | |1 Dom.|& Adv |tus | |D| | | | |Aug. | | | |------------------------------------------------------------------|------| | |xxiii |10 M.|17 Mai.|21 M.| 11 | 28 |29 N. | | |xxii xxi xx xix xviii xvii xvi|17 M.|24 Mai.|28 M.| 10 | 27 |29 | |D|xv xiv xiii xii xi x ix |24 M.|31 Mai.| 4 I.| 9 | 26 |29 | | |viii vii vi v iv iii ii |31 M.| 7 Iun.|11 I.| 8 | 25 |29 | | |i * xxix xxviii xxvii xxvi | 7 I.|14 Iun.|18 I.| 7 | 24 |29 | | | 25 xxv xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii |11 M.|18 Mai.|22 M.| 11 | 28 |30 N. | | |xxi xx xix xviii xvii xvi xv |18 M.|25 Mai.|29 M.| 10 | 27 |30 | |E|xiv xiii xii xi x ix viii |25 M.| 1 Iun.| 5 I.| 9 | 26 |30 | | |vii vi v iv iii ii i | 1 I.| 8 Iun.|12 I.| 8 | 25 |30 | | |* xxix xviii xvii xvi 25 xxv | 8 I.|15 Iun.|19 I.| 7 | 24 |30 | | | xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii xxi |12 M.|19 Mai.|23 M.| 11 | 28 | 1 D. | | |xx xix xviii xvii xvi xv xiv |19 M.|26 Mai.|30 M.| 10 | 27 | 1 | |F|xiii xii xi x ix viii vii |26 M.| 2 Iun.| 6 I.| 9 | 26 | 1 | | |vi v iv iii ii i * | 2 I.| 9 Iun.|13 I.| 8 | 25 | 1 | | |xxix xxviii xxvii xxvi 25 xxv | 9 I.|16 Iun.|20 I.| 7 | 24 | 1 | | | xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx |13 M.|20 Mai.|24 M.| 10 | 28 | 2 D. | | |xix xviii xvii xvi xv xiv xiii|20 M.|27 Mai.|31 M.| 9 | 27 | 2 | |G|xii xi x ix viii vii vi |27 M.| 3 Iun.| 7 I.| 8 | 26 | 2 | | |v iv iii ii i * xxix | 3 I.|10 Iun.|14 I.| 7 | 25 | 2 | | |xxviii xxvii xxvi 25 xxv xxiv |10 I.|17 Iun.|21 I.| 6 | 24 | 2 | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix |14 M.|21 Mai.|25 M.| 10 | 28 | 3 D | | |xviii xvii xvi xv xiv xiii xii|21 M.|28 Mai.| 1 I.| 9 | 27 | 3 | |A|xi x ix viii vii vi v |28 M.| 4 Iun.| 8 I.| 8 | 26 | 3 | | |iv iii ii i * xxix xxviii | 4 I.|11 Iun.|15 I.| 7 | 25 | 3 | | |xxvii xxvi 25 xxv xxiv |11 I.|18 Iun.|22 I.| 6 | 24 | 3 | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix xviii |15 M.|22 Mai.|26 M.| 10 | 27 |27 N. | | |xvii xvi xv xiv xiii xii xi |22 M.|29 Mai.| 2 I.| 9 | 26 |27 | |B|x ix viii vii vi v iv |29 M.| 5 Iun.| 9 I.| 8 | 25 |27 | | |iii ii i * xxix xxviii xxvii | 5 I.|12 Iun.|16 I.| 7 | 24 |27 | | |xxvi 25 xxv xxiv |12 I.|19 Iun.|23 I.| 6 | 23 |27 | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix xviii |16 M.|23 Mai.|27 M.| 10 | 27 |28 N. | | | xvii | | | | | | | | |xvi xv xiv xiii xii xi x |23 M.|30 Mai.| 3 I.| 9 | 26 |28 | |C|ix viii vii vi v iv iii |30 M.| 6 Iun.|10 I.| 8 | 25 |28 | | |ii 1 * xxix xxviii xxvii xxvi | 6 I.|13 Iun.|17 I.| 7 | 24 |28 | | | 25 | | | | | | | | |xxv xxiv |13 I.|20 Iun.|24 I.| 6 | 23 |28 | -------------------------------------------------------------------------
Old Reformed Paschal Table
