Your gun is a .38 Military & Police Model, 4th change. It was shipped in approx. Feb. 1956, and collectors also call it a pre-Model 10, as these guns were made just before 1958 when S&W changed the names of it's guns to Models with numbers, Model 10 was the 1st, and the Model number was stamped on the frame under the yoke. Your gun is somewhat uncommon as it is one of the first of the 4 screw frames for this model. S&W changed from the 5 screw frames to the 4 screw in 1955-56 period. It was a phased in change, so there is an overlap of serial numbers with both 4 & 5 screws in that time. The number with the T symbol is the assembly/work number, not the serial number. That number was used to keep the parts together during assembly, before the serial number was assigned. The letter C is part of the serial number, however, and is on the butt with the digits. The C is not repeated on the barrel & cylinder, just the digits there. Throw away those crude plastic stocks and get a pair of genuine walnut checkered S&W magna grips, with the diamond patern around the escutcheon, which would be correct for this model. It will upgrade the gun considerably! This is not a rare gun, as the Model 10 is the most common revolver made by S&W, however Model 10 collectors will seek a low number 4 screw frame variation for their collections as they are much less common. Good luck, Ed.