Numbers 39. Report of Colonel William M. Stone, Twenty-SECOND Iowa Infantry, commanding SECOND Brigade. HDQRS. SECOND BRIGADE, FOURTEENTH DIVISION, Vicksburg, July 26, 1863.

CAPTAIN: In reporting the doing of this brigade in the recent expedition of our army against Jackson, I shall necessarily be continued to the time I have been in command of it. Since Saturday morning, the 18th instant, up to this time, the brigade has been under command of Brigadier-General Lawler, who on that morning relinquished the command to me, and started for his home on a leave of absence.

For information as to the action of the brigade prior to the time alluded to, I respectfully refer you to the report of Lieutenant-Colonel Whittlesey, of the Eleventh Wisconsin, herewith transmitted.

On Friday morning, the 17th instant, it was ascertained that Jackson was evacuated, and a portion of our forces marched in and occupied the city. At that time this brigade was in the position they had occupied for several days previous, near the enemy's fortifications on the westside of the city. Here we remained until Saturday morning, when we changed our camp about 1 mile to rear. In the afternoon we marched out to the Mississippi Central Railroad, south of the city, where, in connection with the First Brigade, we succeeded in destroying about 5 miles of railroad. This feat we accomplished by Sunday evening, when we laid upon our arms until Monday, and then returned to our camp on the Raymond road. On Tuesday morning we started for Vicksburg. By easy marches, we reached our old camp in the rear of the city on Friday morning, where we rested for about an hour. We then received orders to move to a new camp, and were directed to go down the Warrenton road to find it. After marching a distance of about 10 miles, over a broken country and under a burning sun, we succeeded in reaching our present camp on the river bank in front of Vicksburg, and about 1 1/2 miles from where we started in the morning. Thankful that it is as well for us as it is, and being always ready to obey orders, and to do our full share"in putting down this unholy rebellion," we are now resting contented from long marches and months of unremitting toils and dangers.

I herewith transmit reports of regimental commanders of the killed and wounded, which embrace all the casualties in the brigade in our late expedition.

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

W. M. STONE,

Colonel Twenty-SECOND Iowa, Commanding Brigade.

Captain C. H. DYER,

Assistant Adjutant-General.

Numbers 40. Report of Major Leonard B. Houston, Twenty-THIRD Iowa Infantry. HDQRS. TWENTY-THIRD IOWA INFANTRY VOLUNTEERS,[July 24, 1863.]

Left Vicksburg on the morning of July 5, 1863, with 82 enlisted men and 7 field staff, and commissioned officers. Encamped on Big Black