You have a Smith & Wesson .32 Regulation Police model. The key clue is the "Pat. June 5, 1917" stamp on the bottom of the stocks.
The .32 Regulation Police model was introduced In 1917, at serial number 331,320 (number approximate) within the .32 1903 Hand Ejector number series. Production continued until 1942 and serial number 536,683. Production then resumed after the war. Your revolver is obviously an early one. Standard barrel lengths were 3 1/4, 4 1/4 and 6 inches, with the shorter lengths being more common. Nickel finish in combination with the long barrel was also less common then blue.