I won't go into the doctrinal disputes to which these ambiguities gave rise. The interested reader should consult the "Easter" entry in a good encyclopedia of theology (e.g., the Dictionnaire de Théologie Catholique). The generally favored solution was that Easter should always be on a Sunday, and that there should be some rule for determining a time fairly close to Passover. Just what this rule should be took a long time to hammer out. Relying upon the Jewish definition of Passover was uncongenial to many Christians, and as the Jewish calendar was not yet fixed by rule there was also the practical problem of waiting for the determination of the Sanhedrin in Jerusalem for a date which then had to be transmitted to widely separated churches throughout the Roman empire. To calculate Easter, then, Christians needed to find a lunar month in spring, which required both a definition exactly when spring began and a method of computing lunar months (i.e., a lunar calendar) that could be converted into the Julian calendar.
The rule eventually agreed upon was that Easter should be celebrated on the Sunday after the 14th day of the "Paschal" month. That Paschal, or Easter, month (essentially a Christian version of Nisan) is the one where the 14th day is on or next after the vernal equinox.
Even after this definition was generally accepted, there were still problems. When, exactly is the vernal equinox, and what sort of lunar calendar does one keep to track the Paschal month?
The Romans took the vernal equinox to be on March 25, a traditional date, to which they clung stubbornly for many years. Many of the eastern churches, however, took March 21 as the equinox. This measurement was fixed by direct observation of astronomers in Alexandria in the early third century. During that time, Alexandria was famous as a center of astronomic knowledge, and it was a natural place to go for expert consultation.
The lunar calendar used to track the new moons was also a subject of debate. The earliest surviving Easter tables show that the approximation 8 years = 99 months was used. This approximation results in an error of 1 day every 5.2 years. Clearly, for any long-term calculation of the moon, this rule will very quickly accumulate significant errors. In the early third century, a Roman named Augustalis introduced a new approximation: 84 years = 1039 months. This equation leads to an error of 1 day every 64.6 years—a significant improvement. Meanwhile the eastern churches, undoubtedly advised by Alexandrian astronomers, had found an even more accurate cycle: the familiar Metonic equation of 19 years = 235 months. This approximation has an error of only 1 day in 316.6 years.
Rome did not actually abandon the 84-year cycle or March 25th equinox (which, of course, led to periodic differences in date between the Alexandrian and Roman churches), but often Rome seems to have accepted Alexandrian calculations. Not always, however. From time to time, the Roman church expressed its unhappiness with dates that it considered unsatisfactory. Ironically, every time the Romans consulted experts, they were essentially told that their way was inaccurate, and that they should adopt the Alexandrian computation.
B | M iiii | ii | xxvi | vi | xiii | v i |
xvi k |
xxi |
M v | iii | vii | vii | xv | iiii k |
k |
xvii | |
END | M vi | iiii | xviii | i | xvi | xv k |
xi k |
xviii |
ANNI DNI | INDICT | EPACTE | CCVRR | CICLLVN | XIIIIma LVNA | DIES DOM POST | LVNA IPSIUS | |
---|---|---|---|---|---|---|---|---|
M vii | v | Nvlla | ii | xvii | Non apr |
xvii i |
xv | |
B | M viii | vi | xi | iiii | xviii | viii k |
v k |
xvii |
M viiii | vii | xxi | v | xviiii | I |
xx k |
xviii | |
M x | viii | iii | vi | i | iiii non apr |
v i |
xxi | |
M xi | viiii | xiiii | vii | ii | xi k |
viii k |
xvii | |
B | M xii | x | xxv | ii | iii | iiii i |
i |
xvii |
M xiii | xi | vi | iii | iiii | iii k |
non apr |
xx | |
OGD | M xiiii | xii | xvii | iiii | v | xiiii k |
vii k |
xii |
So, what does it all mean? Let's start with the column headings, which in this case actually come in the middle of the table. Expanding the abbreviations, the headings mean: anni domini (years of the lord); indictiones (indictions); epactæ (epacts); concurrentes; cicli lunae (lunar cycles), 14ma Luna (the 14th moon); dies dominica post (the Sunday afterwards); luna ipsius (this moon).
The indiction we have already seen. It plays no direct role in the calculation of Easter, but note that the cycle remains consistent with that given by Dionysius. The epacts indicate the age of the moon (i.e. days into the lunar month) on March 22, the earliest possible date of Easter Sunday. The concurrentes give the day of the week (the so-called ferial numbers) of March 24th. The lunar cycles track the Metonic, 19-year cycle. Later in the Middle Ages, this cycle will be determined by the numerus aureus, the golden number, so called because it is the key to figuring out the date of Easter. Note, however, that this lunar cycle, while it has the same practical effect as the golden number, is not exactly the same. For example, 1010, which has a golden number 4, is listed as the first year of the lunar cycle. The 14th moon is the 14th day of the lunar month, i.e., the full moon. The Sunday afterwards is Easter. The "moon itself" is the age of the moon, i.e., the day of the lunar month, on Easter.
Apart from the numbers and dates, the other abbreviations in the margin are B, for bisextilis, i.e. a leap-year; END for endecadas and OGD for ogdoadas mark the subdivisions of the Metonic cycle. The first is a period of 11 years, the second of 8. They coordinate the insertion of lunar leap.
Year | Indct | Epct | 3/24 | Gldn# | Full Moon | Easter | Moon on Easter | |
---|---|---|---|---|---|---|---|---|
L | 1004 | 2 | 26 | 6 | 14 | April 9 | March 17 | 21 |
1005 | 3 | 7 | 7 | 15 | March 29 | April 1 | 17 | |
1006 | 4 | 18 | 1 | 16 | April 17 | April 21 | 18 | |
1007 | 5 | 0 | 2 | 17 | April 5 | April 6 | 15 | |
L | 1008 | 6 | 11 | 4 | 18 | March 25 | March 28 | 17 |
1009 | 7 | 22 | 5 | 19 | April 13 | April 17 | 18 | |
1010 | 8 | 3 | 6 | 1 | April 2 | April 9 | 21 | |
1011 | 9 | 14 | 7 | 2 | March 22 | March 25 | 17 | |
L | 1012 | 10 | 25 | 2 | 3 | April 10 | April 13 | 17 |
1013 | 11 | 6 | 3 | 4 | March 29 | April 5 | 20 | |
1014 | 12 | 17 | 4 | 5 | April 18 | April 25 | 21 |
If you check these years (for example with the ChurchCalendar applet) you will find only one (March 17) is wrong. This one is an obvious scribal blunder. Easter must come after the full moon. The scribe wrote 16 Kalends of April when he should have written 16 Kalends of May, which is April 16, the correct date. Further, if you calculate the week day of the 24th, you will find that all of them match up correctly (1 = Sunday, etc.).