Hard to say without some precise measurements, but possibly a .44 Henry or .56 Spencer rimfire. Could well be old enough to be a CW cartridge case (shell casings go into shotguns or cannon).
Jump to the below site and see if the marking in the center of the base matches any of the stampings.
The 10.4 or 41 swiss rimfire has dual firing pins on both sides of the bolt, and this was struck twice. once on the top, and once on the bottom. probably cause it did not fire the first time.
These rifles were sold as surplus since the early 1900's so they are fairly common to most all parts of the country. the case you have looks to be swiss military, the rifles were sold in enough quantity that here in the states that remington produced the ammo for it till after ww2.