_Old Settlers on the River Saint John. New-Brunswick erected into a Government, and settled by the Loyalists in 1783-4. Difficulties of the first Settlers. List of successive Governors and Presidents._ The Province of New-Brunswick formerly formed a part of Nova-Scotia, which was the first European settlement on the Continent of North America.--The first grant of land in it was given by King JAMES the FIRST to Sir WILLIAM ALEXANDER, in 1621--from whom it had the name of Nova-Scotia or New Scotland. It was at that time regarded by the English as a part of CABOT'S discovery of Terra-Nova. The first settlers, however, were emigrants from France, who as early as the year 1604 came to the Country with DE MONT, a French adventurer, and gave it the name of Acadia. This country frequently changed masters; passing from the French to the English, and back again, till it was finally ceded in full sovereignty to the British at the peace of Utrecht in 1713. In 1760, a number of persons from the County of Essex, in Massachusetts, obtained a grant of a Township, twelve miles square, on the River Saint John, from the British Government; and after several delays in exploring and surveying, they commenced a settlement at Maugerville. During the American War of 1775, they were joined by a number of other families from New England: the district adjoining Maugerville was settled, and the whole called by the general name of Sunbury, where the Courts of Justice were held till 1783: when the peace with America left the Loyalists who had followed the British standard, to seek an asylum in some part of the British dominions. Prior to this period a number of families from Yorkshire in England, and others from Massachusetts, had settled in and about Cumberland, where many of their descendants still remain.--These people, actuated by different attachments, lived during the war in a state of hostility with each other;--one part adhering to the British, and the other to the Americans.