Mexican Presidential Election.—The results of the Presidential Election, which is held in Mexico to day, (August 1st,) will be awaited with considerable interest. The two candidates are the present incumbent, Herrera, and Gomez Farias. From the choice of the people in the present canvass, it may be expected that the political destinies of the country will take their complexion for many years to come. Herrera is attached to the principles of Centralism, and to a party disposed to check the changes and ameliorations so necessary for the renovation of Mexico.—Gomez Farias, on the contrary belongs to the most liberal class of Mexican politicians, and has for a long period figured as their head and leader. He has spent many years in the United States, and became thoroughly imbued with our republican notions. The principles avowed by him, and on which he is running as a candidate, are decidedly Federal in character. He advocates the restoration of the Federal Constitution of 1824.—The prospects of his success are said to be much the most flattering of the two candidates. In the event of his election, every confidence is felt in the re-establishment of the Federal institutions. As to the nature of these, as introduced under the new organization in 1824, perhaps some information might not, at the present crisis, be uninteresting. The Constitution of 1824 was formed after the pattern of that of the United States, and in most parts is a complete transcript of it. The divisions of the functions of the government into three departments, of Legislative, Judicial, and Executive, is the same; and so is the assignment to each of their respective duties and the limitation of their powers. The only material difference in the two instruments is, the omission of the right of trial by Jury, and the freedom of religious worship. The ignorance and moral degradation of the Mexicans disqualify them for the exercise of the first of these franchises; and the political influence of the reigning priesthood is an insuperable obstacle to the enjoyment of the last. Perhaps no form of government more liberal than the Constitution of 1824 would be compatible with the existing state of society. We should rejoice to see it the organic law of Mexico, and the happy result secured by the election of Gomez Farias.—N. O. Bulletin.