The cession of the Spanish Province of Louisiana to France, which took place in the course of the late war, will, if carried into effect, make a change in the aspect of our foreign relations which will doubtless have just weight in any deliberations of the Legislature connected with that subject. There was reason not long since to apprehend that the warfare in which we were engaged with Tripoli might be taken up by some other of the Barbary Powers. A reenforcement, therefore, was immediately ordered to the vessels already there. Subsequent information, however, has removed these apprehensions for the present. To secure our commerce in that sea with the smallest force competent, we have supposed it best to watch strictly the harbor of Tripoli. Still, however, the shallowness of their coast and the want of smaller vessels on our part has permitted some cruisers to escape unobserved, and to one of these an American vessel unfortunately fell a prey. The captain, one American seaman, and two others of color remain prisoners with them unless exchanged under an agreement formerly made with the Bashaw, to whom, on the faith of that, some of his captive subjects had been restored. The convention with the State of Georgia has been ratified by their legislature, and a repurchase from the Creeks has been consequently made of a part of the Talasscee country. In this purchase has been also comprehended a part of the lands within the fork of Oconee and Oakmulgee rivers. The particulars of the contract will be laid before Congress so soon as they shall be in a state for communication. In order to remove every ground of difference possible with our Indian neighbors, I have proceeded in the work of settling with them and marking the boundaries between us. That with the Choctaw Nation is fixed in one part and will be through the whole within a short time. The country to which their title had been extinguished before the Revolution is sufficient to receive a very respectable population, which Congress will probably see the expediency of encouraging so soon as the limits shall be declared. We are to view this position as an outpost of the United States, surrounded by strong neighbors and distant from its support; and how far that monopoly which prevents population should here be guarded against and actual habitation made a condition of the continuance of title will be for your consideration. A prompt settlement, too, of all existing rights and claims within this territory presents itself as a preliminary operation. In that part of the Indiana Territory which includes Vincennes the lines settled with the neighboring tribes fix the extinction of their title at a breadth of 24 leagues from east to west and about the same length parallel with and including the Wabash. They have also ceded a tract of 4 miles square, including the salt springs near the mouth of that river.