General Grant's headquarters during the afternoon of the 23d and the day of the 24th were in Wood's redoubt, except when, in the course of the day, he rode along the advanced line, visiting the headquarters of the several commanders in Chattanooga Valley.

At daylight on the 25th the Stars and Stripes were descried on the peak of Lookout. The Rebels had evacuated the mountain. Hooker moved to descend the mountain, striking Missionary Ridge at the Rossville Gap, to sweep both sides and its summit.

The Rebel troops were seen, as soon as it was light enough, streaming regiments and brigades along the narrow summit of Missionary Ridge, either concentrating on the right to overwhelm Sherman, or marching for the railroad to raise the siege.

They had evacuated the valley of Chattanooga. Would they abandon that of Chickamauga?

The twenty-pounders and four-and-a-quarter inch rifles of Wood's redoubt opened on Missionary Ridge. Orchard Knob sent its compliments to the Ridge, which, with rifled Parrotts, answered, and the cannonade, thus commenced, continued all day. Shot and shell screamed from Orchard Knob to Missionary Ridge, and from Missionary Ridge to Orchard Knob, and from Wood's redoubt, over the heads of Generals Grant and Thomas and their staffs, who were with us in this favorable position, from whence the whole battle could be seen as in an amphitheatre. The headquarters were under fire all day long.

Cannonading and musketry were heard from General Sherman, and General Howard marched the Eleventh Corps to join him.

General Thomas sent out skirmishers, who drove in the Rebel pickets and chased them into their entrenchments, and at the foot of Missionary Ridge Sherman made an assault against Bragg's right, entrenched on a high knob next to that on which Sherman himself lay fortified. The assault was gallantly made.

Sherman reached the edge of the crest, and held his ground for (it seemed to me) an hour, but was bloodily repulsed by reserves.

A general advance was ordered, and a strong line of skirmishers followed by a deployed line of battle some two miles in length. At the signal of leaden shots from headquarters on Orchard Knob, the line moved rapidly and orderly forward. The Rebel pickets discharged their muskets and ran into their rifle-pits. Our skirmishers followed on their heels.

The line of battle was not far behind, and we saw the gray Rebels

swarm out of the ledge line of rifle-pits and over the base of the hill A few turned and fired their pieces;

into the many roads which cross

in numbers which surprised us.
but the greater number collected
obliquely up its steep face, and went on to the top.

Some regiments pressed on and swarmed up the steep sides of the Ridge, and here and there a color was advanced beyond the lines. The attempt appeared most dangerous; but the advance was sup ported, and the whole line was ordered to storm the heights, upon which not less than forty pieces of artillery, and no one knew how many muskets, stood ready to slaughter the assailants. With cheers answering to cheers, the men swarmed upward. They gathered to the points least difficult of ascent, and the line was broken. Color after color was planted on the summit, while musket and cannon vomited their thunder upon them.

A well-directed shot from Orchard Knob exploded a Rebel caisson on the summit, and the gun was seen being speedily taken to the right, its driver lashing his horses. A party of our soldiers intercepted them, and the gun was captured, with cheers.

A fierce musketry fight broke out to the left, where, between Thomas and Sherman, a mile or two of the Ridge was still occupied by the Rebels.

Bragg left the house in which he had held his headquarters, and rode to the rear as our troops crowded the hill on either side of him. General Grant proceeded to the summit, and then only did we know its height.

Some of the captured artillery was put into position. Artillerists were sent for to work the guns, and caissons were searched for ammunition.

The Rebel log breastworks were torn to pieces and carried to the other side of the Ridge, and used in forming barricades across.

A strong line of infantry was formed in the rear of Baird's line, and engaged in a musketry contest with the Rebels to the left, and a secure lodgment was soon effected.

The other assault to the right of our center gained the summit, and the Rebels threw down their arms and fled.

Hooker, coming into favorable position, swept the right of the Ridge, and captured many prisoners.

Bragg's remaining troops left early in the night, and the battle of Chattanooga, after days of manoeuvring and fighting, was won. The strength of the Rebellion in the center is broken. Burnside is

relieved from danger in East Tennessee. Kentucky and Tennessee are rescued. Georgia and the Southeast are threatened in the rear, and another victory is added to the chapter of "Unconditional Surrender Grant."

To-night the estimate of captures is several thousand prisoners and thirty pieces of artillery.

Our loss for so great a victory is not severe.

Bragg is firing the railroad as he retreats toward Dalton. Sherman is in hot pursuit.

To-day I viewed the battle-field, which extends for six miles along Missionary Ridge and for several miles on Lookout Mountain.

Probably not so well-directed, so well-ordered a battle, has taken place during the war. But one assault was repulsed; but that assault, by calling to that point the Rebel reserves, prevented them repulsing any of the others.

A few days since Bragg sent to General Grant a flag of truce advising him that it would be prudent to remove any non-combatants who might be still in Chattanooga. No reply has been returned; but the combatants having removed from the vicinity, it is probable that non-combatants can remain without imprudence.

M. C. MEIGS, Quartermaster-General.

In securing this great victory the Union forces had lost 757 killed, 4,529 wounded and 330 missing. The loss of the Confederates has never been ascertained, but reached probably beyond fifteen thousand. General Grant captured 6,142 prisoners, 40 pieces of artillery, 69 artillery carriages, and caissons, and 7,000 stand of small arms.

Not satisfied with the first fruits of this victory Grant ordered the retreating enemy to be hotly pursued, which was successfully accomplished, they being forced back upon Ringgold. Further pursuit was abandoned, owing to the necessity of relieving Burnside at Knoxville.

Grant had by his masterly movement in turning the enemy back upon Dalton and Ringgold thrown Sherman and his corps between Longstreet and Bragg, and he at once dispatched General Granger and other forces under