I already explained that, but I will go into more detail.
In the 1930s law enforcement agencies were looking for a more powerful cartridge that could pierce automobile bodies that the new breed of criminals were using. Smith and Wesson developed a new, higher velocity 38 Special cartridge to fit the bill. This cartridge developed higher pressure, enough that might damage a conventional K frame 38. So Smith turned to the larger N frame, with its larger diameter cylinder that could take the pressure of the new, higher velocity cartridge. Since the N frames had largely been used for 44 caliber cartridges, the new revolvers were called 38-44; 38 for the 38 Special chambering, 44 for the size of the frame. The 38-44 Heavy Duty was the fixed sight version, introduced in 1930.
This is a 38-44 Heavy Duty revolver. It shipped in 1931.
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This is a 38-44 Outdoorsman. Note the adjustable rear sight. It shipped in 1933.
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The problem remained that a shooter might inadvertently load the high velocity 38s into a conventional K frame revolver, possibly causing damage. So in 1935 Smith and Wesson introduced the 357 Magnum cartridge, developed by Winchester. The case of the new cartridge was about 1/10" longer than a conventional 38 Special, so it could not be loaded into a conventional 38 Special revolver. By the way, Douglas Wesson, grandson of Daniel Wesson and a chief promoter of the new cartridge was a wine connoisseur, hence the name magnum, which means a really big bottle of wine in the wine world.
The new revolver, with its longer chambers, was introduced with the new cartridge in 1935. Built on the large N frame like the 38-44 revolvers, it was simply called The 357 Magnum revolver at the time. Nothing fancier than that. However, S&W thought it would be a clever marketing idea to register the new revolvers to their owners. This was an in house program, nothing to do with law enforcement.
When S&W was developing the new revolver they did not anticipate a large amount of sales, this was the height of the Great Depression after all. The new revolvers were the top of the line, costing $60, $15 more than anything else in the catalog at the time. I'm talking 1935 dollars here. So the first 357 Magnum revolvers were the Registered Magnums. A factory certificate was given to the owner, noting the registration number which was stamped on the frame. The checkering on the top of the top strap and barrel rib were meant to reduce glare. The new revolvers were all custom built, the customer had his choice of barrel lengths from 3 1/2" to 8 3/4". There were seven different front sights available, with matching rear sights, any style of service grips or Magna grips, with or without grip adapter. The factory sighted the revolvers in with the customer's choice of ammunition at any distance up to two hundred meters. As I said, each owner's certificate listed his registration number as well as all the special features of his revolver.
Even though this was the height of the Great Depression, sales far exceeded what S&W anticipated. Factory capacity at the time was about 120 Registered Magnums per month. After producing about 5,500 Registered Magnums the Registered Magnum program was discontinued in 1938. The revolver continued to be called The 357 Magnum until 1957 when it became the Model 27.
Good luck finding a 'shooter grade' Registered Magnum. As I said, they were all custom revolvers, and are all expensive. I looked at a beat up Registered Magnum a few years ago. It was very beat up, but still cost more than I wanted to pay.