of the axle); then multiply the power by its distance | The principle of the wheel and axle, or perpetual Fig. 20. for spokes or levers, which the men push against to cause the axle to turn. This is a powerful and convenient machine on shipboard; when not in use, the spokes are taken out and laid aside. An illustration of the wheel and axle, in a combined form, is afterwards given in the case of the crane. OF CORDS AND PULLEYS. The pulley, or cord, is one of the primary mechanical powers. A pulley is a wheel, with a groove in its circumference, and suspended by a central axis. In fixed pulleys, a flexible cord, which is made to pass over and hang from the upper part of the groove, has at one extremity a certain weight to be raised, and at the other extremity a power is attached for the purpose of pulling. pulley, but instead of being placed in a fixed position W Fig. 22. The moveable pulley possesses a mechanical advantage. The first point to be observed is, that the weight hangs in the cord; second, that the weight presses down each side of the cord equally-that is, it draws as hard at A as at C or P; third, that the consequence of this equal pressure is the halving of the weight between the two ends of the cord. The halving of the weight is therefore the mechanical advantage given by the moveable pulley. Example. If the weight W be ten pounds, five pounds is borne by A, and five pounds by P. The case is precisely the same as that of two boys carrying a basket between them. The basket is the weight, and each boy, with his hand upholding the handle, bears only half the load, whatever it may be. If, instead of holding by the handle, the boys slip a cord beneath it, and each take an end of the cord, the case is the same. In order to save expenditure of power in lifting weights by pulleys, it is always contrived to cause some inanimate object, as for instance a beam or roof, to take a share of the weight, leaving only a portion to be borne by the person who pulls. But in this, as in all cases of mechanical advantage, the saving of power is effected only by a certain loss of time, or a longer continuation of labour. To lift a weight one foot from the ground, by the moveable pulley, a man must pull up the cord two feet; therefore, to lift a weight, it will take double the exertion to draw it up a given height in a given time without the pulley, that it would require with the intervention of the pulley. As the power which a man can exert by his hands, is able to overcome a weight greater than the weight of his own person, this circumstance may be taken advantage of in a very peculiar manner, through There are two kinds of pulleys, the fixed and move-the agency of the fixed pulley. As able. The annexed cut, fig. 21, represents a fixed pulley. A is the wheel, B is a beam or roof from which the wheel is suspended. P is the power hanging at one end of the rope, and W is the weight at the other end. This kind of pulley is called a fixed pulley, because it does not shift" from its position. The fixed pulley possesses no mechanical advantage. The wheel is merely a lever with equal arms, and therefore the cord which passes over these arms gains no advantage. To Fig. 21. raise a pound weight from the ground at the one end of the cord, the power of one pound must be exerted at the other. The object of the single fixed pulley is not to save power, but to give convenience in pulling. For instance, by pulling downwards, a weight may be raised upwards, or by pulling in one direction, a load may be made to proceed in another. The same object might be gained by drawing a cord over a fixed post or pivot, but in this case the friction of the cord would chafe or injure it; the wheel or pulley is therefore a simple contrivance to prevent friction, for it turns round along with the cord. The moveable pulley is in form the same as the fixed represented in fig. 23, a man may Fig. 23. The principle upon which pulleys act, is the distribution of weight throughout the different portions of the cord, so as to lessen the power necessary to be exerted by the operator. And along with this principle is the changing of the direction of the power for the sake of convenience in pulling. According to ordinary language, the mechanical power of which we are treating is called the power of the pulley; but, in reality, as has been just shown, the pulley has no power in itself. The power of the ma chine is in the cord. It is in the equal tension of the cord through its whole length, by which the weight is distributed upon intervening points, that the machine offers any In all cases in which cords are drawn tightly, so as the marked 4, supports eight pounds, or 4 pounds on each In working pulleys, the power Fig. 25. W Technically, the wheel of a pulley is called a sheave; will be a loss of power in pro- The power of pulleys is increased by a combination are several, The following are examples of different combinations