42. The "leap of the Moon"
[III. ANOMALIES OF LUNAR RECKONING (CHS. 42^43)]
42. THE ''LEAP OF THE MOON'' 1
Concerning this ''leap [of the Moon]'', it seems to be true that it is produced when the place and time of the appearance of the new Moon comes more quickly than is ordinarily supposed. For how could it be that over [the course of] nineteen years it becomes necessary to subtract one from the usual number of lunar days, were it not that a certain acceleration of the lunar orbit gradually brings it into e¡ect over the whole period of the 19-year cycle? In the same way, but in the opposite sense, the course of the Sun is demonstrably a¡ected by retardation, so that one day is added to its course over the four years of its cycle.2
Although it is not easy to perceive the stages [ordo] of [the Moon's] acceleration, and if I may put it thus, of this ''advance'', its measure is by no means a mystery. For it is agreed that the diminution and removal of one day /408/, regardless of how this takes place, is assembled over nineteen years, augmented each year by one hour, one punctus, and 1
19 of one punctus. For the day has 24 hours, of which 5 remain when you distribute 19 [hours] over the same number of years of the 19-year cycle.
Multiply these by four (because there are four puncti in one hour) and that makes 20. Give one [punctus] to each year, and there is one left over. Divide this by 19, and you will see, as we said, that one adds one hour, one punctus and 1 19 of one punctus each year to make up the ''leap of the Moon'' [saltus lunae]. Therefore the appearance of the new Moon is not observed at one and the same point in time, or region in the heavens, but it always arrives somewhat sooner than in the previous month, whence it is that it springs over one day in the nineteenth year.3
Now various computists have thought that this ''leap of the Moon'' should be interposed at various points in the 19-year cycle cycle; that is, that a lunar month which in other years normally has thirty days should have twenty-nine.
1 For discussion of Bede's sources for this chapter, see Commentary.
2 Cf. ch. 38, n. 341.
3 Cf. Bede, On Times 12. On the implications of this gradual advance, see ch. 43.
THE RECKONING OF TIME
The natural way [ratio naturalis] to calculate this readily, is to assign the beginning and end of all augmentations and diminutions of this type, both of the Sun and of the Moon, /409/ to the equinoxes wherein their beginning and end were ¢rst created: that of the Sun at the spring, and that of the Moon at the place of the autumn equinox.4 Therefore
Anatolius, who rightly perceived that the beginning of the months and the starting-point and end-point of the whole cycle is the spring equinox,5 did not himself place this change of the Moon at the beginning or end of his 19-year cycle, but in its fourteenth year, which is the last one of the ogdoas,6 making [the epact] rise from 8 to 20 at the [spring] equinox. On the other hand, Victorius /410/ considered that this insertion should be made in the third year before the end of the ogdoas, changing the Moon
[i.e. the lunar epact] on the kalends of January from 4 to 16.7 But then the Egyptians, to whose judgement the catholic Church now gives its consent, ¢x the change in the ¢rst year of the 19-year cycle, making the annual lunar epact, whose locus is the 11th kalends of April [22
March],8 to jump from 18 to zero [in nullam]. Hence this same year, if it is not a leap year, is ¢nished /411/ in 353 days.
Dionysius seems to touch upon this in his letter, when he says: For instance from the ¢fteenth Moon of the Paschal feast in the preceding year until the fourteenth in the following year there are 354 days if it is a common year and 384 if it is embolismic. If there is one day more or less, it is a manifest mistake except in the ¢rst year of the oft-mentioned 19year cycle, which it is our concern to calculate from the fourteenth Moon of the last (that is, the nineteenth) year, up to the fourteenth Moon of this
¢rst year. Because of this, that last year, containing an epact (that is, a 4 Cf. ch. 6 above, and the Letter to Wicthed.
5 Anatolius 2, as reported by Ru¢nus in his ed. of Eusebius, HE 7.32.15. (723.15^
19); cf. Letter to Wicthed.
6 The ogdoas is the ¢rst eight years of the 19-year cycle. Since ps.-Anatolius' cycle begins six years before the 19-year cycle, the last year of the Alexandrian ogdoas corresponds to his year 14. This is, of course, the famous 14th-year saltus of the Celtic computus, though Bede was unaware of it. Note that in Krusch's edition of the table of ps.-Anatolius
(Studien I, 325) the saltus is placed in the 13th year. Bede's concordance of ps.-Anatolius' cycle with the 19-year cycle suggests that he thought he knew when ps.-Anatolius' table began, i.e. in the 13th year of the 19-year cycle. Bede's date for Anatolius in the chronicle in Reckoning of Time, ch. 66 is AM 4230, or AD 279, which happens to ¢t this criterion: cf.
Jones, BOT 377.
7 On the problems of Victorius' saltus, see Introduction, section 3.
8 Cf. ch. 50 below; cf. On Times 13.