Well, the enemy has assaulted Lookout Mountain to-day, sure enough, as was intimated in my letter of last night he probably would do. Having accomplished a part of the object of his demonstration yesterday, to wit: the transfer of a portion of our forces on the mountain to the extreme right, he attacked the mountain with a confidence which the sequel will show was not misplaced. The great rise in the Tennessee had carried away his pontoon bridges the night before, but his positions were so well taken, and had been so strongly fortified, that he did not hesitate to make the assault. He opened at 11 o'clock with his batteries in Lookout Valley, directing his fire against our lines along the western side and northern face of the mountain. Our own batteries on the mountain could take no part in the engagement, owing to a dense fog which enveloped Lookout Point and the crest above. At 12 1/2 o'clock the infantry became engaged, and the battle was then fully joined. Very few details have been received -- too few, indeed, for me to attempt to enter into particulars. The impression prevails in well informed circles that the affair has not been well conducted by the Confederate officers in command on the mountain. Our forces had been much weakened the night before by the withdrawal of WALKER's division, which was sent to the right, leaving only STEVENSON's and CHEATHAM's divisions behind, both under command of Gen. STEVENSON. Gen. CHEATHAM arrived on the ground late in the afternoon, having just returned to the army. Up to the time of his return his division was under the command of Gen. JACKSON, the senior brigadier in the division. It was thought that these two divisions would have been sufficient to hold the position against a largely superior force; but not so. The Confederates were steadily pushed back from the moment the infantry opened fire until late in the evening when Gen. BRECKINRIDGE went to the assistance of STEVENSON with a brigade. The Federals, who had driven the Confederates slowly around the north face of the mountain to CRAVEN's house, and thence around almost to the road which leads to the top, were, in their turn, forced back after night some four or five hundred yards. The fight continued until 10 P.M., and even now I can hear an occasional shot while I write. The troops and guns on the mountain were brought down safely, only a few commissary stores being left behind. We lost a considerable number of prisoners, nevertheless, early in the day, and on the western slope of the mountain, the enemy, it is alleged, having got in the rear of WALTHALL's brigade, under cover of the prevailing fog. One account says that WALTHALL lost from 500 to 600 prisoners, including nearly the whole of one regiment -- the Thirty-fourth Mississippi. It is not improbable that our loss has been exaggerated somewhat. Orders have been given to evacuate the mountain, and for the whole army to retire across the Chickamauga, in the direction of the station of that name. The loss of Lookout Valley and Brown's Ferry removed all doubt as to the ability of Gen. GRANT to subsist his army at Chattanooga this Winter, and rendered the longer possession of Lookout Mountain of comparatively little importance, and, now that the mountain has passed into his hands, there is no reason left why we should longer remain in the mud and water around Chattanooga. Besides, Gen. GRANT has been throwing a heavy force up the river, and crossing it over in the boats we neglected to burn all this afternoon. A portion of this force consists of heavy cavalry, which have been landed above the mouth of the Chickamauga. Some infantry had also been landed on the east side of that stream -- the remainder and much more the more numerous body on the west side -- all up the Tennessee and some distance above our right wing. This movement greatly endangers the depot and railroad, and furnishes an additional reason for withdrawing across the Chickamauga. Another danger, and a still more serious one, is the probability that GRANT will turn our right and get between the main army and LONGSTREET at Knoxville. It is now well ascertained that SHERIDAN has not gone to the relief of BURNSIDE, as was fully believed a few days ago; but the whole Federal army is here marshaling for our destruction. Perhaps GRANT has concluded that he could best succor BURNSIDE by forcing BRAGG to retire. I have just heard that our communications with Knoxville have been cut, probably by the Federal cavalry that crossed the river above this afternoon, and that the depot buildings at Joyner's Station, on the Chattanooga and East Tennessee road, have been burnt. NOVEMBER 25 -- 2 A.M. Finding that he could not withdraw his army in time, Gen. BRAGG has given orders to mass his whole available force on the right. A battle may be expected to-day. The situation is critical.

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