NOT 1848. The 22 short cartridge didn't come out until the late 1850's,
and S&W had a lock on the bored through cylinder concept until early 1869.
Also, it's not a derringer. Pocket pistol would come closer to describing it.
DO NOT shoot it with modern 22 ammunition. If you just have to make it
go bang, try some Aguila 22 Colibri.
It is a Colt New Line 1st model, as The GunClinger stated above. SN puts year of manufacture at 1873, so it's an early one!