HEADQUARTERS SECOND CAVALRY BRIGADE, In Camp near Murfreesborough, Tenn., January 6, 1863.

LIEUTENANT: I herewith have the honor to report the part taken and the work performed by my brigade since our departure from Nashville until the close of the battle before Murfreesborough.

I left Nashville on the morning of the 26th ultimo, with three regiments of my brigade, viz, the First, Third, and Fourth Ohio Cavalry, the Fifth Kentucky remaining at Nashville. My force numbered 950 men. We marched out on the Franklin pike, the Third Ohio having the advance. When within 2 miles of Franklin, drove in the rebel pickets, skirmished all the way down to Franklin, drove the enemy out, and pursued him some 2 miles. From the best information received, the enemy were 900 strong (all cavalry), part of Wharton's brigade. We killed 4, wounded several, and took 10 prisoners, among them a lieutenant of General Bragg's escort, several horses and mules, and destroyed their camps, with some tents standing thereon. We retired from Franklin, moved over to the Wilson Creek pike, and picketed said pike.

On the 27th, sent the First Ohio and most of the Fourth Ohio, under command of Colonel Milliken, on the Wilson Creek pike, toward Triune, to reconnoiter. They proceeded within 2 miles of Triune, captured 6 of the rebel pickets, when the enemy opened on them with shells; threw some 50 without damaging us any; then my force retired to camp. I likewise had sent a battalion of the Third to Franklin to reconnoiter, which drove in the rebel pickets, who had returned in force after my command had left the evening previous. Quite a skirmish ensued, in which 3 of the rebels were killed and several wounded. After skirmishing some two hours, and the enemy being too strong to drive, the battalion returned to camp in good order without any loss.

On the 28th, moved with the command to Triune without anything occurring worth mentioning.

On the 29th, proceeded toward Murfreesborough, moving between the Franklin road and the road called Bole Jack road, which General McCook's corps moved on. In divided my brigade into three columns, marching parallel with one another and with the main force, the right (the Fourth Ohio) moving on the Franklin road, the Third in center, and the First on the left, the columns being from 1 to 1 1/2 miles apart, throwing out skirmishers, connecting one column with the other, and connecting on the left with the main column. We thus proceeded for 5 miles, when the center column encountered the enemy's pickets, which they drove in, the different columns steadily advancing.

Shortly after, both the right and the left encountered pickets, driving them in before them. After proceeding about 1 mile farther, we came upon the enemy's cavalry (Wharton's brigade), engaged them for three hours, some time the right wing, then the left, then the center, receiving several charges, which were repulsed, driving the enemy some 2 miles, when the brigade concentrated, repelling a heavy charge from the enemy, driving him back under his guns, which were only a short distance from us. We then retired some 2 miles and went into camp.

Some few casualties occurred this day. The officers and men behaved admirably during the whole day. The Fourth had proceeded until the enemy threw shells into them pretty rapidly, when they retired. We were within 4 miles of Murfreesborough.

On the morning of the 30th was ordered to proceed on the Franklin road toward Murfreesborough, to push the enemy hard. We had encamped that night near the brick church, on the road leading from General McCook's headquarters to the Franklin road. I proceeded that