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Across the Rapidan — The Grand Struggle Commenced.

The nation will be electrified to-day by the announcement that the Army of the Potomac is again in motion. It has been strengthened by reinforcements and material and inspired with new hope, until, under its present leadership, we believe it may be regarded as invincible. Gen. Meade's address is earnest and patriotic, and cannot but inspire to new courage the brave men whom he leads. We dare not state the strength of his army, but with the forces which are to co-operate with it from other points, we have assurance that it will be able to crush all opposition.

On Tuesday, the various corps of the Army of the Potomac crossed the Rapidan at a number of different fords, the rebels falling back without much opposition behind their entrenchments. The next news we receive may be the intelligence that the stern struggle has commenced. What Gen. Grant most fears, however, is, we believe, that the enemy will fall back within his entrenchments at Richmond.

While Gen. Meade moves upon the enemy's front under the eye of Gen. Grant, there is reason to believe that forces from other points are in motion also. A dispatch already received states that a force has reached West Point, at the head of York river, a point within twenty-four miles of Richmond. Even though this report should be untrue, or premature, a strong force is undoubtedly already in motion from Fortress Monroe, up the Peninsula. There are also indications that Gen. Thomas's forces are moving from Chattanooga in search of Joe Johnston. Vaster and better appointed, or more resistless armies have never moved in modern times.

We seem now to be nearing the point which is to decide the fate of the rebellion, and well may the most sanguine tremble for the result. The struggle for the possession of the rebel capital has undoubtedly commenced, and as Gen. Grant never turns his back upon his foe there is reason to believe the struggle will be a final one, because successful. The most intense anxiety will prevail until the result is known. Let the organization of our hundred day troops be hastened in order that they may strengthen the forces in the field, and thus contribute to a glorious triumph.