After refitting his vessels on the coast of Greenland, Captain DE HAVEN, who had the command of the expedition, started again for the North. After passing Baffin's Bay on the 8th of August, he became again hopelessly entangled in the vast masses of ice that were floating around, and was compelled to start for the United States. The expedition is likely to contribute essentially to our knowledge of the natural history of that remote region of the earth, as Dr. KANE, an intelligent naturalist, who went in the vessels as surgeon, has very complete memoranda of every thing of interest especially in this department. Although unable to find any distinct traces of him later than 1846, the officers of the expedition think it far from impossible that Sir JOHN FRANKLIN may be still alive, hemmed in by ice at a point which they were unable to reach. They agree in the opinion that a steamer of some kind should accompany any other expedition that may be sent. A State election took place in GEORGIA, on the 7th of October, which has a general interest on account of the issues which it involved. The old political distinctions were entirely superseded, both candidates for Governor having belonged to the Democratic party--one of them, however, Hon. HOWELL COBB, late Speaker of the U.S. House of Representatives, being in favor of abiding by the Compromise measures of 1850, and his opponent Mr. MCDONALD being opposed to them, and in favor of secession from the Union. Up to the time of closing this record, full returns have not been received; but it is quite certain that Mr. COBB, the Union candidate, has been elected by a very large majority. Full returns of the Congressional canvass, which was held at the same time, have not yet reached us; but it is believed that six Union, and two State Rights members have been elected. The Legislature of VERMONT met at Montpelier on the 9th of October. The House was organized by the election of Mr. Powers, speaker, and Mr. C. T. Davey, clerk. The message of Gov. Williams treats of national topics at considerable length. He insists that the laws must be obeyed, and vindicates the _habeas corpus_ act passed by Vermont at the last session of its Legislature from many of the censures that have been cast upon it.