Great advances have been made of late years in the understanding of ancient artillery, but the difference between the παλíντινιν and the εὐθ⋯τινιν seems to remain a riddle still inviting solution. In tentatively accepting the invitation, we are met at the outset by a certain amount of fog due to the fact that ancient guns were classed by two methods which produce a cross division. It will pay us to dispel this fog, or at any rate to find our bearings in it as exactly as may be, before going further.