If then the first Duach died _c._ 425, it seems probable that he was succeeded by Amolngaid. There seems to be no clear evidence that Dathi was king of Connaught while he was king of Ireland. It is stated in the _Genealogy of the Hy Fiachrach_ (p. 90) that he ruled Connaught and Ireland. It is quite conceivable that he was king of Connaught before 405, and that in that year he secured the succession to the throne of Ireland by agreeing to transfer the kingship of Connaught to his cousin Duach. The hypothesis that Amolngaid immediately followed Duach _c._ 425 is supported by two considerations. 1. Provisionally assuming, for the purpose of the argument, that Amolngaid might have succeeded Dathi, I pointed out that the sum total of regnal years in O’Duinn’s list, from Amolngaid’s accession to Aed’s death, would take us back to the close neighbourhood of Dathi’s death in 428. But there is actually a difference of four years (577 - 153 = 424). If Amolngaid succeeded Duach in 424/5, we may say that the agreement of this date with the total of years in O’Duinn’s reckoning is precise. 2. On this hypothesis we are able to solve the main problem—the interval between Amolngaid and Ailill Molt. For if Amolngaid succeeded in 424/5, and reigned 20 years, his death would fall in 444/5. There would consequently be an interval of 26 or 27 years between his death and the accession of Ailill Molt in 471. Now if Duach mac Briain had a son, we might expect to find him elected to the throne. The prose list in the Book of Ballymote designates Eogan Srem as the son of Duach Galach (that is, Duach mac Briain); and the regnal years assigned to Eogan Srem in O’Duinn’s poem are precisely the number required to fill up the interval between Amolngaid and Ailill Molt. The inference therefore would be that Amolngaid was followed by Eogan, Duach’s son, _c._ 444/5. In order to show the force of the argument, I may say, at the risk of tautology, that it consists of three converging considerations. (_a_) Eogan Srem is introduced, in the lists in the Book of Ballymote, among the Kings of Connaught in the sixth century in defiance of chronology. His appearance in these lists has to be explained, and is most naturally explained by supposing that he was at one time King of Connaught, though not at the time implied in the lists. If the conclusion is right that Duach mac Briain died in 425, then his son Eogan Srem must be moved back into the fifth century. (_b_) The 27 regnal years assigned to Eogan Srem exactly occupy the vacant interval between Amolngaid and Ailill Molt. (_c_) The succession of Eogan Srem, son of Amolngaid’s predecessor, is just what we might expect; it is exactly parallel to the successions in the fifth century to the throne of Ireland. Thus: Niall, Dathi, Loigaire son of Niall; Dathi, Loigaire, Ailill son of Dathi; Loigaire, Ailill, Lugaid son of Loigaire.