Welcome to the forum. S&W introduced that model in 1911 and made it until just before WWII. After the war the model got a slight redesign and went into production again about 1953. After 1957 it was known as the Model 35.
In 1931 S&W introduced a larger .22 revolver based on its mid-sized K-frame, and commercially speaking that is where the company's .22 action has been for 80 years. The small frame .22s are still great shooters, but the larger frame revolvers are more accurate -- or perhaps I should say easier to shoot accurately with minor amounts of practice.
Not that the small-frame .22s were any slouch. Here are a couple of pages from the company catalog of 1925.
By the mid-'20s the standard front sight design had changed and the company had returned to installing the larger extension stocks as the standard grip configuration for the model. The stocks on yours were introduced in 1917 for a .32 fixed sight revolver, but they were also mounted on the .22 and .32 target revolvers of the era.
My guess is that your gun probably shipped in 1919; that year saw a lot of guns in the 27xxxx range leave the factory.
Looks to be a nice specimen. They are fun to shoot, but in my experiences it takes some effort to develop accuracy with them.