The remaining years up to A.D. 577, the year of Aed’s death, would be just accounted for by Eochaid Tirmcharna’s reign of one year and Aed’s reign of twenty-five years (twenty-two years in lists 2 and 4; a confusion here too of II and u). But at this point, after Ailill, occurs the repetition of Duach Tenga Uma: he appears in Tigernach as well as in the lists (except 4); and seven years are assigned to him. Further, the catalogue of O’Duinn inserts Eogan Srem between this second Duach and Eochaid Tirmcharna, and gives him twenty-seven years. Eogan Srem also appears in the prose list in the _Book of Ballymote_, but before Ailill. If we take as fixed points the death of Ailill in 550 and that of Aed in 577, it is obvious that, even if Aed reigned only twenty-two years, there is no room for a second Duach and Eogan Srem in this period. On the other hand, if we take the sum total of all the regnal years as given in O’Duinn’s poem up to Aed’s death, and reckon back from A.D. 577, we find that we are taken back to the neighbourhood of the death of king Dathi. It will be best to give O’Duinn’s list:— Amolngaid reigned 20 years Ailill Molt ” 11 ” Duach, son of Brian ” 20 ” Eogan ” 37 ” Ailill ” 5 ” Eogan Srem ” 27 ” Duach, son of Fergus ” 7 ” Eochaid ” 1 ” Aed ” 25 ” --------- Total 153 ” Reckoning back 153 years from A.D. 577, we reach A.D. 424. The date of Dathi’s death was A.D. 428, but if we take into account the conditions of such a calculation, where incomplete years may be set down as full years, the divergence might be consistent with the conclusion that the list was constructed on the initial assumption that Amolngaid succeeded Dathi in 428—which implies that Dathi was king of Connaught (but see below). We can now see how the chronology was constructed in O’Duinn’s source. It will be simplest, for the purpose of criticism, to tabulate the dates (approximately) implied by that construction:— Amolngaid ceased to reign 444 Ailill I. ” 455 Duach I. ” 475 Eogan I. ” 512 Ailill II. ” 517 Eogan II. ” 544 Duach II. ” 551 Eochaid ” 552 Aed ” 577