effect which putting in motion some particles of a body has upon the rest. Strictly speaking, we ought to say that sound has no existence except in the ideas of the hearer; but, in accordance with common phraseology, we shall speak of a body as sounding when it is in that state in which it would produce the impression of sound, if the proper medium were placed between it and the ear. No body can produce a sound, as we know from observation, unless its parts be put into rapid motion. We have evidence of this in a tuning fork, the string of a musical instrument, the parchment of a drum, &c. Neither will any sound be perceived unless there is a continual supply of solid or fluid matter, possessed of a moderate degree of elasticity, between it and the ear. Thus a bell, when rung in an exhausted receiver, hardly yields any sound; and the small portion which it does give may be altogether destroyed or materially diminished by lining the receiver with cotton or wool. The air is generally the medium through which sound is conveyed; but only because this is most commonly the one with which the tympanum or drum of the ear is in direct communication. A bell rung under water has been very well heard at a distance of 1200 feet by an observer with his head under the same body of water; those who work in one shaft of a mine can often distinctly hear the sound of the pickaxe in another shaft through the solid rock; and persons wholly deaf, who therefore are not at all affected through the ear, have received pleasure from music, by placing their hands upon a shutter or other solid body near the instruments. We confine ourselves particularly to what takes place in air. The body of air which surrounds us produces no sound if it be all moved together, that is. if the velocity of all its particles be the same. The highest wind makes no noise except when it is forced against some obstacle, and the sound of a cannon is heard in whatever direction the wind may blow. Neither does the strongest band of music produce any sensible wind in any direction. It is therefore unto some other sort of motion that we must look for the agent of sound, and the manner in which sonorous bodies move immediately points it out. If a tuning fork or a string be struck, a rapid succession of vibrations is the consequence, which, as we shall see, causes the particles of air to vibrate in a similar manner. And we find, that in order to produce a note, not only must there be a succession, but a rapid succession, of vibrations; experiments show that the ear is not capable of receiving the impression which we call sound, unless the particles of air in contact with it vibrate at least thirty times in a second. The vibration produced in the particles of air by a sonorous body may be distinctly proved by the following experiment. Let a tuning fork be sounded, and while yet in vibration, let it be stopped by the finger. A sensation will be felt for an instant, for which we have no name in our language, arising from the prong of the fork rapidly, but gently, striking the finger, and very different from that produced by merely touching the fork when at rest. Now, blow into a common flute, stopping two or three of the higher holes, gently. The same sort of sensation, though in a much smaller degree, will be felt on that part of the fingers' ends which is in communication with the interior air. The fingers should be warm, and if the observer be not used to the instrument, the effect is made more certain by tuning the string of a violoncello to the note which is to be fingered on the flute, and then sounding the former strongly, while the latter is held over it, with the fingers placed as before. That any very violent and sudden noise produces a concussion in the air even farther than the sound can be heard, is proved by the fact, that the explosion of a large powder-mill will shake the windows in their frames for nearly twenty miles round. AD. The spring being at AC, and the finger or other disturbing cause being removed, the elasticity of the metal makes continued efforts to restore it to its first position AB, by which it is made to move, and with continual accession to its velocity, until it actually does arrive at AB, where, if the velocity were suddenly destroyed, it would rest. But the velocity still continuing, the spring continues to move towards AD, with a change of circumstances, inasmuch as the elasticity, now opposing its motion, gradually destroys the velocity by the same steps as it was before gradually created; so that when the spring comes to AD, it will be again at rest, but will not continue so, since the elasticity will cause the same phenomena to be repeated, and the spring will move back again towards A C. But for friction and the resistance of the air it would again reach AC; it does not, however, get so far, owing to these causes, which always diminish, and never increase, velocity. This alternation will go on until the spring is reduced to a state of rest. Similar phenomena occur in the motion of a pendulum, of the string of a harpsichord, and generally, wherever small vibrations are excited in a body, which remove it, but not much, from its position of rest. We might, perhaps, conclude, that each successive oscillation is performed in a shorter time than the preceding, seeing that a less space is described by the spring. But this is not the fact; it can be observed, as well as demonstrated, that the oscillations which take place before