It would be helpful to know if this is a spur-trigger single-action gun or a double-action gun with a trigger guard.
That said, the "Reissue" patent marking suggests that it is the former, which would make it a
.32 Single Action aka
Model 1½ Centerfire. The serial number range for this model is 1-97574, and they were made from 1878 until 1892, which implies that #10xxx was made ca. 1880. BTW the odd "half model" nomenclature comes from S&W's decision to introduce an earlier tip-up rimfire gun larger than the .22-caliber Model 1 but smaller than the 6-shot .32-caliber Model 2.
If the gun is double-action, it is a
.32 Double Action 2nd Model, also made ca. 1880.
Either way, this gun falls solidly within the black powder era. Firing smokeless powder loads in it is generally inadvisable. The gun is chambered in
.32 Smith & Wesson or .32S&W, an obsolescent caliber that's not stocked by many local gun shops but is slightly easier to find via mail-order; however, AFAIK all currently-produced commercial .32S&W ammo is loaded with smokeless powder. (This cartridge is sometimes called .32S&W "Short" to differentiate it from the more common .32 S&W Long, which won't work in a top-break.)
IIRC Old West Scrounger (OWS for short) produced a run of black powder .32S&W a few years ago, but it appears to no longer be offered. You might be able to find some on Gunbroker or at a local gun show. Winchester offers a black powder blank, but that doesn't help you if you want to make real holes in an actual target.
Most shooters who fire these types of guns on a regular basis handload their own ammo with black powder and cast lead bullets.
Two warnings:
- I would strongly advise you to find a gunsmith who's at least somewhat familiar with top-breaks and verify that it's safe to fire. Although S&W was one of the higher-quality revolver makes from this period, 19th-century guns were generally made of much softer steel than modern firearms, so they tend to "loosen up" a lot more with repeated use.
- Do not, I repeat, do NOT, under any circumstances, even THINK about firing .32ACP (aka .32 Auto or 7.65mm Browning) ammo in this gun! This ammo is commonly available and will chamber in most of these old .32S&W top-breaks, but it is loaded to higher pressure than the original ammo, and it always contains smokeless powder. It will most likely blow the revolver up and possibly take some of the shooter's fingers with it. Don't try it!