longer than the other, is applied in Other applications of of this lever may be traced in all these instruments. (3) The singlearmed lever (fig. 5) differs somewhat from those already considered, the ful k various ways, for moving One of the most familiar Fig. 4. crum c being situ ated at the end of Fig. 5. the lever. The forces k and w act on the unequal arms b c and a c, but in contrary directions, for k acts upwards, and w draws downwards. Equilibrium is likewise established in this case if kx b c = wx a c. Applications of the one-armed lever are found in the chopping a Fig. 6. blade, the nutcrackers, in most lever presses, in the force-pump (fig. 6), and in many safety-valves (fig. 7), wheelbarrows, &c. II. WHEEL AND AXLE.-This is the second mechanical power, by which weights are raised to a far greater height than by the lever. Upon the principle that every part of a revolving body moves with a velocity proportioned to its distance from the axis, it must be quite plain that any point of the circumference or outer rim of a wheel moves with greater velocity than any point of its axle; and consequently that a force applied to the wheel has more power than the same force applied to its axle, in proportion as the circumference or diameter of the wheel is greater than that of the axle. If the diameter of the wheel be ten times that of the axle, any force applied to, the wheel will have the same power as ten times that force applied to the axle. You have probably seen water drawn up from a deep well by means of a bucket fastened to a rope, which coils round a slender revolving cylinder (or bar) of wood or iron, that is put in motion by force applied to a handle affixed to the extremity of it, like the handle of a common roasting-jack, or of a hand-mill, or the key frequently used for a watch. Here it is evident that the man's band, which is applied to the handle, moves round a wide circle in the same time that each point of the cylinder round which the rope is coiled describes only a small one; and that power accordingly is gained in proportion as the circle described by the hand is greater than the circumference of the cylinder. Had the same force been applied to the cylinder itself instead of the handle, the bucket might not have moved at all. Hence, too, the difficulty of drawing up the bucket is continually increased, as one part of the rope coils round another, for this obvious reason, that the difference between the circle described by the hand and that described by the rope is proportionally diminished. The more you increase the length of the handle, and consequently enlarge the circuit of the hand, the more of course you increase the force. But a very long handle of this kind would be extremely inconvenient; and therefore, when considerable force must be employed, recourse is had to a wheel with cogs or spokes sticking out from it, by which it is impelled. Various other inventions, upon a similar principle, have been devised, under the name of capstans, windlasses, &c., such as you may have seen on board ships or on wharfs. Sometimes the wheel is moved by a man or several men placed in the inside, who walk on bars as if going up-stairs, by which the wheel is moved, just in the same manner as you may have seen squirrels or other animals make their cages revolve. This is very hard labour, which has accordingly given rise to the introduction of the tread-mill into houses of correction. III. THE PULLEY.-This is the third mechanical power. You have seen pulleys fixed in a wall for the purpose of drawing up curtains, bird-cages, &c. These fixed pulleys are often very convenient in changing the direction of a power, and enabling us to elevate a body to a considerable height, without putting us under the necessity of ascending thither along with it. But this is all the advantage they confer. They give no increase of power. In the fixed pulley (fig. 8), the forces q and q act at the points a and b, and the line a cb represents nothing more than an equalarmed lever, whose point of support is at c. No power is gained, therefore, in employing the fixed pulley; it is only of use in permitting the application of the force at the most appropriate point, as, for instance, when applied to a draw-well. The moveable pulley (fig. 9) represents a one-armed lever, the fulcrum of which is situated at b, while the force q draws downwards at the distance 1, and the force e upwards at the distance 2 and at the point d. As, however, the latter force acts at double the distance, it is only required to be half as great as the force q, in order to maintain the equilibrium. If, therefore, a weight of 4 lbs. be suspended on the hook of the moveable pulley, a force equal to 2 lbs. applied at e will be sufficient to raise it, and the least excess of power will be sufficient to set the load in motion. By combining a number of moveable pulleys, as seen in fig. 10, we are enabled to raise a considerable weight by the application of a small amount of force. On suspending the weight q, equal to 8 lbs., to a system of three moveable pulleys, 1 lb. will be found sufficient to maintain it in equilibrium. As was shown at fig. 9, the weight of the suspended load decreases one-half for every additional moveable pulley. The most convenient arrangement for raising weights by means of moveable pulleys is shown at fig. 11. In this system the three upper pulleys are stationary, and the three lower ones moveable; and therefore the advantage in its application is likewise that the load q may be counterbalanced by the application of one-eighth of its weight at p. It might be expected that by the application of a great number of pulleys we should be enabled to raise enormous weights with ease, But the results obtained fall short of e:ectation, partly because, by the addition of every pulley, the distance to which the load may be raised is diminished, while the friction, which is a great impediment to motion, is proportionably increased. IV. THE INCLINED PLANE is the fourth mechanical power, by which is meant nothing else than a slope or declivity, employed in order to render the ascent of a heavy body easier than it would have been in a perpendicular direction, when exposed to the full operation of the force of gravity. Of the application of this power you may see daily instances in the sloping planks which are laid for the purpose of lowering or raising packages to or from warehouses below the level of the street. The principle upon which the inclined plane operates differs from that of the other mechanical powers which have already been explained, but is no less obvious. No body, when laid on a declivity, will fall with the same velocity as when descending freely through the atmosphere. You have perhaps all seen a kind of table which, for the purpose of occupying less room when unemployed, is made to fold back by means of a hinge upon its pedestal. Lay a round body-as, for example, a marble-upon the table, when in its horizontal position (that is to say, in the position in which it is ordinarily made use of), and the marble will remain quite stationary; slope the table a little out of its horizontal position, and the marble will roll off; slope it still more, and the marble will roll off with increased velocity; turn it down altogether, and the marble will descend with all the velocity communicated by the full force of gravity. From what has been said, it is clear that a body will roll down the declivity A C with less velocity than it would fall in the perpendicular A B; and that in like manner it would roll down A D A with less velocity than it rolls down A C. For the same reason it will require less force either to sustain it on the declivity A D or to make it ascend that line, than would be B c Ꭰ necessary with reference either to A C or A B. The power gained, accordingly, by the use of the inclined plane, is in proportion as the length of the declivity exceeds its height. Thus, because A C is twice the length of A B, and A D is three times the length of A B, a single pound weight, suspended in the air at A, will be sufficient to sustain two pounds laid on the slope A C, or three pounds upon A D. In actual practice, however, much allowance must be made for the effect of friction. Chisels, and other sharp instruments sloped down to an edge on one side only, are accounted to act on the principle of the inclined plane. V. THE WEDGE is the fifth mechanical power. This is a piece of wood or iron having a sharp edge, and growing continually thicker towards the base, employed by workmen for the purpose of cleaving timber, rocks, &c. Let A B C represent, the surface of this implement. It is obvious that it consists of two |