a body recovers the effects of a small disturbance and resumes the state of rest, are severally performed, if not in the same time, yet so nearly in the same time, that the difference may be entirely neglected in most practical applications: for the reason of which, see OSCILLATION. Such being the case, we may omit the effects of friction and resistance, so far as the time of vibration is concerned, and consider the spring as describing exactly the same path in each successive vibration. Let DC be the line described by the top of the spring, which we may call a straight line, since it is very nearly so, and while the spring moves from D to c, imagine a curve Dyc to be drawn, in such a way that, the spring being at æ, the perpendicular xy is the rate per second at which the tep of the spring is then moving. A little attention will show that the curve we have drawn represents the various changes of motion just alluded to: thus TB, the greatest perpendicular, is over the point B where the spring moves fastest; and at D and c there is no perpendicular, the spring coming to rest when it reaches those points. During the return from c to D, in which the motion is the same, but in a contrary direction, let a similar branch cto be drawn, on the other side of CD. We will call the whole curve DTCTD the type of the double vibration of the spring, the two branches being the types of its two halves. Now, suppose a column of air inclosed in a thin tube AB, which is indefinitely extended towards B, but closed at a by a piston which moves backwards and forwards from A to c, and from c to A, after the manner of a spring, the type of its motion being represented by the curves on a C. And first let the piston be pushed forward from A to c. If the air were solid, we should say that a column of air A c in length would be pushed out of the end в of the tube (Fig. 2.), in the time in which the piston Fig. 2 B is driven in. As to how far we should be justified in saying so, we refer the reader to the article ELASTICITY; we certainly can have no notion that such an effect would be produced upon a column of elastic fluid like the air. ExperiWe now proceed to describe, as far as the same can be ment, as well as mathematical demonstration, show us that simply done, the motion which takes place in the air when though every particle of the fluid will finally be put in mothe impression of sound is communicated; and here we tion, yet that those particles which are nearer the disturbing stop to explain a method of making the eye help the piston receive their first impression sooner than those which reason in many cases. Suppose we wish to register what are more distant; and we find that this successive propagatakes place in the vibration of a spring, of which the position, as it is called, of the disturbance, goes on uniformly tion of rest is AB, but which, having been set in motion, (Fig. 1) passes through all positions between AC and Fig. 1 B C T at the rate of about 1125 feet in a second, the temperature being 62° of Fahrenheit; for example, a second must elapse before those particles, which are 1125 feet distant from A, will have their first news, so to speak, of what is going on at A, and in the same proportion for other distances. It is also shown that the velocity of communication is not affected by the greater or less degree of vio◄ lence with which the air is struck, but remains the same for every sort of disturbance. With such a velocity, we may see that the column of air made up of all the particles which feel, or have felt, the effects of the disturbance, must be very long when compared with a c, the extent of an almost insensible vibration; so that it will lead to no sensible error if we suppose that the effect of the piston at every point of its course is propagated instantaneously to c, and from thence only, with the velocity of 1125 feet per second. We will now consider what this effect is. Divide the whole length A C, fig. 3, into a large number of very small parts, described in equal parts, and instead of the piston moving continuously, and with imperceptible changes of velocity, along AC, let it move by starts from each point to the next, with the proper increase or decrease of velocity. In the figure we have divided AC into ten parts, but the same reasoning applies to any greater number, and the reader may refer to ACCELERATION for an instance in which the truth, as regards motion gradually increased, is come at by a similar supposition. We have much enlarged a c (Fig. 3), to give room Fig. 3. أة A 12 3 6 7 89 C P R s for the figure: the reader may help his ideas by supposing that AC is viewed through a powerful microscope, and the rest of the tube by the naked eye. Whatever may be the common time of moving through each of the parts A1, 12, &c., the portions of the column affected by the starts of the piston will be of the same length, and each will be as much of 1125 feet as the time of each start is of one second. Set off the lengths CP, PQ, QR, &c., each equal to this length, and for the present let us agree to call the common time in which the piston starts through 41, 12, &c. an instant. The reader must bear in mind throughout that we intend to carry the supposition of dividing a C into parts to its utmost limit, by which we shall have to suppose CP, PQ, &c. very small, though still great when compared with A1, 12, &c. We also think it right to repeat, that all the figure on the left of c is immensely magnified, and