subdued by King William, 87;

earl Ragnvald's half conferred on Harald Ungi, 87;

earl Harold slew earl Harald Ungi, 87;

Caithness given to Ragnvald Gudrodson, 88;

who defeated earl Harold at Dalharrold, 89;

Ragnvald's stewards left in charge, their fate, 89;

the lawman, 89;

Ragnvald bought earldom, 89, 90;

extent of earl Harold's earldom, 90;

Scottish policy in the north, 91;