October 12.—Jefferson Davis, accompanied by General Bragg and staff, visited the battle-field of Chickamauga. He complimented the General in the highest terms, remarking that “his soldiers were entitled to the gratitude of the country for their heroism, and promising them that the green fields of Tennessee would shortly again be theirs.”—The Union cavalry, under Colonel Hatch, in pursuit of the rebels, who were retreating from the battle-field of Colliersville, overtook them at Ingham’s Mills, a point on Coldwater River, three miles from Byhalia, Miss. The rebels were posted in a strong position, but were compelled to retreat after a fight of two hours, with a loss of over fifty in killed and wounded.