of pulleys: Figure 24 represents a compound system of pulleys, by which the weight is distributed through four folds of the same cord, so as to leave only a fourth of the weight, whatever it may be, to be raised by the operator. In this illustration, the cord number 1 bears one-fourth of the weight; the cord number 2 bears a second fourth; the cord number 3 bears a third fourth; and the cord number 4 bears a fourth fourth. Here the mechanical advantage ceases. For, although the cord number 4 passes over the topmost fixed pulley down to the hand of the operator, no more distribution of power takes place; this topmost pulley being of use only to change the direction of the power. The person who pulls has thus only a quarter of the weight to draw. If the weight be Fig. 24. one hundred pounds, he has the labour of pulling only twenty-five pounds. W Thus it is observable that the diminution of weight is in proportion to the number of moveable pulleys. To calculate the expenditure of power or diminution of weight, therefore, we have only to multiply the number of moveable pulleys by two, and the product shows the power to be exerted. Two moveable pulleys multiplied by two, gives 4; therefore a fourth of the weight is the power required, and so on. The addition of a single moveable pulley to any system of pulleys, at once lessens the apparent weight one-half, or, in other words, doubles the effect of the power; but every such addition causes more time to be spent in the operation, there being at every additional fold of the cord more cord to draw out, and also more friction to overcome. B Fig. 26 is a representation of a system of pulleys commonly used in practical operations. Three moveable pulleys are enclosed in the block A, and three fixed pulleys are enclosed in the block B. Suppose, therefore, that the weight W, in this case, is six hundred pounds, the hand P pulls it upwards by exerting a force of one hundred pounds. A combination of pulleys resembling this is used in turning kitchen jacks. The weight in sinking draws off the cord from a spindle, by which motion the jack is turned. In order that a considerable weight falling slowly through a comparatively small height may keep the jack in motion for a long time, as many as ten or twelve moveable and fixed pulleys are used. OF THE INCLINED PLANE. W Fig. 26. P A horizontal plane is a plane coinciding with that of the horizon, or parallel to it; when the plane is not level or horizontal, but lies in a sloping direction, with one end higher than the other, it is said to incline, or is called an inclined plane. Fig. 27 is an example. Fig. 27. The inclined plane, as already stated, is a primary mechanical power. The object which is accomplished by it is the raising of weights to considerable elevations, or the overcoming of resistances by the application of lesser weights and resistances; or, making a small power overcome a greater. To raise a load of a hundred pounds to an elevation of fifty feet by a direct perpendicular ascent, and without using any mechanical advantage, the power exerted must be a hundred pounds, or equal to the weights to be overcome. If, instead of raising the load directly upwards, we raise it by the gradual ascent of an inclined plane, the power required is less than a hundred pounds, and the diminution is in proportion to the smallness of rise in the inclined plane. But this saving of power, as in all other instances of mechanical advantage, is accomplished only by a corresponding loss of time. In the annexed system of pulleys, fig. 25, a series of moveable pulleys, with different cords, are made to act successively on one another, and the effect is In drawing a load, as, for instance, a loaded carriage, doubled by each pulley. At the extremity of the first along a horizontal plane, the resistance to be overcome cord, a power of one pound depends. This cord, marked is chiefly the friction of the load upon the plane. If 1, by being drawn below a moveable pulley, supports there were no friction or impediment from inequatwo pounds that is, 1 pound on each side. The next lities of surface, and if the load were once put in mocord, marked 2, in the same manner supports four tion, it would go on moving with the smallest possible pounds, or 2 pounds on each side. The next cord, expenditure of power. In drawing a load up an inclined plane, ordinary | friction has to be overcome, and also the gravity of the body, which gravity gives it a tendency to roll down to the lowest level. In this constant impulse to descend, it is not at liberty to pursue the same line of descent as bodies falling freely from heights. It falls or rolls down as much less speedily than a free falling body (omitting the loss by friction) as the length of the inclined plane is greater than its height. A freely descending body falls about 16 feet in the first second; and a body rolling down an inclined plane, rolls just as many feet the