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in the spout at the same height as in the pot itself; and it must do so, for if the water at B, for instance, were lower than at A, then the pressure under A would be greater than under B, since ($ 2) the pressure is proportional to the depth of the liquid; the water, therefore, could not be at rest, B but a flow must take place into the spout, which would continue till the pressure in it was the same as in the pot, that is, till the water stood at the same level.
This principle is applied to the introduction of water into houses in towns. As fluids always rise to a level,
Fig. 21. no matter what distance the water may be conveyed by pipes, it will rise to the height of the source from which it is brought.
4. A solid body, immersed in a liquid, experiences a pressure equal to the weight of the liquid which it displaces, and this pressure acts vertically upwards through the centre of gravity of the liquid displaced. Let AB be a solid body immersed in water; it is evident that AB occupies the place of a quantity of water equal in volume to itself. Now, suppose AB not yet placed in the water, and AB, as seen in the figure, to be the water about to be displaced ; this part of the liquid is supported by the pressure of the rest around. The pressure on the sides has no
Fig. 22. effect, because it is equal all round, and may therefore be disregarded : it is the pressure from below that properly supports the mass.
And since this mass of water has a certain weight which acts at its centre of gravity g, the upward pressure keeping it in its place must be equal to that weight, and must act through its centre of gravity. Suppose, now, the solid to be substituted for the water, it must experience exactly the same pressure as acted on the water ; that is, the solid AB is acted on by a pressure equal to the weight of the water it displaces, and acting vertically upward through the centre of gravity of the water displaced.
It is an obvious corollary from this, that if a solid be weighed in a liquid, it will be lighter (than its true weight) by the weight of a quantity of the liquid equal in volume to the solid.
This truth was first discovered by the ancient mathematician, Archimedes, and by means of it he was able to discover how much alloy the goldsmith, whom the king of Syracuse had commissioned to make a crown of pure gold, had fraudulently mixed with the metal. It is said that, one day when floating in his bath, it occurred to him that what was supporting his body was that which would support the water displaced by it; and he thought he could, by means of this principle, discover whether the crown was of pure gold. He is reported to have been so overjoyed at the discovery, that he forgot to dress himself, and rushed through the streets, crying: 'I have found it! I have found it !' To test the crown, he first found the absolute weight of a piece of pure gold, and then its weight when immersed in water. He treated the crown in like manner, and found that it displaced more water in proportion to its weight than the piece of pure gold, which proved that the metal had been mixed with something lighter.
5. A floating body displaces its own weight of the liquid. We have seen that, when a body is immersed in water, a pressure equal to the weight of the water displaced acts upon it, pushing it upward, while its own weight tends to make it sink. If, then, these two pressures are equal, the body will rest in any part of the liquid ; if the weight of the body is greater than the weight of an equal volume of water, the body will sink to the bottom ; while, if the weight of a quantity of water, equal in volume to the body, is greater than the weight of the body, it will be forced upward to the surface. When this last takes place, the body is said to float. And, of course, part of it must rise above the surface, because, if it were to rest with its surface exactly level with the surface of the liquid, it might have rested at any part of the liquid ; but it is
supposed to have been forced upward to the surface. The question, then, comes to be, How much of the body will rise above the surface ? or, which is the same thing, How much of it will be in the water? We have seen that a body, immersed in a liquid,
remains at rest when the weight of a quantity of the Fig. 23.
liquid equal in volume to itself, is equal to its own
weight; and from this it is clear that a floating body (as AB) will be at rest, when the weight of the water displaced by the submerged part B is exactly equal to the weight of the body. Thus the heaviest bodies can be made to float on a liquid, if only they can be so arranged as to displace a quantity of the liquid of weight greater than their own. A piece of iron sinks in water, but ships can be made of iron, because they are hollow, and displace a quantity of water of greater weight than their own.
ACOUSTICS. ACOUSTICS1 is the science which treats of sound. Sound is the sensation produced when the vibrations of some sounding body are conveyed directly or indirectly to the organ of hearing. That a body producing sound is in a state of vibration at the time is seen in any stringed musical instrument, the prongs of a tuning-fork, the lip of a bell, &c. These vibrations must be communicated to the ear through some medium connecting the sounding body with the ear, the ordinary medium being the air. This is proved by the fact, that when a bell is struck in a chamber from which the air has been withdrawn, no sound is produced, and that the less dense the air becomes, the fainter are the sounds heard in it, so that on high mountains, where the air is very rare, what would elsewhere be loud talking is heard like whispers. Air, however, is not the only medium, the vibrations being conveyed through water, wood, and other substances. If the head be held under water, any noise at a distance, such as that caused by two stones being knocked against each other, is heard with great distinctness. Or if the ear be placed at one end of a log of wood, the slightest scratch at the other end is heard very distinctly, the vibrations being transmitted through the particles of the wood. Bodies denser than air are better conductors of sound, but, as air is the ordinary medium, the general principles of sound have reference to it. Vibrations are the wave-like motion which is communicated to the air by any shock, such as a shot, the blow of a hammer, or an explosion. The air is not made to change its place, but the compression of its particles caused by the shock is passed along like the undulations of a rope held at one end and moved up and down. These undulations pass outward from the body producing them, in all directions, exactly like those caused on the surface of water by a stone thrown into it, and, like them too, they diminish in force as they proceed outward.
