Easter Principles and a Fifth-Century Lunar Cycle Used in the British Isles

Jones C. W. , Bedae Opera de temporibus (Cambridge, Mass., 1943). Jones offers the most authoritative survey of Bede's computistical works.

Sherley-Price L. , Bede: Ecclesiastical history of the English People (London, 1990). For luna 14–20 or luna 14 references see pp. 104, 109, 138, 146, 149, 170, 190, 197 and 313, and for 84-year cycle references see pp. 104 and 320.

Bede , Historia ecclesiastica, iii. 25; Sherley-Price , op. cit., 186–92.

Walsh M. and Cróinín D. Ó , “Cummian's letter ‘De controversa Paschali’ and the ‘De ratione conputandi’” (Toronto, 1988), 85.

Humphreys C. J. and Waddington W. G. , “Dating the Crucifixion”, Nature, cccvi (1983), 743–6. C. Ruggles , “The moon and the Crucifixion”, ibid., cccxlv (1990), 669–70, p. 670.

Krusch B. , Studien zur christlich-mittelalterlichen Chronologie, i: Der 84-jährige Ostercyclus und seine Quellen (Leipzig, 1880); idem, “Die Einfuhrung des griechischen Paschalritus im Abendlande”, Neues Archiv der Gesellschaft für ältere deutsche Geschichtskunde, ix (1884), 101–69. MacCarthy B. , Introduction, Annals of Ulster, iv (Rolls Series; Dublin, 1901). Schwartz E. , Christliche und jüdische Ostertafeln (Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Phil-Hist. Klasse, Neue Folge, Band 8, no. 6; Berlin, 1905), 17–128. Schmid J. , Die Osterfestberechnung auf den britischen Inseln vom Anfang des vierten bis zum Ende des achten Jahrhunderts (Regensburg 1904). O'Connell D. J. , “Easter cycles in the early Irish Church”, Journal of the Royal Society of Antiquaries of Ireland, lxvi (1936), 67–106. O'Connell remarks that it was a pity that Schwartz did not review Mac Carthy's work, but a close comparison of Schwartz and Mac Carthy's analysis of the latercus of the Munich Computus shows so many correspondences, particularly in their editing of the MS, that I believe they must have collaborated about this matter at least. Mac Carthy's computistic arguments are presented in the same sequence and are always a reduction of Schwartz's. This would imply that, although he did not publish until eight years later, Schwartz provided the source for Mac Carthy's analysis, except of course that he did not go so far as to derive a reconstructed latercus. This vitiates the independence of their dating of the latercus.

For details of this, see below, ref. 35.

See for example Cross F. L. and Livingstone E. A. (eds), The Oxford dictionary of the Christian Church (Oxford, 1983), s. v. “Celtic Church”, p. 260.

Ideler L. , Handbuch der mathematischen und technischen Chronologie (2 vols, Berlin, 1825–26). Ginzel F. K. , Handbuch der mathematischen und technischen Chronologie: Die Zeitrechnungswesen der Völker (3 vols, Leipzig, 1906–14). Samuel A. E. , Greek and Roman chronology: Calendars and years in Classical Antiquity (Munich, 1972), 1–20.

Harrison K. , “Luni-solar cycles: Their accuracy and some types of usage”, in Saints, scholars and heroes, ed. by King M. and Stevens W. (Collegeville, Minnesota, 1979), 65–78, p. 66, gives 29.5306 days as the estimated lunar synodic value for 500 a.d.

See Samuel , op. cit. (ref. 9), 140.

Bede , De temporum ratione, xx and xlv.

Carthy Mac , op. cit. (ref. 6), pp. lxv ff.; Jones , op. cit. (ref. 1), 11.

Carthy Mac , op. cit. (ref. 6), p. lxviii.

McCarthy D. and Cróinín D. Ó , “The lost Irish 84-year Easter table rediscovered”, Peritia (Cork), nos 6–7 (1987–88), 227–42, p. 228.

McCarthy and Cróinín Ó , op. cit. (ref. 15).

McArdle J. , “Computer generation of Easter cycles”, Final year student project report, Computer Science Dept, Trinity College, Dublin, 1988.

McCarthy and Cróinín Ó , op. cit. (ref. 15).

Bayerische Staatsbibliothek, München, Clm. 14456, f. 28r, “Compotus sancti Augustini sancti Hiernonimi sancti Ysidori sancti Dyonisii sancti Quirilli greciae et ceterorum”. With the dearth of information that existed regarding the principles of the latercus it seems remarkable that Krusch, Mac Carthy and O'Connell were all able to pass over without mention this item, which includes also a tabulation of the kalends moons for a latercus year which confirms the structure of the lunation table; see Schwartz , op. cit. (ref. 6), 100.

Ibid.

Ibid. : “so ist es ausgeschlossen dass etwa der münchener Computist sie in den ‘vetus latercus’ hineininterpretirt haben sollte: Sie muss in ihm selbst ebenso drin gestanden haben wie sie im Buch des Ps. Anatolius mit umständlicher Breite auseinandergesetz wird”.

