The S&W No.3 revolver was originally designed for the .44 Henry Rimfire cartridge, but initial US military testing caused it to be changed to a centerfire cartridge, and all serial production would use centerfire ammunition. All serial production, that is, except a couple orders from the Ottoman Empire. The Ottomans had a substantial number of 1866 Henry rifles (chambered for .44 Henry Rimfire) that they rather liked (see also: the Battle of Plevna), and they requested revolvers from Smith & Wesson that could use that same cartridge. S&W obliged, and the result was the only production rimfire pattern.
Ottoman purchases of the rimfire No.3 revolver ran for nearly 10 years, from 1874 until 1883. They included 2nd and 3rd model Russian No.3s, and also 5,000 of the New Model No.3, which is what we are looking at today.
Many thanks to Mike Carrick of Arms Heritage Magazine for providing me access to film this example!