It is not a Model 2. There were two model 2s, first one was a tip-up 32 rimfire and the second was a 38 S&W top-break spur trigger revolver. Yours is a 32 Double Action Fourth Model, made from 1883 to 1909. There were almost 240,000 of this model made and almost 327,000 32 DAs made in all models. Your gun was shipped from the factory somewhere around 1890, so it is an antique. Driven hard and put up wet, but still a neat little revolver. If it is tight and functions well, there is still ammunition available from most manufacturers. The caliber you should look for is 32 S&W.
I see your pivot pin is not properly installed. Look for the mark on the top of the pin and line it up with the mark on the frame. It should be flush when installed correctly. Also, make sure the tension screw on the front of the butt is screwed in until tight.