The Duke of Cumberland Packet arrived a few days ago, from Falmouth, with government despatches for Lord Dunmore. It is said she left England the 23d of January, and bring advice, that Lord Cornwallis sailed about the same time, with a number of transports, under convoy of twelve frigates, the place of their destination uncertain. The packet was at South Carolina, but found that Lord William Campbell had left the province, and joined Governor Martin at Cape Fear. Some Gentlemen from below say, that soon after the arrival 'of this vessel they published a paper which was called a declaration of war against the colonies, and received it with loud acclamations.