------------------------------------------------------------------- |G.|Epact |Dom.|Sep- |Ash |Easter |Ascen-|Pente-|Corpus|Sun.|First| |No|cycle |let. |tua- |Wed. | |sion |cost |Christ|after|Sun. | | | | |ges. | | | | |i |Pent|Advent| | | | |Jan. |Feb. | Mar |Apr | May | May | | | |-------------------------------------------------------------------| |16|xxiii | | | | | | | | | | | 5|xxii | d | 18 | 4 | 22 | 30 | 10 | 21 | 28 |29 n.| | |xxi | e | 19 | 5 | 23 |1 May | 11 | 22 | 28 |30 | |13|xx | f | 20 | 6 | 24 | 2 | 12 | 23 | 28 | 1 d.| |-------------------------------------------------------------------| | 2|xix | g | 21 | 7 | 25 | 3 | 13 | 24 | 28 | 2 | | |xviii | A | 22 | 8 | 26 | 4 | 14 | 25 | 28 | 3 | |10|xvii | b | 23 | 9 | 27 | 5 | 15 | 26 | 27 |27 n.| | |xvi | c | 24 | 10 | 28 | 6 | 16 | 27 | 27 |28 | |-------------------------------------------------------------------| |18|xv | d | 25 | 11 | 29 | 7 | 17 | 28 | 27 |29 | | 7|xiv | e | 26 | 12 | 30 | 8 | 18 | 29 | 27 |30 | | |xiii | f | 27 | 13 | 31 | 9 | 19 | 30 | 27 | 1 d.| |15|xii | g | 28 | 14 |1 Apr| 10 | 20 | 31 | 27 | 2 | |-------------------------------------------------------------------| | 4|xi | A | 29 | 15 | 2 | 11 | 21 |1 Jun| 27 | 3 | | |x | b | 30 | 16 | 3 | 12 | 22 | 2 | 26 |27 n.| |12|ix | c | 31 | 17 | 4 | 13 | 23 | 3 | 26 |28 | | 1|viii | d |1 Feb| 18 | 5 | 14 | 24 | 4 | 26 |29 | |-------------------------------------------------------------------| | |vii | e | 2 | 19 | 6 | 15 | 25 | 5 | 26 |30 | | 9|vi | f | 3 | 20 | 7 | 16 | 26 | 6 | 26 | 1 d.| | |v | g | 4 | 21 | 8 | 17 | 27 | 7 | 26 | 2 | |17|iv | A | 5 | 22 | 9 | 18 | 28 | 8 | 26 | 3 | |-------------------------------------------------------------------| | 6|iii | b | 6 | 23 | 10 | 19 | 29 | 9 | 25 |27 n.| | |ii | c | 7 | 24 | 11 | 20 | 30 | 10 | 25 |28 | |14|i | d | 8 | 25 | 12 | 21 | 31 | 11 | 25 |29 | | 3|* | e | 9 | 26 | 13 | 22 |1 Jun| 12 | 25 |30 | |-------------------------------------------------------------------| | |xxix | f | 10 | 27 | 14 | 23 | 2 | 13 | 25 | 1 d.| |11|xxviii| g | 11 | 28 | 15 | 24 | 3 | 14 | 25 | 2 | | |xxvii | A | 12 |1 Mar| 16 | 25 | 4 | 15 | 25 | 3 | |19|xxvi | b | 13 | 2 | 17 | 26 | 5 | 16 | 24 |27 n.| |-------------------------------------------------------------------| | 8|xxiv | c | 14 | 3 | 18 | 27 | 6 | 17 | 24 |28 | | | | d | 15 | 4 | 19 | 28 | 7 | 18 | 24 |29 | | | | e | 16 | 5 | 20 | 29 | 8 | 19 | 24 |30 | | | | f | 17 | 6 | 21 | 30 | 9 | 20 | 24 | 1 d.| |-------------------------------------------------------------------| | | | g | 18 | 7 | 22 | 31 | 10 | 21 | 24 | 2 | | | | A | 19 | 8 | 23 |1 Jun| 11 | 22 | 24 | 3 | | | | b | 20 | 9 | 24 | 2 | 12 | 23 | 23 |27 n.| | | | c | 21 | 10 | 25 | 3 | 13 | 24 | 23 |28 | -------------------------------------------------------------------
New Reformed Paschal Table
