Speaking of potential energy and momentum, we naturally come upon the question of machine weight. It is a peculiar fact that the weight of the man does not form so important a part in the bicycle exercise as that of the machine, so that if a rider be heavier by twenty pounds than another, it will not generally count against him; but if that weight is in the machine, competition is out of the question. Nature seems to make up in muscle, or supply of energy in some way, for the extra weight in the man, but said nature is not so clever when this weight is outside of him. It is sometimes thought that a heavy man or a heavy machine will descend a hill faster than a lighter. This is not reasonable. The accelerating force of gravity being independent of the mass, the heavy system will have the same velocity at the bottom, and momentum being represented by mass, times velocity, the increased mass will increase the momentum; but the speed is the same: this extra momentum is required in raising the heavier system to the same height as the lighter. But even if the rider should get the benefit of all the energy he stores in climbing a hill, there is still an indisputable objection to a heavy wheel,—to wit, a man can labor long and continuously at a strain within reasonable limits, and can do a large amount of work thereby; but to strain the system beyond those limits, and attempt to store up too much energy in too short a space of time, is to make nature revolt, resist the imposition, and refuse to be appeased for some time to come and often not at all; in short, an overstrain is bad, and by a heavy machine, no matter what amount of energy you may store up at the top of the hill, if in so doing nature has been overtaxed, it will result disastrously. So we see that, outside of all mechanical questions of momentum and potential energy, there is a vital objection to heavy machines on purely physiological grounds. CHAPTER VIII. COMPARISON OF THE CURVES OF TRANSLATION, IN MACHINES OF WHICH THE DIAMETERS OR COMBINATION OF WHEELS DIFFER, OF A POINT TAKEN IN THE SAME RELATIVE POSITION ON THE SEVERAL SADDLES—CONSEQUENT CONCUSSION AND EFFECT UPON MOMENTUM. In discussing this matter it has been taken for granted that the proper point upon which to base calculations is that point in the saddle at which the motion of the machine may be supposed to be transmitted to the rider; this happens to be very near the centre of gravity of the system, and is also quite near the centre of gravity of the man. The motion is of course partially transmitted to the rider at the pedals, but we will for the present waive that modification.