Tuesday a tender belonging to the Antelope, Mr. Willet, commander, arrived at Port Royal; she brought in here a man whom she took up at sea, off the north side of the island, a few days since, who gives the following account of himself: His name, he says, is Thomas Cobham; that he was gunner of an American privateer, called the Lively, of 14 carriage guns, which foundered in a gale of wind, and all on board, except himself, perished. This poor wretch had floated on a piece of one of the masts four days and four nights, with two more, both of whom were washed off. When Mr. Willet descried the piece of the mast, and not knowing what to make of it, he resolved not to delay his time to look after it, until, by the help of his glass, he thought he discerned something alive; and he then ordered the boat out to see what it was. The poor man had lost his senses; so that when they came up to him he struck at them. It was sometime before he was brought to his right mind, and then he related the particulars of the above misfortune. Two evenings before the tender fell in with him, he was within hearing of a Dutch ship, but could ~ot by his shouts make known his distress.