December 22.-7 a. m., open fire upon the enemy's pickets across Duck River. After considerable firing we succeed in crossing the Fifty-first Indiana Infantry across the river in pontoon-boats. They soon drive back the enemy's skirmishers and capture a few prisoners. These skirmishers were left by the enemy as a party of observation. The Fifty-first Indiana behaved very well, and lost 1 man killed and 7 or 8 wounded. 8 a. m., the enemy having been driven from the south bank of the river, Colonel Streight (First Brigade, Third Division) commences to lay the pontoon bridge. There are but three pontoniers with the train, and the troops that are to lay the bridge know nothing about the work. It will, therefore, be necessarily slow. Some of the prisoners captured to-day report that five brigades of the enemy's troops left Columbia very early this morning for Pulaski, and that Hood intends to cross his army over the Tennessee at Decatur. 6.30 p. m., the pontoon bridge just completed. This corps will move over it at once; the cavalry will follow, and commence sot cross at 5 a. m., to-morrow. General Thomas verbally directs that as soon as the cavalry gets over to-morrow we "press on" after the enemy;s to move out the Pulaski pike, and the cavalry will move "on our flanks." 7 p. m., General Beatty's division commences to cross; General Kimball's will follow; then General Elliott's. 12 midnight, owing to delays the last of General Elliott's division is just crossing the pontoon. General Beatty's division bivouacs on the ridge just beyond our old picket-line-the one established when we first arrived at Columbia-General Kimball's division on the right of the Pulaski pike, inside of the same . The pontoon bridge is a very poor one,and may break down before all of our artillery and trains pass over it. The artillery. All must be over by 5 a. m. to-morrow to allow the cavalry to cross.

COLUMBIA, TENN.

December 23.-5 a.m., the bridge is in such a bad condition and the descent and ascent of the banks so slippery that it is most difficult to get on and off of the bridge. Since midnight, when the lest of General Elliott' division crossed, we have been able to cross but three batteries and a few wagons. The rest of our artillery and the greater part of our train is to cross, but the bridge must now be given up to the Cavalry Corps, which is just ready to cross. 7 a. m., directed division commanders to march (to move down the Pulaski pike) as soon as the cavalry passes. It will be at least 9 o'clock before all of the cavalry gets over the river, even if the bridge does not break or have to be repaired. It was very cold last night; this morning it is a little warmer. The road s off the turnpike are yet impassable. 2 p. m., the cavalry is very slow crossing the brigade. It is very probable that it will not all be over before dark, therefore orders are given to division commanders to march down the Pulaski pike about five or six miles and camp for the night. 2.30 p. m., commence to march, Kimball's division leading, followed by Beatty's, then Elliott's. 4 p. m., come up with the rear guard of the enemy, posted in a gorge through which the pike runs, five miles from Columbia. There are high hills on either side of this gorge, running almost at right angels to the road. 4.15 p. m., deploy two regiments as skirmishers and one as support, and then more forward to drive the enemy out of the gorge. A rifle battery is also brought to the front and opens fire. 4.45 p. m, the enemy runs. There was ap-