Sacrobosco and Calendar ReformIn the Compotus (c. 1235), the longest of all his works, Sacrobosco dealt systematically with calendars and the reckoning of time. He discussed the day, its division into hours, and subdivisions, being perhaps the first western author to use sexagesimal fractions (minutes and seconds) in a work on time-keeping. He defined the week, the month (solar, lunar, and calendric), the year (solar and lunar) and the astronomical Great Year. And in sections on the solar cycle and the civil calendar, and the lunar cycle and the ecclesiastical calendar, he treated such essentials as leap years, dominical letters, and the determination of the movable Christian feasts.
Sacrobosco's Compotus stood in a tradition of calendrical treatises dating from the early middle ages, the most authoritative of which was the De temporum ratione (AD 725) of the Venerable Bede. It has been suggested, however, that the work was too sophisticated to have been intended as a university textbook. In common with other authors of his time, Sacrobosco recognised that the Julian calendar year exceeded the tropical or solar year, leading to the backwards drift of the equinoxes and solstices through the civil calendar, and that the Metonic cycle which equated 235 lunar months with 19 calendar years was also inexact, and had produced a similar slippage of the lunar calendar. He proposed solutions for each of these problems. Ten days were to be omitted from the civil calendar to return the date of the vernal equinox to March 25th and, as suggested by his parameters, one leap-day in every 288 years was to be left out of the calendar in order to prevent further drift of the equinoxes. The
Golden Numbers indicating the first appearance of the new moon each year were to be adjusted to take account of the accumulated three or four day discrepancy in the lunar cycle (although Sacrobosco anticipated ecclesiastical resistance to this change). And the 19-year cycle was to be replaced by a succession of four such cycles, producing a 76-year lunar calendar which eliminated the disparity with the Julian reckoning. But Sacrobosco seems not to have addressed the consequences of enacting each of these reforms simultaneously.
Sacrobosco's dependence upon other writers on the calendar, in particular on both Robert Grosseteste (c. 1170-1253) and the unknown author of a more elementary Compotus, is a matter of some dispute. The 76-year lunar cycle was adopted in several calendars of the thirteenth century, but not necessarily as a consequence of his treatise. Other reforms were not enacted until the construction of the Gregorian calendar in the sixteenth century. It is worth noting, however, that Sacrobosco's Compotus was one of the medieval calendrical treatises popular at the time of the Gregorian Reform: it went through at least 35 editions between 1531 and 1673, many of them at Wittenberg, where it was promoted by the reformer Philipp Melanchthon.