We pass now to the third section of the supremacy argument. The district to which we have referred as Lothian was, unquestionably, largely inhabited by men of English race, and it formed part of the Northumbrian kingdom. Within the first quarter of the eleventh century it had passed under the dominion of the Celtic kings of Scotland. When and how this happened is a mystery. The tract _De Northynbrorum Comitibus_ which used to be attributed to Simeon of Durham, asserts that it was ceded by Edgar to Kenneth and that Kenneth did homage, and this story, elaborated by John of Wallingford, has been frequently given as the historical explanation. But Simeon of Durham in his "History"[32] asserts that Malcolm II, about 1016, wrested Lothian from the Earl of Northumbria, and there is internal evidence that the story of Edgar and Kenneth has been constructed out of the known facts of Malcolm's reign. It is, at all events, certain that the Scottish kings in no sense governed Lothian till after the battle of Carham in 1018, when Malcolm and the Strathclyde monarch Owen, defeated the Earl of Northumbria and added Lothian to his dominions. This conquest was confirmed by Canute in 1031, and, in connection with the confirmation, the Chronicle again speaks of a doubtful homage which the Scots king "not long held", and, again, the Chronicle, or one version of it, adds an impossible statement--this time about Macbeth, who had not yet appeared on the stage of history. The year 1018 is also marked by the succession of Malcolm's grandson, Duncan, to the throne of his kinsman, Owen of Strathclyde, and on Malcolm's death in 1034 the whole of Scotland was nominally united under Duncan I.[33] The consolidation of the kingdom was as yet in the future, but from the end of the reign of Malcolm II there was but one Kingdom of Scotland. From this united kingdom we must exclude the islands, which were largely inhabited by Norsemen. Both the Hebrides and the islands of Orkney and Shetland were outside the realm of Scotland. The names of Macbeth and "the gentle Duncan" suggest the great drama which the genius of Shakespeare constructed from the magic tale of Hector Boece; but our path does not lie by the moor near Forres, nor past Birnam Wood or Dunsinane. Nor does the historian of the relations between England and Scotland have anything to tell about the English expedition to restore Malcolm. All such tales emanate from Florence of Worcester, and we know only that Siward of Northumbria made a fruitless invasion of Scotland, and that Macbeth reigned for three years afterwards.