Once a supply line down the Tennessee River was secured, he launched a probe against the Confederate position.
Sherman, attacking on the Union left was unable to take Tunnel Hill. Hooker advancing slowly from Lookout Mountain had little impact. (Well, his troops had captured lookout mountain on the 24th of November, so it is hard to say he had little impact.) Troops under General George Thomas attacked the middle of the line at Missionary Ridge, on 25 November 1863.
Thomas' troops overran the first position held by the Confederates, but they could not hold this line - since they were too exposed.
On their own men began to charge the ridge, only a few at first. Informed of the advance past the picket line Grant and Thomas turned back and watched as the men moved on the fortified rebel position. Fearful that if the charge failed the grays could advance and rout his army, Grant inquired of the men around him who ordered the charge. "I don't know,.." Thomas responded, "I did not."A combination of retreating Confederates, and poorly placed gun emplacements kept the troops under Braxton Bragg from effectively engaging the Federals. Bragg ordered a general retreat.
Failure to stop the Union Army in the vicinity of Chattanooga was a major problem for the South. Sherman resumed the attack in the spring, and Atlanta would fall to Sherman in September of 1864, helping Abraham Lincoln's re-election campaign with a decisive victory. Less than a year after Missionary Ridge, William Tecumseh Sherman would burn Atlanta and start his infamous March to the Sea, destroying much the South's ability - and will - to wage war.