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From 1863 to 1865 he was Medical Director of all the hospitals in the Confederate Army in the Dept. of Tennessee.
http://www.collphyphil.org/FIND_AID/S/stoutsh10a_376.htm
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FORM NO. 3 --- Officer's Pay Voucher
Surgeon S. H. Stout Med Dir of Hospls
From 1 Apr, 1864 To 31 Mar, 1864 One Month, Pay p's Month $162 Amount $162
Paid $162
M331: Compiled Service Records of Confederate General and Staff Officers, and Nonregimental Enlisted Men