O'Leary P. , Irish numerals and how to use them ( Dublin , c. 1920), 1. I am grateful to Dáibhí Ó Cróinín for sending me this item for my examination and for confirming my translation of it; it contains the only occurrence known to him of the use of the word epacht in Irish.

Ibid.: “Cómhrimh síos ón Márta mbán, Go dtí an mí n-a mbeidh tú ann, Cuir aon fé n-a gceann, Lá an mhí, agus an t-epacht. Aon nídh fé bhun nó os cionn trí dheich, Sin agat aois na rae”.

McCluskey S. , “The mid-quarter days and the historical survival of British folk astronomy”, Archaeoastronomy (supplement to Journal for the history of astronomy), no. 13 (1989), S1–19, p. S15.

Op. cit. (ref. 19), f. 28r; Jennifer Moreton kindly provided a translation of this passage.

It is perhaps worth noting that the effect of inserting a saltus into the lunar calendar only shows up in the Padua table in the 1 January epact of the following year. In this respect it resembles the effect of the bissextile upon the ferial of the following 1 January.

Mommsen T. , Chronica minora (Monumenta Germaniae Historica, Auctores Antiquissimi, ix; Berlin, 1892), 679: “tum deinde ii qui cyclum annorum octoginta et quattuor ediderunt, duodecim peractis annis lunam unam … adiciendum legitimo cursui esse praecipunt. Item sunt qui hanc eandem quinto decimo demum incipiente anno magis annumerari definiunt.” Cited by O'Connell , op. cit. (ref. 6), 91.

Op. cit. (ref. 19), f. 42v, lines 7–12.

Bede , De temporum ratione, xx.

This program, which is written in Fortran, is available upon request to the author (Dept of Computer Science, Trinity College, Dublin 2, Ireland).

Wallis F. , Translation of Bede's De ratione temporum, private communication 1991.

The ferial of 1 January increments by 1 following a non-bissextile year because 365 divided by 7 leaves a remainder of 1; following bissextile years it increments by 2 since 366 divided by 7 leaves a remainder of 2.

See McCarthy and Cróinín Ó , op. cit. (ref. 15), 229 where these amendments are discussed in greater detail.

This program, which is also written in Fortran, is available upon request to the author.

All the authorities from Liber Anatolius, S. Columbanus and Colman to Bede agree that these were the limits of the Insular Easter moon; given this, it is remarkable that both Mac Carthy and O'Connell were persuaded to accept the range 14 to 21 by the Acts of the Council of Caesarea and the Tractate of S. Athanasius. They likewise incorrectly imposed the Roman later limit of 21 April, which error Jones (op. cit. (ref. 1), 84, n. 2, and 87, n. 2) has also identified, and which has the consequence that it is impossible always to find a Sunday with luna 14 to 20 in the 28 days between 25 March to 21 April. Both authors mention this problem in passing and it was probably this that persuaded them to accept luna 21. Krusch in his reconstruction (op. cit. (ref. 6), 17), on the other hand, accepted the strict lunar limits, but he extended the termini from 21 March to 23 April in order to overcome the problem. It is hard to understand how he persuaded himself to accept 21 March in the face of the fulminations in Liber Anatolius on this detail. It seems clear that these authors, working from sparse MS evidence, have effectively conflated at least two distinct Paschal traditions.

Carthy Mac , op. cit. (ref. 6), p. lxxvi, and O'Connell , op. cit. (ref. 6), 92.

Article on “Lent”, New Catholic encylopedia (New York, 1967), 634–5, p. 635, and Thurston H. , Lent and Holy Week (London, 1904), 15 and 21.

Schwartz , op. cit. (ref. 6), 103.

Ibid. , 100: “Da die Verteilung der Lunationen aus den Ostervollmonden und den Epakten des 1. Januar nicht abgeleitet werden kann, so ist es ausgeschlossen dass etwa der münchner Computist sie in den ‘vetus latercus’ hineininterpretirt haben sollte: Sie muss in ihm selbst ebenso drin gestanden haben wie sie im Buch des ps. Anatolius mit umständlicher Breite auseinandergesetzt wird”.

Table 3, cyclic nos 27, 35, 70, 81.

The Initium dates of cyclic nos 70, 75 and 81 show evidence of scribal interference; the Easter date of no. 75 has been retarded from xvii k.m (April is just a copying error — it is impossible to have this latercus Easter before 25 March) to xvi k.m, probably due to the ambiguity in the positioning of the embolismic month as discussed in the text. Consequently the Initium has been moved back from i no.mr to viii id.mr and this change has been roughly propagated to the Initium dates of nos 70 and 81.

McCarthy and Cróinín Ó , op. cit. (ref. 15), 241, n. 26.

McCarthy and Cróinín Ó , op. cit. (ref. 15).

Ibid., 232–4. Note that even though the dating analysis there is based on an epact value adjusted to luna 19 on the kalends of January 438, the dating result is unaffected. A forthcoming article in preparation will treat these details.

Sherley-Price , op. cit. (ref. 2), 322.

Carthy Mac , op. cit. (ref. 6), p. lxx.

Schwartz , op. cit. (ref. 6), 102.