that the propagation is supIn the first posed to be instantaneous from 1, 2, &c. to c. instant, the piston moves through a 1, with the velocity pl per second, and forces the column of air a 1 into CP, which, therefore, has its density increased, or is compressed, the air which was held in CP and A1 together being now confined in CP. As the propagation has not travelled farther than P, the effect is just the same as if there had been a solid obstacle at P during the first instant. The portion CP is then compressed, strictly speaking, unequally, that is, the parts near to c are more compressed than those near to P; but on account of the small length of CP, and the rapidity of the transmission, we may suppose all the parts equally compressed. Again, the particles near c begin to move towards P, and for a similar reason we may suppose the velocities of all the particles the same; this velocity being that of A during the first instant. The reader must not confound the absolute velocity of the several particles, which is always small, with the rate at which they transmit their velocities and compressions, which is very great. We will use the phrase that the portion C P has received its first compression. If the piston were stopped at the end of the first instant, the whole effect upon CP would be transferred to PQ in the second instant, both as to compression and velocity, and the particles of CP would return to their first state, and receive no further modification. But in the second instant, the portion CP receives its second compression, which is greater than the first, since a column 12 longer than A1 is forced into it. Similarly the velocity is increased, being 2q per second instead of 1p. If the spring were then stopped, the third instant would see the portion P Q transmit its velocity and compression to QR, CP to PQ, and CP would resume its natural state. But in this instant, CP receives its third compression, which is greater than the former two, and the same process goes on, each portion transmitting its velocity and compression to the succeeding one, receiving in its turn more than it parted with, from the preceding. This continues until the piston has reached the middle point of AC, after which the compression of cp still continues, but becomes less and less in successive instants, because 56, 67, &c. down to 9c decrease in length, in the same way as A1, 12, &c. increased. When the piston begins to return through C9 in the eleventh instant, the portion CP receives its first rarefaction; for the air in CP now occupies CP and c9; the particles in cp therefore move towards c instead of from it, and the preceding modifications are successively repeated in quantity, but changed into their contraries; that is, each portion undergoes successive rarefactions, equal in amount to the former condensations, and the particles move towards c with the same velocities which they formerly had from c. This continues until the piston reaches a again, after which the same phenomena recommence in the same order. Thus it appears that the absolute velocity of each particle is in the direction of the propagation so long as it is compressed; but in the contrary direction, when it is rarefied, and that each particle, during the progress of a double series of compression and rarefaction, moves forward in the direction of propagation, and back again to its former place, where it rests, unless a third vibration follows the first two. When we talk of the compression of a particle, we mean that it is nearer the succeeding particle, than it would have been in its natural state; and vice versa for rarefaction. We may represent these phenomena in the following table, which, to save room, is made on the supposition that AC was divided into four parts, and might be equally well constructed if the number of parts into which AC was divided had been greater. The numbers in the top horizontal line are the successive portions of the tube, those in the left vertical column the successive instants of time, and under any portion of the tube, opposite to any instant of time, will be found the state in which that portion of the tube is at that instant of time: 1 denoting its first compression; 1' its first rarefaction; these latter numbers recommencing when a complete cycle of changes is finished. The blanks denote that the effect has not yet reached the corresponding particles. 4' 3' 2' 1' 4 3 2 1 2 1 2 1 131' 4 142′ 1' 4 15 3 2 1 4 3 164' 3' 2' 1' 4' 3' 21' 4 3 4 3 2 1 4' 3' 2' 1' 4 3 2 1 On casting the eye down any vertical column, we see the state of the same portion in successive instants of time: on looking along a horizontal column, we see the state of all the portions of the tube at the same instant, as far as the effect has reached them. Doing the latter, we see that all the successive states are continually repeated, in such a way that whatever states two portions may be in, the intermediate portions have all the intermediate states. There is also at the beginning an unfinished series in process of formation. If we look down a column, we see that any one particle successively undergoes the different states, from the moment when the effect first reaches it. We shall now suppose the division of AC to go on without end, and examine the final result. The different states of compression or rarefaction will then become more and more numerous, but the difference of quantity between each and its preceding will become less and less, so