By the death of his only daughter, who had been married to the king of Norway, and of his only son in the same year, Alexander the Third found that unless he had a male heir by a second marriage the succession to the throne would devolve upon a little grand-daughter, the Princess of Norway, then only two years old, and on her the succession was settled in a Parliament held at Scone on the 5th February 1283-4, failing such male issue. In the instrument by which the succession was so settled the magnates of Scotland bound themselves to receive Margaret, daughter of Eric, king of Norway, and of Margaret, daughter of King Alexander, as their lady and heir of the kingdom of Scotia; and to acknowledge her and her heirs as their liege lady, and the true heir of their sovereign in the whole kingdom, and in the island of Man, and all the other islands pertaining to the kingdom of Scotia, as well as in Tynedale and Penrith, and other dependencies of the kingdom.[1] Such were the enlarged limits to which the name of Scotia, once confined to the districts between the Firth of Forth and the river Spey, had now extended; and the dependencies of the kingdom, which had then embraced large semi-independent provinces on the south and west of these boundaries, were now reduced to the recently-acquired Western Isles, and to the small districts of Tynedale and Penrith lying beyond her southern frontier. If this process of consolidation, however, may be said to have been completed in the reign of Alexander the Third, it can only be held to have properly commenced with that of David the First. Prior to his accession, although the rule of the Scottish monarchs had extended itself by degrees over the districts south of the Forth and Clyde, and then west of the Drumalban range and the river Spey, yet the name of Scotia was still confined to the eastern districts between these limits. These districts formed the real nucleus and heart of the kingdom, and were more directly associated with her monarchs as kings of the Scots. [Sidenote: Southern frontier of Scotland.] The extension of their power over the southern districts commenced about a century after the establishment of the Scottish dynasty on the Pictish throne, when, in the year 946, the districts forming the kingdom of Cumbria were ceded by Edward the elder to Malcolm king of the Scots. This kingdom extended, at that time, from the river Clyde to the river Derwent in Cumberland, and to the cross at Stanmore on the borders of Westmoreland and Yorkshire, which separated it from the Northumbrian territories. It embraced the western districts of Scotland from the Clyde to the Solway, the present county of Cumberland, with the exception of that part of it which lies on the south of the river Derwent and formed the barony of Copeland, and the whole of Westmoreland exclusive of the barony of Kendal, which, with Copeland and the western districts as far as the borders of Wales, belonged to the Northumbrian kingdom.