Your pistol appears to be a Stevens Model 41 Tip-up, first patented by Joshua Stevens in 1864 - although your gun most likely dates from the 1880's.
At that time, Stevens A&T Co (Arms & Tool) was the world's largest manufacturer of firearms - making rifles, pistols and shotguns in the many hundreds (if not thousands) each day.
Stevens had several multiple-story mill buildings, dedicated to making firearms, at the time, in Chicopee Falls.
The .22 chambering was a blackpowder .22 rimfire Short - the first .22 rimfire invented, and nowhere near as powerful as modern smokeless ammo.
Even though we may not think of .22 rimfires, and .22 Shorts in particular, as being particularly powerful - if chambered & fired in that old gun, it would most likely open under the pressure, or soon break/wear out.
In any event, the bore is also probably like a sewer pipe from shooting BP .22 ammo through it - the only kind available until well after WW I.
The original finish would have been nickle plating - a common & practical pistol finish of the day.
There's no safety, other than a half-cock postion of the hammer.
The cross button on the frame side is the push button to release the barrel lock, to tip up/open the barrel for loading/unloading.
As a point of reference, this is my similar but different Stevens Gould Model 36 Target, ca.1892:
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