CHATTANOOGA, Nov. 24—6 P. M.

Major General H. W. HALLECK, General-in-Chief, Washington, D. C. :— The fighting to-day progressed favorably.

General Sherman carried the end of Missionary Ridge, and his right is now at the tunnel, and his left at Chickamauga Creek.

The troops from Lookout Valley carried the point of the mountain, and now hold the eastern slope and point high up.

I cannot yet tell the amount of casualties, but our loss is not heavy. General Hooker reports two thousand prisoners taken, besides which a small number have fallen into our hands from Missionary Ridge. U. S. GRANT, Major-General.

In the above dispatch General Grant says nothing about himself, or in what manner he had participated in the struggle, although from the correspondent's account it is clearly seen, that notwithstanding his crippled condition he anxiously watched the movements of the troops at a position within cannon shot of the enemy.

The following is the rebel dispatch concerning the con

test:

To General S. COOPER:

MISSION RIDGE, Nov. 24, 1863.

We have had a prolonged struggle for Lookout Mountain to-day, and sustained considerable loss in one division. Elsewhere the enemy has only manœuvred for position.

BRAXTON BRAGG, General.

CHAPTER LI.

THIRD DAY.-TUNNEL HILL.-MISSION RIDGE.

The battle raged as furiously on the third day as on those preceding, and is thus described:

General Hooker pursued the retreating enemy on top of the mountains, but did not succeed in coming up with him. He descended the mountain, however, at Hickajack trace, and, crossing the Chattanooga Creek Valley, made the ascent of Mission Ridge at or near he old battle field of Chickamauga. Here he was to the south of Rossville and in the rear of the rebel line in Chattanooga Valley, entirely cut off from the rest of our army, but perfectly able to take care of himself. He began to move north on top of Mission Ridge, and arrived at an opportune moment in the rear of Fort Breckinridge.

Weary with watching Hooker the night previous, it was late before I reached Orchard Knob on the morning of Wednesday. At the first glance I thought the situation here unchanged; but upon a closer examination I saw that the mask of night had been used to cover very extensive preparations for hard work. The relinquishing of Lookout Mountain had evinced the rebel intention to defend Mission Ridge with vigor, and in answer to this sensible play of the rebels, General Grant had doubled the strength of forces selected to storm the ridge. Wood had been chosen to storm the heights at Blackfords. General Grant had added to his force that of General Baird. Sheridan had been chosen to make the assault at Thurman's house, and a brigade was added to his force. General Palmer had taken command of these in person, while General Gordon Granger assumed command of the divisions of Wood and Baird. Under the cover of the forest in which they rested, these two formidable columns were hid from view from Mission Ridge, and there were no rebels on Mission Ridge to signalize the important information to Bragg, who kept head-quarters at Blackfords. The men were in excellent spirits. They had rested well from their Monday's labor, and their souls had been cheered by seeing Hooker's camp fires on Lookout and Sherman's on Mission Ridge. Daylight had revealed the signa

flags waving on Lookout, and the artillery of Sherman opening from his position on Fort Buckner. General Wood was enjoying himself hugely, and called to me to stay and see the finest work of the day; but I had seen General Rawlings, of Grant's staff, dash away a few minutes before towards Fort Wood, and I knew that he had gone to fire the signal for the assault, and, putting spurs to the (not) noble ass which I had pressed into service in default of a good horse I had broken down the day before, I dashed off to see Sherman's fight.

I found General Howard's Corps moving to the left, taking care to expose itself as much as possible to rebel eyesight. The corps subse. quently reached General Sherman, and were sent to strengthen his left in a movement up Chickamauga Creek.

On reaching the summit of the semi-circular shaped hills, which General Sherman had occupied on Tuesday afternoon, I found he had strengthened his position by strong rifle-pits, and had put four pieces of artillery on the right of his line, on the hills, and a section on the other extreme, thus getting in an enfilading fire on Fort Buckner. I asked the distance from the right position to Fort Buckner, and by the elevation given to the guns it was reported to be a fraction over 900 yards. A short time after my arrival this battery again became rather seriously engaged with a rebel battery in Fort Buckner, which was kept up for half an hour, to the evident discomfiture of the rebels. With the excep. tion of the artillery, the line was as quiet and composed as if in camp, or as-were three of our high privates, whom I saw sitting in a cluster to the left, making entries in their diaries. Three private soldiers, under fire, entering in diaries, in plain, legible chirography, the events of the day, is a spectacle only seen in the army of the Union. It is one of the sights which causes one to reflect, and which will long retain hold upon his memory.