Loudness of Sound.—The loudness of any sound depends upon the force of the concussion of the air, and the force with which this concussion is conveyed to the ear; so that, from the decreasing force of the sound-waves, in a certain ratio, the intensity or loudness of sound diminishes with the distance of the hearer from the object causing it. But a great many other things besides the distance have to be taken into account as affecting the intensity of sound. Thus, sounds at a distance are heard much better at one time than another: this arises from various causes. As was mentioned above, the denser the air is the better are sounds heard ; a dense state of the atmosphere would therefore account for sounds being heard distinctly at a great distance at a particular time. Sounds are also better heard in a dry atmosphere, as moisture seems to interfere with the propagation of sound-waves. Although a simple current of air does not of itself produce sound (it only does so when it comes in contact with obstacles in its way, as trees, houses, &c., by which vibrations are produced), yet it will carry sound-waves in any direction ; sounds are therelore heard more distinctly when there is a breeze blowing from the source of the sound towards the hearer.
1 From Greek akoustikos, relating to hearing or sound, from akouo, to hear.
Velocity of Sound—The velocity with which sound-waves are propagated can be calculated very exactly, owing to the extreme rapidity with which light travels. The velocity of light is so great that for any distance within the limits to which sound could be heard, its passage may be considered as instantaneous. This being the case, the blow, shot, explosion, &c. causing any noise, may be seen to take place before the noise is heard ; and the time that elapses between seeing the cause and hearing the noise is the time that it takes for the propagation of the sound-waves to the distance of the hearer. If a man be observed at a distance striking heavy blows on anything, the blow will be seen to descend some time before the sound of it is heard ; so with the firing of a gun, the flash is seen before the report is heard. It has been found by experiment that sound travels at the rate of about 1142 feet per second, or of a mile in about four seconds and a half. The velocity is somewhat less, however, when the temperature is lower, being only 1090 feet at the freezing-point. In water, sound travels about four times, and in solids, from ten to twenty times more quickly than in air.
Reflection of Sound Echo.—We are now to consider what takes place when a sound-wave meets a large obstacle to its progress. The vibration is to a small degree communicated to the solid, just as light is transmitted through a new medium ; but the principal effect is to reflect the wave, just as a wave of the sea is thrown back from a rock. When a sound-wave is thrown back in this way from a flat surface, the sound is carried back to the point where it was produced, and this return-sound is called an echo. It may be produced by a perpendicular wall of rock, a wood, or other obstacle. If a sound be produced between two faces of rock, for instance, it will first be echoed by both ; and then those echoed sounds (the sound being now doubled) will be thrown back from one to the other again and again, becoming fainter each time; so much so, that a shot in such a situation may be repeated forty or fifty times. The best echo is produced by a concave surface, such as the roof of a cave, by which the sound-wave is reflected to a focus, as in the case of rays of light. If one happen to stand so as to bring one's ear into the focus, the whole of the sound, concentrated at that point, falls upon
and the effect is astounding.
The ears of animals are admirably adapted to receive impressions from the vibrations of the air caused by so-called sounding bodies. The external ear collects part of the sound-wave, and turns it into the passage which conducts it to the membrane from which the vibrations are conveyed to the auditory nerves. The ear-trumpet, which is a trumpet-shaped instrument, having a wide mouth at the end of a tube, is simply a contrivance by which a greater volume of the sound-wave is collected and conveyed into the ear.
Musical Notes.—We have hitherto spoken only of a single shock transmitted through the atmosphere as producing a single sound. The sensation conveyed to the ear when blows are struck with a hammer is a succession of distinct sounds. When sounds are produced in such quick succession that the successive pulses of the air cannot be distinguished by the ear, a musical note is produced. For example, if a toothed-wheel, with a plate of some thin elastic substance resting on the teeth, be turned slowly, the shock produced by the plate falling off each tooth is conveyed separately to the ear, and separate sounds are heard ; but when it is turned more rapidly, the shocks all blend into one, and the sound heard is a continued 'whir;' and the more rapidly the wheel is turned the more sharp and shrill the 'whir' becomes. It is on this principle that notes are produced from the strings of musical instruments. When a string stretched between two objects is pulled aside in the middle, its elasticity causes it to return to its proper position; but the momentum it has meantime acquired carries it past to about the same distance on the other side. Its elasticity here comes into play again, and it is again carried past the middle straight position almost as far as it was pulled aside at first : the same thing is repeated; and this goes on, the vibrations on each side gradually becoming less and less, till the string at last comes to rest. When this is done with a slack string, the vibrations are slow; but when the string is tight, the vibrations are quick that, as in the case of the toothed-wheel when turned rapidly, the separate pulses are blended into a continuous note; and the tighter the string is pulled, the sharper is the sound produced by its vibrations. A good illustration of successive vibrations blending to cause a continuous sound, is the 'buzz' of a fly, which is supposed to be not the voice of the insect, but the sound produced by the rapid vihrations of its wings. It is on this rapidity of vibration that the difference of sounds depends. We observed that the "whir' of a toothed-wheel striking an elastic plate becomes more shrill the quicker the wheel is turned, and that the sound produced by a vibrating string is sharper the quicker the vibrations are made. Now, a short string will evidently vibrate more quickly than a long one; therefore, every degree of sharpness of sound can be produced from strings by making them of different lengths and of