Hi Tom,
Serial # should be same on receiver and underside of barrel . . . your Spencer may have been altered, repaired at some time in its ownership. Spencer Carbine with serial # 20777 may have been issued to Company D, 12th Illinois Volunteer Cavalry in 1864.
Email me JUST A FEW photos of your Spencer, especially of the receiver area, top, bottom, and sides. fsgrand2@fairpoint.net Send me NICE, SHARP, Well-exposed photos. NO white background.
Two Flints