The Connacht kings continued, however, to extend their conquests and their power. A grandson of Muiredach Tirech was king of Tara at the beginning of the fifth century (_c._ A.D. 400), Niall of the Nine Hostages. His brother, Brión (or Brian) took possession of a south-western section of Ulster, comprising a large part of the counties of Leitrim and Cavan, afterwards called Brian's Land--Tír Briúin. Three sons of Niall took possession of what remained of western Ulster, now comprised in the county of Donegal. Their names were Eoghan, Conall, and 'Enda, and the territories occupied by them were called Eoghan's Land, Conall's Land, and 'Enda's land. Another son of Niall, named Coirbre, obtained a piece of Leinster, now the barony of Carbury in Co. Kildare. The Connacht dynasty and its branches now ruled over the northern half of Ireland, with the exception of the eastern seaboard region from Ardee to the Giant's Causeway. It ruled in Tara, and its chief kings were recognised also as Monarchs of Ireland. The Connacht power, after the time of Niall, was regarded as comprising three chief divisions--the kingdom of Connacht, the Airgialla, and the territory of the descendants of Niall (Uí Néill). All Leinster was laid under tribute to them, and a note in the Book of Leinster says that this Leinster tribute was divided equally among the three sections. This subdivision of the Connacht power, in my opinion, was what gave rise to the ancient term _Teora Connachta_, "the Three Connachts"--a term which seems to have caused some trouble for its explanation to writers of a later age. An unpublished tract in the Book of Lecan, also found in the introductory part of the Book of Genealogies by MacFir Bhisigh, tells us that during this period, the succession to the Monarchy was regulated in this way: On the death of the Ardri, the king of Connacht took his place as king of Tara. A new king of the same family was elected in Connacht, and this process went on during several generations. Niall was king of Connacht first, of Tara afterwards. And so, in like manner, the high kingship was filled from Connacht until the death of Ailill Molt in A.D. 483 or thereabouts. The two facts, then, that explain the transformation of the Pentarchy at the beginning of the Christian Era into the Monarchy and seven principal kingdoms of St. Patrick's time, are these: In the northern half of Ireland, the gradual conquest achieved by the Connacht dynasty; in southern Ireland, the rise of a new power, that of the Eoghanacht kings, centred in Cashel. Along with the direct control of northern Ireland, the Connacht dynasty obtained predominance over the country in general, and this predominance found its natural expression in the high kingship.