From the memoirs of William Tecumseh Sherman:
Resuming our march eastward by the large road, we soon reached Elk River, which was wide and deep, and could only be crossed by a ferry, a process entirely too slow for the occasion; so I changed the route more by the north, to Elkton, Winchester, and Deckerd. At this point we came in communication with the Army of the Cumberland, and by telegraph with General Grant, who was at Chattanooga. He reiterated his orders for me and my command to hurry forward with all possible dispatch, and in person I reached Bridgeport during the night of November 13th, my troops following behind by several roads. At Bridgeport I found a garrison guarding the railroad-bridge and pontoon bridge there, and staid with the quartermaster, Colonel William G. Le Due (who was my school-mate at How's School in 1836). There I received a dispatch from General Grant, at Chattanooga, to come up in person, leaving my troops to follow as fast as possible. At that time there were two or three small steamboats on the river, engaged in carrying stores up as far as Kelly's Ferry. In one of these I took passage, and on reaching Kelly's Ferry found orderlies, with one of General Grant's private horses, waiting for me, on which I rode into Chattanooga, November 14th. Of course, I was heartily welcomed by Generals Grant, Thomas, and all, who realized the extraordinary efforts we had made to come to their relief. The next morning we walked out to Fort Wood, a prominent salient of the defenses of the place, and from its parapet we had a magnificent view of the panorama. Lookout Mountain, with its rebel flags and batteries, stood out boldly, and an occasional shot fired toward Wauhatchee or Moccasin Point gave life to the scene. These shots could barely reach Chattanooga, and I was told that one or more shot had struck a hospital inside the lines. All along Missionary Ridge were the tents of the rebel beleaguering force; the lines of trench from Lookout up toward the Chickamauga were plainly visible; and rebel sentinels, in a continuous chain, were walking their posts in plain view, not a thousand yards off. "Why," said I, "General Grant, you are besieged;" and he said, "It is too true." Up to that moment I had no idea that things were so bad. The rebel lines actually extended from the river, below the town, to the river above, and the Army of the Cumberland was closely held to the town and its immediate defenses. General Grant pointed out to me a house on Missionary Ridge, where General Bragg's headquarters were known to be. He also explained the situation of affairs generally; that the mules and horses of Thomas's army were so starved that they could not haul his guns; that forage, corn, and provisions, were so scarce that the men in hunger stole the few grains of corn that were given to favorite horses; that the men of Thomas's army had been so demoralized by the battle of Chickamauga that he feared they could not be got out of their trenches to assume the offensive; that Bragg had detached Longstreet with a considerable force up into East Tennessee, to defeat and capture Burnside; that Burnside was in danger, etc.; and that he (Grant) was extremely anxious to attack Bragg in position, to defeat him, or at least to force him to recall Longstreet. The Army of the Cumberland had so long been in the trenches that he wanted my troops to hurry up, to take the offensive first; after which, he had no doubt the Cumberland army would fight well. Meantime the Eleventh and Twelfth Corps, under General Hooker, had been advanced from Bridgeport along the railroad to Wauhatchee, but could not as yet pass Lookout Mountain. A pontoon-bridge had been thrown across the Tennessee River at Brown's Ferry, by which supplies were hauled into Chattanooga from Kelly's and Wauhatchee..
Another bridge was in course of construction at Chattanooga, under the immediate direction of Quartermaster-General Meigs, but at the time all wagons, etc., had to be ferried across by a flying-bridge. Men were busy and hard at work everywhere inside our lines, and boats for another pontoon-bridge were being rapidly constructed under Brigadier-General W. F. Smith, familiarly known as "Baldy Smith," and this bridge was destined to be used by my troops, at a point of the river about four miles above Chattanooga, just below the mouth of the Chickamauga River. General Grant explained to me that he had reconnoitred the rebel line from Lookout Mountain up to Chickamauga, and he believed that the northern portion of Missionary Ridge was not fortified at all; and he wanted me, as soon as my troops got up, to lay the new pontoon-bridge by night, cross over, and attack Bragg's right flank on that part of the ridge abutting on Chickamauga Creek, near the tunnel; and he proposed that we should go at once to look at the ground. In company with Generals Thomas, W. F. Smith, Brannan, and others, we crossed by the flying-bridge, rode back of the hills some four miles, left our horses, and got on a hill overlooking the whole ground about the mouth of the Chickamauga River, and across to the Missionary Hills near the tunnel. Smith and I crept down behind a fringe of trees that lined the river-bank, to the very point selected for the new bridge, where we sat for some time, seeing the rebel pickets on the opposite bank, and almost hearing their words.
Having seen enough, we returned to Chattanooga; and in order to hurry up my command, on which so much depended, I started back to Kelly's in hopes to catch the steamboat that same evening; but on my arrival the boat had gone. I applied to the commanding officer, got a rough boat manned by four soldiers, and started down the river by night. I occasionally took a turn at the oars to relieve some tired man, and about midnight we reached Shell Mound, where General Whittaker, of Kentucky, furnished us a new and good crew, with which we reached Bridgeport by daylight.