The Loss Esat Chickamauga

New York, Oct. 19. - A special to the Tribune from Chattanooga, Oct. 12ih via Nashville, I8th, contains the iollowing: "Complete official returns from the Infuntry engaged in the late battles are received, and give the following statistics: "Thomas' Corps- Officers killed, 36; wounded, 266; missing, 120. Men killed, 686; wounded, 3,297; missing, 2,127. Total, 6 301. "McCook's Corps- Oflicers killed, 40; wounded, 168; missing, 70. Men killed, 363; wounded, 2,367; missing, ],503 Total, 4,520. "Crittenden's Corps- Officers killed, 39; wounded, 131; missing, 22. Men killed, 296; wounded, 2,158; missing, 655. Total, 3,300. "Two brigades of Granger's reserve corps, engagt'd only in the afternoon of the second day's fight, lost - officers killed, 16; men 230; wounded officers 59; men 877; officera missing 34. men 527;- total 1,732. 'The losses cf our cavalry, not reported, wil] inake the grand aggregate about 17,000. Of the 4,685 missing, about 3,500 are wounded 36 pieces of artülery were lost and a few wagons. "Southern papers of Oct. 9th are received. They still insist that their whole loss will not exceed 12,000; but partial returns published by thein indícate that it is Hindman's División alone lost 2,100 out of 2,400 men.