CASTLE-BAY, a borough and market-town, capital of the county of Mayo in Ireland, is a well-inhabited place, and carries on a brisk trade: it has a barrack for a troop of horse; and there is here a charter-school capable of receiving fifty children, and endowed with two acres of land, rent-free, by the Right Honourable Lord Lucan, who has also granted a lease of twenty acres more at a pepper-corn yearly.