I believe Mud Hut is correct... because your button's back greatly resembles the extremely common Scovill back found on US Army "general service" eagle-buttons for Enlisted-mens' ranks (non-officers). It will have the name "Scovill Mfg. Co Waterbury" in raised lettering. The version of "general service" button you found was issued from 1854 through 1874... when it was replaced by a slightly different-shaped eagle having a very high-relief shield on its chest.