that when we at last give to the piston a continuous or gradually increasing and decreasing velocity, we must also suppose a continuous or gradually increasing and decreasing compression or rarefaction of the air in the tube. This being premised, we return to the figure, and construct the type of the motion of the piston, both backwards and forwards, and also the type of the state in which the particles of air actually are for two or three several positions of the spring; N 2 as in the figure below, which we proceed to explain., density of undisturbed air. This follows from the investi(Fig. 4.) Fig. 4. gation attached to fig. 3: for, in the fourth instant for example, the column 34 of air is forced into C P, and 34 and CP being spaces described in equal times with velocities Fig. 5. In fig. 4 (1), the piston has travelled from A to the small perpendicular, through something more than a quarter of a vibration: the first disturbance has reached D, and the curve DK is the type of the state of each particle as to velocity; that is, the perpendicular FG is the rate per second at which the particle F is moving from c, and the same for every other perpendicular. 48 and 1125 feet per second, are spaces proportional to these velocities. And the compression will be the same if we increase CP in any proportion, provided we increase the quantity of air forced into it in the same proportion. A similar proposition holds for rarefactions. Or, in other words, FK being the velocity with which the particle at F is moving towards c, the rarefaction of the particles at F is that which would be obtained by allowing the air naturally contained in a tube GF, 1125 feet long, to expand into the length GK. Similarly, the compression at is that which would be obtained by compressing the air in a tube NL into the shorter tube N M. If we wish to see the state of these particles at any succeeding instant, let the curvilinear part of the figure travel uniformly forward at the rate of 1125 feet per second, new curves being continually formed and finished at c: we shall thus have the state of the whole tube at any succeeding moment. Before proceeding to apply this explanation to the phenomena of sound, we must see what will take place if the tube be agitated by several different undulations at once. If the piston be performing its third complete vibration, or its second vibration forwards, there will have been a preceding series of compressions and rarefactions propagated onwards, as in the figure 4 (1). In fig. 4 (2), a vibration forwards has been completed; the curve on CD now represents a complete undulation, as far as the compressions are concerned. In fig. 4 (3), the return of the piston has commenced, and the particles between C and D are rarefied, and moving towards c; this we explain by placing the type beneath the tube, and dotting the curve; FG expressing the velocity per second of the particle F towards c. The length of the whole wave CD is easily calculated. If, for example, the single vibrations of the piston are made in of a second, the first impulse will have travelled through one hundredth part of 1125 feet, or 11 of a foot. This is the length of CD, in fig. 4 (2). The complete series of compressions is called a wave of compression; and that of rarefactions a wave of rarefaction. And the same type which represents to the eye the velocities All readers, however little acquainted with Mechanics, of the various particles, will also serve to represent the are aware, that if a body be impressed by two forces in the degrees of compression or rarefaction. For those particles same direction, it will proceed with the sum of the velocities which are moving quickest from c are most compressed, produced by the two forces; and with the difference of the and those which move quickest towards c are most rarefied. velocities, if the forces strike in contrary directions, the moIn returning to figure 3, we see that A1, 12, 23, &c., tion in the latter case being in the direction of the greater are spaces described in equal times, and are therefore in of the forces. Hence, if there be different undulations exthe same proportions as the velocities, that is as 1p, 2q, 3r, cited in the same column of air, the velocities of each par&c. But these spaces, in the preceding explanation, are ticle will be made up of the sum or difference of those proportional to the degrees of condensation; these latter which it would have received from each undulation, had then are proportional to the velocities. If, then, we suppose each acted alone; the sum when it would have been comthe series of compressions and rarefactions to have gone on pressed by both, or rarefied by both, and the difference for some time, and an unfinished wave of compression to when it would have been compressed by one and rarefied by have been formed at the instant we are considering, we may the other. And the compressions or rarefactions being pro represent the whole state of the particles in the tube at portional to the velocities, a similar proposition will hold of that instant by the following figure (Fig. 5):-R GN them. Underneath we have represented the state in which is a line parallel to the tube, and therefore GF is of the a column of air would be at a given instant from two differsame length for all positions of F. It is to be made 1125 ent waves, the types of which are drawn, and the broad feet in length. Its use depends upon the following pro-line is the type of their