The classic revolvers of the Old West were single-action revolvers. Pulling the trigger released the hammer and fired a shot, but the shooter had to cock the hammer manually, which also advanced the cylinder to the next round.
Later models were double-action. Pulling the trigger cocked the hammer, advanced the cylinder, and then released the hammer. This made for a long, “heavy” trigger-pull.
Then semi-automatic pistols started using the energy of one shot to load the next.
It turns out that some revolvers were designed to do this too, like the Webley-Fosbery Automatic Revolver:
Semi-automatic pistols were just beginning to appear when Colonel Fosbery (1832–1907) devised a revolver that cocked the hammer and rotated the cylinder by sliding the action, cylinder, and barrel assembly back on the frame. The prototype was a modified Colt Single Action Army revolver. Fosbery patented his invention August 16, 1895 and further improvements were patented in June and October 1896. [...] Webley further developed the design and the Webley-Fosbery Automatic Revolver was introduced at the matches at Bisley of July 1900.
The Webley-Fosbery makes an appearance in the classic film The Maltese Falcon. It is the gun linked to the killing of Sam Spade’s partner, Miles Archer. Spade, played by Humphrey Bogart, erroneously identifies the gun (and mispronounces the name as “Foresby”), saying, “It’s a Webley-Foresby, .45 automatic, eight shot. They don’t make ‘em anymore.” While the .38 caliber did have an eight-round capacity, the .455 (not .45) did not. And though some .455 Webleys were modified to fire the more common .45 ACP cartridge by use of half-moon clips, unless specially modified on an individual basis, there was never a .45 caliber eight-shot Webley-Fosbery Automatic Revolver. In the original Dashiell Hammett novel the gun is correctly identified as a “Thirty-eight, eight shot”.
The Webley-Fosbery also makes an appearance in the motion picture Zardoz, where it is used by Sean Connery’s character “Zed”. The two-handed method of manually cocking the revolver can be seen several times in the film. As a movie prop firing blanks and not live ammunition, the absence of adequate recoil would not allow for automatic recoil cocking.
Modern metallic cartridges feed just fine from a spring-loaded box magazine, but revolver cylinders still make some sense for finicky ammo, like shotgun shells. The Pancor Jackhammer was designed as an automatic revolver shotgun.