Previously Unpublished Works, Fascicles VI-VII

As Christianity grew, it broke all ties with Judaism, and the rule for determining Easter came to depend on the fourteenth day of the moon following a fixed spring equinox The date in spring when day and night are approximately equal in length; traditionally used as the marker for the start of the ecclesiastical year.. This introduced a new source of disagreement. The date of the equinox was slowly shifting over time; while one part of the world might keep the traditional date (March 25), another would adopt a date that was astronomically accurate (such as March 21). If the fourteenth day of the moon fell between these two dates, Easter would be celebrated in some countries in March, while others kept it in April. To avoid these kinds of errors, it early on became necessary to make arrangements for calculating the date of Easter in advance and communicating it to Christians all over the world. This seems to have been done in the Churches of Alexandria and of Rome through Paschal letters Formal letters sent by the bishops of major Christian centers to notify other bishops of the correct date for Easter. sent to the various bishops. The calculations were made using cycles—tables showing the number of years that would pass before the "Paschal" new moon would occur again on the same day of the week and the same day of the calendar month. As the Roman Empire collapsed and the custom of sending Paschal letters faded, the question of which cycle to adopt became very important.

An ancient astronomical cycle of great accuracy was the nineteen-year cycle original: decennovennalis of Euctemon and Meton, created in 432 B.C. They calculated the solar year as 365¼ days (making 19 years equal to 6,939.75 days), while 235 average lunations The time from one new moon to the next, which is the basis of a lunar month. would be 6,939.70146 days. Since they treated these as exactly 6,940 days, the error compared to 19 solar years was 6 hours, and compared to 235 lunar months was 7½ hours. To reduce this error, Calippus introduced a cycle of 76 years (consisting of 4 Metonic cycles), which, along with other adjustments, removed one day. This made the error only 6 hours when compared with 940 lunar months and eliminated the error entirely when compared with 76 solar years of 365¼ days each. It is unnecessary to describe the system of intercalary months Extra months inserted into a calendar to keep the lunar phases in line with the solar seasons. that this system required, because by the time Christianity was firmly established, the Julian system The solar calendar introduced by Julius Caesar, which eventually became the standard for the Western world. with its purely solar months was the only one we need to consider.

The calendar, however, could not ignore the position of the moon. Not only was the date of the new moon during the season of the spring equinox necessary to set the date of Easter, but it was also necessary in the ordinary affairs of life to know the "age" of the moon on any given date. For convenience, the length of a lunar month was taken as 29½ days (which is a little too long), which in practice resulted in months alternating between 29 and 30 days. The difference between 235 of these lunar months and 19 solar years was reconciled by adding one day to seven of the 29-day months, making them 30-day months—these being