My first thought was 10.4 mm rimfire Swiss Vetterli. Back when I was a teenager I acquired a Vetterli and a box of old corroded cartridges. I was dumb enough to fire one.
A somewhat similar looking cartridge is a Ward-Burton .45-85 experimental cartridge. This cartridge dates to the period 1871-1875. The Ward-Burton was a bolt action rifle that was part of the evaluation that accepted the trap-door Springfield for the army. The experimental cartridge is center-fire, not rim-fire.
A general selection of military items from the Civil War through World War II with an emphasis on Civil War cartridges and early American military buttons.