united effects. We know [see position:-That in the simple undulation which we are INCOMMENSURABLE] that any two lengths are either in now considering, so long as the disturbance is small, the the proportion of two whole numbers, or if not, two whole velocity of any particle bears to the velocity of propagation numbers can be found, which are as nearly proportional to (two very distinct things, as we have before observed) the them as we please. We have, to take a simple case, drawn same proportion as the change in the density bears to the the lengths of the waves in the proportion of 5 to 4. (Fig. 6.) The types of the waves are different portions of straight | have been, if the preceding figures had been rounded. And lines, one whole condensation and rarefaction taking place, the supposition of rectilinear types facilitates the drawing of as indicated by Aaвbс in the first, and by AppqQ in the such figures, (which we would recommend to our readers,) second. We suppose the waves to commence together. since, as they will observe, the type of the combined wave This supposition, of the condensation and rarefaction pro- consists also of portions of straight lines which break off ceeding in such a way that their types shall be parts of only when the type of one of the single waves changes straight lines, is not to be obtained in practice, since, as we from one line to another. The general rule for forming have seen, such motion as that of a spring, and we may the broad line, derived from a preceding observation, is add of a string or drum, would produce regular curves.-let the perpendicular or ordinate [See ABSCISSA] be But it is as allowable in illustrating the effects of combined the sum of the perpendiculars of the types of the waves, undulations as any other; and if, moreover, we round the when they fall on the same side of AP, and the differcorners of the types of the single waves, thus making them ence when they fall on different sides; observing, in the present an appearance similar to that in the preceding latter case, to let the broad line fall on the side of that wave figures, a slight rounding of the corners of the broad line which has the greatest perpendicular. Thus at the first M, will show sufficiently well what the combined wave would MT is the sum of мu and м v, and particles at м are in a greater state of compression than the first wave would give them, which arises from the second; similarly at the second м there is an increase of rarefaction. At N, the air is compressed by one wave, and rarefied by the other, but more compressed than rarefied. At P, B, Q, C, &c., where one of the waves causes neither compression nor rarefaction, the broad line coincides with the other wave. On looking at the figure thus produced, we see 1. That it is composed of a cycle of successive compressions and rarefactions, in which, however, the rarefactions differ in kind from the preceding compressions; so that we must not give the term wave to each set of compressions or rarefactions, as we reserve this word to denote cycles of changes, which are following by similar cycles of contrary changes. 2. That when the lengths of two waves are as five and four, four of the first will be as long as five of the second; so that the waves recommence together at w, but not exactly as before, the wave of condensation from the first being accompanied by the wave of rarefaction from the second. This difference, however, is not found at the end of the second similar cycle of four and five; so that after eight of the first waves, corresponding to ten of the second, the combined wave begins again to have the same form as at first. 3. The complete cycle denoted by the broad line may be divided into two, joining at w; in the second of which a series of rarefactions is found similar to every series of compressions in the first, and vice versa. We may, therefore, give the name of wave to the part of the broad line intercepted between A and w, consistently with our definition of this word. 4. If the waves had not begun together, a wave would have resulted of the same length as the preceding, if we began at any point where the compression from one was exactly compensated by the rarefaction from the other. We subjoin a cut, representing a wave contained three times in another wave, and the resulting wave. (Fig. 7.) Fig. 7. We have hitherto considered combined undulations as propagated in the same direction: let us now take two waves of equal lengths propagated in opposite directions, arising, as we may suppose, from two pistons, one at each end of the tube. After a certain time, depending on the length of the tube, two waves will meet, by which we mean that the particles will begin to be affected by the motion of both pistons, and the manner in which the joint effect is represented is the same as before, though the phenomena are very different. In the former case, having represented the resulting wave at one instant, we could trace the change of state throughout every particle of the fluid, by supposing the type of that resulting wave, or a succession of such types, to move along the tube at the rate of 1125 feet per second; in the present case, the waves are propagated in contrary direction, so that any given effect from the first wave is no longer continually accompanied by another given effect from the second wave. We must also recollect, that the motion of the particles in each wave of compression is in the direction of the propagation; so