Upon the first ballot for a candidate for President, ABRAHAM LINCOLN received the vote of every State, except Missouri, whose delegates voted for Gen. Grant. The nomination having, on motion of a Missourian, been made unanimous, a scene of the wildest enthusiasm followed, the whole convention being on their feet shouting, and the band playing “Hail Columbia.” For Vice-President, the following names were presented: Andrew Johnson, of Tennessee; Hannibal Hamlin, of Maine; Gen. L. H. Rousseau, of Kentucky; and Daniel S. Dickinson, of New York. As the vote proceeded, it was soon apparent that ANDREW JOHNSON was to be the nominee; and before the result was announced the various States whose delegations had been divided, commenced changing their votes, and went unanimously for Mr. Johnson, amid the greatest enthusiasm. On the 9th of June, Mr. Lincoln was waited on by a committee of the convention, and notified of his nomination by the chairman, ex-Governor Dennison, of Ohio, who, in the course of his address, said: “I need not say to you, sir, that the Convention, in thus unanimously nominating you for re-election, but gave utterance to the almost universal voice of the loyal people of the country. To doubt of your triumphant election would be little short of abandoning the hope of a final suppression of the rebellion and the restoration of the Government over the insurgent States. Neither the Convention nor those represented by that body entertained any doubt as to the final result, under your administration, sustained by the loyal people, and by our noble army and gallant navy. Neither did the Convention, nor do this Committee doubt the speedy suppression of this most wicked and unprovoked rebellion.” In reply the President said: “MR. CHAIRMAN AND GENTLEMEN OF THE COMMITTEE:--I will neither conceal my gratification nor restrain the expression of my gratitude that the Union people, through their Convention, in the continued effort to save and advance the nation, have deemed me not unworthy to remain in my present position. I know no reason to doubt that I shall accept the nomination tendered; and yet, perhaps, I should not declare definitely before reading and considering what is called the platform. “I will say now, however, that I approve the declaration in favor of so amending the Constitution as to prohibit slavery throughout the nation. When the people in revolt, with the hundred days explicit notice that they could within those days resume their allegiance without the overthrow of their institutions, and that they could not resume it afterward, elected to stand out, such an amendment of the Constitution as is now proposed became a fitting and necessary conclusion to the final success of the Union cause.