Some of the petty dynasties thus created were themselves in later times subjected to the same process and reduced to a lower degree. Thus when the O'Conor family, which was itself a branch of the sept of Brión above-mentioned, acquired exclusive succession to the kingdom of Connacht, one of its branches, bearing the distinctive name of O'Conchubhair Ruadh, obtained the lordship of Cairbre in north-eastern Connacht, over the heads of the ancient lords descended from Cairbre son of Niall. In like manner, Ailill's land, Tirerrill, after having been ruled for centuries by his descendants, passed under the lordship of the families of MacDonnchadha and MacDiarmada, descendants of his brother Brión, whose line held the kingship of all Connacht. The sept of Ailill, reduced in degree, gradually passes into obscurity. About the thirteenth century, even the genealogists cease to be interested in them; and in the seventeenth century, the last genealogist of the old school, Dubhaltach Mac Fir-Bhisigh, says that those who then remained of Ailill's race are no longer reckoned among the nobles of the territory. Let me repeat that, with the help of the genealogies, it is possible to trace this process at work in various parts of Ireland from the fifth century until the abolition of Irish law in the sixteenth century. I shall have to recur to these facts when I come to deal with the so-called "clan-system" or "tribal system," convenient terms with which some modern writers contrive to fill up the vacuum of their knowledge in regard to the general political condition of ancient and medieval Ireland. Breifne, under the rule of Brión's sept, was regarded as permanently annexed to Connacht. In its early extent Breifne comprised about the northern half of Co. Leitrim and the western half of Co. Cavan; these territories having been annexed from the ancient Ulster. In later times, when the O'Ruairc and O'Raghallaigh chiefs extended their power, Breifne comprised the whole of the present counties of Leitrim and Cavan. The territories of the sons of Niall were separated by Breifne and Oriel into two groups, a north-western group and a Meath group. The north-western group of Niall's descendants are called the Northern Ui Néill, the Meath group the Southern Ui Néill. One frequently meets with the error of supposing Ui Néill to mean the Ó'Néills--I find it in a paper of Zimmer's published after his death. It is true that Ui Néill, as a matter of grammar, is the plural of Ó'Néill, but it is not the plural of the surname Ó'Néill in Irish usage. The sept-names with Ui prefixed belong to an earlier age than surnames like O'Neill. The surname O'Neill belongs to the descendants of Niall Glúndubh, king of Ireland, who was reigning a thousand years ago. The sept-name Ui Néill includes all the descendants in the male line of Niall of the Nine Hostages who reigned 500 years earlier.