first second as the number of feet of inclination is in sixteen feet. If the inclination be one foot in sixteen, the body rolls down one foot, and so on. B A D Fig. 28. C M Q Figure 30 represents a supposed case of two inclined planes of the same height, but different slopes, meeting together at the top, with a weight resting on each, P and Q, hanging by a string, which passes over the pulley M. If the length of the longest plane from A to M be two feet, and that of the shorter from B to M be one foot, then two pounds at Q, Fig. 30. on the short side, will balance four pounds at P, on the long side; and so on in this proportion, whether the planes be longer or shorter. A B In this manner, weights moving on two adjoining inclined planes may be adjusted so as to balance each other, although the inclinations be different; and they are so made to act on various sloping railways connected with public works, where one waggon descending on one plane is made to draw up another waggon on another plane. An inattention on the part of our forefathers to these exceedingly simple principles of mechanical science, led them to form roads over steep hills, pursuing, as it was imagined, the best routes, because they were the straightest in a forward direction. In modern times, this error has been avoided by enlightened engineers, and roads are now constructed with as few risings and fallings as possible. When roads have necessarily to be carried to the summits of heights, they are very -D properly made either to wind round the ascent, or to describe a zig-zag line of direction. Any body in being drawn up an inclined plane, by a power parallel with the plane, presses at right angles with the plane. The common expression is, that the reaction of the plane upon the object is perpendicular ot the plane. When an object, as a ball, rests upon a horizontal plane, its pressure is at right angles with the plane; or, what is the same thing, the reaction or resistance of the plane is at right angles with it. This is seen in fig. 28, in which a ball is represented lying on a level plane, with the line of pressure A passing down to B, which line is at right angles with the plane. Suppose, then, that the end of the plane at C is elevated to D, as in fig. 29, so as to form a slope; in this case the line of pressure of the ball on the plane is also moved, so as still to be at right angles with the inclination. The power which is required to be sustained for the purpose of overcoming friction or inequalities of surface on level planes, is for the purpose of drawing the load up or over the inequalities. B Fig. 29. The amount of the power corresponding to different weights and inclinations of the plane has been correctly ascertained, and the following are the rules upon the subject: First. The quantity of weight is great in proportion to the inclination of the plane; consequently, so is the difficulty of raising greater, and the rate of elevation or motion slower. Second.-To overcome the weight or resistance, and the slowness of movement, a corresponding increase of power must be given. Third.-The smaller the inclination, so is the pressure of the weight on the plane the greater. Fourth, or Special Rule of Calculation.-Whatever is the unit of inclination in a given length, the same is the unit of weight that can be lifted, and the unit of power to be exerted. If the inclination of a road be one foot in ten, onetenth is called the unit of inclination; hence, one-tenth part of the nominal weight of the load has to be lifted; and a power to draw this one-tenth part of the load has to be exerted. Or, to put the case in other words:-If the road rise one foot in ten, there is in the ten only one foot of perpendicular height to be lifted through; and the weight at any point of the ten feet is only a tenth of what would be if it were to be lifted through a perfect perpendicular ascent of ten feet. The reason is now perceived why a small power overcomes a greater in the case of draughts upon inclined planes. The load is, as it were, lifted by instalments, Partly supported as it advances, and always supported more completely the smaller the inclination, the weight of the burden is apparently lessened by merely taking the rise gradually and slowly. If we suppose a case of two roads, the first rising one foot in twenty, and the second rising one foot in filty, a loaded carriage will be found to go over the fifty feet of the one with precisely the same expenditure of power that would be required to make it go over the twenty feet of the other—that is, always providing that friction and other circumstances are alike. The drivers of carts are aware of the saving of labour to their horses by causing them to wind or zig-zag up steep roads instead of leading them directly forward. The inclined plane is resorted to for a saving of labour in many of the ordinary occupations of life. By it loaded wheelbarrows are with comparative