H&R made top breaks from 1871 to about 1941. The .32 S&W caridge was designed in 1878 so you revolver could be made in any if that time period.
Also the serial number is usually on the but of the gun. So if the grips covers the bottom try removing the grips. If it doesn't have a serial number don't worry the law doesn't require any gun made beofre 1968 to have one.
As for tracking the manufacture date, You can't find the exact day, month or even year.
Here's something to look to help you identify by the markings on the gun:
1. Top of Barrel Rib: Company Name, Address and patent dates.
1885-1890=Company Name and Address in one line.
1891-1919=Company Name, Address and 1 to 5 patent dates in two lines.
1919-1941=Company Name and Address in two lines.
2. Left side of barrel: Model Name and/or Caliber, after 1905 (Black powder models do not Have these markings).
3. Bottom of Top strap: Serial Number, this is the location that will have a letter code usually on model manufactured between 1890 and 1905/06.
4. Left side of grip strap at bottom: Serial Number 1890-1906 (grips must be removed to see).
5 Bottom of Butt: Serial number 1905-1941 (1905-1906 production may have serial number in locations
You have your gun with you so you could use this information better. Judging from what you gave us tough I would say you gun was made between 1919 to 1941.
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Does anyone have any further information on this revolver?
thanks, JT
Hillbillies loved them.....