Olaf left two sons, Halfdan and Ingiald. The former, on the tragical death of his father, was with his grandfather in Soleyr, but he was followed by the Swedes, and demanded from the old king. The latter, however, having no desire to surrender his grandson to the murderers of the father, resisted, and a battle ensued, in which he lost his life. _Halfdan_ was raised to the government of both states, and, with the aid of both, he subdued Raumarik, a country west of Soleyr. The three formed a compact and scarcely accessible kingdom, which, when governed by chiefs of enterprise and policy, could not fail to extend its limits to the west and north. Like his father, Halfdan studied how to promote the interest of his new state by a matrimonial alliance. North of Raumarik lies Hedmark, a small province subject to a king named Eystein. Its situation was so convenient in respect to Raumarik and Soleyr, that Halfdan eagerly sought and obtained the hand of Esa, daughter of Eystein. This union affording him a pretext for interfering in the affairs of that province, half of it, by force or policy, he soon added to his other states; and he afterwards subdued a considerable portion of Westfold, which he claimed in right of Hilda, princess of Westfold, the wife of his son. He died at Thotnia, one of his new acquisitions; but his body was carried to Westfold, and there interred. Over Vermeland was his brother Ingiald; and after the death of this chief the province was administered by jarls. [Sidenote: 730 to 840.]