...y and artillery, and 4849 cavalry,--total, 56,671. In each army these figures were diminished by the usual details for hospital and transportation service, train guards, and other purposes, so that Rosecrans reported his force actually engaged, December 31st, at 43,400, while Bragg placed his own force at 37,712. Rosecrans's left wing, under Crittenden, bivouacked on the night of the 29th within se...