NASHVILLE, TENN., December 15, 1864-10.30 p. m.

(Received 11 p. m.)

Major T. T. ECKERT:

Our line advanced and engaged the rebel line at 9 this a. m. The line was formed thus: Steedman on the left; T. J. Wood, with the Fourth Corps, next; A. J. Smith next; with Cox, in reserve, next; and the cavalry, under Wilson, fighting dismounted, occupying the extreme right, aided by gun-boats on the river. The artillery practice has been fine, and at times the musketry firing continuous and heavy, and, though the casualties have been slight, the results are very fair. The left occupies the same ground as at morning, but right has advanced five miles, driving enemy from river, from his entrenchments, from the range of hills on which his left rested, and forced back upon his right and center. His center pushed back from one to three miles, with loss, in all, of 17 guns and about 1,500 prisoners, and his whole line of earth-works, except about a mile on his extreme right, where no serious attempt was made to dislodge him. From our new line General Thomas expects to be able to drive the enemy at daylight east of the road to Franklin, and so open communication with our forces at Murfreesborough. The whole of Hood's army is here, except the cavalry and one division, which has been detached to threaten or attack Murfreesborough. The whole action of to-day was splendidly successful. The divisions commanded by General Kimball, of the Fourth Corps, by General Garrard, of the command under General A. J. Smith, and the cavalry division under General Knipe, were under my observation, and I have never seen better work. General Kimball's division carried two fortified positions by assault, with very slight loss, capturing at one point 400 prisoners and 6 guns. No doubt the other parts of the line did as well; I only speak of what I saw.

J. C. VAN DUZER.

CLARKSVILLE, December 15, 1864.

General THOMAS:

I sent two gun-bats at 4 o'clock this morning, accompanied by an army transport, and twenty-men furnished by Colonel Smith, which destroyed about twenty of Lyon's canoes and skiffs, and brought away two artillery barges, found near Cumberland and int eh creeks. None of burnt transports interfere with channel.

S. P. LEE,

Acting Rear-Admiral, &c.

CLARKSVILLE, December 15, 1864-5.30 p. m.

Major-General THOMAS:

Telegram just received from commanding officer Black Hawk, at Smithland, reports force of 900 rebels, with two guns, at Eddyville. Three gun-boats convoying transports from here had got off before it was received here. I have ordered an iron-clad and heavy gun-boats, just arrived at Mound City, from there to Eddyville, thence as far up as stage of water will allow.

S. P. LEE,

Acting Rear-Admiral, Commanding Mississippi Squadron.