with it, therefore undulations received by the air, whether it be from a sudden impulse, such as an explosion, or the vibrations of a musical chord, are propagated equally in every direction, and produce the sensation of sound upon the auditory nerves. In the small undulations of deep water in a calm, the vibrations of the liquid particles are made in the vertical plane, that is, at right angles to the direction of the transmission of the waves; but the vibrations of the particles of air which produce sound differ, being performed in the same direction in which the waves of sound travel. The propagation of sound may be illustrated by a field of corn agitated by a gust of wind; for however irregular the motion of the corn may seem, on a superficial view, it will be found, if the intensity of the wind be constant, that the waves are all precisely similar and equal, and that all are separated by equal intervals, and move in equal times.

A sudden blast depresses each ear equally and successively in the direction of the wind, but in consequence of the elasticity of the stalks and the force of the impulse, each ear not only rises again as soon as the pressure is removed, but bends back nearly as much in the contrary direction, and then continues to oscillate backwards and forwards in equal times like a pendulum, to a less and less extent, till the resistance of the air puts a stop to the motion. These vibrations are the same for every individual ear of corn; yet as their oscillations do not all commence at the same time, but successively, the ears will have a variety of positions at any one instant. Some of the advancing ears will meet others in their returning vibrations, and as the times of oscillation are equal for all, they will be crowded together at regular intervals; be

tween these, there will occur equal spaces where the ears will be few, in consequence of being bent in opposite directions; and at other equal intervals they will be in their natural upright positions; so that over the whole field there will be a regular series of condensations and rarefactions among the ears of corn, separated by equal intervals where they will be in their natural state of density. In consequence of these changes the field will be marked by an alternation of bright and dark bands. Thus the successive waves which fly over the corn with the speed of the wind are totally distinct from, and entirely independent of, the extent of the oscillations of each individual ear, though both take place in the same direction. The length of a wave is equal to the space between two ears precisely in the same state of motion, or which are moving similarly, and the time of the vibration of each ear, is equal to that which elapses between the arrival of two successive waves at the same point. The only difference between the undulations of a corn-field and those of the air which produce sound is, that each ear of corn is set in motion by an external cause, and is uninfluenced by the motion of the rest, whereas in air, which is a compressible and elastic fluid, when one particle begins to oscillate, it communicates its vibrations to the surrounding particles, which transmit them to those adjacent, and so on continually. Hence, from the successive vibrations of the particles of air, the same regular condensations and rarefactions take place as in the field of corn, producing waves throughout the whole mass of air, though each molecule, like each individual ear of corn, never moves far from its state of rest. The small waves of a liquid, and the undulations of the air, like waves in the corn, are evidently not

real masses moving in the direction in which they are advancing, but merely outlines, motions, or forms rushing along, and comprehending all the particles of an undulating fluid, which are at once in a vibratory state. Or, in other words, an undulation is merely the continued transmission in one direction of particles bearing a relative position to one another. It is thus that an impulse given to any one point of the atmosphere is successively propagated in all directions, in waves diverging as from the centre of a sphere to greater and greater distances, but with decreasing intensity, in consequence of the increasing number of particles of inert matter which the force has to move; like the waves formed in still water by a falling stone, which are propagated circularly all round the centre of disturbance. These successive spherical waves are only the repercussions of the condensations and motions of the first particles to which the impulse was given.

The intensity of sound depends upon the violence and extent of the initial vibrations of air, but whatever they may be, each undulation, when once formed, can only be transmitted straight forwards, and never returns back again. unless when reflected by an opposing obstacle. The vibrations of the aerial molecules are always extremely small whereas the waves of sound vary from a few inches to several feet. The various kinds of musical instruments, the human voice, and that of animals, the singing of birds, the hum of insects, the roar of the cataract, the whistling of the wind, and the other nameless peculiarities of sound, at once show an infinite variety in the modes of aërial vibrations, and the astonishing acuteness and delicacy of the ear, thus capable of appreciating the minutest differences in the laws of molecular oscillation.

All mere noises are occasioned by irregular impulses communicated to the ear, and if they be short, sudden, and repeated beyond a certain degree of quickness, the ear loses the intervals of silence, and the sound appears continuous, because, like the eye, it retains the perception of excitement for a moment after the impulse has ceased. Qr, in other words, the auditory nerves continue their vibrations for an extremely short period after the impulse, before they return to a state of repose. Still such sounds will be mere noise; in order to produce a musical sound, the impulses, and, consequently, the undulations of the air, must be all exactly similar in duration and intensity, and must recur after exactly equal intervals of time. The quality of a musical note depends upon the abruptness, and its intensity upon the violence and extent of the original impulse. But the whole theory of harmonics is founded upon the pitch which varies with the rapidity of the vibrations. The grave, or low tones are produced by very slow vibrations, which increase in frequency progressively, as the note becomes more acute. When the vibrations of a musical chord, for example, are less than sixteen in a second, it will not communicate a continued sound to the ear; the vibrations or pulses increase in number with the acuteness of the note till, at last, all sense of pitch is lost. The whole extent of human hearing, from the lowest note of the organ to the highest known cry of insects, as of the cricket, includes about nine octaves. All ears, however, are by no means gifted with so great a range of hearing; many people, though not at all deaf, are quite insensible to the cry of the bat or the cricket, while to others it is painfully shrill. According to recent experiments by M. Savart, the human ear is capable of

hearing sounds arising from about 24000 vibrations in a second, and is consequently able to appreciate a sound which only lasts the twenty-four thousandth part of a second. All people do not hear the deep sounds alike; that faculty seems to depend upon the frequency of the vibrations, and not on the intensity or loudness. But, although there are limits to the variations of our auditory nerves, Dr. Wollaston, who has investigated this curious subject with his usual originality, observes, that as there is nothing in the nature of the atmosphere to prevent the existence of vibrations incomparably more frequent than any of which we are conscious, we may imagine that animals, like the Grylli, whose powers appear to commence nearly where ours terminate, may have the faculty of hearing still sharper sounds which we do not know to exist, and that there may be other insects hearing nothing in common with us, but endowed with a power of exciting, and a sense which perceives vibrations of the same nature indeed as those which constitute our ordinary sounds, but so remote, that the animals who perceive them may be said to possess another sense agreeing with our own solely in the medium by which it is excited.'

The velocity of sound is uniform, and is independent of the nature, extent, and intensity of the primitive disturbance. Consequently sounds, of every quality and pitch, travel with equal speed; the smallest difference in their velocity is incompatible either with harmony or melody, for notes of different pitches and intensities, sounded together at a little distance, would arrive at the ear in different times; and a rapid succession of notes would produce confusion and discord. But as the rapidity with which sound is transmitted depends upon the elasticity of