22. A formula for any Moon or weekday
TRANSLATION
however, you use the number which is going to be dropped in January and February, but on the ¢rst of March, you start to compute with that [number] contained in the solar cycle.213
So if you wish to ¢nd out, for example, the weekday of the kalends of January, you say ''January 2'',214 add the concurrent days of the week which occur in the year for which you are calculating, for instance, 3: this makes 5. The kalends of January starts on the ¢fth weekday
[Thursday]. Again, in a year which has 6 concurrents, take the 5 regulars for the month of March, add the 6 concurrents, and they make 11. Take away 7,215 and 4 remain. The kalends of March is on the fourth weekday
[Wednesday].
22. A FORMULA FOR ANY MOON OR WEEKDAY
There is an old formula devised for ¢nding the Moon or the weekday not only for the kalends, but for any day between kalends. It is somewhat more di⁄cult to learn, but it was passed down to us by the authority of our elders, /351/ and so ought to be handed on conscientiously to our juniors. If you wish to know how old the Moon is on this or that day, count the days from the beginning of January up to the day you want, and when you know this, add in the age of the Moon on the kalends of January.216 Divide the total by 59, and if more than 30 remain, subtract
30.217 What is left over is the day of the Moon you are seeking. Again, if you wish to know what the weekday is on such and such a day, calculate the days from the beginning of January up to the day in question, and when you have found out what [the total] is, add the weekday on which the kalends of January fell.218 If it is a leap year, remember also to add
213 I.e. the ''o⁄cial'' concurrent for that year, as found in the Paschal table. The concurrent valid in January and February will be one less. The insertion of the extra day in February pushes the remaining dates of the year ahead by one weekday.
214 The solar regular for January is 2.
215 In other words, should the sum of the concurrents and regulars exceed the number of days in a week, i.e. 7, these must be deducted, and the remainder will be the weekday of the kalends.
216 Using the formula given in ch. 20.
217 The synodic lunar month is 29ˆ~˜ days, but as this is an awkward ¢gure to compute with, the formula uses 59, the number of days in two synodic lunar months. Since no lunar month can be longer than 30 days,this ¢gure must be deducted from the remainder if it exceeds 30.
218 This can be ascertained using the formula described in ch. 21.
THE RECKONING OF TIME
the leap-year day after it has passed. Divide the total by seven and the remainder will show you what day of the week it is, in every case.219
This formula only works without di⁄culty if you are accustomed to reciting by heart the number of each of the months by kalends, nones and ides:
January: 1 on the kalends, 5 on the nones, 13 on the ides; February: 32 on the kalends, 36 on the nones, 44 on the ides;
March: 60 on the kalends, 66 on the nones, 74 on the ides; April: 91 on the kalends, 95 on the nones, 103 on the ides;
May: 121 on the kalends, 127 on the nones, 135 on the ides; June: 152 on the kalends, 156 on the nones, 164 on the ides;
July: 182 on the kalends, 188 on the nones, 196 on the ides; August: 213 on the kalends, 217 on the nones, 225 on the ides;
September: 244 on the kalends, 248 on the nones, 256 on the ides; October:274onthekalends,280onthenones,288ontheides;/352/
November: 305 on the kalends, 309 on the nones, 317 on the ides; December:335onthekalends,339onthenones,347ontheides.220
So for example, if you wish to know what the age of the Moon is on the kalends of May in a year in which the Moon is nine days old on the kalends of January, say ''May: 121 on the kalends''. Subtract the [day of the] kalends, and 120 remains; add 9, and that makes 129. Divide by 59:
59 times 2 is 118. Subtract 118 and 11 remain. The Moon is 11 days old on the kalends of May. If you want to know how old the Moon is on the 15th kalends of June [May 18], say ''June: 152 on the kalends''.
Subtract the ¢fteen kalends of June and 137 remain. Add 9, which makes 146. Divide by 59: 59 times 2 is 118. Subtract 118 and 28 remain.
The Moon on the 15th kalends of June is 28 days old. If you want to know what the Moon is on the 7th ides of December [December 7], say
219 ''Again, if you wish to know . . . in every case.'' Dionysius Exiguus, Argumentum 10, ed. Krusch, Studien II, 77.
220 The source of this table is ps.-Anatolius 10 (323^324). It also appears in later computus anthologies in a number of variant forms. One version begins in March rather than January (e.g. PL 90.706D, or the ''Bobbio computus'' in PL 129.1279D^1282A), and this form came to be labelled as secundum Dionysium, on the assumption that Dionysius, the champion of Alexandrian reckoning, would have devised his table according to the Alexandrian custom of beginning the computistical year in March. Ironically, Bede's version was baptised secundum Victorium, the logic being that Victorius championed
Roman methods of computus against the Alexandrian, including beginning the year in January. Cf Jones, BOT 358.