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tremity, you raise it with much more ease, than if you were to attempt to raise it at a part of the bench, more nearly approaching to that on which the person sits. Every door, too, or shutter, which turns upon hinges, is an example of this species of lever, of which the hinge is the fulcrum: here, also, you will close the door with more ease, by applying your strength to the fartherend, than by applying it to any part of the door nearer the hinge. The oar of a boat is also a lever of this kind, having the water for a fulcrum. A pair of nutcrackers is a double lever of the same kind, having the fulcrum at the hinge.--The 3d kind of lever is that, in which the fulcrum is placed at one extremity, the weight to be raised at the other, and the power between them. In this case there is an evident loss of force by the position of the power. Thus let BF represent a lever of this kind having the fulcrum at F, the weight to be raised suspended at B, and the force applied at
D A. Here it is evident that the point A moves with only a fourth part of the velocity of B, and consequently that it will require a weight of 4
A pounds at A to balance a weight of 1 pound at B. You may believe that the power is never so placed except in cases of absolute necessity, as for example, in raising a ladder against a wall. Anatomists have shown that the lower part of the human arm is a lever of the third kind, having the elbow for the fulcrum: and though, by such an arrangement, force is obviously lost, this is far more than counterbalanced by other most important advantages.
MECHANICAL POWERS(continued). II. The second Mechanical Power is the WHEEL AND AXLE, by which weights are raised to a fargreater height than by the lever. Upon the principle formerly ex
plained, 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 evi. dent that the man's hand, 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 next mechanical power is the PULLEY. 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. The hand, which draws the weight, moves with no greater velocity than the weight itself: and accordingly to balance each other, the power and the weight must be precisely equal. It is quite different however with regard to the moveable pulley, by which we mean one that, besides revolving round its own axis (as is the case with all pulleys), moves along with the weight. By means of one of these pulleys, the power is doubled, and by a combination of them may be greatly multiplied. Let C represent a moveable pulley, and the line ABCD a rope, one end of which is fixed to a hook at D, and the other passes over the fixed pulley B, placed there merely for the
B D purpose of altering the direction of the rope: weight of one pound suspended at A will be sufficient to balance two pounds suspended from the moveable pulley C. Here you will observe that the power at A has not to А support the whole weight suspended from the moveable pulley; for one half of that weight is borne by the other end of the rope fixed at the hook D.
When the rope is set in motion, it will be found that the power at A moves with just double the velocity of the moveable pulley and weight attached to it: be. cause, when the pulley has been raised one inch, the parts of the rope BC and CD will both have been shortened one inch; therefore two inches of rope altogether must have passed overthe fixed pulley, and the power at A must have advanced two inches in the same time that the weight suspended at C has advanced only one inch. When several of these moveable pulleys are combined, a still greater power is acquired. Thus a power of one pound is by means of two of these pulleys, enabled to support a weight of four, and by means of five of them, is enabled to support a weight of ten. Such combinations of pulleys you may see employed in cranes for raising goods into warehouses, and aboard ships to raise the sails. The principal objection to pulleys is, that, in consequence of friction, they lose so much of their natural power. By friction is meant that obstacle, which bodies encounterin their movements, from rubbing against each other. It may here, once for all, be remarked, that it more or less affects our calculations with regard to the power of all kinds of machinery, as well as of the pulley.-IV. The fourth mechanical power is the INCLINED PLANE, 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 theapplication 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 this 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 ; urn 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 AC with less velocity than it would fall in the perpendicular AB; and that, in like manner, it would roll down AD with less velocity than it rolls down AC. For the same reason, it will require less force either to sustain it on the declivity AD or to make it ascend that line, than would be necessary with reference either to AC or AB. 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 AC is twice the length of AB, and AD is three times the length of AB, a single pound weight, suspended in the air
at A, will be sufficient to sustain two pounds laid on the slope AC, or three pounds upon AD. In actual practice, however, much allowance must be made for the effect of friction. Chisels, and other sharp instruments A sloped down to an edge on one side only, are accounted to act on the principle of the inclined plane.
D V. The fifth mechanical power is the WEDGE, which 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 ABC represent the surface of this implement. It is obvious that it consists of two inclined planes, meeting at the point C, and united at the base AB. The point C is inserted into the body to be cleft, and, by means of violent blows of a hammer upon the