Upon the 30th, the whole Union force, in mass, was prepared to move upon Tullahoma; but on the next day a dispatch was received by General Rosecrans from General Thomas, announcing to him that the enemy had evacuated Tullahoma during the night. Pursuit was ordered instantly. The divisions of Brannan, Negley, and Sheridan entered Tullahoma, and took possession. The infantry arrived about noon; and the divisions of Negley and Rousseau pushed on after the retreating rebels, and overtook their rear-guard at Bethpage Bridge, two miles above the railroad crossing. The rebels, in strong force, occupied the heights at this place; and the Unionists engaged in a brisk skirmish with them, in which the National forces entirely routed the rebels. General McCook, in command of two divisions, pursued the enemy, on the next day, along the road which lay west of the railroad. The Elk river was found to be almost unfordable by the cavalry; while the rebel cavalry on the opposite side did everything in their power to resist the attempted crossing by the Union forces. But the rebels were speedily driven away, and the National troops took possession of the ford. General Thomas, with similar difficulty, effected a crossing, the enemy having during the night burned the bridge by which he had expected to cross. The small cavalry force under General Turchin pushed forward to Hillsboro,’ on the Deckhard road; and finding the enemy’s cavalry at Elk Ford, near Morris Ferry, engaged them, and being very soon reinforced by General Mitchell’s troops they forced a passage across the river, after a sharp conflict. Night then closed the pursuit. Upon the 3d July, General Sheridan succeeded in crossing Elk river, and, supported by General J. C. Davis’s division, pushed the enemy to Cowan, where he learned that the rebels, with their artillery and infantry, had crossed the mountains by University and Sweden’s Cove, and that the cavalry alone would be found covering their rear. On the same day General Thomas got his troops across, also; portions of the cavalry from Sheridan’s division, and also from the main column were sent forward, but they only learned that the enemy was gone. The roads were found to be almost impassable from the heavy rains, and the troops being well-nigh out of provisions a halt was ordered until supplies could be forwarded from Murfreesboro’. Thus ended a campaign of nine days’ duration, in which the enemy had been driven from two strongly fortified positions, and which had resulted in giving the Union forces possession of the whole of Middle Tennessee, and preserving Kentucky from the danger of a second invasion. * * * * *