In the year 1779, when the navy of England was less triumphant than during the revolutionary wars, several engagements took place in the British seas, and the inhabitants of the coast were frequently thrown into a state of alarm by Paul Jones, the intrepid Anglo American Buccaneer. This man had formerly been in the service of the Earl of Selkirk, whence he was expelled with disgrace; and, having repaired to America, he volunteered to make a descent on the British coast. Being at first entrusted with the command of a privateer, he landed on the coast of Scotland, and in resentment plundered the mansion of his old master; he also burnt several vessels at Whitehaven, and performed a number of other daring exploits. These services insured his promotion, and procured him the command of a small squadron, consisting of the Bon Homme Richard, and the Alliance, each of 40 guns; the Pallas, of 32 guns; and the Vengeance armed brig. - With this force he made many valuable captures, insulted the coast of Ireland, and even threatened the city of Edinburgh. - On Monday the 20th of September, 1779, an express arrived at Bridlington, from the Bailiffs of Scarborough, with intelligence that an enemy was cruising off the coast. - The same night the hostile squadron was descried off Flamborough Head, and it was soon discovered that Paul Jones was the commander. In the night of Tuesday, a large fleet of British coasting vessels sailed into the bay, and the harbour became so completely crowded, that a great number could only find security in being chained to each other on the outside of the piers. Two companies of the Northumberland militia, then quartered in the town, were called to arms by beat of drum, after midnight, and the inhabitants, armed with such weapons as could be most readily procured, proceeded to muster at the Quay, while a number of the more opulent were making preparations for sending their families into the interior. Business was now completely at a stand, and the attention of all was directed to the expected invasion. On Thursday a valuable fleet of British merchantmen, from the Baltic, under the convoy of the Serapis, Captain Pearson, of forty-four guns; and the Countess of Scarborough, Captain Piercy, of twenty-two guns, hove in sight, and were chased by the enemy. The first care of Captain Pearson was to place himself between the enemy and his convoy, by which manoeuvre he enabled the whole, or the merchantmen to escape in safety into the port of Scarborough. - Night had now come on, but the moon shone with unusual brightness. About half past seven o'clock the thunder of the cannon announced that the engagement had commenced, and the inhabitants of the coast, on hastening to the cliffs, were presented with the sublime spectacle of a naval engagement by moonlight. The battle raged with unabated fury for two hours, when at length Captain Pearson, who was engaged by the two largest of the enemy's frigates was compelled to surrender. Captain Piercy made also a long and gallant defence against a superior force, but he was in the end obliged to strike to the Pallas. The enemy purchased his victory at a prodigious price, not less than 300 men being killed or wounded in the Bon Homme Richard alone, which vessel received so much injury that she sank the next day, with many of the wounded on board.