Harald appears to have governed the Western Isles by Norwegian Jarls, but his hold upon them was slight, and apparently ceased with his death, and they became merely the haunt of stray Vikings until the middle of the following century, when their possession was contested between the Danes of Dublin and Limerick, who had got a firm hold of the Island of Man, and the Norwegian Jarls of Orkney. One of the principal leaders of the Danes of Dublin, Anlaf Cuaran, had become connected with the Scottish King Constantine, and appears to have exercised some authority over the islands; but at the great battle of Brunanburgh, in which he and his father-in-law Constantine were engaged, we find the death of Geleachan, King of the Isles, recorded, as well as that of Cellach, a prince or Mormaer of Scotland,[23] names which undoubtedly show a Gaelic form. Soon after we find Maccus or Magnus, son of Aralt, a leader of the Danes of Limerick, called King of Many Islands, and a struggle took place between his brother and successor Godfred, son of Aralt, called King of Innsigall, and Sigurd, Norwegian Jarl of Orkney, for the possession of the western Isles, when the former was slain by the Gaelic people of Dalriada or Argyll, and the Isles were acquired by the Orkney Jarl, who soon after added to his territories the western and northern districts of Scotland. His territories are said in the Sagas to have consisted, besides Orkney and the Sudreys, of Katanes, Sudrland, Myrhaevi or Moray, and Dali or the glens of Argyll, on the west, and we find a Jarl Gilli apparently ruling the Isles, whose principal seat was the island of Coll, and whose name has a Gaelic form.[24] He pays scatt or tribute to Sigurd, and obtained his sister in marriage. Under Sigurd’s son Thorfinn, the most powerful of the Orkney Jarls, after the defeat and death of King Duncan in 1040, the whole of the northern districts of Scotland, as far as the river Tay, fell under the power of the Norwegians, who likewise possessed the Sudreys or Western Isles and the Gaelic district of Galloway, while Macbeth, the Mormaer of Moray, ruled as king over the dominions left to him, and the other districts south of the Firths of Forth and Clyde adhered to the family of Duncan; but on the death of Thorfinn, we are told that the additional territories acquired by him fell back to their native lords. Malcolm, the son and heir of Duncan, succeeded in defeating and killing the usurper Macbeth, and his successor Lulach, also of the family of the Mormaers of Moray, and establishing himself as king over the same territories which had been possessed by his father. The Western Isles pass for a time under the power of an Irish king of Leinster, which shows how powerful the Gaelic element in their populations still was, and on his death fell under the authority of the Crown. At this time the Isle of Man was in the possession of the Danish kings of Dublin, but a