Rognvald "The Wise" Eysteinsson (son of Eystein Ivarsson) is the founder of the Earldom of Orkney in the Norse Sagas. Three quite different accounts of the creation of the Norse earldom on Orkney and Shetland exist. The best known is that found in the Heimskringla, but other older traditions are found in the Historia Norvegiae and the Fragmentary Annals of Ireland.
The saga accounts are the best known, and the latest, of the three surviving traditions concerning Rognvald and the foundation of the Earldom of Orkney. Recorded in the 13th century, their views are informed by Norwegian politics of the day. Once, historians could write that no-one denied the reality of Harald Fairhair's expeditions to the west recounted in Heimskringla, but this is no longer the case. The Norwegian contest with the Kings of Scots over the Hebrides and the Isle of Man in the middle 13th century underlies the sagas.
In the Heimskringla, Rognvald is Earl of Møre. He accompanies Harald Fairhair on his great expeditions to the west, to Ireland and to Scotland. Here, Rognvald's son Ivarr is killed. In compensation King Harald grants Rognvald Orkney and Shetland. Rognvald himself returns to Norway, giving the northern isles to his brother Sigurd Eysteinsson.
The Heimskringla recounts other tales of Rognvald. It tells how he causes Harald Finehair to be given his byname Fairhair by cutting and dressing his hair, which had been uncut for ten years on account of Harald's vow never to cut it until he was ruler of all Norway, and it makes him the father of Ganger-Hrólf, identified by saga writers with the Rollo (Hrólfr), ancestor of the Dukes of Normandy, who was said to have been established as Count of Rouen by King Charles the Simple in 931.
Historia Norvegiae 
The Historia Norvegiae's account of Rognvald and the foundation of the Orkney earldom is the next oldest, probably dating from the 12th century. This account contains much curious detail on Orkney, including the earliest account of the Picts as small people who hid in the daytime, but it has little to say about Rognvald.
In the days of Harald Fairhair, king of Norway, certain pirates, of the family of the most vigorous prince Ronald [Rognvald], set out with a great fleet, and crossed the Solundic sea..., and subdued the islands to themselves. And being there provided with safe winter seats, they went in summer-time working tyranny upon the English, and the Scots, and sometimes also upon the Irish, so that they took under their rule, from England, Northumbria; from Scotland, Caithness; from Ireland, Dublin, and the other sea-side towns.
This account does not associate Rognvald with the earldom, but instead attributes it to his anonymous kinfolk.
Fragmentary Annals of Ireland 
|...for it was not long before this that there had been every war and every trouble in Norway, and this was the source of that war in Norway: two younger sons of Albdan, king of Norway, drove out the eldest son, i.e. Ragnall son of Albdan, for fear that he would seize the kingship of Norway after their father. So Ragnall came with his three sons to the Orkney Islands. Ragnall stayed there then, with his youngest son.|
|Fragmentary Annals of Ireland, FA 330. Edited and translated by Joan N. Radnor.|
The oldest account of the Rognvald and the earldom of Orkney is that found in the Fragmentary Annals of Ireland. The annals survive only in incomplete copies made by Dubhaltach Mac Fhirbhisigh in the 17th century, but the original annals are believed to date from the lifetime of Donnchad mac Gilla Pátraic (died 1039). The annals are known to have had an influence on later writings in Iceland.
The annals make Rognvald the son of "Halfdan, King of Lochlann." This is generally understood to mean Halfdan the Black, which would make the Rognvald of the annals the brother of Harald Finehair. However, the sagas claim that Rognvald's grandfather was named Halfdan.
These events are placed after an account of the devastation of Fortriu, dated to around 866, and the fall of York, reliably dated to late 867. However, such an early date makes it difficult to reconcile the saga claims that Harald Fairhair was involved in Rognvald's conquest of the northern isles.
Harald Finehair's victory in the Battle of Hafrsfjord, which gave him dominion over parts of Norway, is traditionally dated to 872, but was probably later, perhaps as late as 900. What little is known of Scottish events in the period from the Chronicle of the Kings of Alba would correspond equally well with Harald's attacks on Scotland in the reign of Domnall mac Causantín (ruled 889–900). However, this would not correspond with the sequence in the earliest account of the origins of the Orkney earldom, which places this a generation earlier.
Orkney inheritance 
Rognvald having given his earldom to Sigurd, according to the Orkneyinga Saga, the latter died in a curious fashion after a battle with Máel Brigte of Moray. Sigurd's son Gurthorm ruled for a single winter after this and died childless.
In addition to Hrólfr/Rollo and Turf-Einar, Rognvald had a third son called Hallad who then inherited the title. However, unable to constrain Danish raids on Orkney, he gave up the earldom and returned to Norway, which "everyone thought was a huge joke." The predations of the Danish pirates led to Rognvald flying into a rage and summoning his sons Thorir and Hrolluag. He predicted that Thorir's path would keep him in Norway and that Hrolluag was destined seek his fortune in Iceland. Turf-Einar, the youngest, then came forward and offered to go to the islands. Rognvald said: "Considering the kind of mother you have, slave-born on each side of her family, you are not likely to make much of a ruler. But I agree, the sooner you leave and the later you return the happier I'll be." His father's misgivings notwithstanding, Torf-Einarr succeeded in defeating the Danes and founded a dynasty which retained control of the islands for centuries after his death.
- Crawford, pp. 52–53.
- Anderson, pp. 332–334; Saga of Harald Fairhair, c. 22.
- Saga of Harald Fairhair, cc. 4 & 23.
- Saga of Harald Fairhair, c. 24.
- Saga of Harald Fairhair, cc. 29–30.
- Anderson, pp. 330–331.
- Crawford, pp. 53–54.
- Anderson, p. 296; Annals of Ulster, s.a. 865.
- Crawford, p. 55–56.
- Anderson, pp. 395–396.
- Thomson (2008) p. 28.
- Pálsson and Edwards (1981) "A poisoned tooth". pp. 27-28.
- Thomson (2008) p. 30 quoting chapter 5 of the Orkneyinga Saga.
- Pálsson and Edwards (1981) "Forecasts". pp. 28-29.
- Thomson (2008) p. 29.
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- Radner, Joan N. "Writing history: Early Irish historiography and the significance of form", Celtica, volume 23, pp. 312–325. (etext (pdf))
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- Thomson, William P. L. (2008) The New History of Orkney, Edinburgh, Birlinn. ISBN 978-1-84158-696-0