I herewith report the following list of casualties,to wit:

Command. Killed. Wounded. Missing.

Company A 2 4 ---

Company B 1 8 5

Company C 1 4 ---

Company E 1 7 ---

Total 5 23 5

I have the honor to be, captain your obedient servant,

J. A. ROSS,

Major Fourth Arkansas Battalion.

Capt. R. E. FOOTE,

Assistant Adjutant-General, Third Brigade, McCown's Division.

No. 300. Report of Capt. John T. Humphreys, Arkansas battery.

CAMP NEAR SHELBYVILLE, TENN., January 10, 1863.

SIR: In obedience to orders, at daylight on the morning of December 31 [1862,] my battery advanced to the position occupied the day previous by Robertson's battery. Your brigade, then advancing, engaged the enemy and was rapidly driving him back. I followed as closely as the nature of the ground would admit, but, turning to the right too suddenly, became separated from your brigade, and, having advanced in a northern direction about 1 mile, engaged a battery of the enemy, a part of which was soon after captured by our advancing lines. I then passed through an interval in our infantry lines caused by our left swinging too far in that direction, and, taking position near Mr. Cowan's house, some 3 miles form and northwest of our original lines, opened fire upon the enemy's batteries, some 500 yards distant, in position on an elevation equal to our own and partially concealed by a narrow skirt of timber intervening between our position and his. The enemy's guns (supposed to have been sixteen in number), then firing upon our infantry and other troops in his front, were immediately turned upon us with great precision and rapidity. We responded as fast as our guns could be served, and for more than half an hour drew the entire fire of all the guns on the opposite hill. Two of my guns were rendered useless by ammunition too large, and two others were, during the action, disabled by the enemy's shot, one having a wheel shot off and otherwise injured, and the cannoneers of the other being in the same way disabled. Five horses were killed by an exploding shell. With two pieces (a 3-inch rifle and 6-pounder gun) we maintained the fight until our advancing lines were charging the enemy's guns, when we were ordered to fall back, which we did, to a point some 300 yards in rear of that position. Eight men were disabled by wounds.

During the engagement there were many acts of individual gallantry displayed, some of which I beg leave to mention. Lieut. John W. Rivers, when the cannoneers at a piece were disabled, seized the sponge-staff, and, calling other to his aid, filled the post of No. 1 with energy and determination.