Thanks, does it say anything about rarity?
I can not locate this particular button in the RECORD OF AMERICAN UNIFORM AND HISTORICAL BUTTONS BICENTENNIAL EDITION, BY Alphaeus H. Albert. Are you sure that it a GW button? More buttons were produced in 1879 for the centennial. In 1902 the army had several buttons that look very similar, but the shield seems to be a little longer before the V.