------------------------------------------------------------------------- |L| |Sun. |Septua-|Ash |Easter|Roga- |Ascen-| |e| Epact Cycle |betw.|gesima |Wed. | |tions |sion | |t| |Epiph| | | | | | |D| |& Sep| | | | | | |------------------------------------------------------------------|------| | |xxiii | 1 |18 Jan.| 4 f.|22 Mar|27 Apr|30 Apr| | |xxii xxi xx xix xviii xvii xvi| 2 |25 Jan.|11 f.|29 Mar| 4 May| 7 May| |D|xv xiv xiii xii xi x ix | 3 | 1 Feb.|18 f.| 5 Apr|11 May|14 May| | |viii vii vi v iv iii ii | 4 | 8 Feb.|25 f.|12 Apr|18 May|21 May| | |i * xxix xxviii xxvii xxvi | 5 |15 Feb.| 4 m.|19 Apr|25 May|28 May| | | 25 xxv xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii | 1 |19 Jan.| 5 f.|23 Mar|28 Apr| 1 May| | |xxi xx xix xviii xvii xvi xv | 2 |26 Jan.|12 f.|30 Mar| 5 May| 8 May| |E|xiv xiii xii xi x ix viii | 3 | 2 Feb.|19 f.| 6 Apr|12 May|15 May| | |vii vi v iv iii ii i | 4 | 9 Feb.|26 f.|13 Apr|19 May|22 May| | |* xxix xviii xvii xvi 25 xxv | 5 |16 Feb.| 5 m.|20 Apr|26 May|29 May| | | xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii xxi | 1 |20 Jan.| 6 f.|24 Mar|29 Apr| 2 May| | |xx xix xviii xvii xvi xv xiv | 2 |27 Jan.|13 f.|31 Mar| 6 May| 9 May| |F|xiii xii xi x ix viii vii | 3 | 3 Feb.|20 f.| 7 Apr|13 May|16 May| | |vi v iv iii ii i * | 4 |10 Feb.|27 f.|14 Apr|20 May|23 May| | |xxix xxviii xxvii xxvi 25 xxv | 5 |17 Feb.| 6 m.|21 Apr|27 May|30 May| | | xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx | 2 |21 Jan.| 7 f.|25 Mar|30 Apr| 3 May| | |xix xviii xvii xvi xv xiv xiii| 3 |28 Jan.|14 f.| 1 Apr| 7 May|10 May| |G|xii xi x ix viii vii vi | 4 | 4 Feb.|21 f.| 8 Apr|14 May|17 May| | |v iv iii ii i * xxix | 5 |11 Feb.|28 f.|15 Apr|21 May|24 May| | |xxviii xxvii xxvi 25 xxv xxiv | 6 |18 Feb.| 7 m.|22 Apr|28 May|31 May| |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix | 2 |22 Jan.| 8 f.|26 Mar| 1 May| 4 May| | |xviii xvii xvi xv xiv xiii xii| 3 |29 Jan.|15 f.| 2 Apr| 8 May|11 May| |A|xi x ix viii vii vi v | 4 | 5 Feb.|22 f.| 9 Apr|15 May|18 May| | |iv iii ii i * xxix xxviii | 5 |12 Feb.| 1 m.|16 Apr|22 May|25 May| | |xxvii xxvi 25 xxv xxiv | 6 |19 Feb.| 8 m.|23 Apr|29 May| 1 jun| |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix xviii | 2 |23 Jan.| 9 f.|27 Mar| 2 May| 5 May| | |xvii xvi xv xiv xiii xii xi | 3 |30 Jan.|16 f.| 3 Apr| 9 May|12 May| |B|x ix viii vii vi v iv | 4 | 6 Feb.|23 f.|10 Apr|16 May|19 May| | |iii ii i * xxix xxviii xxvii | 5 |13 Feb.| 2 m.|17 Apr|23 May|26 May| | |xxvi 25 xxv xxiv | 6 |20 Feb.| 9 m.|24 Apr|30 May| 2 jun| |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix xviii | 2 |24 Jan.|10 f.|28 Mar| 3 May| 6 May| | | xvii | | | | | | | | |xvi xv xiv xiii xii xi x | 3 |31 Jan.|17 f.| 4 Apr|10 May|13 May| |C|ix viii vii vi v iv iii | 4 | 7 Feb.|24 f.|11 Apr|17 May|20 May| | |ii 1 * xxix xxviii xxvii xxvi | 5 |14 Feb.| 3 m.|18 Apr|24 May|27 May| | | 25 | | | | | | | | |xxv xxiv | 6 |21 Feb.|10 m.|25 Apr|31 May| 3 jun| -------------------------------------------------------------------------
New Reformed Paschal Table (continued)
