The capital of one of them is Tara, that of the other is Dinn Riogh on the Barrow. We learn from Keating and all other authorities and traditions that, in the period of Cú Chulainn and the Ulster hero tales, the river Boyne, in its lower course, separated Ulster from Leinster. Tara, on the south side of the Boyne, was in Leinster territory. Hence it is plain that Leinster and not Munster comprised two of the Five Great Fifths. People sometimes say to me and have said to me since these lectures began, "You are very ruthless in tearing away from us some of our most cherished traditions." Now, if I showed any contempt for tradition, this reproach would be altogether too mild. Tradition, if it is indeed tradition, is worthy of all reverence. It is not infallible. Tradition is a people's memory, and a people's memory, like yours or mine, has its limitations. We are all agreed that the Gaels are of Celtic origin and that their language is a Celtic language, but there is no tradition for it. From the earliest recorded traditions of Ireland and Britain down to the writing of the history of Scotland by Buchanan, not the faintest trace of such a tradition has been found. Nevertheless there are fields of historical inquiry in which tradition is the most faithful witness, and one such field is the internal polity of Ireland during the centuries that precede the written record. In that field, so far am I from despising tradition, that my main effort is to find tradition and establish its authority. We must get away from the notion that everything that is written by Keating or the Four Masters or in the Book of Invasions about that early time is tradition. The Scythian origin of the Gaels, the geographical details of their wanderings, the tower of Bregon, the landing at an unknown Inbhear Scéine--these things do not belong to tradition, they are the inventions of Latin scholars, suggested to them by ancient Latin writers. The evidence on which I rely with regard to the Five Fifths of ancient Ireland is unquestionably traditional. The evidence that I have quoted on the point does not stand alone. It is not singular and inconsistent. On the contrary, it will be found to fit in with the whole body of ancient tradition, and taken along with the other evidences, it will be found to give life and reality to the history of an obscure yet most interesting period.