The fact that it is an S&W .32 top break with that high a serial number points to the .32 Double Action Fourth or Fifth Model. The problem is that the serial is in a transition range, so we need one more piece of info. If the front sight is pinned in, it is a Fourth Model; if the sight is machined as part of the barrel, it is the Fifth Model. The last patent date should be 1889 and the gun was probably made in 1909 or 1910.
Jim