is. The elbow being the centre round which the lower part of the arm turns, the muscle, therefore, must exert a force ten times as great as the weight to be raised. At first view this may appear a disadvantage, but the loss of power is compensated by the gain of velocity, and by the beauty and compactness of the limb. QUESTIONS.-1. What are mechanical powers? 2. What four things are necessary to be considered in order to understand the power of a machine? 3. When do the power and weight balance each other? 4. What is a lever? 3. Describe the lever of the first kind. 6. What are some instances of it, and to what purposes are they applicable? 7. What is said of a balance? 8. Describe the second kind of lever. 9. What does it explain? 10. What is the third kind of lever? 11. Show how the bones of a man's arm make a lever of this kind. 12. How is the loss of power compensated? 13. Give an illustration by fig. 7. of the first kind of lever. 14. Of the second kind, by figures. 9 and 5. 15. Of the third kind, by figures 10 and 2. LESSON 21. The Pulley, Wheel and Axle, and Inclined Plane. THE pulley is formed by a small wheel, made of wood or metal, with a groove in its circumference, which is placed in a frame and turns on an axis. The wheel is usually called a sheeve, and is so fixed in the frame, or block, as to move round a pin passing through its centre. Pullies are of two kinds; fixed, which do not move out of their places; and moveable, which rise and fall with the weight. A single fixed pulley gives no mechanical advantage, but it is of great importance in changing the direction of power, and is much used in buildings for drawing up small weights, for a man may raise a weight to any height without the fatigue of ascending a ladder. In the single moveable pulley, the advantage gained is as two to one; that is, a power exerted by the hand of ten pounds will balance a weight of twenty pounds. In a system of pullies, the power gained must be estimated, by doubling the number of pullies in the lower or moveable block. So that when the fixed block contains two pullies which only turn on their axes, and the lower block also contains two, which not only turn on their axes, but rise with the weight, the advantage gained is as four to one. In an THE INCLINED PLANE. 43 example of this kind, you will perceive, that by raising the weight an inch, there are four ropes shortened each an inch, and therefore the hand must have passed through four inches of space in raising the weight a single inch; which establishes the maxim, that what is gained in power is lost in space. The next mechanical power is the wheel and axle, which consists of a cylinder, and a wheel fastened to it, or of a cylinder with projecting spokes. The power being applied at the circumference of the wheel, the weight to be raised is fastened to a rope that coils round the axle. The advantage gained is in proportion as the diameter of the wheel exceeds that of the axle. Suppose a wheel to be twelve feet diameter, and the axle one foot, the power acting at the circumference of the wheel moves over twelve times the space which the circumference of the axle does. Hence, twelve hundred weight may be raised with the power of one hundred weight. The wheel and axle may be considered as a perpetual lever, the centre of the axle being the fulcrum, half the diameter of the wheel the long arm, and half the diameter of the axle the short arm. Now, from this it is evident, that the greater the diameter of the wheel, and the smaller the diameter of the axle, the stronger is the power of this machine; but then the weight must rise slower in proportion. A useful appli cation of the wheel and axle is the crane used on wharfs for drawing goods up from a ship. A man sets a great wheel in motion by pressing on the spokes at the rim, and the rope to which the goods are attached is wound round the axle. The wheel is sometimes put in motion by a man in the inside, who is in an upright position, and keeps walking on the bars, as if ascending stairs, which keeps the wheel revolving. The inclined plane is nothing more than a slope, or declivity, frequently used to facilitate the drawing up of weights. The increase of the power is in the proportion of the length of the plane to its height; that is, the more the plane is lengthened, or its height shortened, the less is the resistance to be overcome. If a plane be twenty feet long, and the perpendicular height be four feet, or one-fifth of the length, then five hundred pounds would be balanced on it by one hundred, because the plane is five times the length of the perpendicular height to which the weight is to be raised. If the height be two feet, or one-tenth of the length, then fifty 44 THE WEDGE AND SCREW, pounds will balance the five hundred. It is much less laborious to ascend a hill by a winding gentle ascent than to climb up a steep declivity. In addition to there being a greater force required in ascending a hill, horses, that draw a load, are placed in a position in which they can exert but a small part of their usual strength. The principle of the inclined plane is applied to the construction of carriage-ways, for the conveyance of heavy loads up steep elevations. It is applied also in rail-ways, the use of which has been hitherto confined, almost exclusively, to coal-works, and other mines. Inven tions, whose only recommendations are simplicity and usefulness, are often suffered to lie long in a state of public neglect, while others of more imposing aspect are readily adopted. It has been remarked with respect to Great Britain, that the time has at length arrived, when carriages moving on level surfaces, or on gently inclining planes, with little friction, and without obstructions, are fast spreading over the face of the country. QUESTIONS.-1. How is the pulley formed? 2. What are the two kinds of pullies? 3. What is said of the single fixed pulley? 4. What advantage is gained in a single moveable pulley? 