------------------------------------------------------------------------- |L| |Pen- |Trini- |Corpus|Sun. |Sun. |First | |e| |tecost|ty |Christ|between|between|Sun. | |t| Epact Cycle | | |i |Pent.& |Pent. |Advent| | | | | | |1 Sun. |& Adv.| | |D| | | | |Aug. | | | |-------------------------------------------------------------------------| | |xxiii |10 m.|17 May |21 m.| 11 | 28 |29 n. | | |xxii xxi xx xix xviii xvii xvi|17 m.|24 May |28 m.| 10 | 27 |29 | |D|xv xiv xiii xii xi x ix |24 m.|31 May | 4 j.| 9 | 26 |29 | | |viii vii vi v iv iii ii |31 m.| 7 Jun|11 j.| 8 | 25 |29 | | |i * xxix xxviii xxvii xxvi | 7 j.|14 Jun|18 j.| 7 | 24 |29 | | | 25 xxv xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii |11 m.|18 May |22 m.| 11 | 28 |30 n. | | |xxi xx xix xviii xvii xvi xv |18 m.|25 May |29 m.| 10 | 27 |30 | |E|xiv xiii xii xi x ix viii |25 m.| 1 Jun| 5 j.| 9 | 26 |30 | | |vii vi v iv iii ii i | 1 j.| 8 Jun|12 j.| 8 | 25 |30 | | |* xxix xviii xvii xvi 25 xxv | 8 j.|15 Jun|19 j.| 7 | 24 |30 | | | xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii xxi |12 m.|19 May |23 m.| 11 | 28 | 1 d. | | |xx xix xviii xvii xvi xv xiv |19 m.|26 May |30 m.| 10 | 27 | 1 | |F|xiii xii xi x ix viii vii |26 m.| 2 Jun| 6 j.| 9 | 26 | 1 | | |vi v iv iii ii i * | 2 j.| 9 Jun|13 j.| 8 | 25 | 1 | | |xxix xxviii xxvii xxvi 25 xxv | 9 j.|16 Jun|20 j.| 7 | 24 | 1 | | | xxiv | | | | | | | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx |13 m.|20 May |24 m.| 10 | 28 | 2 d. | | |xix xviii xvii xvi xv xiv xiii|20 m.|27 May |31 m.| 9 | 27 | 2 | |G|xii xi x ix viii vii vi |27 m.| 3 Jun| 7 j.| 8 | 26 | 2 | | |v iv iii ii i * xxix | 3 j.|10 Jun|14 j.| 7 | 25 | 2 | | |xxviii xxvii xxvi 25 xxv xxiv |10 j.|17 Jun|21 j.| 6 | 24 | 2 | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix |14 m.|21 May |25 m.| 10 | 28 | 3 d | | |xviii xvii xvi xv xiv xiii xii|21 m.|28 May | 1 j.| 9 | 27 | 3 | |A|xi x ix viii vii vi v |28 m.| 4 Jun| 8 j.| 8 | 26 | 3 | | |iv iii ii i * xxix xxviii | 4 j.|11 Jun|15 j.| 7 | 25 | 3 | | |xxvii xxvi 25 xxv xxiv |11 j.|18 Jun|22 j.| 6 | 24 | 3 | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix xviii |15 m.|22 May |26 m.| 10 | 27 |27 n. | | |xvii xvi xv xiv xiii xii xi |22 m.|29 May | 2 j.| 9 | 26 |27 | |B|x ix viii vii vi v iv |29 m.| 5 Jun| 9 j.| 8 | 25 |27 | | |iii ii i * xxix xxviii xxvii | 5 j.|12 Jun|16 j.| 7 | 24 |27 | | |xxvi 25 xxv xxiv |12 j.|19 Jun|23 j.| 6 | 23 |27 | |-------------------------------------------------------------------------| | |xxiii xxii xxi xx xix xviii |16 m.|23 May |27 m.| 10 | 27 |28 n. | | | xvii | | | | | | | | |xvi xv xiv xiii xii xi x |23 m.|30 May | 3 j.| 9 | 26 |28 | |C|ix viii vii vi v iv iii |30 m.| 6 Jun|10 j.| 8 | 25 |28 | | |ii 1 * xxix xxviii xxvii xxvi | 6 j.|13 Jun|17 j.| 7 | 24 |28 | | | 25 | | | | | | | | |xxv xxiv |13 j.|20 Jun|24 j.| 6 | 23 |28 | -------------------------------------------------------------------------
