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.

Deeply interested as we are in the prosperity of our sister Republics, and more particularly in that of our immediate neighbor, it would be most gratifying to me were I permitted to say that the treatment which we have received at her hands has been as universally friendly as the early and constant solicitude manifested by the United States for her success gave us a right to expect. But it becomes my duty to inform you that prejudices long indulged by a portion of the inhabitants of Mexico against the envoy extraordinary and minister plenipotentiary of the United States have had an unfortunate influence upon the affairs of the two countries, and have diminished that usefulness to his own which was justly to be expected from his talents and zeal. To this cause, in a great degree, is to be imputed the failure of several measures equally interesting to both parties, but particularly that of the Mexican Government to ratify a treaty negotiated and concluded in its own capital and under its own eye. Under these circumstances it appeared expedient to give to Mr. Poinsett the option either to return or not, as in his judgment the interest of his country might require, and instructions to that end were prepared; but before they could be dispatched a communication was received from the Government of Mexico, through its charge d'affaires here, requesting the recall of our minister. This was promptly complied with, and a representative of a rank corresponding with that of the Mexican diplomatic agent near this Government was appointed. Our conduct toward that Republic has been uniformly of the most friendly character, and having thus removed the only alleged obstacle to harmonious intercourse, I can not but hope that an advantageous change will occur in our affairs.

In justice to Mr. Poinsett it is proper to say that my immediate compliance with the application for his recall and the appointment of a successor are not to be ascribed to any evidence that the imputation of an improper interference by him in the local politics of Mexico was well founded, nor to a want of confidence in his talents or integrity, and to add that the truth of the charges has never been affirmed by the federal Government of Mexico in its communications with us.

I consider it one of the most urgent of my duties to bring to your attention the propriety of amending that part of the Constitution which relates to the election of President and Vice-President. Our system of government was by its framers deemed an experiment, and they therefore consistently provided a mode of remedying its defects.

To the people belongs the right of electing their Chief Magistrate; it was never designed that their choice should in any case be defeated, either by the intervention of electoral colleges or by the agency confided, under certain contingencies, to the House of Representatives. Experience proves that in proportion as agents to execute the will of the people are multiplied there is danger of their wishes being frustrated. Some may be unfaithful; all are liable to err. So far, therefore, as the people can with convenience speak, it is safer for them to express their own will.

The number of aspirants to the Presidency and the diversity of the interests which may influence their claims leave little reason to expect a choice in the first instance, and in that event the election must devolve on the House of Representatives, where it is obvious the will of the people may not be always ascertained, or, if ascertained, may not be regarded. From the mode of voting by States the choice is to be made by 24 votes, and it may often occur that one of these will be controlled by an individual Representative. Honors and offices are at the disposal of the successful candidate. Repeated ballotings may make it apparent that a single individual holds the cast in his hand. May he not be tempted to name his reward?

But even without corruption, supposing the probity of the Representative to be proof against the powerful motives by which it may be assailed, the will of the people is still constantly liable to be misrepresented. One may err from ignorance of the wishes of his constituents; another from a conviction that it is his duty to be governed by his own judgment of the fitness of the candidates; finally, although all were inflexibly honest, all accurately informed of the wishes of their constituents, yet under the present mode of election a minority may often elect a President, and when this happens it may reasonably be expected that efforts will be made on the part of the majority to rectify this injurious operation of their institutions. But although no evil of this character should result from such a perversion of the first principle of our system--that the majority is to govern--it must be very certain that a President elected by a minority can not enjoy the confidence necessary to the successful discharge of his duties.