Our relations with the Barbary Powers continue, as they have long been, of the most favorable character. The policy of keeping an adequate force in the Mediterranean, as security for the continuance of this tranquillity, will be persevered in, as well as a similar one for the protection of our commerce and fisheries in the Pacific. The southern Republics of our own hemisphere have not yet realized all the advantages for which they have been so long struggling. We trust, however, that the day is not distant when the restoration of peace and internal quiet, under permanent systems of government, securing the liberty and promoting the happiness of the citizens, will crown with complete success their long and arduous efforts in the cause of self-government, and enable us to salute them as friendly rivals in all that is truly great and glorious. The recent invasion of Mexico, and the effect thereby produced upon her domestic policy, must have a controlling influence upon the great question of South American emancipation. We have seen the fell spirit of civil dissension rebuked, and perhaps for ever stifled, in that Republic by the love of independence. If it be true, as appearances strongly indicate, the spirit of independence is the master spirit, and if a corresponding sentiment prevails in the other States, this devotion to liberty can not be without a proper effect upon the counsels of the mother country. The adoption by Spain of a pacific policy toward her former colonies--an event consoling to humanity, and a blessing to the world, in which she herself can not fail largely to participate--may be most reasonably expected. The claims of our citizens upon the South American Governments generally are in a train of settlement, while the principal part of those upon Brazil have been adjusted, and a decree in council ordering bonds to be issued by the minister of the treasury for their amount has received the sanction of His Imperial Majesty. This event, together with the exchange of the ratifications of the treaty negotiated and concluded in 1828, happily terminates all serious causes of difference with that power. Measures have been taken to place our commercial relations with Peru upon a better footing than that upon which they have hitherto rested, and if met by a proper disposition on the part of that Government important benefits may be secured to both countries.