The operations of the day, on General Sherman's part, began by an attack on his right upon the enemy posted behind the railroad bank at Glass Station. This attack was made at ten o'clock, and resulted in a repulse of the assaulting Union troops, after a short fight, so weakly made and so early dropped that I imagine it was intended to develop the enemy and his strength for the benefit of the artillery on the hill which began to pour upon the rebels a very destructive fire of shells, which exploded above them in handsome style. The Union commander recalled his troops after they had fully drawn the fire of the enemy, and awaited further developments on the left.

I find myself using the pronoun of the egotist rather oftener than is

modest, perhaps; but the history of the first events of the battle must necessarily be matters of personal observation-and that must be my apology. On going to the left of the ridge I found gathered together there Generals Sherman, Blair, M. L. Smith and Lightburn, watching the re-enforcement by General Corse's command of three regiments of General Lightburn's Brigade, which had succeeded in effecting a lodgment on Tunnel Hill, and upon which the enemy was still at work on Fort Buckner. General Blair pointed out the situation to me, remarking, "When we take one hill it looks as if there was another to be taken." But, after a moment's pause and silent observation of Tunnel Hill, he added, "When we've got that we'll be done." I don't know that General Blair thought we should be repulsed; but I imagine he did when he made that last remark.

General Corse, with his command, mounted the hill in good style, and reached the crest without any difficulty or opposition, as other troops had also succeeded in doing; for you must understand that Fort Buckner was not built immediately on the edge of the hill. That is, you reached the top and the plateau before you got under the fire of the fort; but the moment you began to move over the plateau the fire of the enemy was likely to open out upon you. General Corse, taking command, formed the whole force under the crest of the hill, his own immediate command on the right, with the other three regiments on the left. It was just eleven o'clock when a tremendous volley from the enemy revealed the fact, patent only to good field-glasses, that Corse had marched over the crest, was on the plateau, and was charging on Fort Buckner. The opening chorus was well worthy to be the prologue of the day's drama, for it had all the merit of brevity and briskness. It lasted but ten minutes. The men fell back under the crest of the hill, but they left their dead and wounded in the enemy's rifle-pits. As they retreated our batteries opened upon the pursuing enemy, who appeared in heavy force. This ably-directed fire covered the retreat so well that the enemy were unable to pursue to the crest of the hill.

This column had hardly fallen back to its position when from the right appeared another Union brigade, pushing steadily and rapidly across some open fields in a persistent and stronger attack upon the railroad bank at this station. The enemy gave him a warm reception in front; but one of the Union regiments appearing upon their left flank, and our batteries opening on them from their right, they failed to stand the assault, and hastily abandoning it fled up the hill to the fort. Our men were seen in permanent occupation of the

bank, and from it continued to fire on the retreating rebels until the last one found safety behind the mud walls of Fort Buckner.

While this had been going on, General Corse was re-enforced by a portion, perhaps all, of another brigade, and the position vacated by him was then filled by the Eleventh Corps of General Howard, which about this time double-quicked across the ridge and went into position on the left extreme. A second assault was now ordered, and General Lightburn, who had been anxiously watching the action, joined the portion of his brigade on the hill, and assumed command of the whole assaulting column. He ordered the movement to begin immediately, and a more desperate and bloody assault than the former was made. The combat had no salient point to be described; it was simply a steady and slow advance of the whole line to within a few dozen yårds of the fort, occupying three quarters of an hour, and then a rapid retreat to the former position at the crest of the hill, leaving the dead and wounded in the hands of the enemy; and between their outer rifle pits and Fort Buckner, Generals Corse and Giles Smith. seriously wounded, were carried into the valley in the rear-the one to lose his leg, and the other probably to die. Corse and Smith gone, the troops were reformed in a new line of battle by Lightburn, and under orders the line lay down to rest and await the attack of the enemy should he venture to make one. From this time-quarter after twelve, was the time which this repulse took place—until half-past one there was a pause in Sherman's battle. This he occupied in inditing a message to Grant, and in preparing for a more determined assault. The centre of the line at Orchard Knob noted the time by rapid and vigorous firing. I employed the time by examining the hospitals in rear of the lately assaulting party, and I found at the old log hut, which was being used as an hospital, and in the side at the foot of the hill, many a brave heart that had grown suddenly silent to the praises which comrades were murmuring over them.

On leaving the valley and the hospitals I returned to the point on the right of the ridge, where the guns were posted. Here I found that a Union brigade had, disdaining the protection of the railroad bank, rushed forward and was now skirmishing with the enemy for the possession of an abrupt ledge of rocks, which, outcropping from the hill side, afforded a secure position to an attacking column, at a point not more than fifty yards from Fort Buckner, which, let it be noticed, was hear the crest of the west side of the hill, up which the brigade was now moving. The brigade eventually gained possession of this by half.