As indicated in my other reply about buttons with "chicken-head" eagle and raised shield, it is a Model-1874/75 US Army "general service" Enlisted-men's uniform button. This one's particular backmark, saying "SCOVILL MFG CO . WATERBURY" (note that the dot is not a period after CO) with a ring of dots around the loop but no other rings of any kind, dates from 1880 and later. Because the Model-1874/75 eagle button was discontinued in 1902, this one of your buttons would only have been made sometime between 1880 and 1902.