Matches a bunch of my civil war pistol rounds. I'll get the info out of the book in the morning for you, I just forget the name off hand. Someone might also chime in before I get back.
Invest in some calipers so you can get some good measurements. They are not expensive. The closest I can find, based on the looks, is a 40 cal. Derringer. Really need measurements.
Agree. Looks like a .36 cal variant of some kind. If you grab some length measurements I can narrow it down in my book. There's a bunch in that caliber range. Hard to tell in your photos, how many grooves can you count? that will help too.
There's not an exact match, but the colt rounds seem to come closest. Back then there were a ton of rounds floating around and the direct answer might be outside my book. But if you look for 36cal pistol rounds you might find an exact match.