The Genealogical Record of the Barnum Family calls him Jeduthen Barnum, and states that he fought in the Civil War as Dewitt C. Barnum. He was supposedly a corporal in Company "E", 1st Michigan Cavalry from Aug 1861 to 1864, and was captured at the Second Battle of Bull Run, 30 Aug 1862.
Civil War Pension Index: General Index to Pension Files, 1861-1934. Name: Dewitt C. Barnum/Eduthen [sic] F. Barnum; Widow: Sarah Barnum; Minor: Winnie M. Barnum