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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 height by driving a wedge below it. As all instruments, 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 instru. ment. It is usual in separating large mill-stones from the siliceous sand-rocks, in some parts of Derbyshire, in Eng, land, 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 à 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 forins 4 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 mechanical 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, thai 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 knite ? 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
are required to balance any weight with a mechanical power, 80 pounds will be wanted to put the machine in motion.] 13. How does oil lessen friction ? 14. What are the two kinds of friction ? 15. How does it appear that in the pulley what is gained in power is lost in time? 16. Explain the principle of the wedge by fig. 6. 17. Of the screw by fig. 3.
The Laws of Fluids. Hydrostat'ics, a term formed of two Greek words, which signify water, and the science which considers the weight of bodics,
viz. statics. Gas, all kinds of air differing from the atmosphere are called gas. Cu bical, having six square and cqual sides. Or'ifice, any opening or perforation. A Fluid is a body, the parts of which yield to any impression, and are easily moved among each other. Philosophers have generally imagined that the particles of which Auids are composed must be exceedingly small, because with their best glasses, they have never been able to discern them. And they contend that these particles must be round and smooth, since they are so easily moved among o. e another. This supposition will account for many circumstances which belong to them. If they are round, there nust be vacant spaces between them. If a number of cannon balls were placed in a large vessel so as to fill it up even with the edge; though it would hold no more of these balls, yet a great number of smaller shot might be placed in the vacuit between them: and when the vessel would contain no more small shot, a great quantity of sand might be shaken in, and between the pores of these, water or other fluids would readily insinuate themselves. In a similar inanner, a certain quantity of particles of sugar can be taken up in water without increasing the bulk, and when the water has dissolved the sugar, salt may be dissolved in it, and yet the bulk remain the same.
And this is easily accounted for, if we admit the particles of water to be round.
Fluids are either non-elastic and incompressible, as water, oil, mercury, and others, or elastic and compressible, as air, steam, and the different gases. The science which treats of
PRESSURE OF FLUIDS.
the nature, gravity, pressure, and motion of fluids, in general, and of the methods of weighing solids in them, is called hydrostatics. The non-elastic fluids are said to be incompresa sible, not because they are absolutely so, but because their compressibility is so very small as to make no sensible difference in calculations relative to their several properties. It has been found that water will find its way through the pores of gold, rather than suffer itself to be compressed into a smaller space.
At Florence, a celebrated city in Italy, a globe made of gold was filled with water, and closed so accurately that none of it could escape. The globe was then put into a press, and a little flattened at the sides : the consequence of which was, that the water came through the fine pores of the golden globe, and stood upon its surface like drops of dew. It was concluded at that time that water was incompressible. Later experiments, however, have shown, that those fluids which were esteemed incompressible, are, in a very small degree, as, perhaps, one part in twenty thousand, capable of compression.
Fluids are subject to the same laws of gravity as solids ; but their want of cohesion occasions some peculiarities. The parts of a solid are so connected as to form a whole, and their weight is concentrated in a single point, called the centre of gravity; but the atoms of a fluid gravitate independently of each other. It is on this account that water always finds its level; for when any particle accidentally finds itself elevated above the rest, it is attracted down to the level of the surface, and the readiness with which water yields to the slightest impression, will enable the particle by its weight to penetrate the surface and mix with it. The particles of a Auid acting thus independently, press against each other in every direction, not only downwards but upwards, and laterally or sideways, and in consequence of this equality of pressure, every particle remains at rest in the fluid. If you agitate the fluid you disturb this equality of pressure, and it will not rest till its equilibrium or level is restored. The pressure downwards is the effect of gravity, and if there were no lateral pressure, water would not run out of an opening on the side of a vessel. The lateral pressure proceeds entirely from the downward pressure, or the weight of the liquid above; and consequently the lower an orifice is made in a vessel, the greater will be the velocity of the water rushing
PRESSURE OF FLUIDS.
out of it. In a cubical vessel the pressure downwards will be double the lateral pressure on one side; for every particle at the bottom of the vessel is pressed upon by a column of the whole depth of the fluid, whilst the lateral pressure diminishes from the bottom upwards to the surface, where the particles have no pressure. The upward pressure of fluids may be shown by a machine, called the hydrostatic "bellows. It consists of two oval or round boards, covered with leather so as to rise and fall like the common bellows, but without valves. A long tube is fixed to the upper board and weights placed upon it. When the tube is supplied with water, it will, by its upward pressure, sustain and lift up the weights. The pressure of water and other fluids differs from the gravity or weight, in this respect; the weight is according to the quantity; but the pressure is according to the perpendicular height. Dr. Goldsmith relates that he once saw a strong hogshead split by the following experiment. A strong small tube, made of tin, about twenty feet long, was cemented into it, and then water was poured in to fill the cask; when it was full and the water had risen nearly to the top of the tube, the vessel burst with a prodigious force. This extraordinary power may be greatly increased by a forcing piston placed in the tube. A similar method has been adopted in forming a machine, called a hydrostatic press, by which hay or cotton may be brought into a compass twenty or thirty times less than it usually occupies.
QUESTIONS.—1. What is a fluid ? 2. What have philosophers generally imagined respecting the particles of fluids ? 3. What illustration is given respecting the vacant spaces between the particles of fluids? 4. What are the two kinds of fluids ? 5. Define Hydrostatics. 6. Why are the non-elastic fluids said to be incompres. sible? 7. Describe the experiment made at Florence. 8. What was concluded at the time, and what have later experiments shown ? 9. What is the difference between the gravity of fluids and solids? 10. Why does water always find its level? 11. What is said of the direction in which fluids press ? 12. What is the cause of the downward and lateral pressure? 13. What is said of the lateral pressure in a cubical vessel ? 14. How may the downward pressure, be shown? 15. How does the pressure of a fluid differ from the weight ? 16 What is related by Dr. Goldsmith ? 17. What is said of the hydrostatic press? 18. Illustrate the pressure of fluids by figures 25. 24. and 23. 19 What is said of what is called the hydrostatical paradox?