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NOTE 6. p. 119.
Mechanical powers are simple arrangements by which we gain power at the expense of time; thus, if a certain weight can be raised to a certain height by unassisted strength, and the same thing is afterwards done with one tenth part of the exertion, through the use of a mechanic power, it will be found to occupy ten times as much time. In many cases, however, loss of time is not to be put in competition with the ability to do a thing; and since the advantages which the mechanical powers afford to man, by enabling him to perform feats which, without their assistance, would have been for ever beyond his reach, are incalculably great, the waste of time is overlooked, and is much more than balanced in the general result. It is true that, if there are several sınall weights, manageable by human strength, to be raised to a certain height, it may be full as convenient to elevate them one by one, as to take the advantage of the mechanical powers in raising them all at once; because the same time will be necessary in both cases : but suppose we should have an enormous block of stone, or a great tree to raise; bodies of this description cannot be separated into parts proportionable to the human strength, without immense labour, nor, perhaps, without rendering them unfit for those purposes to which they are to be applied; hence then the great importance of the mechanical powers, by the use of which a man is able to manage with ease a weight many times greater than himself.
To understand the principle of a mechanical power, we must revert to the doctrine of momentum. It will be remembered, that a small ball, weighing only two pounds, and moving at the rate of 500 feet in a second, will produce as much effect as a cannon ball of ten pounds in weight, provided it only moved at the rate of 100 feet in the same time; in like manner a ball weighing one pound may be made to balance another of five pounds, by placing it five times farther from the centre of motion; for in such a case, for every inch of space through which the large ball
passes, the small one will traverse five inches, and will thus generate five times the momentum. This may be rendered still more evident by turning to page 273., where the see-saw is described, which, in fact, is a true mechanical power. It will be at once evident, from an inspection of the figure, that the lesser boy will pass over a much greater space, in equal time, than the greater boy, and thus generate more momentum, which compensates for his defect in weight, and renders him a balance for his heavier companion. It is curious to reflect upon what a simple, and apparently trivial truth the mechanical powers are founded, viz.that the lengths of circles are in proportion to their diameters; for it is an immediate consequence of this property of the circle, that if a rod of iron, or beam of wood, be placed on a point or pivot, so that it may move, as a see-saw board does, round its prop, the two ends will go through parts of circles, each proportioned to that arm of the beam to which it belongs; the two circles will be equal if the pivot is in the centre or middle point of the beam; but if it is nearer one end than the other, say five times, that end will pass through a circular space, or arc, five times shorter than the circular space the other end goes through in the same time. If, then, the end of the long beam goes
through five times the space, it must move with five times the swiftness of the short end, since both move in the same time; and, therefore, any force applied to the long end must overcome the resistance of five times that force applied at the opposite end, since the two ends move in contrary directions; hence one pound placed at the long end would balance five placed at the short end. The beam we have been describing constitutes the first of the mechanical powers, and is termed the LEVER. There are, besides five others, viz. the wheel and axle ; the inclined plane ; the screw ;
the pulley; and the wedge ; out of the whole, or a part of which, it will be found that every mechanical engine or piece of machinery is constructed.
THE LEVER being the simplest of all the mechanic powers, is in general considered the first. It is an inflexible rod or bar of any kind, so disposed as to turn on a pivot or prop, which is always called its fulcrum. It has the weight or resistance to be overcome attached to some one part of its length, and the power which is to over, come that resistance applied to another; and, since the power, resistance, and fulcrum admit of various positions with regard to each other, so is the lever divided into three kinds or modifications, distinguished as the first, second, and third kinds of lever. That portion of it which is contained between the fulcrum and the power, is called the acting part or arm of the lever ; and that part which is between the fulcrum and resistance, its resisting part or arm.
In the lever of the first kind, the fulcrum is placed between the power and the resistance. A poker, in the
act of stirring the fire, well illustrates this subject; the bar is the fulcrum, the hand the power, and the coals the resistance to be overcome. Another common application of this kind of lever is the crow-bar, or hand-spike, used for raising a large stone or weight. In all these cases, power is gained in proportion as the distance from the fulcrum to the power, or part where the men apply their strength, is greater than the distance froin the fulcrum to that end under the stone or weight. A moment's reflection will show the rationale of this fact; for it is evident that if both the arms of the lever be equal, that is to say, if the fulcrum be midway between the power and weight, no advantage can be gained by it, because they pass over equal spaces in the same time; and, according to the fundamental principle already laid down, as advantage or power is gained, time must be lost ; but, since no time is lost under such circumstances, there cannot be any power gained. If now, we suppose the fulcrum to be so removed towards the weight, as to make the acting arm of the lever three times the length of the resisting arm, we shall obtain a lever which gains power in the proportion of three to one, that is, a single pound-weight applied at the upper end will balance three pounds suspended at the other. A pair of scissors consists of two levers of this kind, united in one common fulcrum ; thus the point at which the two levers are screwed together is the fulcrum; the handles to which the power of the fingers is applied, are the extremities of the acting part of the levers, and the cutting part of the scissors are the resisting parts of the levers ; the longer, therefore, the handles, and the shorter the
points of the scissors, the more easily you cut with them. A person who has
hard substance to cut, without any knowledge of the theory, diminishes as much as possible the length of the resisting arms, or cutting part of the scissors, by making use of that part of the instrument nearest the screw or rivet. Snuffers are levers of a similar description; so are most kind of pincers, the power of which consists in the resisting arm being very short in comparison with the acting one.
In the lever of the second kind, the resistance or weight is between the fulcrum and the power. Numberless instances of its application daily present themselves to our notice; amongst which may be enumerated the common cutting knife, used by last and patten makers, one end of which is fixed to the work-bench by a swivel-hook. Two men carrying a load between them, by one or more poles, as a sedan chair, or as brewers carrying a cask of beer, in which case either the back or front man may be considered as the fulcrum, and the other as the power. Every door which turns upon its hinges is a lever of this kind; the hinges may be considered as the fulcrum, or centre of motion, the whole door is the weight to be moved, and the power is applied to that side on which the handle is usually fixed. Nut-crackers, oars, rudders of ships, likewise fall under the same division. The boat is the weight to be moved, the water is the fulcrum, and the waterman at the oar is the power. The masts of ships are also levers of the second kind, for the bottom of the vessel is the fulcrum, the ship the weight, and the wind acting against the sail is the moving power. In this kind of lever the power or ad