From this point it marched with the army, via Bolton and Clinton, to Jackson, MISS., arriving at the position assigned it on the morning of the 10th instant. it remained in reserve until the morning of the 15th, when it marched to the front and relieved a brigade belonging to General Osterhaus' DIVISION.

On the 16th, in compliance with an order from DIVISION commander, I ordered my line of skirmishers to feel the enemy's works. It soon became hotly engaged, and was obliged to halt, fully demonstrating the fact that the enemy was still in force. in this attack the brigade suffered a loss of 1 killed and 11 wounded. Early on the morning of the 17th instant, I received information that Jackson had been evacuated, and without delay advanced my skirmishers and occupied the enemy's works in my front, being among the first to reach the city.

On the 18th, the One hundred and fourteenth Illinois and the seventy-SECOND Ohio Volunteer Infantry, with Waterhouse's battery, marched in the expedition to Brandon, under command of Colonel Gedded, of the Eighth Iowa, who, I suppose, will report the part taken by them in the engagement at that place.

In the mean time the Ninety-FIFTH Ohio was used as a rear guard on the main Clinton road, and the Ninety-THIRD Indiana were destroying railroad in the city.

On the 23rd, the brigade marched with the corps to which it is attached for its present camp, reaching this vicinity on the evening of the 25th instant. I cannot speak too highly of the endurance, spirit and courage of the troops comprising my command, officers and men having acquitted themselves nobly.

I am, &c.,

W. L. McMILLEN,

Colonel, Commanding First Brigade.

Captain J. B. SAMPLE, Assistant Adjutant-General.

Numbers 45. Report of Captain Samuel A. J. Snyder, Seventy-SECOND Ohio Infantry. NEAR MARKHAM'S, July 30, 1863.

COLONEL: I have the honor to submit the following report of the operations of this regiment, which composed a part of the brigade under your command, in the expedition to Brandon, MISS., July 19, 1863:

Making no mention of the march, I would state that the part taken by the regiment was unimportant. When the line of battle was formed, and skirmishers thrown forward from the Eighth Iowa and One hundred and fourteenth Illinois, I was ordered forward to support those regiments on the left of the road. The ground over which my command had to advance in battle order was very rough and traversed by deep cuts, yet the advance was in good order and my line was not once broken. After advancing in support for about 1 mile, I was ordered to fill the interval between the Eighth Iowa and one hundred and fourteenth Illinois, when the line again advanced, but men no enemy, he having taken advantage of a hard rain-shower to retreat. Upon arriving at Brandon, my regiment was thrown forward to support the skirmishers in the eastern limits of the town, when we bivouacked for the night.