HEADQUARTERS FIRST DIVISION, FOURTH ARMY CORPS, Huntsville, Ala., January 6, 1865.

COLONEL: I have the honor to report that on the evening of the 14th of December last I received the order of the general commanding the corps to be ready to march at 6 o'clock the next morning, for the purpose of attacking the rebel army, then entrenched before Nashville. At that hour my command was under arms, and immediately after daybreak it was moved toward the right and out through our line of works on the Hillsborough pike, and put in position-the Third Brigade, Brigadier General William Grose commanding, on the right, his right extending to the position taken by the left of the Second Division of this corps, and the First Brigade, Colonel I. M. Kirby commanidng, on the left, his left resting on the Hillsborough pike; the Second Brigade, Brigadier General Walter C. Whitaker commanding, was placed in reserve opposite my center. All of my brigades were formed in two lines of battle. During the forenoon my line was advanced, driving the enemy's skirmishers before it to a ridge fronting and about, 1,000 yards form Montgomery's Hill, where the enemy had strong works and a battery commanding the Hillsborough pike. In this advance my command had oblique to the left, conforming its movements to adjacent commands, and nearly all of the First Brigade crossed s the turnpike and took position to the left of it. Ziegler's battery (B, Second Independent Pennsylvania Artillery) had been ordered to report to me, and was placed in position on the ridge before spoken of, near the pike, and on the left it. About midway between this position and Montgomery's Hill, in front of my left, intervened a small ridge of ground, which almost disappeared at the Hillsborough pike, in front of my left center. The country between my position and the enemy's works was open, and every movement of my troops could be plainly seen by him. At 2 p. m. I was ordered to occupy this ridge, which was promptly done by Kirby's brigade, Grose's brigade connecting which his right. The right of Grose's brigade in this movement was retired to protect my right flank, which was left exposed in consequence of the Second Division not having moved at the same time. Ziegler was sent forward with his battery, and took position on the Hillsborough pike, on the right of First Brigade, and within easy musket-range of the enemy's works. From this point he kept up a galling and continuous fire upon the enemy, sending many of his shells through the rebel embrasures into their ranks. Upon securing the ridge of ground referred to it was discovered that at the foot of the slope toward the enemy there was an old road, somewhat worn by rains and long use, and which Kirby's front line was ordered to occupy. A good protection to a part of my line was thus procured for the time being within 250 yards of the enemy's works.

At 4 p. m. I asked and received permission of the general commanding the corps ot assault this hill. The command, "forward," was immediately given. Grose's brigade advanced along the turnpike, and, crossing it, passed a stone fence which had been used by the enemy, and charged up the steep hill at double-quick. The right of his brigade reached around and inclosed the south westerly or left end of the enemy's works on Montgomery's Hill. Kirby's brigade moved directly forward, with an unbroken line, across a corn-field where the ground was very heavy, and through the brush and fallen timber on the hill-side, never halting until his front line was inside the enemy's works. Both brigades moved in the face of a murderous fire of canister and rifled-balls, and both reached the hill-top at nearly the same moment. Kirby lost heavily while crossing the corn-field, as he was necessarily much exposed