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Ignore the 19200, which is a process control number. The serial number is the one from the butt -- 34288. That number indicates that this gun is a .32 Hand Ejector Model of 1903, First change. The gun was probably shipped in 1904 or 1905.
Note the second flat spring in the grip. This gun has the early trigger rebound mechanism that does not involve a rebound slide and coil spring. The rebound slide mechanism was introduced with the Second Change of his model in 1906.
The gun has been refinished. Frame edges look a little rounded over, but the real giveaway are the hammer and trigger. Those parts were never plated or blued on S&W revolvers, even in factory refinishes. Color case hardening is the standard original finish for hammers and triggers.
The original stocks were probably hard rubber.