Your S&W appears to be a .32 Single Action Model 1 1/2 centerfire. There will be a serial number on the butt, on the back of the cylinder, on the bottom of the barrel latch and on the barrel between the rear "ears." These number should match. If the grips are original to the gun, the back side of the right panel will have the serial number there also. The style of the grips indicate the gun's serial number is over 29,000. The original finish is almost gone from improper care, however it it's in good mechanical condition and the cylinder locks up tight when the gun is cocked, it is probably safe to fire, using .32 S&W centerfire ammo. Ed.