ease wheeled to considerable elevations in house building and other works of art; hogsheads are rolled out of or into waggons, and ships are launched into or drawn from the water, the inclined plane being as useful in giving facilities for letting down loads as in drawing them up. It is also by inclined planes that we reach the higher floors of a house from the ground, or attain other elevations. For all such purposes, the inclined plane formed with steps to ensure our safe footing. All stairs or flights of steps are inclined planes. A ladder forms a steep inclined plane. OF THE WEDGE. The inclined plane has been described as being fixed or stationary, as, for instance, a common ascending road, or a sloping plank, upon which the weights are moved. It has now to be viewed as a moveable plane, in which form it suits many useful purposes. When an inclined plane is moveable, and the load or weight which it affects is at rest, it receives the name of a wedge. The wedge is, therefore, a mechanical power, founded on the principle of the inclined plane. B The wedge is an instrument or simple machine, consisting of a solid body of wood, iron, or some other hard material, and is triangular in form. See fig. 31. Here the wedge is seen to taper from a thick end or head at B to a thin edge or point at A. This, however, is only the more common form of the wedge. It is made with sides of various angularities or degrees of slope; and, in some cases, it possesses a flat and a sloping side. When it slopes on both sides, it consists of two inclined planes joined together; and when one of its sides is Fig. 31. flat, it acts as only one inclined plane. The wedge is employed as an instrument for cleaving solid masses asunder, to compress bodies more closely together, and to move great weights through small spaces. Fig. 3is a front view of a wedge in the act of splitting asunder a piece of timber. The power employed to The rules for calculating the power of at the centre. Fig. 32. Fig. 33. It is difficult to calculate the precise power of the wedge, for much depends on the force or the number of blows which may be given to it, together with the obliquity of the sides, and the power of resistance in the object to be split. In the splitting of timber, for instance, the divided parts act as levers, and assist in opening a passage for the wedge. The wedge is the least used of the simple machines, but the principle upon which it acts is in extensive application. Needles, awls, bodkins, and driving nails, are the most common examples. Knives, swords, razors, the axe, chisel, and other cutting instruments, also act on the principle of the wedge; so likewise does the saw, the teeth of which are small wedges, and act by being drawn along while pressed against the object operated upon. The principle of the inclined plane, which is the basis of that of the wedge, is particularly observable in the action of the razor and the scythe, both of which cut best by being drawn along the materials against which they are applied. When the edge of a scythe or razor is examined with a microscope, it is seen to be a series of small sharp angularities of the nature of the teeth of a saw. The principle of the wedge operates in the case of two glass tumblers, one placed within the other, as in fig. 34. A very gentle pressure applied to the uppermost tumbler would be sufficient to burst the lower. At every little advance of the uppermost tumbler, it acts more and more as a lever power on the rim of the lower, and at last overcomes the resistance, and fractures the vessel. OF THE SCREW. Fig. 34. The screw is the fifth, and usually the last mentioned mechanical power. Like the wedge, it is founded on the principle of the inclined plane. The screw consists of a projecting ridge winding in the form of an inclined plane, and in a spiral direction, round a central cylinder or spindle, similar to a spiral road winding round a precipitous mountain. Fig. 35 is a representation of a common strong screw used in various mechanical operations. The projecting ridge on the spindle is technically called the thread. The thread is not always made in this square projecting form; it is frequently sharpened to a single thin edge, as in fig. 58, but this does not affect the principle of the machine. Fig. 35. One circumvolution or turn of a thread of a screw is, in scientific language, termed a helir (plural helices), from a Greek word signifying winding or wreathing. The spiral winding of the thread is called the helical line. The helices of a screw do not necessarily require to have a central spindle. They may form a screw of themselves, and do so in the case of the common cork-screw (fig. 36). A screw of this pointed or tapering form, in penetrating a substance, possesses the advantage of the inclined plane in three ways-first, by the gradual thickening of the substance of the thread from a sharp point; second, the gradual widening; and, third, the