The next advance of General Rosecrans was against Chattanooga. General Bragg retreating on the south side of the Tennessee had reached this place, and had there thrown up defensive fortifications. General Rosecrans commenced his movement on the 16th of August; having spent the time from July 3d to the middle of August in making the necessary preparations. The advance was made, of course, across the mountains, its front extending from the head of Sequatchie Valley in East Tennessee to Athens in Alabama, a distance of about one hundred and fifty miles. The army advanced in divisions, availing itself of various gaps in the mountains, and crossing the Tennessee at various points. In the early days of September the army of the Cumberland was threatening the rebels under Bragg, all along that river from Whitesburg to Blythe’s Ferry. General Rosecrans, having become convinced, from evidence gathered from various sources, that General Bragg had commenced on the 6th of September, to move on Rome, directed General Crittenden to hold Chattanooga with one brigade and to pursue the enemy vigorously with the remaining force at his disposal. General Crittenden occupied Ringgold on the 11th, but Wilder’s mounted infantry pushed forward, skirmishing sharply with the enemy as far as Tunnel Hill. Logan having joined Crittenden, the whole corps advanced rapidly, on the twelfth, to Gordon’s Mill. Wilder, while engaged in covering this movement, had a desperate struggle with the enemy at Letts’ Tanyard. Negley, who had, in the mean time, been reconnoitering in the vicinity of Dug Gap, where he found the enemy in heavy force, was joined on the 11th by Baird’s division, and, after a severe skirmish with the rebels, secured a strong position in front of Stevens’ Gap. On the twelfth Reynolds and Brennan closed up to sustain these two advanced positions.