20. What the age of the Moon is on any given first day of the month
THE RECKONING OF TIME
which the sequence of letters is laid out, and having found the year196 from the inscription at the top, ¢nd the letter pertaining to that day which you seek. Then, looking backwards and forwards,197 you will discover what region, month and sign the Moon is in from its position.
Reader, we will give you something to serve as an example. Suppose you are looking for the location of the Moon on the kalends of April in the sixth year of the 19-year cycle. Open the [calendar-] codex and look up that particular date. You will ¢nd written in front of it the letter E. Turn to the Table of Regulars. Look at the sixth year and ¢nd the letter E by looking through its alphabet. Now run your eye along to the margins.
You will discover that the end of Gemini /345/ is noted on one side and the beginning of the month of June on the other.198 And reader, whether you are learned or unschooled, you will rejoice to have tracked down what you were looking for, right before your eyes. Moreover, during that whole year, on whatever days you ¢nd the letter E inscribed, you will know that the Moon, whether waxing or waning, is occupying that part of the sky. You cannot discover by this formula whether the Moon is waning /346/ or waxing, in conjunction with or in opposition to the Sun; but if you want to know this, refer to the formula of the Egyptians, handed down by ancient observance.199
20. WHAT THE AGE OF THE MOON IS ON ANY GIVEN
FIRST DAY OF THE MONTH
In the ¢rst year of the 19-year cycle, in which the epact201 is zero, the Moon on the kalends of January is 9 days old; on the ¢rst of February,
10; on the ¢rst of March, 9; on the ¢rst of April, 10; on the ¢rst of May, 11; on the ¢rst of June, 12; on the ¢rst of July, 13; on the ¢rst of August,
14; on the ¢rst of September, 16; on the ¢rst of October, 16; on the ¢rst of November, 18; on the ¢rst of December, 18. Take these numbers as the ''regulars'' of each month. By adding the annual epacts to them, you
196 That is, the year of the 19-year cycle. Bede gives a formula for translating annus Domini into year of the 19-year cycle in ch. 47. Alternately, one could simply look it up in a Paschal table (Appendix 2).
197 I.e. to the left and to the right.
198 It is still, of course, April 1! What Bede means is that the Moon is in the zodiac sign in which the Sun will be found in June.
199 Cf. ch. 24.
201 I.e. the age of the Moon on March 22; see ch. 50 below.
TRANSLATION
200 For explanation of the theory behind the pagina regularis, see Commentary. Since Bede himself did not explain why some zodiac signs have two, and some three spaces alloted to them, there are a number of variations, many seemingly arbitrary, in the way in which this table appears in the manuscripts.The version presented by Jones in his critical edition is, as he admits, an arbitrary reconstruction (BOT 354); but it is also erroneous, in that it does not position the ''long signs'' at three month intervals. The version presented here is based on the reconstruction by John Armstrong III, ''The Old Welsh Computus Fragment
Virgo k e m g b o i d l September Scorpio m g b o i d l f A n November Sagittarius k e m g b o i d l f A December Aquarius m g b o i d l f A n h c February Libra l f A n h c k e m October Capricorn l f A n h c k e m g b January Leo o i d l f A n h c k August Pisces n h c k e m g b o i d March
Aries A n h c k e m g b April Taurus b o i d l f A n h c May Gemini c k e m g b o i d June Cancer d l f A n h c k e July Cancer m g b o i d l f A n h Sagittarius n h c k e m g b o Gemini l f A n h c k e m g Aries o i d l f A n h c k e Taurus k e m g b o i d l f Cancer n h c k e m g b o i Leo e m g b o i d l f A Virgo f A n h c k e m g b Scorpio h c k e m g b o i d Scorpio i d l f A n h c k e Libra g b o i d l f A n h c Pisces m g b o i d l f A Aquarius k e m g b o i d Capricorn o i d l f A n h c Pisces l f A n h c k e and Bede's Pagina regularis [Part 1]'', Proceedings of the Harvard Celtic Colloquium 2 (1982):219.
PAGINA REGULARIS200
THE RECKONING OF TIME
will discover without error what the age of the Moon is on any given kalends.
If you wish to know the age of the Moon for the kalends of January in the second year of the decennovennal cycle, take the regular [of January]
^ 9 ^ and add the epact ^ 11 ^202 and that makes 20: it is the twentieth Moon. If you want to know what Moon it is on the kalends of June in the third year, take the regular 12, add the epact for that year ^ 22 ^ and that makes 34. Subtract 30,203 and 4 remain; on the kalends in question, the Moon is four days old.
