If the gun has a round butt, you have a .32 Hand Ejector 3rd Model manufactured between 1917 & 1920 in the serial range 263001 to 321000. If a square butt, with the grips stamped with a 1917 patent date, then you have a .32 Regulation Police manufactured in the same serial range and time frame. Either way the gun predates heat treatment of cylinders, so dont try to shoot hot handloads in it. It also predates the modern hammer block safety. If dropped it could fire, so leave the chamber under the hammer empty.
Your gun predates model numbers, which were introduced in 1957 with the .32 Regulation Police becoming the Model 31 & the .32 Hand Ejector becoming the Model 30.
The numbers under the cylinder yoke are assembly numbers, used to track parts in the factory. They were not recorded and had no meaning after the gun was completed.
The patent date is correct for the changes introduced in 1917.
If a Regulation Police there is a 'step' in the back strap that allows fitting of special round to square butt conversion grips.
The gun is built on S&Ws I frame.
Hope this helps.