First, welcome to TreasureNet's "What-Is-It?" forum, the best place on the internet to get correct ID of unknown objects. Second, your button shows the Great Seal of the United States. The "Great Seal" button has been the primary uniform button of the US Army since 1902, through today. As Fyrffyrt1 mentioned, "rimless" (or "borderless") ones date from 1902 to 1910. Ones with a "black finish" on the brass date from World War One to 1923. I can't be sure from your photos of the uncleaned button, but it looks like it has "black finish" on the brass. If it does, you now know the exact time-period of your button. If it doesn't, it is from later than 1923.