If all riding were done in a vacuum, we would more nearly get back our energy, but somehow or other the vacuum is generally in the rider and doesn’t count, so there is an end to that. The rider, then, loses the momentum he would acquire from gravity because the friction of the air is resisting his progress at the rate of, or according to, the square of his velocity. In order to store up all the energy in a falling body we must allow gravity to increase the velocity as the square root of the distance. But it is easily seen that a rate of speed will soon be reached such that the air by impact will entirely annul all increase of velocity, and therefore all of the momentum we can expect to have at the bottom of the hill is just that which was acquired at the time and point at which the impact of the air balanced the accelerating force of gravity. This will soon come to pass, even omitting other friction, which, in connection with hill-climbing, we can afford to omit with good reason, because we should expect to have that to overcome if the road were level. The mere difference in the length of the surface travelled over will not bother a cyclist if it be a good level road, so we must blame it all on the air; I see no other way out of it. No manner of springs or anti-vibrators will help us out of this difficulty. If our rider puts on the brake, then of course there is no question as to where the work goes; but, as we all know, with a safe machine and an expert rider this is not often done in an ordinary country. In defence of our theory of loss of energy on very long hills, observe the fact that a mere rolling road is not generally despised by the cyclist; in fact, many prefer it to a dead level, the writer being decidedly one of their number. The short intervals of labor and rest, the continual barter and sale with gravity, in the transfer of energy to and fro, is not by any means an uncomfortable diversion to either our minds or bodies; but when we come to suffer the usurious interest demanded by the action of the air against us, we simply draw the line, and go by another road, even though the surface thereof be not of the most inviting character. Some ingenious mechanics have devised mechanism whereby they propose to store up the power lost in the brake action; but it is doubtful if any riders would care for it after they become expert and daring, which they all do in course of time in spite of all admonition against undue risk.