Joe, I can't find any record of a W. J. or Joseph Birchum/Burchum who was conscripted in 1863-1864. However, I did find a record of a man by that name in the Johnson County Militia. Pvt. William J. Birchum was enrolled in Co. G, 10th Regiment Arkansas Militia, and was marked as "present" during the militia's annual muster for inspection and drill at Clarksville during the period February 27 to March 19, 1862. After the Spring 1862 muster, all of the militia regiments ceased to exist, for all practical purposes, as most of the men subsequently enlisted or were conscripted into Confederate service.