ment. 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 which is produced by merely touching the fork when at rest. Now, blow into a common flute, and at the same time stop gently two or three of the higher holes. 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. For this purpose the fingers should be warm, but 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. The column of air in the flute will be made to vibrate by the motions of the string, forming a case of what is called sympathetic vibration. 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 around. We now proceed to describe, as far as can be simply done, the motion which takes place in the air when the impression of sound is communicated; and here we stop to explain a method which may be adopted in many cases, of making the eye assist the reason. Suppose we wish to register what takes place in the vibration of a spring, of which the position of rest is A B (fig. 1), but which, having been set in motion, passes through all the positions between AC and A D. The Fig. 1. Fig. 2. put in motion, yet that those particles which are nearer the disturbing piston receive their first impression sooner than those which are more Fig. 3. B distant; and we find that this successive propagation, as it is called, of the disturbance, goes on uniformly 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 violence 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 AC, 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 thence only, with the velocity of 1125 feet per second. We will now consider what this effect is. Divide the whole length ac, fig. 4, into a large number of very small parts, described in equal times, and instead of the piston moving continuously, and with imperceptible changes of velocity, along A c, 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 a c into ten parts, but the same reasoning applies to any greater number. We have much enlarged a 0 (fig. 4), to give room for the figure: the reader Fig. 4. A 12 3 4 5 6 7 89 C P R A spring being drawn aside by the finger or other disturbing cause to a α, and then released, the elasticity of the metal makes continued efforts to restore it to its first position a B, by which it is made to move, and may help his ideas by supposing that a C is viewed through a powerful with continual accession to its velocity, until it actually does arrive at microscope, and the rest of the tube by the naked eye. Whatever may A B, where, if the velocity were suddenly destroyed, it would remain at be the common time of moving through each of the parts a 1, 12, &c., rest. But the velocity still continuing, the spring continues to move the portions of the column affected by the starts of the piston will be towards a D, with a change of circumstances, inasmuch as the elasticity, of the same length, and each will be as much of 1125 feet as the time now opposing its motion, gradually destroys the velocity by the same of each start is of one second. Set off the lengths CP, PQ, QR, &c., steps as it was before gradually created; so that when the spring each equal to this length, and for the present let us agree to call the comes to a D, it will be again at rest, but will not continue so, since common time in which the piston starts through a 1, 12, &c., an instant. the elasticity will cause the same phenomena to be repeated, and the The reader must bear in mind throughout that we intend to carry the spring will move back again towards a C. But for friction and the supposition of dividing AC into parts to its utmost limit, by which we resistance of the air it would again reach AC; it does not, however, get shall have to suppose CP, PQ, &c., to be very small, though still great so far, owing to these causes, which always diminish, and never increase, when compared with A1, 12, &c. We also think it right to repeat, velocity. This alternation will go on until the spring is reduced to a that all the figure on the left of c is immensely magnified, and that the state of rest. Similar phenomena occur in the motion of a pendulum, propagation is supposed to be instantaneous from 1, 2, &c., to c. In of the string of a harpsichord, and gene: ally, wherever small vibrations the first instant, the piston moves through a 1, with the velocity p 1 per are excited in a body, which remove it, but not much, from its position second, and forces the column of air a 1 into CP, which therefore has of rest. We might, perhaps, conclude, that each successive oscillation its density increased, or is compressed, the air which was held in CP is performed in a shorter time than the preceding, seeing that a less and a 1 together being now confined in OP. As the propagation has space is described by the spring. But this is not the fact; it can be not travelled farther than P, the effect is just the same as if there had observed, as well as demonstrated, that the oscillations which take been a solid obstacle at P during the first instant. The portion CP is place before a body recovers the effects of a small disturbance and then compressed, strictly speaking, unequally; that is, the parts near resumes the state of rest, are severally performed, if not in the same to c are more compressed than those near to P; but on account of the time, yet so nearly in the same time, that the difference may be small length of CP, and the rapidity of the transmission, we may supentirely neglected in most practical applications. Such being the case, pose all the parts to be equally compressed. Again, the particles near we may omit the effects of friction and resistance, so far as the time c begin to move towards P, and for a similar reason we may suppose of vibration is concerned, and consider