From the Internet Movie Firearms Database
The "superweapon" that is the focus of the film's action is a belt-fed Gatling-style cannon (similar to an oversized, clunkier CIWS system) supposedly invented by Eli Whitney (the father of the cotton gin). The weapon is designed to blanket an area with a volley of explosive shells, which are then detonated simultaneously by firing a glowing orange "trigger" shell from the central barrel. Quentin Turnbull (John Malkovich) mounts the weapon on an ironclad and plans to use it to level Washington, D.C.
From the same page:
Detail of the multiple barrels. Note the design seems to assume a cannonball works the same way as a modern artillery shell; there is no system for replacing propellant charges behind the cannonballs, and nowhere for charges to actually go even if there was such a system.
Ultimately, a lot of digging hasn't turned up anything concrete other than the charges might be 'Magic Dragon Balls' - so I think we can chalk this one up to sloppy writing and badly thought out plot devices.