NEW ALBANY, August 7, 1864.

LIEUTENANT: I have the honor to report the operations of my command from June 14 to July 6, inclusive.

On the morning of the 14th we advanced in line of battle toward the Marietta road, the objective point being Pine Mountain, upon which the enemy had fortifications and artillery. After a difficult and circuitous march through the woods to prevent the development of the movement, we at once debouched from the woods and moved by the right flank, and formed in front of the road and open field in the edge of the woods. A sharp skirmish attended the formation, and for a time my line was enfiladed, until General Baird moved up on my right. Breast-works were thrown up, and a battery placed in position near my right, which opened on Pine Mountain, farther to the right and near other positions of the army. Joining in the movement on the right and left of the mountain, the enemy were compelled to either fall back or be captured. They chose the former. Our forces had now gained Lost and Pine Mountains, and the right, from day to day, continued to swing round to the left, toward Kenesaw Mountain and Marietta. In this movement my command participated. On the 17th I was ordered by General King to take a position on the edge of the woods facing south and perpendicular to the front. The ground was previously examined by Generals Baird, King, and myself, and the object of the movement fully explained. A battery was placed on my left, and the whole line intrenched after night-fall, without developing the movement to the enemy, who occupied the wood across the open field in my front. On the morning of the 18th one of my regiments, the Thirty-eighth Indiana, deployed in front of this wood and at right angles with my new line. Everything being ready, the battery on my left commenced a terrific shelling of the woods. The Thirty-eighth Indiana simultaneously rushed in, surprising the enemy, who were lying close behind their breast-works, to protect themselves from the artillery. Many prisoners were taken, and the woods cleared of rebels. My right now swung up, General Baird forming on my right. My skirmishers had advanced to an open field, across which we discovered the enemy behind the strongest fortifications we had observed during the campaign. The next morning the whole line advanced in a violent rain and thunder storm. As soon as our movements became developed, the enemy opened their batteries, as well as volley of musketry, from their works. The flash and roar of artillery mingled with the lightning and thunder, as if nature had conspired with man in work of destruction. Captain Dilger, commanding Company I, First Ohio Artillery, moved up on my right in the open field, exposed to the enemy's artillery and musketry, returned their fire, and with great heroism and skill succeeded in silencing the battery on his front. Breast-works thrown up, and various movements and dispositions were made during the day and night, which were rendered useless the next morning by the retreat of the enemy. On the night of the 20th I relieved General Harker in front of Kenesaw. The whole night was spent in strengthening the position. Three batteries were disposed along my line. For two days my command lay under the most furious artillery fire that it has ever been my lot to experience. The enemy, from various directions, concentrated their fire on the batteries in my line. The night of the 23rd was occupied in relieving General Cruft's brigade, farther to the right, and in forti-