"in their cracked, secret meetings having several times descended from heaven by the way of a trap-door, announcing the speedy opening of the seventh vial"

This is a reference to the Book of Revelations: "And I saw another sign in heaven, great and marvelous, seven angels having the seven last plagues; for in them is filled up the wrath of God And I heard a great voice out of the temple saying to the seven angels, Go your ways, and pour out the vials of the wrath of God upon the earth."