gradual ascending, of the thread. Fig. 36. The screw acts on the principle of the inclined plane, and this is obvious from the consideration of the nature of the threads. If we were to cut through the turns of the threads straight from top to bottom, and draw them out to their full extent, each separate and retaining its own inclination, we should find that they were so many inclined planes. In the c annexed cut, fig. 37, one entire turn of the thread is thus drawn out, reaching from b to a, and is seen to form an inclined plane. If not drawn out, it would wind down to c; therefore, while a weight is raised by one turn of the screw over the limits of one thread, or from c to b, it has actually been carried up the inclined plane from a to b. Fig. 37. a The screw has no power by itself. It can operate only by means of pressure against the threads of another screw which overlaps it and holds L it. This exterior screw, which is technically called a box or a nut, consists of a block with a central tube cut out in spiral grooves so as to fit with perfect exactness to the screw which has to work in it. Fig. 38 represents both screws in combination. M is the box or nut through which the Fig. 38. screw passes. L is a lever inserted into the head of the screw, for the purpose of turning it. M The object required by the use of the screw is to apply force or pressure. To produce the intended effect, either the outer or inner screw, that is, either the nut or the screw, must be fixed. If the screw be fixed at one extremity, say at the top, to a solid body, the nut may be turned round it so as to move from the bottom to the top; and if the nut be fixed, held fast by some solid body, the screw in the same manner may be turned round till it reach its extremity. Thus, either the point of the screw, or the nut, may be forced in such a way as to squeeze or press any object presented to them. Practically, the screw is never used as a simple machine; the power being always applied by means of a lever, passing either through the head of the screw, or through the nut. The screw, therefore, acts with the combined power of the lever and inclined plane; and, in investigating the effects, we must take into account both these simple mechanical powers, so that the screw now becomes really a compound machine. In the inclined plane, as has been seen, the less it is inclined, the more easy is the ascent, though the slower is the process of rising to a certain elevation. In applying the same principle to the screw, it is obvious that the greater the distance is betwixt the threads, the greater or more rapid is the inclination, and, consequently, the greater must be the power to turn it under a given weight. On the contrary, if the thread inclines downwards but slightly, it will describe a greater number of revolutions in a given space, so as to diminish the distance betwixt the threads, and the smaller will be the power required to turn the machine under a given weight. Therefore, the finer the screw, or the nearer the threads to each other, the less the power will require to be for a given resistance. tention of the pressure; and this quality of constancy is always procurable from the great friction which takes place in the pressure of the threads on the nut, or on any substance, such as wood, through which the screw penetrates. Suppose a case of two screws, one having the threads | pressure accompanied with constancy of action, or reone inch apart, and the other half an inch apart; then, the force which the first screw will give with the same power at the lever, will be only half that given by the second. The second screw must be turned twice as many times round as the first, to go through the same space. At the lever of the first, two men would raise a weight to a given height, by making one revolution; while at the lever of the second, one man would raise the same weight to the same height, by making two revolutions. It is apparent, that the length of the inclined plane up which a body moves in one revolution, is the circumference of the screw, and its height the interval between the threads. The proportion of the power would therefore be " as the circumference of the screw is to the distance between the threads, so is the weight to the power." By this rule, the power of the screw could alone be found, provided the action of the machine was not affected by the lever which works it. As that is the case, the circumference described by the outer end of the lever employed is taken instead of the circumference of the screw itself. B 1:|:ཀགཞནA༦ H The common standing-press used by bookbinders for pressing their books, affords one of the best examples of the application of the screw to produce great pressure (fig. 39). The screw A has a thick round lower extremity B, into holes in which the lever is inserted. This extremity B is attached by a socket joint to the pressing-table C, so that when the