the spring as describing exactly the velocities of all the particles to be the same; this velocity being the same path in each successive vibration. Let D C (fig. 2) be the that of a during the first instant. The reader must not confound the line described by the top of the spring, which we may call a straight absolute velocity of the several particles, which is always small, with line, since it is very nearly so, and while the spring roves from D to C, the rate at which they transmit their velocities and compressions, which imagine a curve Dy c to be drawn, in such a way that, the spring being is very great. We will use the phrase that the portion C P has received at x, the perpendicular xy is the rate per second at which the top of its first compression. If the piston were stopped at the end of the first the spring is then moving. A little attention will show that the curve instant, the whole effect upon CP would be transferred to P Q in the which we have drawn represents the various changes of motion just second instant, both as to compression and velocity, and the particles of alluded to: thus TB, the greatest perpendicular, is over the point B, CP would return to their first state, and receive no further modification. where the spring moves fastest; and at D and c there is no perpen- But in the second instant, the portion C P receives its second compression, dicular, because the spring comes to rest when it reaches those points. which is greater than the first, since a column 1 2 longer than a 1 is During the return from c to D, in which the motion is the same, but forced into it. Similarly, the velocity is increased, being 2 q per second in a contrary direction, let a similar branch ctD be drawn, on the instead of 1p. If the spring were then stopped, the third instant other side of C D. We will call the whole curve DTCtD the type of would see the portion P Q transmit its velocity and compression to Q R, the double vibration of the spring, the two branches being the types of CP to PQ, and CP would resume its natural state. But in this instant, its two halves. Now, suppose a column of air inclosed in a thin tube CP receives its third compression, which is greater than the former A B (fig. 3), which is indefinitely extended towards B, but closed at a two, and the same process goes on, each portion transmitting its velocity by a piston which can be moved backwards and forwards from A to C, and compression to the succeeding one, receiving in its turn more than and from c to A, after the manner of a spring, the type of its motion it parted with, from the preceding. This continues until the piston has being represented by the curves on a C. And first let the piston be reached the middle point of a c, after which the compression of CP still pushed forward from A to c. If the air were solid, we should say that continues, but becomes less and less in successive instants, because 56, a column of air A c in length would be pushed out of the end B of the 67, &c., down to 9 c, decrease in length, in the same way as a 1, 12, tube in the time in which the piston is driven in, but we certainly can &c., increased. When the piston begins to return through c 9, in the have no notion that such an effect would be produced upon a column of eleventh instant, the portion CP receives its first rarefaction; for the elastic fluid like the air. Experiment, as well as mathematical demon-air in CP now occupies C P and c9; the particles in CP therefore move stration, show us that though every particle of the fluid will finally be towards c instead of from it, and the preceding modifications are suo cessively 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 compressions and rarefactions, moves forward in the direction of propagation, and back again to its former place, where it rests, unless a third vibration follow 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 a C 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, l' 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. dicular, through something more than a quarter of a vibration: the first disturbance has reached D, and the curve D K is the type of the state of each particle as to velocity; that is, the perpendicular F G is the rate per second at which the particle F is moving from c, and the same for every other perpendicular. 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 fig. 5 (1). In fig. 5 (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. 5 (3), the return of the piston has commenced, and the particles between C and D are rarefied, and moving towards o; this we explain by placing the type beneath the tube, and dotting the curves 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 feet. This is the length of CD, in fig. 5 (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 of the various particles, will also serve to represent the degrees of compression or rarefaction. For those particles which are moving quickest from c are most compressed, and those which move quickest towards c are most rarefied. In returning to fig. 4, we see that a 1, 12, 23, &c., are spaces described in equal times, and are therefore in the same proportions as the velocities, that is, as 1p, 2q, 3 r, &c. But these spaces, in the preceding explanation, are proportional to the degrees of condensation; these latter then are proportional to the velocities. If, then, we suppose the series of compressions and rarefactions to have gone on for some time, and an unfinished wave of compression to have been formed at the instant we are considering, we may represent the whole state of the particles in the tube at that instant by the following figure (fig. 6):-R G N is a line parallel to the tube, and therefore GF is of the same length for all positions of F. It is to be made 1125 feet in length. Its use depends upon the following proposition:-That in the simple undulation which we are now considering, so long as the disturbance is small, the velocity of any particle bears to the velocity of propagation (two very distinct things, as we have before observed) the same proportion as the change in the density bears to the density of undisturbed air. This follows from the investigation attached to fig. 4: for, in the fourth instant for example, the column 3 4 of air is forced into o P, and 3 4 and C P being spaces described in equal 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. In the latter case, 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; as in the figure below, which we proceed to explain. (Fig. 5.) K G C C G F D Fig. 5. 