The Memoirs of General Ulysses S. Grant, Part 4‪.‬

Extended biography of Grant : As stated before, after the fall of Vicksburg I urged strongly upon the government the propriety of a movement against Mobile. General Rosecrans had been at Murfreesboro', Tennessee, with a large and well-equipped army from early in the year 1863, with Bragg confronting him with a force quite equal to his own at first, considering it was on the defensive. But after the investment of Vicksburg Bragg's army was largely depleted to strengthen Johnston, in Mississippi, who was being reinforced to raise the siege. It would be bad to be defeated in two decisive battles fought the same day, but it would not be bad to win them. I, however, was fighting no battle, and the siege of Vicksburg had drawn from Rosecrans' front so many of the enemy that his chances of victory were much greater than they would be if he waited until the siege was over, when these troops could be returned. Rosecrans was ordered to move against the army that was detaching troops to raise the siege. Finally he did move, on the 24th of June, but ten days afterwards Vicksburg surrendered, and the troops sent from Bragg were free to return.