The second morning after leaving Monterey, we were off Point Conception. It was a bright, sunny day, and the wind, though strong, was fair; and everything was in striking contrast with our experience in the same place two months before, when we were drifting off from a northwester under a fore and main spencer. ``Sail ho!'' cried a man who was rigging out a top-gallant studding-sail boom.-- ``Where away?''-- ``Weather beam, sir!'' and in a few minutes a full-rigged brig was seen standing out from under Point Conception. The studding-sail halyards were let go, and the yards boom-ended, the after yards braced aback, and we waited her coming down. She rounded to, backed her main topsail, and showed her decks full of men, four guns on a side, hammock nettings, and everything man-of-war fashion, except that there was no boatswain's whistle, and no uniforms on the quarter-deck. A short, square-built man, in a rough gray jacket, with a speaking-trumpet in hand, stood in the weather hammock nettings. ``Ship ahoy!''-- ``Hallo!''-- ``What ship is that, pray?''-- ``Alert.''-- ``Where are you from, pray?'' &c., &c. She proved to be the brig Convoy, from the Sandwich Islands, engaged in otter-hunting among the islands which lie along the coast. Her armament was because of her being a contrabandista. The otter are very numerous among these islands, and, being of great value, the government require a heavy sum for a license to hunt them, and lay a high duty upon every one shot or carried out of the country. This vessel had no license, and paid no duty, besides being engaged in smuggling goods on board other vessels trading on the coast, and belonging to the same owners in Oahu. Our captain told him to look out for the Mexicans, but he said that they had not an armed vessel of his size in the whole Pacific. This was without doubt the same vessel that showed herself off Santa Barbara a few months before. These vessels frequently remain on the coast for years, without making port, except at the islands for wood and water, and an occasional visit to Oahu for a new outfit. Sunday, January 10th. Arrived at Santa Barbara, and on the following Wednesday slipped our cable and went to sea, on account of a southeaster. Returned to our anchorage the next day. We were the only vessel in the port. The Pilgrim had passed through the Canal and hove-to off the town, nearly six weeks before, on her passage down from Monterey, and was now at the leeward. She heard here of our safe arrival at San Francisco.