Suppose that a heavy stamper or hammer is to be raised to a certain height, and thence to be allowed to fall, and that the power used for this purpose is a water-wheel. While the stamper ascends, the power of the wheel is nearly balanced by its weight, and the motion of the machine is slow. But the moment the stamper is disengaged and allowed to fall, the power of the wheel, having no resistance, nor any object on which to expend itself, suddenly accelerates the machine, which moves with a speed proportioned to the amount of the power, until it again engages the stamper, when its velocity is as suddenly checked. Every part suffers a strain, and the machine moves again slowly until it discharges its load, when it is again accelerated, and so on. In this case, besides the certainty of injury and wear, and the probability of fracture from the sudden and frequent changes of velocity, nearly the whole force exerted by the power in the intervals between the commencement of each descent of the stamper and the next ascent is lost. These defects are removed by a fly-wheel. When the stamper is discharged, the energy of the power is expended in moving the wheel, which, by reason of its great mass, will not receive an undue velocity. In the interval between the descent and ascent of the stamper, the force of the power is lodged in the heavy rim of the fly-wheel. When the stamper is again taken up by the machine, this force is brought to bear upon it, combined with the immediate power of the water-wheel, and the stamper is elevated with nearly the same velocity as that with which the machine moved in the interval of its descent. (311.) In many cases, when the moving power is not subject to variation, the efficacy of the machine to transmit it to the working point is subject to continual change. The several parts of every machine have certain periods of motion, in which they pass through a variety of positions, to which they continually return after stated intervals. In these different positions the effect of the power transmitted to the working point is different; and cases even occur in which this effect is altogether annihilated, and the machine is brought into a predicament in which the power loses all influence over the weight. In such cases the aid of a fly-wheel is effectual and indispensable. In those phases of the machine, which are most favourable to the transmission of force, the fly-wheel shares the effect of the power with the load, and retaining the force thus received directs it upon the load at the moments when the transmission of power by the machine is either feeble or altogether suspended. These general observations will, perhaps, be more clearly apprehended by an example of an application of the fly-wheel, in a case such as those now alluded to.