Judging from the serial number and patent dates, you have a
Smith & Wesson .38 Double Action, 2nd Model.
These were made between 1880 and 1884, within a serial number range running from 4,001 to approximately 119,000. The 5-shot cylinder was chambered to use the .38 S&W cartridge. Standard barrel lengths were 3 1/4, 4, 5, and 6 inches (measure from the front of the cylinder to the end of the muzzle). Cataloged finishes were blue, or nickel plated with a blued trigger guard and barrel latch. The hammer and trigger were color case-hardened. Stocks were usually black hard rubber.
These revolvers were intended to be used with black powder cartridges, and while current smokeless powder rounds will fit in the chambers, it is strongly suggested that they not be fired in a revolver as old as this one.
If you want more specific information you can have Smith & Wesson research their original records. This is how to go about it.
To do so you will need a snapshot of the gun, a full description including the serial number on the butt, and a check in the amount of $50.00 made out to Smith & Wesson. In exchange the company's historian, Roy G. Jinks, will research the original records (which are not computerized by the way) and send you a letter containing the details of what he finds.
This comprehensive document will contain an overview of the model’s history, followed by the details of your particular gun. This usually includes the caliber, barrel length, finish, and the exact date it was shipped from the factory, and to what distributor or dealer. If there are any special features they will be listed too. This information is often invaluable to both you and future generations.
Additional information on a historical letter will be found at the Smith & Wesson company website at:
http://www.smith-wesson.com/webapp/...catalogId=11101&content=25301§ionId=10504