In this order the column moved steadily forward, flanked on either side by cavalry. After relieving the cavalry line of pickets by our advanced line of skirmishers, the skirmishers were soon engaged with the pickets of the enemy, but they, getting a sight of the series of lines, which really looked formidable as well as beautiful, offered but feeble resistance to our advance. The object of the movement being simply to drive the enemy from a hill, so that we could occupy it as an encampment to protect our supply train, to follow in our rear; we did more than that, advancing some half a mile farther, where we found excellent ground for our camp. The First and THIRD Brigades then encamped for the night, the supply train and First DIVISION, with our Second Brigade, coming up the same day. On Monday, the 22d, we were ordered to advance, preceded by the First DIVISION, General Mower, my brigade taking the advance of the THIRD DIVISION. After marching about three miles, and within a mile or two of Oxford, Miss., we halted, and the same p. m. were ordered to countermarch for the rear. We returned, crossing the Hurricane and encamping on the north bank for the night. The next day, the THIRD DIVISION being in the advance and my brigade in the rear of it, we marched to the vicinity of the Tallahatchie, where we were halted on account of the want of a bridge, and the same p. m., by orders of Colonel Shaw, I was ordered to report my brigade to Major-General Smith. Doing so we were moved and drawn up in line of battle at the edge of a wood south of General Smith's headquarters, and a heavy line of skirmishers thrown out. In this position we remained until the 25th. At 6 o'clock of that morning I received orders to move at 7 a. m. After considerable delay at the crossing of the Tallahatchie we succeeded in crossing, and moved on the Holly Springs road, passing about one mile this side of Waterford, where we were encamped for the night, and on the 26th returned to this place. I have no casualties to report save 1 man of the Twenty-first Missouri, who was knocked over by a spent ball in the skirmish of the 21st, but not injured, and the loss of 2 wagons and mules of the Ninth Indiana Battery, captured by the enemy near Abbeville on our return while our foraging for corn.

I have the honor to be, lieutenant, very respectfully, &c.,

C. D. MURRAY,

Colonel Eighty-ninth Indiana, Commanding Brigade.

Lieutenant JAMES B. COMSTOCK,

Acting Assistant Adjutant-General.

Numbers 9. Reports of Colonel Thomas J. Kinney, One hundred and nineteenth Illinois Infantry.

LA GRANGE, August 15, 1864.

Thirty-three men of the Seventh Indiana Cavalry had a skirmish with enemy at Lamar at 12 o'clock last night. Sergeant and twelve men came here; report quite a force, more than they could manage; charged the rebels; were repulsed and scattered. I have sent them back with FIFTY men of Seventh Illinois Cavalry. This morning, if necessary, will send more men down.

T. J. KINNEY,

Colonel 119th Illinois Volunteers, Commanding Post.

Major-General WASHBURN.