On the Earldom of Caithness:
Around the close of the first millennium the territory in the northernmost part of Scotland over which the Earls of Caithness later held sway was frequently divided in two, each part being in the possession of different Norse Jarls or Earls of Orkney, though each Jarl seems to have been a member of the same extended family. The Earldom (as it came to be called) of Orkney and that of Caithness differed to a certain extent in that the former was held of the Kings of Norway while the latter was held of the Kings of Scots. This meant that different customs were observed in each territory, specifically in the case of the Earldoms that the Orkney one was held jointly while the Caithness one was only sometimes so held. The Earldom of Caithness could be (and frequently was) disposed of by the Kings of Scots to different persons in the lifetime of the original grantee or grantee's heir, either jointly or solely, which makes it pointless, however tempting, to assign any ordinal numbering to the Earldom at this time. [Burke's Peerage]
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EARLDOM of ORKNEY [NOR] - subject to King of Norway until after 1379
Sigurd II Digri, as Jarl of Orkney and Caithness, In the winter of 988-89 he went from Hrossey (Pomona or Mainland of Orkney) to Caithness in order to fight Earl Hundi and Earl Melsnati, who had slain his brother-in-law Havard, his Steward for Caithness, at Freswick, and he defeated them at Dungalspeak. Melsnati was killed and Hundi fled and was pursued "until they learned that Malcolm, the Scottish King, was collecting an army at Duncansby." Before 995 Sigurd defeated "Findlaech, the Earl of the Scots," at the second battle of Skidmoor in Caithness, and in return for their support gave back to his Orkneymen the udal rights which they had surrendered to his great-grandfather, Jarl Turf-Einar, in the summer of (?) 895. At this time, in addition to Orkney, Shetland and Caithness, he had "this dominion in Scotland, Ross and Moray, Sutherland and the Dales," and "laid a tax on the inhabited lands of Man." He frequently engaged in piracy among the Sudreys and on the coasts of Scotland and Ireland. In 995 under great pressure from Olaf Tryggvesson, who was on his way to become King of Norway (995-1000), Sigurd and the Orkneymen accepted baptism. He made an alliance with King Olaf Tryggvesson, in virtue of which the payment of tribute to Norway on the udal lands in Orkney was discontinued; and after his son Hundi-Hiodveís death, while a hostage in Norway, he paid no allegiance to the King. He made alliance with Sihtric Silkbeard, King of Dublin (who came to Hrossey before Yule 1013), against Brian, High King of Ireland (1002-1014), who had married Sihtricís mother, Gormflaeth (da. of Morugh MacFinn, King of Leinster (?) 965-972). By this alliance, which was instigated by Gormflaeth, who was "bitter against King Brian," King Sihtric agreed that if they killed King Brian, Sigurd should marry Gormflaeth and be High King of Ireland. Sigurd landed at Dublin on Palm Wednesday (21 Apr. 1014] and was killed at the battle of Clontarf on Good Friday [23 Apr. 1014]. He had three sons by an unnamed mother or mothers: Somerled, Brusi and Einar Rangmund (Wrymouth). By Donada, dau. of Malcolm MacKenneth, King of Scots, whom he m. probably in or after 1005, he had a 4th son, Thorfinn, who was b. circa 1009. Sigurd, who had left his three elder sons to rule Orkney, when he started for Dublin, was suc. in Orkney by all three, who divided the Earldom among themselves; but Caithness and Sutherland were seized by King Malcolm MacKenneth for (their half-brother) his grandson Thorfinn whom he created Earl of Caithness in 1014, and he "set men to govern the dominion with him." [Complete Peerage, X:Appendix A:8-9]