This Morning arrived off the Harbour the Lexington Privateer, taken by Captain John Bazely, off the Lizard, in Lat: 27. There being but little Wind, Capt. Bazely, in the Alert, rowed up with the Privateer, who, thinking him an easy Prey, fired a Broadside into him, and ordered him to strike. Bazely answered he would, but was not near enough. He then received his second Broadside, and being then near to each other, a very hot Engagement continued between three and four Hours; at length the Privateer struck to the superior Valour of the Dover Boys. The Privateer is gone into the Downs to put her Wounded into the Hospital at Deal, several of whom stand in need of Amputation of Arms or Legs; Tomorrow she comes into this Harbour to be repaired before she can proceed to the River. The Lieutenant of the Privateer lost one of his Hands. By the Copy of a Letter found in the Captain's Chest, the Lexington appears to be one of the three which did the Mischief in the Irish Seas; he directs his Agent in France to dispose of the 14 Prizes for the joint Benefit of the three Privateers. The Midshipman who now commands the Prize is a Nephew of General Schuyler, and entered with Bazely about six Weeks ago. The Alert stood for Plymouth to repair, having sustained some Damage in the Engagement. The Lexington had been but three Days out of St. Maloes, and was chiefly manned with Scotch and Irish.