FROM LIVERPOOL. - On Sunday last a very ordinary, dirty looking schooner, with the British ensign flying from her masthead, made her way up the river and quietly anchored off the Great Western Railway depot. She was evidently a stranger in our waters, and naturally attracted considerable attention, as it was apparent that no Yankee shipbuilder had a hand in the modelling of her hull, the bow being extremely blunt, and only partially relieved by a heavy unsightly cut-water. On going on board, we were politely received by Capt. Crang [sic], and informed that we stood on the deck of the "Madiera Pet," of Guernsey, and that she was bound for Chicago with a cargo of crockery ware, paints oils, iron, steel, &c. She was 36 days in making the passage from Liverpool to Quebec, and 28 days from Quebec to this port. Her dimensions are, length 101 feet, width 17 feet 6 inches, depth of hold 11 feet. She carries 123 tons, custom house measurement, and draws 9 feet of water. Capt. Crang informed us that he should load at Chicago with hams, bacon, tallow, &c. for Liverpool. She sailed last evening for Chicago.