HDQRS. SECOND Brigadier, THIRD DIV., 20TH ARMY CORPS, Camp in front of Atlanta, Ga., July 28, 1864.

CAPTAIN: I have the honor to make the following report of the operations of the Second Brigade, Third Division of the Twentieth Corps, from the 29th day of June to this date, July 28, 1864:

On the 29th day of June the brigade was encamped on the Powder Springs road, north side, about three and a half miles west of Marietta, Ga., behind earth-works recently erected by it. Major-General Butterfield having leave of absence, Brigadier-General Ward assumed command of the division. On the 30th of June the brigade remained in the same camp, the enemy remaining, as before, close in front in their works. On the 30th of June the brigade was relieved by the First Brigade of the division,and moved a short distance to the rear. On the 1st of July we remained in same camp, the men washing and cleaning clothes and arms. On 2nd of July remained in same camp. On the 3rd of July the enemy at 2 o'clock in the morning evacuated his position in front, abandoning the lines by which he held Kenesaw Mountain and Marietta, which our forces at once occupied. The brigade at an early hour moved out with the division on the Marietta road to the intersection of the Sandtown road, three-fourth of a mile from Marietta. Here we came under fire of two batteries of the enemy, stationed southeast of us, toward the railroad. The First Brigade was halted here, and this brigade directed to advance on the Sandtown road a mile upon a reconnaissance. The enemy wa snot found on this road, and a short advance farther brought us to the Second Division, Twentieth Corps, who were advancing directly east and at right angles to our direction, and skirmishing in front of our left. The brigade passed the Second Division, and throwing out skirmishers and flankers advanced some five miles south, to a point quite near the enemy's works on the left. Here they appeared in strong force, and opened upon us with artillery. We halted;the brigade was formed in two lines and fortified. The shells of the enemy did comparatively little harm, wounding but 2 men in the brigade. At 4 p.m. the brigade was relieved by Morgan's brigade, of Davis' division, of the Fourteenth Corps, and moved to the right of the road, crossing a branch of Nickajack Creek, and encamping for the night with the division at a point near, seven miles west of south of Marietta. On the 4th of July the brigade moved two and a half miles to the south, and near to Mill Grove, leaving the rebel works to the left, and encamped here for the night,near to portions of the Sixteenth and Twenty-third Corps. On the 5th of July the brigade moved southeast, passing through the works of the enemy which had been evacuated the night before, meeting a portion of the Sixteenth Corps, who passed to our right. The brigade crossed Nickajack Creek at 3 p.m., and advanced about two miles and encamped, on a high range of hills overlooking the Chattahoochee River, with the division and corps. July 6, the brigade moved two miles east, encamping on the same range, the enemy being within his last line of works this side the Chattahoochee River. The brigade remained in this camp until the 17th of July, resting, refitting, and preparing for the advance. On the 10th of July the enemy evacuated their position this side of the river in our front. On the 17th day of July the brigade, with the division, marched eastwardly, passing Vining's Station, on the Chattanooga and Atlanta Railroad, and going to the river, crossed it at Pace's Ferry on two parallel pontoon bridges without resistance,