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ing fault with Gen. Bragg. The following estimate of the strength of the Federal army is based upon reports obtained from three different and well informed sources just before the battle, and I am satisfied, as you would be if you were in possession of all the facts, that it approximates the truth very nearly: McCook's corps, three divisions, (Sherman's Davis's, and R. R. Johnson's,)18,000 Thomas's corps, four divisions, (Rousseau's, Negley's, Brannan's, and Reynolds's.)25,000 Crittenden's corps, three divisions, (Palmer's, Van-Cleve's, and Wood's,)18,000 Granger's reserve corps, three divisions, (Morgan's, Steadman's, and Granger's,)15,000 77,000 This is exclusive of Stanley's corps of cavalry composed of three divisions. Some small detachments from this large force, say 12,000 in all, were on duty in the rear, leaving 65,000 fighting men who were actually present and engaged in the battle. Opposed to this formidable Army Gen. Bragg did not have, exclusive o