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This here is a Volcanic repeating pistol, a particularly fancy example.
The Volcanic was one of the earliest forerunners to the lever-action rifle, these used a special kind of caseless cartridge, the .41 Rocketball, where there's the lead bullet, a hollow out in the back of it, which is filled with black powder and has a primer and sealant cap added on.
The idea is simple, the hammer hits the primer, the primer ignites the black powder, and the gas pressure sends the bullet going, burning up the sealant cap, the hollow back of the bullet expanding to seal against the rifling, then you work the lever to load the next cartridge.
Problem is, this didn't work out too well. For one, the sealant cap would often actually stay in the chamber, or stick to the bullet partially and then stay in the bore, etc, and worse is that you actually can not fit very much blackpowder in the cavity made in the ass of a conical lead bullet. The .41 Rocketball is a slow bullet, very slow, for comparison the full length Volcanic rifles could produce ballistics which are dwarfed by a 1900's pocket pistol in .25ACP, which is comparable to .22LR in energy, assuming a pistol barrel, though probably with much worse sectional density. There is at least one story of a man failing to commit suicide with a Volcanic pistol, shooting himself multiple times in the head.
If you had a dud cartridge, there also wasn't really any easy way to clear the chamber, because the Volcanic had no facilities for ejecting, as the entire cartridge was expected to go out the barrel.
The concept of cycling a manually repeating action with a lever sitting alongside the grip or stock is pretty solid, and the mechanical concepts would live on in the Henry and Winchester rifles, to this day even, but the Volcanic itself failed horribly, and Rocketball cartridges are remembered only as a weird and useless curiosity from before the age of self-contained metallic rimfire and centerfire cartridges.