Welcome to the Forum. You have a Model 2 Old Model or Army, 32 Long rimfire revolver. These guns were made from 1861 to 1874, with over 77,000 total manufactured. Your serial number puts yours at the very first year of production. The most common barrel lengths were 5" and 5", but a 4" barrel was also available.
These were very popular private purchase revolvers in the Civil War and chances are good that yours was a Civil War gun. Yours appears to be in nice shape and a very historic S&W model that led the way for the development of the top-break large frame Model 3 American in 44 caliber.