Smith & Wesson “Bicycle model” 3rd model
Based on the shape of the barrel latch, what we have here is a .32 Safety Hammerless model, a.k.a "Lemon Squeezer".
Smith&Wesson issued 5 different variants of the .38 and 3 of the .32 caliber. There are only small variations, though.
The Safety Hammerless revolvers were the last of the topbreak series and come immediately before the Hand Ejector model with swing-out cylinder.
Production started in 1886 and the very last of these revolvers left the factory in 1940, long after production was resumed. The 3rd Model was introduced in 1890 at approx. serial# 42484 and was produced until 1898 (highest known serial# is 116002).
Most of the production feature short barrels, the 2" one being nicknamed "Bicycle Model".
Technically, those revolvers were quite advanced because they included an "inertia-type" firing pin, developed by Joe Wesson, son of Daniel B. This type of firing pin was mounted in the frame and spring-loaded. It could only hit the primer upon receiving a sufficient blow from the hammer, which transferred the momentum from the hammer to the firing pin itself. When the concealed hammer was at rest against the firing pin, the pin would not protrude through the frame.
I don't know who invented the system at first, but it wasn't Joe Wesson anyway. The "inertia-type" firing pins were at the same period already in use in the Belgian Leclercq shotguns, and probably in numerous other weapons.
Marcel
