THE authors of this research on the vibrations of gun barrels were induced to make an experimental investigation of the behaviour of rifle barrels, in order to clear up certain difficulties connected with that which is oknown in ballistics as the error of departure. It had been noticed that in shooting with a rifle (whether held loosely, or firmly fixed), that the initial tangent to the trajectory —“die Anfangstangente der Flugbahn”—does not coincide, as would be expected, with the axis of the bore of the barrel, when produced, but is more or less inclined to it at a small angle; this is called the angle of error of departure. The authors, working with photo-chronographic methods, determined the movements of the muzzle end of a rifle in a vertical plane, and a vibrational movement of the barrel was detected, and recorded on a moving photographic plate, on the same plate; a trace from a tuning-fork of known period was also formed, so that the position of the muzzle was known at any instant. The rifle used was of the Mauser type M 71.