The problem which the Franklins and the Kanes, of Arctic science and discovery, have labored so long and with such heroism to solve, has had no new light thrown upon it by the voyage from which Dr. Hayes has just returned. When, in July of last year, he left our shores in the small schooner United States, having on board only sixteen persons and the usual outfit, we felt in no way sanguine that the expedition would be successful in clearing away the mystery which surrounds the North pole, and the result is, therefore, only in accordance with our anticipations. This conveys no ill compliment to its projector, whose enthusiasm, talent and perseverance are undoubted; but we formed our opinion from the weakness of the exploring force. It was an attempt, with very inadequate means, to achieve a great object. Everything about the expedition was on far too small a scale; and, being insufficient, it became a foregone conclusion that it would fail. We are still wanting in scientific data relating to the geography and meteorology of the Arctic region, and even of its navigation and zoology. We are only slightly informed; but this expedition has discovered nothing before unknown on these points, and the death of its astronomer has only added another to the long list of Arctic victims. Had the expedition been larger, and provided with a good scientific party, much might have been attained, where, for want of it, the result has been simply a blank. Dr. Hayes succeeded in making his way by dog sledges no farther north than latitude 81 degrees 35 minutes, which is a lower degree than even Hendrik Hudson reached about the year 1600. We refer to these facts simply to show the folly of fitting out Polar expeditions that, from their very diminutiveness, are unequal to the work for which they are designed.