Should anyone object that the order of either this or the preceding formula204 is shaky at any point [alicubi ordinem uacillare], then let him teach a more accurate and handy formula for investigating questions of this kind, and we will gladly and gratefully accept it. /347/ We have given out the formula which we explained earlier on to several people to be copied, and have also recommended that it be pre¢xed to this present work.205 Indeed, let the present formula that we set forth for ¢nding the Moon on the kalends su⁄ce for learning and teaching, at least at this point. For when the age of the Moon on the kalends is known, it will
202 The epact in the ¢rst year of the 19-year cycle, as Bede observes in the ¢rst sentence of this chapter, is zero: that means that the Moon on 22 March in year 1 of the cycle is a new Moon, in conjunction with the Sun. Because the lunar year is 354 days long, or 11 days shorter than the solar year, the Moon on 22 March in year 2 of the 19-year cycle will be 11 days old. Thus the epact of year 2 is 11.
203 No Moon can be more than 30 days old, so when the total exceeds this ¢gure, 30 must be deducted.
204 uel huius uel praecedentis argumenti. Bede usually employs argumentum in the conventional way to mean ''formula'' (cf. Jones, BOT 357): his term for ''table'' is pagina.
Nonetheless from what follows, it seems plain that a table is what Bede is referring to, one which he has included in the front matter of the manuscript of The Reckoning of Time.
205 The Laon-Metz glossator understood the argumentum referred to here as the pagina regularis from the preceding chapter (p. 346, ad lineam 18). Jones (BOT 355^356) however, claims it must have been a table which showed the ages of the Moon on the kalends of each month, i.e. a table corresponding to the formula explained in this chapter; his argument is supported by Armstrong, ''The Old Welsh Computus Fragment'', 193. But Bede explicitly refers to the ''preceding formula'' which he has ''already explained'' (praecedens quod commemorauimus argumentum), so he must be referring to something discussed before ch. 20. Curiously, Jones also claims that Bede is refusing to place this argumentum in front of the book (BOT 355), though the sense of the Latin suggests exactly the opposite: etnonnullisadtranscribendumiamdedimusetinprincipiishuiusnostriopusculi prae¢gendum esse censemus. (347.19^21). Since in ch.19, he expressly states that he has prefaced his book withthe pagina regularis, I think that the reading of the Laon-Metz glossator is the correct one.
TRANSLATION
easily be seen what its age is on the other days of any month by reciting on one's ¢ngers that month and its concurrents.206 However, there are three years in the 19-year cycle when this formula cannot preserve the stability of its course, namely the eighth, the eleventh and the nineteenth. The cause of this discrepancy is the insertion, distributed throughout the year in various ways, of the embolismic [month].207 Now in the eighth year, the Moon on the kalends of May, according to the logic of this formula, is calculated as being in its twenty-eighth day, but because of the embolism inserted into the month of March, it is actually in its twenty-seventh. Again, according to the formula the Moon ought to be in its thirtieth day on the kalends of July, but because of the addition of the day which the super£uity of the embolism introduced, it is the twenty-ninth. Again in the eleventh year, because the Moon of the embolismic [month] is kindled on the day before the nones of December [4
December], it makes the Moon on the kalends of March to be in its twenty-eighth day, while the logic of the formula teaches that the Moon then is the twenty-ninth. Again in the nineteenth year, because the Moon of the embolismic [month] begins on the 3rd nones of March [5
March], it dictates that the Moon on the kalends of May be calculated as in its twenty-eighth day, when according to the calculation of the formula /348/ it is tallied as the twenty-ninth.
Moreover, in this [nineteenth] year the computation of the ''leap of the Moon'', of which we shall say more later on,208 vitiates the reliability of this formula. But if you start [to use] this formula at the month of September, after the manner of the Egyptians, whose year begins at that point, it is necessary that the Moon of July in that year have twenty-nine days and never more,209 one day having been removed because of the ''leap of the Moon''. In consequence, the Moon of the kalends of August, calculated as the second according to the rule of the formula, will be assigned as the third. But if, following what we taught above, you prefer to begin the formula in January, according to the same sequence the seventh day of the Moon will fall on the kalends of December, which 206 Bede rather confusingly uses the term concurrentes here to mean ''successive days of the month''; cf. Jones, BOT 357. It has a more common computistical meaning, which is explained in the next chapter.
207 Why the insertion of the embolismic month disrupts lunar reckoning is described in the Introduction, section 3.
208 See ch. 42.
209 The lunation of July is normally a ''full'' one of 30 days.