A header cannot result from stopping the rotation of the rear wheel, as generally supposed, because the point of contact of the same being in the rear of the rider and centre of gravity, the system cannot revolve about the said point in a forward direction, or direction of momentum. It will be seen, then, that if from any cause the rear wheel leaves the ground, which it can do from a rebound against some obstruction, the instant it does so the system will be simply carried forward by the rolling of the front wheel. Headers have been said to result from the above cause in the ordinary bicycle, but the writer after several experiments has been unable to attain such a result. Yet it is quite possible that it might occur from the rebound of the rear wheel in striking an object with great force, though it is altogether improbable if the drive-wheel were kept fully in motion. An obstruction so great as to bodily raise the wheel sufficiently high to throw the centre of gravity over never gets a chance to act, since the forward wheel must surmount it first, and this is where the header occurs. It can be easily seen that when the rear wheel, from any cause, is raised from the ground, there can be no action within the system to make it raise any higher or to prevent the forward wheel from rolling onward as usual; hence it is evident that as soon as the former leaves the ground it will simply drop back and rebound again at will. But in the other case, if the front wheel is locked, the rear wheel cannot go on in a straight line and it must therefore go on over the top. In the writer’s experiments on the rear wheel, he had an attendant throw a stick between the spokes while in motion; it was not tried at very high speed, however, for the reason, perhaps, that any failure in the theory above provided might end rather disastrously to the experimenter and thereby cause an act of ingratitude to be perpetrated upon the prospective patron of this book, through an inability to ever finish it. If some ambitious cyclist will kindly complete these experiments, the writer will gladly incorporate an account of them in future editions of this work, together with an appropriate obituary notice in large type. CHAPTER XIII. GEARING UP AND DOWN.