screw is turned in one direction, the table sinks, and when turned in another, the table rises. The books D lie upon a fixed sole S, and are thus between the table and the sole. His a cross beam above, in which is the box or overlapping screw to give the necessary resistance. S Fig. 39. MECHANICAL COMBINATION AND STRUCTURE. Mechanical action is applied to the action of forces that produce no change in the constitution of bodies, and is therefore distinguished from chemical or any other species of action, in which change of constitution is less or more effected. The rule by which the true force of the screw is calculated, is, by multiplying the circumference which the lever describes by the power. Thus-The power multiplied by the circumference which it describes, is equal to the weight or resistance multiplied by the distance between the two contiguous threads. Hence, the efficacy of the screw may be increased, by increasing the length of the lever by which it is turned, or by diminishing the distance between the threads. If, then, Great changes are continually taking place in nature we know the length of the lever, the distance between and art by mechanical action. Mechanical action ge the threads, and the weight to be raised, we can rea-nerally implies movement or change of place, and in dily calculate the power; or, the power being given, and the distance of the threads and the length of the lever known, we can estimate the weight which the screw will raise. Suppose the length of the lever to be forty inches, the distance of the threads one inch, and the weight 8000; required the power, at the end of the lever, to raise the weight. The lever being 40 inches, the diameter of the circle which the lever describes is double that, or 80 inches. Reckoning the circumference at thrice the diameter (though it is a little more), we multiply 80 by 3, which gives 240 inches for the circumference of the circle. The distance of the threads is one inch, and the weight 8000 pounds. To find the power, multiply the weight by the distance of the threads, and divide by the circumference of the circle. 8000 weight 1 distance 240)8000 334 Thirty-three and a third is the product, and it would require that power or number of pounds to raise the weight. This, however, is only in theory. In practice, a third of the amount of power would require to be added to overcome the friction of the machine. most cases alteration of external features and circumstances. The whole of the planetary movements are mechanical; the motions of water and winds are me chanical; and the new appearances produced in art by placing different objects together, are mechanical. The action of forces upon solids, or mechanical action, is taken advantage of by mankind for the production of numerous useful results in the arts. And success in attaining these results depends in a great measure upon the knowledge we have of the principles of mechanics, and the skill and care we use in applying them. When skill, care, and ingenuity, are brought fully into operation for these results, very great wonders are in many instances achieved. But where there is ignorance or negligence, the object in view may not only be defeated, but very mischievous consequences may take place. Example first.-If a tall mast or beam break through at two-thirds of its height, and the two fractured ends be simply placed together and tied with a rope, the upper piece will, by the action of a small force, again fall. It will act like the arm of power of a lever against the rope, which is the weight; and as this weight is inconsiderable, the arm of power will preponderate. But if we take the two pieces and saw each of them lengthwise, so as In the ordinary working of the screw, velocity is incompatible with great power. This is a truth, how-to make four pieces, and then, as represented in ever, which applies only to a screw with one thread. There is a way of making a screw, by which great velocity and power may be combined. This is done by forming the screw with two, three, or more threads. To understand how this is accomplished, we have only to conceive the idea of a screw with one thread, very wide betwixt its turns, and then imagine one or two other threads placed so as to fill up the intervals; thus composing a fine close screw. And as by this means all the threads descend with equal rapidity, we have a screw which will not only descend with great velocity, but which will apply a very great degree of pressure. A screw of this nature is used in the printing press, by which a pressure of a ton weight is applied instantaneously by a single pull of a lever. The most common purpose for which the screw is applied in mechanical operations, is to produce great fig. 40, lay a short piece alongside of a long Example second.-If a man, in making repairs upon the outside of a building, project a plank from a window for the purpose of standing upon it, and if he proceed |