Previously Unpublished Works, Fascicles VI-VII

...known as embolismic lunations These are "intercalary" or extra lunar months added to a calendar to keep the lunar phases in sync with the solar seasons.. And to make the cycles of lunations and solar years coincide, a lunation at the end of the cycle, which should have contained 30 days, had to be one of 29 days; this breach of rule was called the leap of the moon original: saltus lune; a technical adjustment where a day is "skipped" in the lunar count to prevent the calendar from drifting away from the actual moon phases.. The dates of this leap of the moon were the 15th day before the Kalends of December In the Roman calendar, the Kalends is the 1st of the month; this date corresponds to November 17th. (according to Victorius and the Latin Churches); the 11th day before the Kalends of April (the Greeks); the 6th day before the Kalends of October (the Egyptians); and the 15th day before the Kalends of May (Dionysius). It does not interfere with the regular order of the days of the week or of the calendar month; it only brings the calendar new moon a day earlier.

The earliest Easter table A chronological chart used to calculate the date of Easter Sunday for many years into the future. we have is that of Hippolytus (217 A.D.) for 112 years starting from 222 A.D. It is not connected with the 19-year cycle Also known as the Metonic cycle, this is a period of 19 years after which the phases of the moon recur on the same days of the year., but was based on the suppositions that by inserting three lunations of 30 days each in 8 Julian years The calendar introduced by Julius Caesar, which assumes a year is exactly 365.25 days long., the new moons would fall on the same day of the month, and that in 16 years they would fall one day earlier in the week, so that in 112 years the moon would come back to the same day of the same calendar month. A statue of Hippolytus with the cycle engraved on it was discovered at Rome in 1551 A.D. After the first 8-year period, the error became increasingly great.

St. Cyprian (243 A.D.) composed a 112-year Easter table (241–352 A.D.) on the basis of a 56-year cycle, and Dionysius of Alexandria (248–266 A.D.) published a canon for an 8-year table in a Paschal letter A formal letter sent by a bishop to notify other clergy of the dates for upcoming religious observances. (as mentioned in original: Eusebius, Hist. Eccl. vii. 20 Eusebius’s Ecclesiastical History, Book 7, Chapter 20). The most important of the early cycles, however, is the 84-year cycle, which is said to have been originally used by the Jews; it exists in two forms. It is founded on a combination of the 76-year and the 8-year cycles, and has the advantage that not only the new moon but also Easter recurs on the same days at the conclusion of a cycle. The earliest form of this cycle that is actually found is one in which a leap of the moon occurs every 12 years except at the close of the cycle. In the other form, the leap of the moon occurs every 14 years. The relative age of these forms is still under discussion and depends on whether a lost document described in a later one is or is not the Augustan Calendar original: Laterculus Augustalis; a specific 5th-century list used for calculating the dates of Easter.. What we have is an 84-year table for 100 years beginning from 213 A.D., but doubtless calculated back to that year. The general opinion seems to be that the first form was the only one ever used at Rome, that it was probably at first used in Ireland, that the second form was a piece of Irish theorizing, and that it was finally adopted by them. The question is affected by another Easter controversy—that as to the limits of the age of the moon during which Easter may be celebrated.

It is popularly supposed that the Council of Nicaea, 325 A.D., fixed the date on which Easter was to be celebrated, and that the duty of...