I have been searching! The 8th Arkansas Infantry, Company B, listed H. C. Baker (the letter writer) wounded and captured 31 Dec 1862 at Stones River, TN, and he died of his wounds 15 Jan 1863 at Murfreesboro, TN
In the letter from Corinth, H. C. told of the death of his brother, Ben. B. J. Baker was also in Co. B, 8th Arkansas Infantry, and he died 16 April 1862.
Both men enlisted 10 Sept 1861 at Camp Price, AR.
Thanks for everybody who helped me!