subjected to that of England. William acknowledged this by signing the Treaty of Falaise, and was then allowed to return to Scotland. In 1175 he swore fealty to Henry II at York Castle. The humiliation of the Treaty of Falaise triggered a revolt in Galloway which lasted until 1186, and prompted the construction of a castle at Dumfries. In 1179, meanwhile, William and his brother David personally led a force northwards into Easter Ross, establishing two further castles, north of the Beauly and Cromarty Firths: one on the Black Isle at Ederdour; and the other at Dunkeath, near the mouth of the Cromarty Firth opposite Cromarty. The aim was to discourage the Norse earls of Orkney from expanding beyond Caithness. A further rising in 1181 involved Donald Meic Uilleim, descendant of King Duncan II. Donald briefly took over Ross; not until his death in 1187 was William able to reclaim Donald's stronghold of Inverness. Further royal expeditions were required in 1197 and 1202 to fully neutralise the Orcadian threat. William also quarrelled with Pope Alexander III, a quarrel which arose out of a double choice for the vacant bishopric of St Andrews. The king put forward his chaplain, Hugh, while the pope supported the archdeacon, John Scotus, who had been canonically elected. A hostile interchange followed; then after the death of Alexander in 1181 his successor, Lucius III, consented to a compromise by which Hugh got the bishopric and John became bishop of Dunkeld. In 1188 William secured a papal bull which declared that the Church of Scotland was directly subject only to Rome, thus rejecting the claims to supremacy put forward by the English archbishop. The Treaty of Falaise remained in force for the next fifteen years. Then the English king Richard the Lionheart, needing money to take part in the Third Crusade, agreed to terminate it in return for 10,000 silver marks (£), on 5 December 1189. William then was able to address the turbulent chiefs in the outlying parts of his kingdom. His authority was recognized in Galloway which, hitherto, had been practically independent; he put an end to a formidable insurrection in Moray and Inverness; and a series of campaigns brought the far north, Caithness and Sutherland, under the power of the crown. William attempted to purchase Northumbria from Richard in 1194, as he had a strong claim over it. However, his offer of 15,000 marks