The 15th inst. the Prosperus, an American privateer, of 18 carriage guns, was brought in here by a sloop and schooner, both of which were fitted out at Kingston, and this was their first cruise. The Provincial vessel had been some time cruising about this island, and had several times sent her boats on shore in the night, and robbed the planters of their live stock, &c. She had 160 men on board, some of whom wear red jackets, and are called marines.