About eleven o'clock on the next morning the battle was resumed with fury. Polk again assailed Thomas, and Thomas urgently asked for reinforcements with which to repel the assault. On that part of the line the struggle continued for hours with varying and not unequal success, the advantage lying on the whole with the Confederates. But later in the day Longstreet, who commanded the right center of Bragg's line, made a tremendous assault of that kind which had been rendered familiar to the fighters in Virginia by repeated experience. He swept everything before him. He made a gap in Rosecrans's line crushing its center, separating its wings from each other and driving it into confused retreat. Thomas alone held his force together, and fought the matter out to a finish. In spite of the fact clearly apparent to him that Rosecrans was defeated, and three fifths of his army destroyed, Thomas continued the bloody contest with a fury that knew no flinching, and hesitated at nothing of human sacrifice in the achievement of its purposes. But for Thomas's obstinacy, skill and courage the Federal defeat at Chickamauga would have been a repetition of the disaster at Chancellorsville. During the night Thomas succeeded in withdrawing his command, and the Federal army fell back to Chattanooga, taking refuge behind the fortifications there. Each army had lost in this struggle from 15,000 to 20,000 men. The exact figures are nowhere procurable. Bragg had won a great victory, but he had not succeeded in regaining possession of Chattanooga. His enemy held that strong, strategic position. It was therefore his next task to besiege the foe there, and either by fighting or by maneuvering to drive him out of the place. Two mountain heights, the one known as Lookout mountain and the other as Missionary Ridge, overlook the town, and command many of its approaches. When the battle was over Bragg promptly advanced and seized upon these heights. By doing so he succeeded in placing Chattanooga in a state of siege, stopping the navigation of the river, and cutting off all of Rosecrans's communications, with the exception of one highly inadequate mud road. It is a maxim of military science that the army which can besiege a position can always capture it in the end unless the beleaguered place is relieved from the outside. Chattanooga was relieved from the outside in an exceedingly quiet, but exceedingly effective way. Ulysses S. Grant--at last a major general in the regular army and in full command of the western department--went thither to supersede Rosecrans in command. The coming of this one silent and unostentatious man meant more to the Federal forces in that quarter than the arrival of half a dozen army corps would have signified. Grant got to Chattanooga on the twenty-third of October, 1863, and set to work at once with his practical common sense to meet and solve the problems of the situation.