The result of the election shows, with great distinctness, the following facts: 1st. That Mr. Buchanan was chosen President, because he received the electoral votes of the five free States of Pennsylvania, New Jersey, Indiana, Illinois and California (62 in all), and that without them he could not have been elected. 2d. That his Southern vote (that of every slave-holding State excepting Maryland) was partly given to him because of his conservative opinions and position, and partly because the candidate for the Vice-Presidency, Mr. Breckinridge, was a Southern man. 3d. That General Fremont received the electoral vote of no Southern State, and that this was due partly to the character of the Republican party and its Northern tone, and partly to the fact that the Republican candidate for the Vice Presidency (Mr. Dayton, of New Jersey), was a citizen of a non-slaveholding State. General Fremont himself was nominally a citizen of California. This election, therefore, foreshadowed the sectional division which would be almost certain to happen in the next one, if the four years of Mr. Buchanan’s administration should not witness a subsidence in the sectional feelings between the North and the South. It would only be necessary for the Republicans to wrest from the Democratic party the five free States which had voted for Mr. Buchanan, and they would elect the President in 1860. Whether this was to happen, would depend upon the ability of the Democratic party to avoid a rupture into factions that would themselves be representatives of irreconcilable dogmas on the subject of slavery in the Territories. Hence it is that Mr. Buchanan’s course as President, for the three first years of his term, is to be judged, with reference to the responsibility that was upon him to so conduct the Government as to disarm, if possible, the antagonism of section to section. His administration of affairs after the election of Mr. Lincoln is to be judged simply by his duty as the Executive, in the most extraordinary and anomalous crisis in which the country had ever been placed. I take from the multitude of private letters written or received during and after the election, a few of the most interesting:— [FROM THE HON. JAMES MACGREGOR.] HOUSE OF COMMONS, June 20, 1856. MY DEAR SIR:— I am, indeed, very happy to receive to-day the decision with regard to you at Cincinnati, and God grant the result be as successful as I wish. The feeling in this house, and I am sure in the country, is, I believe firmly, such as you could wish. I wish that miserable dispute about Central America were dissipated; for my part, I believe that if not only Central America, but all Spanish America, south of California, were possessed and governed by an Anglo-Saxon or Anglo-American race, the more would the progress of civilization, the progress of industry and commerce, and the happiness of mankind be advanced.