This day, about two o'clock, the Right Hon. the Countess of Dunmore, with the rest of the Governor's family, who have for some time past been on board the Fowey man of war, arrived at the palace in this city, to the great joy of the inhabitants, and, we make no doubt, of the whole country, who have the most unfeigned regard for her Ladyship, and wish her long to live amongst us.