The great question of the hour is, that of rebuilding the edifice of the Republic, which has been rudely shaken and partly thrown down by the rebellion. All patriotic hearts, in anticipation of the speedy close of the war, are turned with intense interest to this important work. Opinions divide upon this as upon all other great subjects, and we have two antagonistic ideas, organizing their respective parties with reference to it. One party maintains that the rebellious States have forfeited all their rights, and can under no circumstances claim to be recognized in their former relations, except on a re-admission into the Union upon the terms prescribed by the Constitution for the admission of new States. The other party denies that any of the States, as such, have forfeited, or can forfeit any of their rights, and maintains the duty of the Federal Government to protect all the States in their constitutional integrity, to put down the rebellion within them, and to restore to them the republican forms which have been violently overthrown. In each of these positions, there seems to be a combination of truth and error. So long as any State is in a belligerent and treasonable attitude, disclaiming and repudiating her obligations under the Constitution, she is obviously not entitled to the benefits of the system which she thus assails and defies. The State being sustained in rebellion by its whole people, it is vain to say the Government can only regard the people as individuals, for these are the State, and must be treated accordingly. But if, laying down her arms, or even after being conquered, a State returns to her allegiance, to reject her demands would be to admit that secession had been effectual. It would be a recognition of the validity, if not of the rightfulness of the movement which assumed to carry the State out of the Union.