5. How is the power gained to be estimated in a system of pullies? 6. How is this explained and what maxim does it establish? 7. Describe the wheel and axle. 8. In what proportion is advantage gained in this mechanical power? 9. What is the example? 10. Why may the wheel and axle be considered as a perpetual lever? 11. What application is made of this power? 12. What is an inclined plane? 13. In what proportion is the increase of power? 14. What is the example for illustrating this? 15. What application is made of the principle of the inclined plane? 16. What has been remarked concerning the use of rail-ways? 17. With respect to Great Britain? 18. Explain the single moveable pulley by fig. 13.-system of pullies by fig. 15. 19. Illustrate the power of the wheel and axle by fig. 11. 20. Inclined plane by fig. 8. LESSON 22. The Wedge and Screw. Percussion, the impression a body makes in falling or striking THE wedge may be considered as two equally inclined planes united at their bases. The advantage gained by it is in the proportion of the slant side to half the thickness of the back; so that if the back of a wedge be two inches thick, and the side twenty inches long, any weight pressing on the back will balance twenty times as much acting on the sides. But the great use of a wedge lies in its being urged, not by pressure, but usually by percussion, as by the blow of a hammer or mallet; for the momentum of the blow is greater, beyond comparison, than the application of any dead weight, or pressure, such as is employed in the other mechanical powers. Hence it is used in splitting wood and rocks, and even a large ship may be raised to a small As all instruments, height by driving a wedge below it. which slope off to an edge on one side only, may be explained by the principle of the inclined plane; so those that decline to an edge on both sides, may be referred to the principle of the wedge. A saw is a series of wedges, on which the motion is oblique to the resistance. A knife cuts best when it is drawn across the substance which it is to divide ; and the reason is, that the edge of a knife is in reality a very fine saw, and therefore acts best when used like that instrument. It is usual in separating large mill-stones from the siliceous sand-rocks, in some parts of Derbyshire, in England, to bore horizontal holes under them in a circle, and fill these with wedges made of dry wood, which gradually swell as they imbibe moisture, and in a day or two lift up the mill-stone without breaking it. The last mechanical power is the screw, which is a kind of perpetual inclined plane, the power of which is still farther assisted by the addition of a handle or lever, where the power acts; so that the advantage gained is in proportion as the circumference of the circle, made by the handle or lever, is greater than the distance between thread and thread in the screw. The screw may be conceived to be made by cutting a piece of paper into the form of an inclined plane, and then wrapping it round a cylinder. The edge of the paper will form a spiral line round the cylinder, which will answer to the thread of the screw. With the addition of the lever, the screw forms a very powerful machine, employed either for compressions, or to raise heavy weights. It is used by book-binders to press the leaves of books together; and is the principal machine used for coining money; for taking off copper-plate prints; and for printing in general. All machines are composed of one or more of the six me chanical powers which we have examined. Their force is diminished in a considerable degree by friction, by which is meant the resistance with which bodies meet in rubbing against each other. There is no such thing as perfect smoothness or evenness in nature: polished metals, though they wear that appearance more than any other bodies, are far from possessing it in reality, and through a good magnifyingglass their inequalities may frequently be perceived. When the surfaces of two bodies, therefore, come into contact, the prominent parts of the one will often fall into the hollow parts of the other, and occasion more or less resistance to motion. Friction is usually computed to destroy one third of the power of the machine. The application of oil lessens friction, because it acts as a polish by filling up the cavities of the rubbing surfaces, and thus making them slide over each other the more easily. There are two kinds of friction, the one occasioned by the sliding of the flat surface of a body, and the other by the rolling of a circular body. The resistance resulting from the first is much the most considerable; whilst in the latter the rough parts roll over each other with comparative facility; hence it is that wheels are often used for the sole purpose of diminishing the resistance of friction. The power of a machine is considerably affected by the resistance of the air. In all machines what is gained in power is lost in time. If a man can raise, by a single fixed pulley, a beam to the top of a house in two minutes, he will be able to raise six such beams in twelve minutes; but with six pullies, the three lower ones being moveable, he will raise six beams with the same ease at once; but he will be six times as long about it, that is, twelve minutes, because his hand will have six times as much space to pass over. One capital advantage in the mechanical powers is, that if the six beams were in one piece, it might be raised at once, though it would be impossible to move it by the unassisted strength of a single man. QUESTIONS.-1. What is the wedge? 2. The advantage gained by it? 3. In what does its great use lie? 4. What is said of instruments? 5. A saw? 6. A knife? 7. How are mill-stones obtained in Derbyshire? 7. What is the screw? 8. What is the advantage gained by it? 9. How may the screw be conceived to be made? 10. For what uses is it employed? 11. What is friction? 12. What part of a machine's power does friction destroy? [NOTE. If 60 pounds |