Here's info on the .22 you showed. That's not an 8-3/8" barrel, that's a 6" barrel. The gun is a 5- screw K-22 Masterpiece. The serial number on the back of the cylinder (K 259281) dates it to about 1955. The number you see in the yoke cut is an assembly number, which can also be seen on the left side of the grip frame if you remove the stocks.
During this timeframe, the serial number can be found on the butt of the gun, on the back of the cylinder, on the barrel flat above the ejector rod and on the back of the yoke arm (in from of the cylinder). If the gun had Magna stocks instead of target stocks, you would also find the numeric part of the serial number on the inside of the right grip panel. Target stocks like those were not numbered.