Wug:
The Registered Magnum was and is S&W's finest product. introduced in 1935, each one was registered to the owner by S&W. These were expensive, made to order, hand made quality firearm. In mint condition one could be worth over $10,000 today. Even a poor condition (rusty, unsafe to fire) gun would be worth $500 or more.
The .357 registered Magnum introduced the .357 magnum and was built on the large N frame used for the .44 Special. The same frame size was later used for the .44 Magnum. It came with a target barrel, adjustable sights and fine checkering on the barrel rib, topstrap, forestrap and backstrap. Inside the yoke cut it should say Regxxxx, being the registration number.
According to the Standard Catalog of S&W the Registered Magnum range ran between serial number 45768 and 62489 between 1935 & 1939.
Your gun is well past the serial range for the Registered magnum. In 1948 production began again as the .357 Magnum (no registration number). Yours should be one of these made between 1948 & 1850 and considered a transitional model between the old 'long action' and the new 'short action' introduced around serial number S75514 around November 1950.
There is supposed to be an S prefix to the serial number to denote the new hammer block safety introduced in 1944. If yours lacks the S then it may not have the hammer block.
The Standard Catalog of S&W noted the following values in 2006:
ANIB $1200, Excellent $850, Very Good $500, Good $375, Fair $275, Poor $125. Prices have increased since then. The SCSW also notes that there were 6 or fewer transitional models made with an 8 inch or longer barrel, so your gun may be worth a considerable premium as three are already accounted for: one went to President Truman, one went to Remington as a test gun and one went to Major General Julian Hatcher at the NRA.
I would recommend you spend $50 and get a factory letter from Roy Jinks the S&W historian. He will look up the original shipping records and tell you where it was shipped to, when, and in what configuration.
Also please post some pictures. You have an interesting rarity. I'm sure Oro, Oyeboten, Saxon Pig, Peter M. Eick and the other S&W collectors will be very interested.