When a cyclist climbs a hill, he not only overcomes the friction which would be generated if he travelled over the same length of level road surface, but he ought to be supposed to establish a certain amount of potential energy, or energy against gravity, and therefore should lose none. Yet he does lose considerable somewhere or he would not dread the hilly road as he does. In this matter of potential energy in hill-climbing upon a cycle, the subject assumes a different aspect from that of rolling on or off obstructions, as in rough-road riding treated of elsewhere. In climbing a hill there is no loss of momentum from a too sudden change in its direction; the matter of inertia does not figure in the case in any way, and we have a mere question of the rise and fall of a weight under certain modifications, said weight being the rider and his machine, said rise the ascent of the hill, and the fall the descent thereof. In a purely physical sense, then, we store up a certain amount of energy, or, in other words, put so much energy to our credit as against gravity, and theoretically we have a right to expect to get the benefit of it. To illustrate this potential energy, suppose we place a pulley at the top of a hill and a rider at each end of a rope running over the pulley, with one man at the bottom starting up and the other at the top starting down the same hill. The descent of one man would draw the other up, excepting that each would have to work only just enough to make up the loss from friction, as he would in case the road were level and of equal length. I have little doubt that in such a pulley arrangement there would be much less loss of power and energy than riders now experience in the actual practice of hill-climbing. To illustrate with one man how the potential energy should be returned and thereby benefit the rider, let us place him at the top of a hill at the bottom of which another hill of the same height begins, whence, by the acceleration of gravity, the rider ought to find himself at the bottom of the first hill with an amount of momentum acquired that would send him to the top of the next; in other words, we might naturally expect when we roll down one incline to roll just as far up another of the same grade, or of the same vertical height regardless of the grade, or else we should expect a return of the energy in sending us capering over a level road without further labor, until the kinetic energy is exhausted. We find, however, that such a desirable result does not appear, and we notice that, however long, beyond a certain limit, the hill may be, we have no more momentum or kinetic energy at our disposal than we would in the case of a shorter hill. To what can this loss be attributed? There is but one visible cause,—to wit, our work against the air.