General Lee,
Your Spencer Carbine serial # is 10640. The closest # I show to yours is #10621 which was issued to Co. F, 6th Michigan Volunteer Cavalry on/or/about 02-01-1865. After that I have a serial # 10763 which was issued to the Tonkawa Scouts, Ft Griffin on/or/about 07-27-1873.
Two Flints