EIGHTEEN MILES FROM PULASKI, TENN., LEXINGTON ROAD.

December 28.-6.30 a. m., issued orders for the corps to march at 8 a. m., provided the cavalry is out of the way; General Elliott will lead, General Kimball. The cavalry will start at 5 a. m. 10 a. m., the head of our column starts. The rear of the cavalry command is just moving out the way. The road to-day is no better. The troops cannot move upon it at all, but pass through the thick undergrowth of timber and brush on either side. The country through which we are passing is barren ad desolate; there are also many swamp flats. 3.15 p. m.., our advance reaches a point a miles and a half beyond Levington, eleven miles and a half from our camp of last night. Here we halt and the command commences to go into camp. The cavalry has been in our way all day, and we now overlap the rear brigade of the same . Have not heard one word from General Wilson to-day, therefore it is supposed that he has had no trouble and does not need our assistance. 7 p. m., received a report from Captain Kaldenbaugh (five miles in the rear), who says that none of our trains (headquarters, ammunition, &c.) can get beyond that point to-night. They are stuck fast in the mud and cannot move, and the mules ae exhausted. Received note from General Wilson, dated headquarters Cavalry Corps, Bull's Mills, December 27, 1864, 4.30 as follows:

General T. J. WOOD,

Commanding Fourth Corps:

GENERAL: I am directed to inform you that information has been received that the last of the enemy's forces crossed the Tennessee River last evening, and that the bridge was taken up this morning. General Wilson has sent a staff to General Thomas with this information and for orders.

Very respectfully, your obedient servant,

A. J. ALEXANDER,

Lieutenant-Colonel and Chief of Staff.

9.30 p .m., sent dispatch to General Thomas, stating that General Wilson has reported the enemy across the Tennessee River, and, as it is no use to move farther as a matte of pursuit, that we will wait here in our present camp for further orders from him. He is also informed of the condition of our transportation; that our ammunition trains, hospital train, &c., are in the rear, stuck in the mud, and cannot possibly reach us to-night. Very cold to-night; freezing hard.

LEXINGTON, ALA.

December 29.-7 a. m., directed commanders of divisions and batteries to send out to a creek two miles east of Lexington, and to one four miles west, large foraging parties, to get whatever corn there may be in the country. Enough corn was found last night in the vicinity of Lexington to feed the horses of our batteries and of the rest of the command one day. No forage train has yet arrived from the rear, nor is there at present a prospect of one reaching us. The three day's rations that were started from Pulaski yesterday morning, or the morning of day before yesterday, will not reach Lexington before to-morrow morning. The men will have no rations in their haversacks by to-morrow night. At present we are remaining quietly in camp, awaiting orders from General Thomas, the pursuit of the enemy being over.

11 a. m., received a note from General Wilson, saying that he will remain in camp where he is to-day, that his command may obtain for-