September 10.-Moved on the Chattanooga and Ringgold road 9 miles, and encamped at 5 p.m.

September 12.-Moved to Lee and Gordon's Mills, Ga., on the Chickamauga River, at the crossing of the Chattanooga and La Fayette road.

September 19.-Moved 1 1/2 miles toward Chattanooga, Tenn., Engaged the enemy from 4 p.m. until 6.30 p.m.

September 20.-At 2 a.m. moved 2 miles in the direction of Chattanooga. Engaged the enemy two hours, from 10 a.m. until 12 m. Moved 7 miles, to Rossville, and encamped at 7.30 p.m.

September 22.-At 1 a.m. moved 3 1/2 miles, to Chattanooga, Tenn.

No. 138.

Reports of Colonel George P. Buell, Fifty-eighth Indiana Infantry, commanding First Brigade.

TRACY CITY, August 24, 1863.

SIR: About 11 a.m. of the 22nd instant I received orders to take a force of about 400 men and march to the Tennessee River, for the purpose of capturing the steamer Paint Rock, there disabled, and lying partially guarded somewhere between Suck and Skillet, on said river. Immediately selected 100 men from each regiment, Twenty-sixth Ohio, Fifty-eighth Indiana, One hundredth Illinois, and Thirteenth Michigan, well officered and equipped with three days' rations. In accordance with my request Lieutenant-Colonel Embree accompanied me as second in command, accompanied by 8 or 10 mountain scouts. We started on the expedition. When 3 miles from camp we received orders to halt a short time, news having been received orders to advance at 5 p.m. We marched about 10 miles down the Sequatchie Valley road to Keller's Mill, thence 8 miles on a very indistinct trail over Walden's Ridge to Bob White's house, on the road known as Haley's road, leading from Jasper to Chattanooga, which point we reached at 3 a.m. of the 23rd.

We were then within 2 miles of shore. The steamboat had been disabled. We had intended capturing it before daylight of this morning, but the enemy had within the preceding twenty-four hours secured and passed the vessel above the Suck and out of our reach.

During were this morning about 100 men on the south side of river guarding Kelley's Ferry. It could be surprised and taken without the loss of a half dozen men. The river from the point up to the Suck is from 400 to 500 yards wide. A scout, who came from the south side of the river, reported that the enemy were being re-enforced, and that he was intrenching Lookout Mountain.

Having obtained what information we could, we retraced our steps and reached camp at 8 o'clock this evening. Too much praise cannot be given to the officers and men of my command for their prompt obedience to orders, their endurance of so fatiguing a march, and their energy and zeal in the undertaking.

GEO. P. BUELL,

Colonel Fifty-eighth Indiana Infantry.

Brig. General JAMES A. GARFIELD.