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Fairly recently I acquired "Vicksburg" by Samuel W. Mitcham Jr. A pretty good read about the Sieges (plural) and it speaks to the pettiness of some southern generals who were guilty of not supporting the defenders. It is told from a Southern perspective.
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Soul of the Lion by Wallace ? Its about Joshua Chamberlin's biography and career pre and post war other good reads are Hard marching everyday by Wilbur Fisk a volunteer who wrote home to the local newspaper of his activities during the war. Full Duty Vermont in the civil war by state historian Howard Coffin.