In my opinion, your cartridge-casing's .509" diameter and its 1.8" length indicate it is a .50-70 rifle casing. Go to the following link, scroll a bit more than halfway down the webpage, and look at the cartridge on the far right of the four in the photo. THE CARTRIDGE COLLECTOR
Your .50-70 casing having no "headstamp" on its base dates it to being from the 1870s into the early 1880s.