Exploring Expedition. The United States Corvette Vincennes, Captain Charles Wilkes, the flag ship of the Exploring Expedition, arrived at New York on Friday, June 10th, from a cruise of nearly four years. The Brigs Porpoise and Oregon may shortly be expected. The Expedition has executed every part of the duties confided to it by the Government. A long list of ports, harbors, islands, reefs, and shoals, named in the list, have been visited and examined or surveyed. The positions assigned on the charts to several vigias, reefs, shoals, and islands, have been carefully looked for, run over, and found to have no existence in or near the places assigned them. Several of the principal groups and islands in the Pacific Ocean have been visited, examined, and surveyed; and friendly intercourse, and protective commercial regulations, established with the chiefs and natives. The discoveries in the Antarctic Ocean (Antarctic continent, — Observations for fixing the Southern Magnetic pole, &c.) preceded those of the French and English expeditions. The Expedition, during its absence, has also examined and surveyed a large portion of the Oregon Territory, a part of Upper California, including the Columbia and Sacramento Rivers, with their various tributaries. Several exploring parties from the Squadron have explored, examined, and fixed those portions of the Oregon Territory least known. A map of the Ter............