BeepingforCoins, your member-name suggests you might not have much interest in Military buttons. But, if you think there's some likelihood you'll continue to find buttons like that one, you might want to buy a copy of the button-collector photo-guidebook titled "Record of American Military Uniform Buttons, with Supplement" by Alphaeus H. Albert. It shows and identifies your button as GI-80, US Army Infantry... a very unusual variety in that the eagle is looking to the opposite direction from almost all other US Army "eagle-button" versions, AND it is a silver-plated brass US Army button. Put a dab of Tarn-X on it to bring out the silver.
Another helpful guidebook for you to own is "American Military Button Makers And Dealers; Their Backmarks & Dates" by McGuinn & Bazelon. That book says, as Fyrffytr1 told you, your button was made during 1834 to 1836, because the button manufacturer Ives, Scott & Co. of Waterbury CT was only in business under that name during that very short time. Trust this advice: that book will pay for itself many times.