Last Thursday arrived here, in about 18 days from St. Lucia, the brig Ludlow-Castle, Capt. Darling who informs that, a little before he sailed, there was a warm engagement in the West-Indies, between an American privateer, name unknown; and the British sloop of war, named Hawke, a well-known bird of prey; in which the Hawke was so much damaged, that she was obliged to make the best use of all her wings, to escape the American bird of justice; which we must confess, has not had that agility of motion necessary for the detection and ample punishment of the enemies to this country: ー Otherwise many a rascal who fled hither, to prevent being hanged in his own country, and some natives among us, would have had much longer necks before this day.