About 1 p. m. on the 23d, the infantry advanced, under cover of the guns, and carried the rebel rifle-pits, situated about 1 1/2 miles to our front. Such batteries as could be mounted were immediately thrown out on Orchard Knoll, Brush Knob, and such other elevations as the country afforded.

With the assistance of General Sherman, who furnished me with horses for three batteries (the battery horses of the Department of the Cumberland having either died, or become so emaciated from starvation as to render but few of them fit for service), I had succeeded in mounting seven batteries; four, however, were only brought into action. These did excellent service during the attack of the 25th instant, as, being in easy range of the rebel intrenchments, they did considerable execution and aided materially in forcing the enemy to abandon those works.

On the 24th, Sherman crossed the river and formed a junction with Howard near Citico Creek, the batteries on the north side of the river effectually preventing any masses of troops intercepting them. It was, however, found too hazardous to endeavor to enfilade the rebel line from these batteries as was at first proposed, our troops being in such close proximity.

During the 24th and the morning of the 25th, the guns of Forts Wood and Cheatham opened on all bodies of troops observed to be concentrating or moving on Missionary Ridge, distance 2 1/2 miles; sometimes with good effect.

At about 3.30 p. m. on the 25th instant, the line made the advance that ultimately resulted in carrying the enemy's position. The guns from the intrenchments continued to play on the rebel line at the foot of the ridge until the proximity of our troops rendered such fire dangerous, when they turned their attention to the crest of Missionary Ridge, and made some excellent practice on the rebel troops moving on that position.

This engagement has proved beyond doubt the utter worthlessness of the projectile known as the Rodman projectile, furnished the Rodman 4 1/2-inch guns, and unless other and better projectiles be obtained I consider that these guns will be little better than useless.

There is a radical defect in the fuses of the shells furnished this department, which I believe to originate in the inequality of their composition, rendering the explosion of the shell at the calculated time very uncertain. I have also remarked that the partitions in the fuses are very thin and liable to burst, thus causing the explosion of the shell in a shorter period than the time for which the fuse was cut. In fact, the entire practice with shell was very unsatisfactory, the shell either exploding too soon or not at all.

The following guns, carriages, caissons, limbers, ammunition, &c.,

were captured from the rebels during the engagement of the 24th and 25th and subsequent pursuit of the enemy:

By General Davis' division,

at Chickamauga Station 24-pounder guns 2

By General Geary's division, on Lookout Mountain

field pieces 2

By General Osterhaus' division, on Missionary Ridge do 1

By General Wood's division, on Missionary Ridge do 12

By General Sheridan's division, on Missionary Ridge do 6

By General Johnson's division, at Graysville do 4

By General Baird's division, on Missionary Ridge do 1

Claimed by Generals Baird and Wood do 6

Claimed by Generals Wood and Sheridan do 6

Total 40