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, 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.
Read more about this topic: Rognvald Eysteinsson