After the battle of Chickamauga, the Union army fell back to Chattanooga, and assumed a strong position in front of that place, abandoning, however, the passes of Lookout Mountain, which were immediately occupied by the rebels. The Army of the Cumberland at this time received its supplies, by way of Stevenson, and Bridgeport, from depots at Louisville and Nashville. To cut railroad communication with those points, and thus to paralyze the Union forces, was now the aim of the Confederate commander; and to this labor he addressed his efforts, with promptitude and with courage. But the line of railroad was well defended. On the 23d of September, General Hooker was sent to Tennessee, in command of the Eleventh and Twelfth corps of the Army of the Potomac, and was assigned to the protection of the line of communication between Bridgeport and Nashville. The rebels, in their vain endeavors to intercept the Union communications, brought about several small engagements, in which the Unionists were invariably victorious. Thus, on the 2d of October a rebel force, four thousand strong, under Wheeler, was defeated, at Anderson’s Cross Roads, by the First Missouri and Second Indiana cavalry, under Colonel Edward McCook. The enemy lost one hundred and twenty men, killed and wounded, eighty-seven prisoners, and upwards of eight hundred mules; and was completely routed, and driven back for miles. Thus, also, on the 6th of October, General Mitchell attacked the enemy, in strong force, at Shelbyville, and put them to flight, with heavy loss. They were, likewise, defeated at Farrington, on the 8th of October, by the National troops under General Crook, who captured on this occasion two hundred and forty prisoners, four pieces of artillery, and one hundred stand of arms. But other and more important movements were in contemplation at this time. The Government at Washington, hearing that Bragg was to receive reinforcements, and feeling that the crisis demanded an infallible commander, determined to relieve General Rosecrans, and entirely to reorganize the conduct of the war in the west. With this view General Grant was directed to advance with his forces from Vicksburg, and to assume command of the Departments of Tennessee, Cumberland, and Ohio. On the 18th of October, General Grant arrived at Louisville, and entered upon his new duties. The immediate direction of affairs in the Department of the Cumberland was committed to Major-General G. H. Thomas. The Department of Tennessee was assigned to Major-General W. T. Sherman. The corps of Generals McCook and Crittenden were consolidated, and stationed at Cincinnati. General Burnside, commanding the Department of Ohio, was, at this time, with a considerable Union force, in the vicinity of Knoxville, in the eastern part of the State.