The .41 Magnum was introduced in 1964. This was before the 10MM had been invented and before the hi-cap 9MMs became popular. The revolver was king with the cops.
However, ammo was not nearly as advanced as it is now. Hollow point bullets were rare in handgun calibers and usually didn't work very well. Many agencies issued round-nose lead ammo and this was found wanting.
Some people, including Bill Jordan and Skeeter Skelton, both cops and writers for various firearms journals, argued in favor of revolvers using lead, semi-wadcutter ammo. The problem was that the .38 Special was not a great man-stopper with this load, and the high velocity of the .357 Magnum caused the bore to become terribly leaded after only a few rounds, ruining accuracy and requiring strenuous cleaning. They envisioned a big bore revolver using lead semi-wadcutters that would deliver good energy at lower velocities avoiding the leading problems. They felt that the .44 and .45 calibers using 240-250 grain bullets might be a bit much on recoil. So, they argued for a .41 caliber using 200 grain bullets as this combo would recoil less.
Now, a .44 can shoot 200 grain bullets, but this is a bit light for the bore and penetration would not be as good as with the same weight in a bullet of a smaller frontal area. In other words, a 200 grain .41 outperforms a 200 grain .44 bullet, hence the decision to create a new caliber. Of course, marketing had a lot to do with it as well, and that's why the "Magnum" name got hung on the new cartridge. There was no readily available non-Magnum .41, but S&W wanted to sell to folks other than cops, and the word Magnum would increase sales.
Unfortunately, Jordan and Skelton wanted a cartridge throwing that 200 grain slug at about 900 FPS, and what the ammo makers delivered actually clocked about 1,300 FPS. This was too much for most shooters, especially female officers and the guns were not popular. The large size and weight of the N frame gun was also unpleasant for many cops.
The .41 was used by a number of law agencies around the country. The San Antonio PD used it, as did the San Francisco PD. A sheriff's Dept. in PA used it, and my M58 is a veteran of this agency. There were a few others, but it never really caught on. It was replaced by .357s when better HP ammo became available, and all revolvers fell from favor when the hi-cap semi-autos started appearing.
Some shooters like the .41 because it tends to have a flatter trajectory than the .44 Magnum. A .41 will take a little more pressure than the .44 (in S&W products) because the chamber walls are a touch thicker on the smaller bore.
So, to answer your question, the .41 was meant to be an efficient big bore round with less recoil than the .44 using lead bullets. In theory it is a neat idea. In reality, it was not the best choice for police work, afterall.
I like my .41, and it has enough power to settle anything's hash that I feel the need to shoot with it. The M58 is lighter and more compact than other N frame Magnums due to its fixed sights and unshrouded ejector rod. To me, it is a top choice when maximum power in the lightest and most compact package is desired.
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