Your find is a US Navy uniform button. According to the book by McGuinn & Bazelon on dating buttons by their backmark, your button's double-ring backmark saying "Waterbury Button Co. ** Waterbury Conn" was in use from 1860 to 1890. However, speaking as a 40+ years civil war relic digger and Military Buttons dealer, my opinion is that since we do not dig buttons with that backmark at civil war battlesites or encampments, that backmark is more likely 1870-90.