MACON, GA., August 5, 1864.

SIR: I have the honor to submit the following report of the part taken by my brigade in the action near Atlanta, Ga., on the 22nd of July, 1864:

Owing to the long march the night before and the heavy fire it had been subjected to throughout the previous day, the brigade was much worn and exhausted when it went into action. After advancing in line for about a mile and a half through an almost impenetrable thicket of undergrowth, we struck the enemy, who, after a feeble resistance of a few minutes, fled in great confusion, abandoning his artillery, ordnance, and tool wagons and ambulances. Many prisoners were captured at this point, among them Colonel Scott, commanding a brigade in my front. Owing to the rapidity of the pursuit, the ungovernable enthusiasm of the men, and an almost impassable morass through which the brigade passed, it became much lengthened and thereby weakened, presenting a front scarcely more formidable than that of a strong skirmish line. The pursuit was, however, continued with great spirit and vigor until we had carried three lines of their temporary works, when we came upon them in heavy force and strongly intrenched in an open field. Finding that my brigade was far in advance of the troops on my right and left, and that the position was insecure, I dispatched an officer to communicate the same to the major-general commanding, with the request that re-enforcements be sent forward. In the mean time, the enemy opening a cross-fire on us, I soon found the position untenable, and ordered the brigade to fall back a short distance. A portion of the command either did not receive the order, or failed to comply with it, and under the direction of Major R. J. Person, of the Fifth Confederate Regiment, surrendered to the enemy. This was after I was wounded and forced to leave the field.

Up to this time both officers and men of the brigade bore themselves in the most creditable manner. Two stand of colors were captured by the Twenty-fourth and Twenty-fifth Texas Cavalry (dismounted), 15 pieces of artillery, many of them with horses and harness complete, caissons, ordnance, and tool wagons and ambulances.

Owing to the fact that every regimental commander in the brigade but one was either killed, wounded, or captured, and the commands devolving on inexperienced officers, their reports are meager and imperfect. The list of casualties is, therefore, only approximate, and is as follows: Killed, 23; wounded, 100; captured and missing, 75. Among the killed was the cool and intrepid Captain William M. Allison, of the Eighteenth Texas Regiment, commanding the skirmish line. Among the severely wounded was Colonel R. Q. Mills, Tenth Texas Regiment, a worthy and efficient officer. The command of the brigade then devolved upon Lieutenant-Colonel Young, of the Tenth Texas Regiment.

To Lieutenant S. G. Sneed, acting assistant adjutant-general; Captain J. L. Leonard, acting assistant inspector-general, and Lieutenants William H. Hardy and W. P. Wilson, aides-de-camp (the latter of whom lost his right arm), of my staff, for their zeal and activity displayed on the field, much credit is due.

J. A. SMITH,

Brigadier-General.

Captain I. A. BUCK,

Asst. Adjt. General, Cleburne's Div., Army of Tennessee.