Major-General Lew. Wallace’s Division—Right of Army.—First Brigade—Col. Morgan L. Smith, commanding; 8th Missouri, Col. Morgan L. Smith, Lieut.-Col. James Peckham, commanding; 11th Indiana, Col. George F. McGinnis; 24th Indiana, Col. Alvin P. Hovey; Thurber’s Missouri battery. Second Brigade—Col. Thayer (1st Nebraska) commanding; 1st Nebraska, Lieut.-Col. McCord, commanding; 23d Indiana, Col. Sanderson; 58th Ohio, Col. Bausenwein; 68th Ohio, Col. Steadman; Thompson’s Indiana battery. Third Brigade—Col. Chas. Whittlesey (20th Ohio) commanding; 20th Ohio, Lieut.-Col. —— commanding; 56th Ohio, Col. Peter Kinney; 76th Ohio, Col. Chas. R. Woods; 78th Ohio, Col. Leggett.

At daylight it became evident that the gunboat bombardment through the night had not been without a most important effect. It had changed the position of the rebel army. The sun had gone down with the enemy’s lines encircling the Union forces closely on the centre and left, pushing them to the river, and leaving them little over half a mile of all the broad space they had held in the morning. The gunboats had cut the coils and loosened the anaconda-like constriction. Their shells had made the old position on the extreme Union left, which the rebels had been occupying, utterly untenable. Instead of stealing upon their foe in the night, which was doubtless their intention, they were compelled to fall back from point to point out of range of the shells which came dropping in; go where they would within range, the troublesome visitors would find them out, and they fell back beyond the inner Union camps, and thus lost more than half the ground they had gained the afternoon before.

Less easily accounted for was a movement of theirs on the right. Here they had held a steep bluff, covered with underbrush, as their advanced line. Through the night they abandoned this, the best possible position for opposing Lew. Wallace, and had fallen back across some open fields to the scrub oak woods beyond.

To those who had looked despairingly at the prospects on Sunday evening, it seemed unaccountable that the rebels did not open the contest by daybreak. Their retreat before the bombshells of the gunboats, however, explained the delay. The Union divisions were put in motion almost simultaneously. By seven o’clock Lew. Wallace opened the day by shelling the rebel battery, of which mention has been made, from the positions he had selected the night before. A brisk artillery duel was followed by a rapid movement of infantry across a shallow ravine, as if to storm; and the rebels, enfiladed and menaced in front, limbered up and made the opening of their Monday’s retreating.

NELSON’S ADVANCE.

Nelson, who was assigned the left wing, moved his division about the same time Wallace opened on the rebel battery, forming in line of battle, Ammon’s brigade on the extreme left, Bruce’s in the centre, and Hazen’s to the right. Skirmishers were thrown out, and for nearly a mile the division thus swept the country, pushing a few outlying rebels before it, till it came upon them in force. Then a general engagement broke out along the line, and again the rattle of musketry and thunder of artillery echoed over the late silent fields. There was no straggling this morning. These men were well drilled, and strict measures were taken to prevent miscellaneous thronging back out of harm’s way. They stood up to their work and did their duty manfully.

It soon became evident that, whether from change of commanders or some other cause, the rebels were pursuing a new policy in massing their forces. On Sunday the heaviest fighting had been done on the left. In the morning they seemed to make a less determined resistance here, while toward the centre and right the ground was more obstinately contested, and the struggle fiercely prolonged.

Until half-past ten o’clock Nelson advanced slowly but steadily, sweeping his long lines over the ground of defeat on Sunday morning, moving over scores of dead rebels, and resistlessly pressing back the jaded and wearied enemy. The rebels had received but few reinforcements during the night. Their men were exhausted with the desperate contest of the day before, and manifestly dispirited by the fact that they were fighting Grant and Buell combined.

Gradually, as Nelson pushed forward his lines under heavy musketry, the enemy fell back, till about half-past ten, when, under cover of the heavy timber and a furious cannonading, they made a general rally. The Union forces, flushed with their easy success, were scarcely prepared for the sudden onset, when the rebel masses were hurled against them with tremendous force. The men halted, wavered, and were driven back. At this critical juncture Captain Terry’s regular battery came dashing up. Scarcely taking time to unlimber, he was loading and sighting his pieces before the caissons had turned, and in an instant was tossing in shell from twenty-four-pound howitzers in to the compact and advancing rebel ranks.

Here was the turning point of the battle on the left. The rebels were checked, not halted. On they came. Horse after horse from the batteries was picked off. Every private at one of the howitzers was shot down, and the gun was worked by Captain Terry himself and a corporal. A regiment dashed up from the Union line, and saved the disabled piece. Then for two hours artillery and musketry raged at close range. At last the enemy began to waver. The Federals pressed on, pouring in deadly volleys. Just then Buell, who assumed the general direction of his troops in the field, came up. At a glance he saw the position of things, and gave a prompt order. “Forward at double-quick by brigades.” The men leaped forward with the eagerness of unleashed hounds. For a quarter of a mile the rebels fell back. Faster and faster they ran; less and less resistance was made to the advance. At last the front camps on the left were reached, and by half-past two that point was cleared. The rebels had been steadily swept back over the ground they had won, with heavy loss, and fell into confusion. The Unionists had retaken all their own guns lost here the day before, and one or two from the rebels were left to attest how bravely that great victory in Tennessee was won.