8 K L times with velocities 4 s and 1125 feet per second, are spaces propor- If we All readers, however little acquainted with Mechanics, are aware, that if a body be impressed by two forces in the same direction, it will proceed with the sum of the velocities produced by the two forces; and with the difference of the velocities, if the forces act in contrary directions, the motion in the latter case being in the direction of the greater of the forces. Hence, if there be different undulations excited in the same column of air, the velocities of each particle will be made up of the sum or difference of those which it would have received from cach undulation, had each acted alone; the sum when it would have been compressed by both, or rarefied by both, and the difference when it would have been compressed by one and rarefied by the other. And the compressions or rarefactions being proportional to the velocities, a similar proposition will hold of them. We have represented in fig. 7, In fig. 5 (1) the piston has travelled from A to the small perpen- the state in which a column of air would be at a given instant from such motion as that of a spring, and (we may add) of a string or of a drum, would produce regular curves. But it is as allowable in illustrating the effects of combined undulations as any other; and if, moreover, we round the corners of the types of the single waves, thus making them present an appearance similar to that in the preceding figures, a slight rounding of the corners of the broad line will show sufficiently well what the combined wave would have been, if the preceding figures had been rounded. And the supposition of rectilinear types facilitates the drawing of such figures (which we would recommend to our readers), since, as they will observe, the type of the combined wave consists also of portions of straight lines which break off only when the type of one of the single waves changes from one line to another. The general rule for forming the broad line, derived from a preceding observation, is-let the perpendicular or ordinate [ABSCISSA] be the sum of the perpendiculars of the types of the waves, when they fall on the same side of a P, and the difference when they fall on different sides; observing, in the latter case, to let the broad line fall on the side of that wave which has the greatest perpendicular. Thus at the first M, M T is the sum of M U 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 rai faction. 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 he figure thus produced, we see1. 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 followed 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 ▲ 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. 5. If both waves had been of the same length, the resulting wave would have had that length; or if the first wave had been contained an exact number of times in the second, the resulting wave would have been of the length of the second. We subjoin a cut (fig. 8) representing a wave contained three times in another wave, and the resulting wave. Fig. 8. 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, rising, 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; ard 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 9). 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 P p 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 Q q; 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, for we are considering the case of particles, and not of rigid bodies, where such opposite equal forces would form a "couple," and produce rotatory motion. But when P has come over c, the compression, answering to Pp, is doubled by that answering to Q q. 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 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 R r, 8 will have come over it from the other, with the equal rare faction answering to s s; 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 versû, as in fig. 10, where the coincidence is denoted by a continued and dotted line together, the latter being, of course, a little displaced. 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 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 Fig. 10. 