contusing and jarring the muscular system, which makes him less able to do the work. In so far as the machine is concerned, the loss of energy goes into vibration and into extra friction of the machine; we cannot see any other means by which it can escape; but as to the rider, while energy is of course similarly lost, the motive power is also interfered with. Now, the application I wish to make of this fact, _i.e._, that the annoyance or shock felt by the rider in wheeling over rough roads is comparable to an actual loss of kinetic energy, as well as in addition thereto, is that the nearer we can approach to an even rolling motion affecting the rider least disastrously, the nearer we will come to a perfect road bicycle without loss of momentum. In other words, the dynamical and physiological considerations lead us to the same end,—to relieve the annoyance by means of proper springs, and to so distribute the inequalities of the momentum and modify the change in direction thereof as to minimize the loss of energy. From experiments tried with properly-constructed springs, I find that momentum can be diverted in striking the obstacle into its required new course, upward and forward, with very slight loss indeed, and that much waste of power in rolling off the obstacle can also be saved, the desired conditions and effect being as follows: The wheel strikes the obstacle, springs back a little, and begins to rise upon it; at the same time an upward thrust is given, additionally compressing the vertical components of the springs, the man going on forward at the usual pace of momentum and being gradually raised. When the top is reached and the wheel starts down, the weight of man and machine causes the wheel to spring forward a little at first, and then, when the weight would drop too slowly and the momentum would otherwise pull the wheel bodily off, the vertical spring, being compressed, will, by its quick action, together with the pressure backward of the horizontal spring against the obstruction, hold the wheel in contact and make it roll off. This action is reversed in the case of a rut, and is quite similar in either fore or hind wheel. The principle is to avoid a too sudden attack upon the inertia, to change the course of momentum gradually, and to avoid concussion against inelastic parts.