I should have joined General Negley at 7 a. m. had Colonel King moved with more promptness.

I am, colonel, very respectfully, your obedient servant,

J. M. BRANNAN,

Brigadier-General, Commanding.

Lieutenant Colonel GEORGE E. FLYNT,

Assistant Adjutant-General, and Chief of Staff.

HDQRS. THIRD DIVISION, 14TH ARMY CORPS, Near Chattanooga, Tenn., September 29, 1863.

COLONEL: I have the honor to forward, for the information of the major-general commanding, the following report of the part taken by my division (Third, Fourteenth Army Corps) during the engagement of the 19th and 20th September, 1863, on Chickamauga Creek. In accordance with orders I struck the camp of my division at Gower's Ford, Chickamauga Creek, at about 5 p. m. on the 18th instant, and advanced by the Chattanooga road to the junction of the La Fayette road about 3 miles above Crawfish Spring, whence, taking the latter road, I arrived by daylight at a point about 2 1/2 miles distant from its junction with the Chattanooga road. I was much retarded in this march, which continued during the entire night, by the delay of the Twenty-first Corps in getting into position, having frequently to halt for a considerable time to enable portions of that command to come up from the rear of my column.

On arriving at a point on the La Fayette road known as Kelly's house, I received orders from Major-General Thomas to capture, if possible, a rebel force represented by Colonel Dan. McCook to be a brigade cut off on the west side of the Chickamauga Creek; failing in this, to drive it across the creek. In obedience to these instructions, I advanced the Second Brigade of my division (Colonel John T. Croxton, Fourth Regiment, Kentucky Volunteer Infantry, commanding) by the Reed's Bridge road toward the rebel left, while the remaining brigades of my command advanced by the Daffron's Ford road to strike the supposed right of the enemy's position.

Shortly after 7 a. m. on the 19th instant the Second Brigade, having advanced about three-quarters of a mile toward the Chickamauga, came upon a strong force of the enemy, consisting of two divisions instead of the supposed brigade, who made a furious attack, repulsing Colonel Croxton's first advance. The rebels following this up with a much superior force, a desperate conflict ensued, Colonel Croxton maintaining his ground with great determination, and though suffering considerable loss, refusing to yield his position to the most furious efforts of the rebels. At this point Colonel Carroll, Tenth Regiment Indiana Volunteer Infantry, fell mortally wounded, while gallantly leading his regiment, and Lieutenant Colonel P. B. Hunt, commanding Fourth Kentucky Volunteer Infantry, was carried from the field in a scarcely less precarious condition. On Colonel Hunt being wounded, I sent Major R. M. Kelly, division inspector, at his own request, to command the Fourth Kentucky, which he did that day and the following in the most gallant manner.

I here re-enforced Colonel Croxton with the Thirty-first Ohio Volunteer Infantry (Lieutenant-Colonel Lister commanding) from the left, being the only force available.