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 India-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 B D motion, their only change being condensation or rarefaction; while a, b, c, &c., are never compressed or rarefied, their only change being that of place. We exhibit side by side the successive appearances of the tube, and the relative situations of the types between A and c, the arrows always representing the direction of the motion of the particles. A half-wave elapses between each two configurations. (Fig. 11.) These phenomena will recur in the same order, and this 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 B, 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 ARTS AND SCI. DIV. VOL. L 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, 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 forwards out of the gun, which the instant afterwards is allowed to return. If feathers or dust be floating in the air, they have been observed to move forwards, and then back again, just as we have found the particles of air around them would do in the course of a double wave. The intensity or loudness of the sound seems to depend upon the greatest absolute velocity of the particles, and not at all upon the velocity of propagation, which is found to be the same for all sounds. Thus in a musical chord, spring or drum, the harder the metal or parchment is struck, the louder is the sound, but without any difference of tone, character, or velocity of propagation. There is no instrument of which the sound may not be made louder or weaker without any other change than giving greater velocity to the immediate cause of sound. We will not enter further into this part of the subject than to observe, that, generally speaking, we are not authorised to say that sound travels with equal loudness in all directions. It might do so in the case where it was communicated by the sudden contraction and expansion of an elastic sphere, as above supposed; but this is a supposition which we cannot put in practice. If a tuning fork be sounded and turned round in the hand while held up before the ear, very perceptible diminutions and augmentations of loudness will be perceived. This is however explained otherwise on the principle of Interference, by the fact that when the branches coincide, or are equidistant from the ear, the waves of sound combine their effects, while in all intermediate positions, as they reach the ear in different phases of vibration, they interfere, and produce partial silence. The immediate communicator of sound is the tympanum or drum of the ear, an elastic membrane, which is set in vibration by the motion of the particles of air against it, and vibrates in the same time with filling the labyrinth of the ear, through the air in the tympanic cavity, and probably not, as was formerly supposed, through the delicate chain of bones connecting them. [EAR, in NAT. HIST. DIV. of ENG. CYC.] We might expect, that when the wave of sound is of considerable length, we should hear its different parts, that is, feel a difference between the beginning and end where the velocities and compressions are small, and the middle where they are greatest. This happens to a small extent in the difference, for example, between the 'roar' of a cannon and the 'report' of a musket. No explanation can convey a better idea of the difference than these two words. These simple uncontinuing sounds are the result of few waves, there being no cause for their continuance. them. From this membrane vibrations are communicated to the fluid We have not space in this article for any discussion of the manner in which sounds are conveyed through other bodies besides air, for which see VIBRATION. Noises conveyed through solid bodies travel in general more quickly, and are heard better; the scratch of a pin may be distinctly perceived through a long spar of wood, though inaudible by the person who makes it. With regard to gases, both theory and experiment agree in enabling us to assert, that any two of the same pressure and temperature, (that is, where the barometer and the thermometer would present similar indications in each gas,) convey sound with velocities which are inversely as their densities. Thus, air being about fifteen times as heavy as hydrogen, the velocity of propagation in the latter is about fifteen times that in the former. Such a result cannot be directly submitted to experiment; but, as we shall see in the article PIPE, there are methods equally certain for ascertaining the truth. The velocity of sound had been determined by experiment before the time of Newton, who gave the first mathematical solution of the question, with the following result; that if the atmosphere, instead of decreasing in density as we ascend it, were all to be reduced to the density at the earth's surface, but to be so diminished in height, that the pressure at the earth's surface should not be altered, the velocity of propagation would be that acquired by a heavy body falling unresisted from half the height of this homogeneous atmosphere. This reasoning, however, gave the velocity nearly one-sixth too small; and the cause of the difference was afterwards supplied by the sagacity of Laplace. This we shall try to explain. We know that air and all gases resist compression, and will expand themselves if the pressure of the superincumbent atmosphere be removed. This tendency is what we mean by the elastic force of the air or gas. If we take a column of air reaching from the earth's surface to the top of the atmosphere, the elastic force at any one stratum is equal to the weight of the superincumbent column, since it balances that weight. Moreover, it is observed, that, at the same temperatures, the elastic forces of two different strata are as their densities, that is, for air of half the density of common air, the elastic force is only half as great, and so on. It is also observed that any increase of temperature increases the elastic force if the density remain the same, and also that compression always increases the temperature; and vice versa. If, therefore, a vessel of air were pressed into half its dimensions, it would double its elastic force from the condensation, which would also receive a further addition from the increase of temperature. Again, if the same were rarefied into double its first dimensions, the elastic force would be halved by the