The Paschal lunar limits in this text are those ascribed to Theophilus and the Council of Caesarea, in the spurious _Acta_ composed by an Irish computist[427] (possibly towards the beginning of the sixth century). The probability, however, seems to be that the text of Cummian has suffered corruption in the numbers, and the question is whether (1) xiv. is an error for xv.,[428] and the Alexandrine cycle is implied, or (2) xiv. and xxi. are errors for xvi. and xxii. respectively, and the _supputatio Romana_ (with 84 cycle) is intended. Both these alternatives are possible, for, though we should expect Patrick to have accepted the Gallic usage, he _might_ have been prepossessed in favour of the Alexandrine system at Lérins, where there was probably Eastern influence. In any case, we can hardly feel prepared to reject the statement of Cummian[429] that Patrick “brought” and sought to introduce a different Paschal computation from that which prevailed among the Celts in Cummian’s own time. We may fairly cite in confirmation the express mention of his studies of the calendar (at Auxerre) in the Hymn of Fíacc (l. 11, as interpreted by Thurneysen, _Rev. celt._ vi. 233; see above, p. 264). 18. _The Organisation of the Episcopate_[430] Todd showed in great detail that bishops without sees were common in the Irish Church in the sixth, seventh, and eighth centuries (_St. Patrick_, pp. 1 _sqq._). Strictly speaking, he did not prove it for the fifth century; nor did he show that there were no bishops with sees, even in the times to which his instances and illustrations apply. Loofs has maintained that both in Patrick’s time and in later times there were “_episcopi paruchiales_” in Ireland. I hardly think that the positive arguments which he brings forward are very convincing; the inscription of the letter of Pope John IV. (Bede, _H.E._ 2, 19) proves nothing. But the passage which he cites from the letter of Columbanus (A.D. 603 or 604) to a synod of Gallic bishops and clergy may be quoted in this connexion. The Irish monk writes: Inde sanctus Hieronymus haec sciens iussit episcopos imitari apostolos, monachos uero docuit sequi patres perfectos. Alia enim sunt et alia clericorum et monachorum documenta, ea et longe ab inuicem separata.[431] Had the Abbot of Luxueil who writes with such approbation of the separate functions and ideals of sequestered monks, and active clergy (including bishops), whether regular or secular—had he been accustomed in his native country to a system in which there were no bishops who were not members of monasteries? This bears on the question whether the Irish Church in the sixth century was as exclusively monastic as it is generally represented.