38. The calculation of the leap-year day
TRANSLATION
says amongst other things: Lest it seem incredible that a year should be calculated in a di¡erent way then, they add that among many writers of history it is found that the Egyptians had a year of four months, the Acarnians of six months, and the Lavinians of 13 months. Pliny, although he records that it is related in documents that someone lived to be 152, and another person ten years longer, and that others had a life of 200 years and others of 300, or that some reached 500, others 600 and a few 800, judges that all these arise from ignorance of chronology [inscitia temporum]. 'Some indeed', he says, 'start one year in the summer, and another in the winter, others at the four seasons, so that their years are three months long, like the Arcadians.' He adds, moreover, that the Egyptians, whose short years, as we said above, were four months long, ¢nished a year at the end of the moon. 'Therefore amongst them', he says, 'it is claimed that men live a thousand years.'337 /399/
38. THE CALCULATION OF THE LEAP-YEAR DAY338
I have no wish to contrive anything new on the subject of the leap-year day, but rather to incorporate into this little work what I once said in a letter responding to a friend's inquiry.339 There, after the appropriate introduction, I added this: I said, that just as that anticipated place and time of the appearance of [the new Moon] which they call the ''leap of the Moon'' is produced over a period of 19 years,340 so in the opposite way the leap-year day is produced by nothing other than a retardation of the Sun's course.341 Some people are so clever at computation that they understand without any di⁄culty how many fractions of the growing leap-year day are relentlessly added on each year, or month, or even week or day. Nonetheless, they would not be able to say how this same fraction increases, or what is its cause, or how the increase is calcu337 Augustine, DCD 15.12 (468.48^50, 469.36^51). The passage from Pliny is from HN 7.48.155 (2.608^610). This same quotation appears in the Letter to Plegwin 11.
338 This chapter is an expanded version of On Times 10, and possibly inspired by the anonymous text on leap year in the ''Sirmond Manuscript'', MS Bodleian Library,
Bodley 309, fols. 74r^76r (Jones, BOT 371; see Introduction, section 5). Analogous treatments of the leap year are common in computus anthologies, e.g. the ''Bobbio computus'', chs. 40^44 (PL 129.1295^1296).
339 Bede is referring to his Letter to Helmwald (Appendix 3.2).
340 See below, ch. 42.
341 See Commentary on ch. 42.
THE RECKONING OF TIME
lated, or what troublesome error is engendered if the leap-year day is not intercalated in its sequence in the necessary way.342 For the leap-year day is made up from the calculation of quarter[-days] [quadrantes] over four years. It is customary to call a quarter of something ^ for example money, time or space ^ a quadrans,343 and therefore the fourth part of a day, which with its night is completed in 24 hours, that is, 6 hours, is usually called a quadrans. /400/ The reason why this quarter[-day] is collected over four years into a whole day and intercalated into its place, is that the Sun is held to complete its annual circuit of heaven (that is, the 12 conspicuous signs of the zodiacal circle) not in 365 days, but in 6 hours more. Hence it happens that if, for example, the Sun now enters the equinoctial part of the sky344 when it rises in the morning, it will return to that point next year at noon, in the third year at evening, in the fourth at midnight, and in the ¢fth at daybreak again, that is, with the course of a whole day completed. We should therefore bear in mind that the extra day should be inserted whenever it is necessary, and that it is to be added to the total sum of the fourth year.345 The Egyptians are accustomed to solemnly intercalate it at the end of their year, that is, on the 4th kalends of September [29 August], but the Romans do it on the 6th kalends of March [24 February], whence they call it bissextus.346 For should any computist neglect to make [this intercalation], and think that all years ought to have only 365 days, he will subsequently discover that a great shortfall occurs in the course of the year; after a certain number of years have come and gone, the erring computist will be aghast to encounter spring time in the summer months, winter in the spring months, autumn in the winter months, and summer in the autumn months.
Should anyone perchance not know what we have truthfully and succinctly stated concerning the zodiac and the circuit of the 342 ''Some people are so clever . . .'': Jones argues (BOT 371) that Bede is referring to some particular text here, perhaps the one contained in the Irish-inspired ''Bobbio computus'' 87 (PL 129.1315), which works out the leap-year increment down to the level of the day!
343 See above, ch.4.
344 I.e. crosses the equator at the spring equinox.
345 ''Hence it happens . . .'': cf. Bede, Letter to Wicthed 3.
346 I.e. ''twice six'', because the 6th kalends of March is doubled in leap years, and the second day is designated bis sextus kal. mar. Cf. Isidore, DNR 6.7 (197.50^52).