rarefaction, and receive a further decrease from the diminution of temperature. The increase or decrease arising from temperature would not last long, since the altered mass would communicate heat to the surrounding bodies in the first case, and receive it from them in the second; but in calculating such instantaneous effects as the propaga tion of sound, it is evident they ought not to be neglected. The supposition on which Newton went was, that the elastic forces of two strata of air are always in the same proportion as their densities, which is not true, unless the temperatures are the same. We may also hers remark, that an alteration in the barometer only, produces no alteration in the velocity of air; for, if the barometer rise, though the pressure of the air is increased, yet the density is increased in the same proportion; that is, the force which is to set each mass in motion receives no greater increase in proportion than the mass which is to be moved. But a rise in the thermometer, accompanied by no change in the barometer, increases the velocity of sound, for there is an increase in the elastic force, without any increase in the density. A very good measure of this velocity made near Paris in 1822, under the directions of the Academy of Sciences, gave 1118 feet per second at the temperature of 61° of Fahrenheit. Earlier experiments had given 1130 feet, which, if the French measure is assumed as accurate, represents the velocity at a somewhat higher temperature. The number which we have adopted, viz., 1125 feet per second, at 62° of Fahrenheit, is shown by Sir John Herschel, in his masterly treatise on 'Sound' in the Encyclopædia Metropolitana,' to accord very nearly with the mean of the best experiments. The formula for calculating this velocity is now given as follows:— V = 1090.8 3 { (1 + 0·003665 × t) (1 + 0·375} where t is the centigrade temperature, T the density of vapour, and П that of air, at the time. Every increase or decrease of temperature of 10 of Fahrenheit, causes a corresponding increase or decrease of 114 of a foot in the velocity of sound, which gives about 1090 for the velocity when the air is at the freezing point. We may add, that in the present state of our knowledge of the manner in which the temperature and elastic force of the atmosphere are connected, observation and theory give results which differ from one another by about a hundredth part of the whole. When the exciting cause of sound is continued, as for example, when a board is scratched with a pin, we have a continued sound, caused by the succession of waves which the ear receives, which waves we have no reason to believe are all of the same length. But whenever the exciting cause is one, the vibrations of which can be shown to be performed in exactly the same time, so that the waves caused by them are all of the same length, we perceive a sound which gives pleasure to the ear, and has the name of harmonious or musical. This, however, only happens when the vibrations are at least thirty in a second, or the wave of a sound at most about 38 feet long. This fact is so well established, musical sounds is a consequence of the perfectly equal times of the that we may consider it as certain that the pleasure arising from vibrations which produce them, and of its result, the equal lengths of the sonorous waves propagated from them through the atmosphere. This will not appear so extraordinary, if we consider the very delicate nature of our organ of hearing. A person of tolerable ear can distinguish between two sounds, which only differ in that the one is a consequence of 400 vibrations in a second, and the other of 405. We must therefore grant to the ear a much higher power of perception as to sounds than the eye has to length or surface. Some increase of the perceptive power may arise from the very great number of vibrations, since a result in some degree corresponding is observed in vision. If we look at a large number of parallel lines ruled close together at equal distances, any little deviation from parallelism or equidistance is much more sensibly seen than when the number of lines is small. And even to the eye, any moderately rapid succession of objects of the same kind is much more pleasing when they follow at equal distances and periods of time. The difference between two musical sounds, which we express by saying that one is higher or lower than the other, is a consequence of the different number of vibrations performed by the two in the same time, and the sound which we call higher has the greater number of vibrations. And some sounds, when made together, produce an effect utterly unbearable, while others can be tolerated; others again are extremely pleasant, while some, though very different in pitch, appear so alike, that we call them the same, only higher. It is found by experiment that two sounds are more or less consmant, when heard together, according as the relation between their vibrations is more or less simple. Thus, when two vibrations of the first are made in one vibration of the second (which is the simplest ratio possible, when the have just alluded; the first sound is called the octare of the second, sounds are really different), that similarity is observed to which we and both are denoted in music by the same letter. When the number of vibrations of the two are as 3 to 2, the one which vibrates three times while the other vibrates two, is called a fifth above the other: because in the musical scale of notes CDEFGA B C D' &c. the vibrations of c and G are in this proportion, and a is the fifth sound reckoned from c. If the ratio of the vibrations be that of 3 to 4, that is, if the higher note makes four vibrations, while the lower |