How large could a Puckle-style naval gun be made in the eighteenth or nineteenth century?
Short answerIt could be enlarged in theory, but heavy recoil, chamber weight, and the need to pause for reloading would erase most of the promised rate-of-fire advantage.
NotesThe Puckle principle offers several preloaded chambers that can rotate behind one barrel. Scaling it toward naval artillery allows another chamber to be prepared while the gun fires, but it does not automatically complete the whole loading cycle. Recoil might help eject a spent charge, yet the system still has to pause for safe manual replenishment and alignment. At battleship calibres the rotating assembly becomes so heavy and complex that it adds machinery without providing the continuous fire implied by a true automatic weapon.