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The Battle of Sunday — Interesting Details.

CHATTANOOGA, Sept. 21. — The battle on the 19th resulted well for us, having held our own as established on the left, and contracted forces during the day. In the morning we held a handsome line, with the right on a ridge of hills, and the left protected by rude works of logs thrown up during the night.

The left rested on the east side of the Rossville and Lafayette roads, about four miles south of Rossville. In the fight of the 19th we lost about 600 killed and 2,000 wounded and were ahead three pieces of artillery. The men were in splendid spirits.

The engagement was resumed at 9 A. M. on the 20th, by an attempt of the rebels to storm Thomas' left and front. Several times they were repulsed with heavy loss to them and very little to us.

This fight lasted an hour and a half, and was one of the most terrific of the war, a continuous fire of musketry and infantry being kept up with deadly effect.

During this the right and center were not engaged, skirmishers keeping up a halting fire for a time. The enemy, finding the assault in vain, maneuvred to the left with the intention of throwing a force on the Rossville road and attacking Thomas on the right flank.

At this juncture Thomas ordered Brannon, who had one brigade in reserve, and two with Reynolds holding the key of the position which was Thomas' right, to move to the left of the line and protect the flank.

Rosecrans at the same time sent Davis and Van Cleve from the right and center to support Brannon in the effort to hold the line to Rossville and protect Thomas' left flank.

On perceiving the withdrawal of skirmishers from the front of the divisions, and moving form right and center, the enemy made a rigorous attack on that part of the line, piercing the center and putting off Davis and Sherridan from the left, and driving the center into the mountains, both right and center being much scattered, without very serious loss in killed and wounded.

The right and centre gone, Thomas' right became exposed to a most terrific flank attack, and Reynolds and Brannon and their right of Thomas' line swung round, his extreme left being as at first.

This also fell back a short distance on the Rossville road. Parts of the center were gathered up and reported to Thomas, who made several stands, but was unable to check the rebel advance until the arrival of reinforcements.

At 1 o'clock Gen. Granger, with one division of reserves, came up and were at once thrown into the centre, driving the enemy handsomely form his position on a strong ridge and with heavy loss — the fire from one of Granger's batteries mowing them down.

This fight only lasted half an hour or so, with a slight loss to us. We regret to say Captain Russell, General Granger's adjutant, was killed ere he had been in the fight ten minutes.

After this bloody repulse the enemy remained quiet until about four o'clock, persisting, however, in maneuvering on both flanks, their full and correct information regarding this country enabling them to do so with great facility.

Having gathered again on the flanks, the enemy made a vigorous attack, and a fight ensued which has no parallel in the history of this army.

Colonel Harker's brigade, Wood's division, both Wood and Harker and Gen. Garfield being present, and the remnant of Johnston's division holding the left, covered themselves with glory; and on the right and centre Brannon, Baird, Reynolds and Palmer, with parts of their divisions, fought most gallantly; while Steadman and Granger with the reserves drove the enemy at every point where they went. At five o'clock, Thomas was still triumphant and on the left held his line of the morning, but with night fell back to a line nearly at right angles with that of the morning.

Two lines of retreat were open to him to Chattanooga, on one of which he fell back to Rossville during the night. Our losses have necessarily been heavy, but the list of killed will be surprisingly light, and in the two days engagement we have not suffered more in men than the enemy in the charge by Thomas. On the first day the enemy lost as many in killed as we did in the whole day. What the loss in prisoners and material are, we cannot say. Our killed will reach 1,200.

Our wounded will amount to 7,000, most of them slight wounds. Among the general-officers killed, are Gen. Lytle, Colonel Key, Col. King and Col. Bartleson. 101st Illinois. Among the wounded were Col. Funkhouser, 98th Illinois, and Maj. Johnson, 22d Illinois.