This is the Percival & Smith Repeating Magazine Pistol, patented in 1850. If I understand the description correctly, the cylinder in the front holds 24 bullets and the cylinder in the back holds powder and primer. To chamber a round, the user twists them up, then back down:
After cocking hammer, both chambers swivel upward 180 degrees allowing lead ball to fall into breech from front magazine and loose powder into chamber behind ball from rear magazine; primer pellet also seats itself.
It looks like an advanced version of the Lorenzoni, an amazing gravity-fed seven-shot repeating flintlock pistol designed in the 1680s.