 Complete the following phrase:  During the Battle of Chickamauga, Mitchell led a brigade under James B. Steedman which arrived late on the second day and played a leading role in aiding George H. Thomas in holding onto his delaying position atop Horsehoe Ridge. At the Battle of Missionary Ridge near Chattanooga, Tennessee, Mitchell supported Maj. Gen. William T. Shermans assault column. Later he moved to Ambrose Burnsides relief during the Siege of Knoxville. During the 1864 Atlanta Campaign, Mitchell led the advance on the enemy positions in the Battle of Rocky Face Ridge. His regiment suffered severely at the Battle of Resaca and played a prominent role in the battles of 