SIR: The country upon the southern shore of Lake Superior, and upon the water communication between that Lake and the Mississippi, has been but little explored, and its natural features are imperfectly known. We have no correct topographical delineation of it, and the little information we possess relating to it has been derived from the reports of the Indian traders. It has occurred to me that a tour through that country, with a view to examine the productions of its animal, vegetable, and mineral kingdoms, to explore its facilities for water communication, to delineate its natural objects, and to ascertain its present and future probable value, would not be uninteresting in itself, nor useless to the Government. Such an expedition would not be wholly unimportant in the public opinion, and would well accord with that zeal for inquiries of this nature which has recently marked the administration of the War Department. But, however interesting such a tour might be in itself, or however important in its result, either in a political or geographical point of view, I should not have ventured to suggest the subject, nor to solicit your permission to carry it into effect, were it not, in other respects, intimately connected with the discharge of my official duties. Mr. Woodbridge, the delegate from this Territory, at my request, takes charge of this letter, and he is so intimately acquainted with the subject, and every way so competent to enter into any explanations you may require, that I shall not be compelled to go as much into detail as, under other circumstances, might be necessary. The route which I propose to take, is from here to Michilimackinac, and from thence, by the Straits of St. Mary's, to the river which contains the body of copper ore (specimens of which have been transmitted to the Government), and to the extremity of Lake Superior. From that point, up the river which forms the water communication between that lake and the Mississippi, to the latter river, and, by the way of Prairie du Chien and Green Bay, to Lake Michigan. The political objects which require attention upon this route are:-- 1. A personal examination of the different Indian tribes who occupy the country; of their moral and social condition; of their feelings towards the United States; of their numerical strength; and of the various objects connected with them, of which humanity and sound policy require that the Government should possess an intimate knowledge. We are very little acquainted with these Indians, and I indulge the expectation that such a visit would be productive of beneficial effects. The extract from the letter of Colonel Leavenworth, herewith inclosed, and the speech of the Winnebago Indians, transmitted to the War Department by Mr. Graham, from Rock Island, February 24, 1819, will show how much we have yet to learn respecting these tribes, which are comparatively near to us.