"Soft-fitting" number used for the serial number
jester,
It just occurred to me that it's very possible that whoever modified/refinished your gun assumed that the #178xx you found in the yoke is your gun's serial #. Because S&W started stamping the serial # in that location after the 1950's, many people, especially younger gun store clerks assume on older guns that it is the serial #. Many S&W guns have been registered using that #!
That #178XX should be located in three locations on your gun:
1. on the yoke arm and seen when opened,
2. on the inside of the sideplate (must be removed to see the #), and
3. on the frame opposite the location of the # on the yoke arm on pre model revolvers.
k22fan's suggestion below is a good one. To confirm which frame you have, you should check for a serial # on the back side of the yoke to verify if it matches the #633XXX on your cylinder.
Look for it on the rear facing surface of the yoke arm with cyl swung open by looking thru one chamber with a flashlight. If you know how, you can pull the cyl off to see it but that's not necessary if you use a good light aimed at the space between the yoke and front of the cyl.
If the numbers match, you can be 99% certain the cyl and frame are original to each other and came from a pre war K22 Outdoorsman .22 revolver from the early 1930's as most posters have suggested. If they don't match, it's even more of a Frankengun and k22fan's M&P possibility could very well be the case.
If this is a converted M&P the only secondary serial number that could even possibly be original would be on the yoke. The OP needs to check for a relocated serial number on the sides of the gripframe.
Please let us know what you find!
P.S. Could we also see a photo of the hammer cocked and the open yoke. Thx.