Queen Auðr djúpauðga (deeply-wealthy) or djúpúðga (deeply-wise), passed through Orkney, in the ninth century, on her way to Iceland, with twenty freed Irish thralls. After this, Einarr, grandson of earl Torf-Einarr, went to Iceland from Orkney with two Vestmenn (Irishmen). _Írar_, Irish, occurs in place-names in Iceland, Orkney and Shetland, in each of which latter there is an _Ireland_. It will now be proved that there were only three possible pure-bred Norse earls of Orkney and Shetland, viz., the first three--Sigurðr hinn ríki, his son, GuÞormr, and his nephew, Hallaðr. The first earl of the main line was Torf-Einarr, who was half Norse and half thrall, his mother being probably of the pre-Norse dark race. His son, the next earl, married a Gael, and after this, through repeated Gaelic marriages, the succeeding earls in the Norse male line were never more than a cross between Norse and Gael, sometimes almost approaching pure-bred Gaels, if the rules of a modern breeding society are to be observed. The same holds good of earl St. Rögnvaldr, a Norwegian, who succeeded on the distaff side, his mother being of Gaelic extraction. The Gaelic conversion of the earls was completed on the succession of the Gaelic earls in 1139. The next step will be to show that the leading families, some of which were related to the earls, were also mainly of Gaelic descent, and in some cases probably in the male line. As the Gaels did not give up patronymics and begin to assume permanent surnames (usually those of their chiefs), until after 1350, those who settled in Orkney before that, and became Norse in language and customs, of course adopted the Norse, in place of the Gaelic, patronymic, _i.e._, _-son_ for _mac-_. This was done by the Gaelic earls in Orkney, in precisely the same way as had been done by the Irish settlers in Iceland. In reply to a query, Sir Herbert Maxwell writes: “You ask me to fix a date ‘when patronymics flourished and ceased in the Highlands?’ I think it would be impossible to do so. There were few, if any, fixed surnames in England or Lowland Scotland before the middle of the thirteenth century, other than territorial ones, derived from the feudal tenure of land. In the Highlands, the adoption of fixed names appears to have been indefinitely deferred. Such counties as Perth and Dumbarton, being nearest the frontier of civilisation, their people would find it convenient to conform to the habit of their neighbours. In more remote districts the shifting patronymic prevailed much longer, and when it was abandoned individuals frequently assumed the surname of their chief or the name of his clan, which accounts for the old patronymic ‘Macdonald’ being the third commonest surname in Scotland; Smith and Brown being first and second.” In the following description particular attention will be called to personal appearance, character, habits, superstitions, etc., as indications of descent. THE NORSE EARLS.