that a particle under the action of two waves of compression, has opposite velocities impressed upon it, and therefore moves with the difference of the velocities; and so on. Now let A, B, C, D, &c., be the points where the two series of waves meet in the axis, and let us choose the instant of meeting for the time under consideration. Let the continued line represent the waves propagated from left to right, and the dotted line those propagated from right to left, as marked by the arrows at the parts at which they end; the arrows above them representing the directions of the absolute velocities which the waves over which they are placed give to the particles. (Fig. 8.) All the particles are now neither compressed nor rarefied; for it is evident that, whatever condensation or rarefaction a particle experiences from the wave moving to the right, there is a contrary rarefaction or condensation from that which moves to the left. But every particle has the velocity derived from either wave doubled by the other. Again, the particular points A, B, C, D, &c., are never put in motion; for it is plain that by the time any point P comes over c, giving it the velocity of Pp to the left, the point q, similarly placed on the other wave, will also have come over c, giving it the equal and contrary velocity qq; so that, as far as velocity is concerned, all the impression produced on A, B, C, D, &c., is equivalent to two equal and contrary velocities, or to no velocity at all. But when P has come over c, the compression, answering to pp, is doubled by that answering to qq. So that the particles at A, B, C, &c., undergo no change of place, but only condensation or rarefaction. Also the particles at a, b, &c., halfway between A and B, B and C, &c., never Half a wave since, all compression and rarefaction had disappeared throughout the tube, the velocity of every particle being double that which either wave would have caused. The case is now altered; no particle has any velocity, since there are the signs of equal and contrary velocities at every point of the tube; but every particle is either doubly compressed, or doubly rarefied, except a, b, &c., which, as we proved, are never either compressed or rarefied. In one more half wave, the phenomena of the first supposition will be repeated; that is, all condensation or rarefaction will be destroyed throughout, the particles, however, being all in motion, except A, B, &c., but in directions contrary to those undergo compression or rarefaction, but only change of velocity. For by the time any point R, from one wave, has come over a, with the condensation answering to RT, s will have come over it from the other, with the equal rarefaction answering to ss; so that the effect of the combined waves upon a, is always that answering to equal condensation and rarefaction, or no change at all. But the velocities answering to Rr and ss are equal, and in the same direction; so that the points a, b, &c., have the velocities which one wave would have given them doubled by the other. Hence at a, b, c, &c., the particles suffer no change of state, but are only moved backwards and forwards. Now, let the time of half a wave elapse, in which case the types of the undulations will coincide, and those parts will be over the capitals on the axis, which are now over the small letters, and vice versa, as in fig. 9, where the coincidence is denoted by a continued and dotted line together, the latter being, of course, a little displaced. (Fig. 9.) D they had at first; while, at the end of a fourth half wave, the phenomena of the second supposition will be repeated, that is, all velocity will be destroyed, the particles being all condensed or rarefied, according as they were before rarefied or condensed. The reader may easily convince himself of these facts by drawing the corresponding figures. To put the results before the eye, suppose the tube to be of a highly elastic material (thin Indian rubber, for example), so as to bulge outwards a little when compressed from the interior, or to contract in diameter by the pressure of the outward air when the inward is rarefied. Recollect, also, that A, B, C, D, &c., remain without motion, their only change being con mode of undulation, though it is necessary to show how it arises from the combination of two waves, is nevertheless more easy to be explained by itself than either of these two. For if we recollect that when particles of air move away on both sides from a given point, there must be a condensation in the parts towards which they move, and a rarefaction in those which they quit, (2) will evidently follow from (1). At this second period, the elasticity of the air will have opposed and destroyed the velocities of the particles; so that there now only remains a tube of particles at rest for the moment, condensed towards the ends and rarefied in the middle. There will, therefore, immediately commence a rush of air towards the rarefied parts, which will end by producing the state represented in (3), where equilibrium is restored, as far as compression and rarefaction are concerned; but where, at the moment under consideration, nothing has yet taken place to deprive the particles of the velocity which they received from the elasticity of the air before the natural state was recovered. There is now a motion of particles, in all directions, towards B, which will go on producing compression at B, and rarefaction at A and c, until all the velocity is