[420] See B. Krusch, Der 84jährige Ostercyclus und seine Quellen, 1880.

[421] Columbanus, Epp. ed. Gundlach, Ep. 4, p. 162.

[422] Ib. Ep. 1 (to Gregory I.), p. 157; Catal. Sanct. Hib., unum Pascha, quarta decima luna post aequinoctium vernale (H. and S., Councils, ii. 292, 293).

[423] Dr. MacCarthy’s explanation (Introd. to Annals of Ulster, iv. p. lxxix) of an entry in the Chronicle of Marius Aventicensis (ad ann. A.D. 560), as implying a survival of the old 84 cycle in Gaul, does not seem tenable (see A. Anscombe, Z. f. Celtische Philologie, iv. p. 333).

[424] I have omitted all reference to the abstruse technique of the computations, and the question as to the difference between the two cycles of 84 (differing in the number of the saltus), for which see MacCarthy, op. cit. pp. lxv. sqq.; Krusch, op. cit.

[425] For dating, see MacCarthy, op. cit. cxl. cxli.

[426] Migne, Patrol. 87, 969.

[427] Krusch, 302 sqq. For dating, see MacCarthy, op. cit. cxvii., where the proof of fabrication will be found.

[428] So MacCarthy, cxxxvii., note 2.

[429] Dr. MacCarthy shows that Cummian was uncritical (cxl.), but I cannot go quite so far as he. He accepts, as genuine tradition, the statement that Patrick brought a cycle with him (rightly observing that the addition of et fecit cannot be pressed), but holds that it was identical with the Celtic cycle of later times. It is with much diffidence that I venture to differ from him on this point; but I owe it to his investigations that I have been able to reach a definite conclusion.