,
the middle, and the north of Pictland through the fathers of Duncan,
Macbeth, and Thorfinn respectively; and we may note that from Thorfinn
are descended all subsequent Jarls and Earls of Orkney and Shetland
and Caithness of the so-called Norse line.

Duncan I, Macbeth, and Thorfinn Sigurd's son were thus first cousins,
and, in spite of the fiction of Holinshed, Boece, and William
Shakespeare, they were all about the same age, being born within seven
years of each other; and none of them lived to old age.

By the victory of Carham in 1018 Malcolm II secured for ever the line
of the Tweed as Scotland's southern frontier; and this success in the
south, one of the most important events in Scottish history, left
him free to extend his kingdom and sovereignty towards the north, his
object being to unite into one realm the whole mainland at least
of Scotland. To accomplish this, he would have to bring under the
supremacy of the Scottish crown in addition to the Picts of Atholl,
whom the Scots had absorbed, the Gallgaels of Argyll, the Picts of
Moray and of Ross within and beyond the Grampians, and those of
the province of Cat, with the Norsemen there as well. He could thus
ultimately hope to oust Somarled, Brusi and Einar, Jarl Sigurd's sons
by his first wife, and their overlords, the Norse kings, from Orkney
and Shetland, and to add those islands to his dominions. Meantime,
Somarled, Brusi and Einar took no share in Cat. Thorfinn had Cat, all
for himself, as a fief of the Scottish king.

Although the history of the time of Thorfinn Sigurdson, the first
Scottish Earl of Caithness and Sutherland,[4] would have been of
great interest to inhabitants of those counties, the _Orkneyinga Saga_
contains but little information about his doings in them, because he
bent all his efforts towards extending his dominion over the islands
which formed his father Sigurd's jarldom, his policy, in his youth at
least, being directed to this object by his grandfather, Malcolm
II. Indeed during the life of that king, Thorfinn appears to have
established himself at Duncansby in Caithness, on the shore of the
Pentland Firth, and to have occupied himself in endeavouring to induce
his three surviving half-brothers, Somarled, Brusi, and Einar, to part
with as large a share as possible of Orkney and Shetland, and cede
it to himself. In this he had much assistance from King Malcolm.
Thorfinn, whose mother probably died in his infancy if we are to
cr