destroyed. This is the state represented in (4), from which (1) follows again; and so on. The states of the column intermediate between the times of (1), (2), &c., are easily imagined. Between (1) and (2) the compression at the extremities will have begun; but not yet to the complete destruction of the velocities. Between (2) and (3) the motion of the particles towards the middle will have begun but will not yet have placed them in their natural positions; and so on. The particle at в is evidently never in motion, being always equally pressed on both sides. The same would be seen of A and c, if the tube were extended on both sides. It is evident also, that except at the instant when compression and rarefaction are all destroyed, there must be a point at which the transition occurs from condensation to rarefaction; and vice versa. It is not, however, so evident, in this way of viewing the subject, that these points always remain in the same position at a and b, which is the result of our previous investigation. The reader must however recollect, that, when we talk of the points a and b being always free from condensation or rarefaction, we do not say that it is the same air which is always uncondensed or unrarefied, but only that the different portions of air, which pass by a and b, are in their natural state at the instant of the passage. Now it must be evident, that if, in the motion of a fluid, there be certain particles which remain at rest, it is indifferent whether we suppose those particles to be fluid or solid; for all that we know of a solid, as distinguished from a fluid, is, that the particles of the latter yield sensibly to any applied force, while those of the former do not. Hence, when such impulses are communicated to a fluid, that some of its particles must remain at rest, the question never arises, so to speak, as to whether those particles would, or would not, move with the fluid, or resist, if the conditions of motion were so altered, that forces, which did not counterbalance, would be applied to those particles. Let us now suppose that a solid diaphragm is stretched across the tube at A; the motion will still continue exactly as before; and we may produce this species of complex undulation by a piston at one end only of the tube, provided the other end be closed. For, on this supposition, all the successive states into which the air at the end furthest from the piston is brought, cannot be communicated to the outside air, and must, therefore, be either retained, or returned back again through the column of air. The latter effect results; and the returning wave, which is of the same kind as the advancing wave, produces the phenomena just explained. If A and B were both closed during an undulation, no piston would be necessary if it were not that there is no substance but what will vibrate in some small degree, and the vibrations communicated to the tube from the internal air gradually destroy the internal motion, by the communication of motion to the external air. We have hitherto considered only the motion of air in a small tube, and have found that the velocity of the particles, as well as the condensation and rarefaction, may be propagated undiminished to any extent. The case is somewhat different when we consider undulations propagated in all directions at once. Imagine a small sphere, which is uniformly elastic in every part, and which, by some interior mechanism, is suddenly diminished in its dimensions, and afterwards as suddenly restored. A wave of rarefaction and condensation will be propagated in every direction; which wave, at any instant, will be contained between two spheres, concentric with the sphere already mentioned, the radii of which differ by the length of the double wave: at least, unless there be some reason in the state of the atmosphere, why the propagation should take place more quickly in one direction than another. We have no reason, at first sight, to suppose that the velocity of propagation would be exactly, or even nearly the same as if a portion of the air through which the waves pass had been contained in a tube, unconnected with the exterior air. But it is found, both by mathematical analysis and experiment, that the velocity of propagation remains unaltered in both cases; and also that the absolute velocities of the particles diminish. This last is a natural consequence of a very simple principle-namely, that when one body, or collection of bodies, strikes a larger body, or collection of bodies, in such a way that its whole motion is destroyed, the velocity of the larger body will not be so great as that of the communicating body, but less in the same proportion as its mass is greater. The law of this diminution should be, from theory, inversely as the distance; that is, by the time the wave has moved from 3 miles to 5 miles, the compressions and velocities should be as 5 to 3; but we have no direct means of submitting this to experiment, the absolute velocities being imperceptible. We now proceed to the application of these principles. We know that when the air is violently or rapidly propelled in any direction, that undulations such as we have described are produced, and that the impression called sound is produced also. When a gun is fired, the great elasticity of the gases which are disengaged by igniting the gunpowder, forces the air forward out of the gun, which the instant afterwards is allowed to return. If feathers or dust be floating in the |