§ 52. The alternate action and reaction of mechanical force and elasticity, and the consequent propagation of force to a distance, by vibration, are beautifully illustrated by the phenomena of SOUND. This is another adjustment of the properties of the atmosphere which constitutes a most important feature in the evident and wonderful design of its constitution. The complete developement of the subject constitutes a distinct branch of science, under the name of Acoustics: we can only here advert to the play of the forces which are concerned in its production.

When the particles of an elastic body are suddenly disturbed by an impulse at a particular point, the force spreads throughout their substance from that point, as a centre, and they return to their state of rest, by a series of isochronous vibrations, or rapid movements to and fro; equal numbers of which take place in equal times. The rapidity, force, and permanence of these vibrations depend upon the elasticity, the form, and the mode of aggregation, of the particles of the vibrating body (13). They are not confined to the substance in which they are produced, but they communicate themselves to the surrounding air in which, on account of its elasticity, they excite equivalent condensations and dilatations which again are propagated to a distance. The corresponding impulses produced upon the ear constitute sound. If the successive impulses form a connected series, following each other too rapidly to be separately distinguished, they constitute a continued sound like that of the voice in speaking; and if they are equal among themselves in duration they produce

(13) A B represent the two prongs of a tuning-fork, made of steel; if one of them, A, be struck against a solid substance, it will momentarily assume the position 6, nearer to the other prong, B, but from its elasticity it will immediately return to its former position, beyond which it will be carried by its momentum to the position a, about as far from A as the second position, b, and thus a series of rapid vibrations is brought about, which being propagated through the air to the ear produces the sensation of a musical note. The vibrations of A alone are represented in the figure for the sake of clearness; but the other prong, B, will also be in a similar state of vibration.

a musical or equable sound, as that of a vibrating string, or of the voice in singing. A quill striking against a piece of wood causes a noise, but striking against the teeth of a wheel, or of a comb, a continued sound; and if the teeth of the wheel be at equal distances, and the velocity of the motion of a certain amount, and constant, a musical note. The lowest sound which can be called musical, is produced by 16 vibrations in a second of time; though according to the observation of Dr. Wollaston, some ears are so constituted as to be able to appreciate notes at both extremities of the scale, which are inaudible to others. The higher octave to this sound is produced by double the number of vibrations, and the double octave by four times the number in the same time, and so on in the progression 16, 32, 64, 128, 256; the last of which produces the note which is designated as the middle C on the pianoforte. The fixedness of these relations is such that the wellknown sound of the different musical notes has been employed by Professor Wheatstone as the measure of velocities in machines which are utterly inappreciable by ordinary mechanical means.

A certain time is always required for the transmission of an impulse through a material substance, and this time varies with its hardness and compressibility. The velocity of sound in air has been found by experiment to be 1130 feet in a second; in water, 4900 feet; and along a deal rod, 17,400 feet.

As the force from the original impulse diverges in air, and spreads through a spherical space, its intensity must decrease as the square of the distance, but it is capable of being turned back or reflected from the surface of any solid obstacle.

§ 53. A musical string gives a very feeble sound when vibrating alone, on account of the small quantity of air set in motion; but when attached to a large surface of wood, or to what is called a sounding-board in musical instruments, it communicates its oscillations immediately to that surface, and the whole system vibrates isochronously. The extensive vibrating surface again transmits its motions to the surrounding mass of the air, and the sound is much increased.

§ 54. The oscillations of a solid body are not confined to one direction, but may be longitudinal, transverse, or rotatory; in every plane, or confined to one plane, accordingly as the impulse is communicated. Differences in the structure of a

body may influence the direction of its vibrations. If a little fine dry sand be strewed over a vibrating surface, it will be thrown into violent agitation by the force communicated to it in parti cular situations, but in other situations it will remain at rest, and it will thus enable the eye to distinguish the vibrating from the quiescent parts. Thus, if vibrations be excited in a plate of glass or metal, by drawing the bow of a violin across its edge, it will emit a musical sound, and the sand will immediately arrange itself in certain lines regularly disposed, where it will accumulate from other parts, and remain at rest. It is thus found that the adjacent divisions of the surface are in different states of vibration, some being always elevated while others are depressed; and the oppositely vibrating parts are separated by lines of rest. These lines of rest are termed nodal lines, and they vary in form and position with the part where the bow is drawn across; but the point by which the plate is held being necessarily in a state of rest, must be included in a nodal line (14). Similar points of rest, or nodal points, are found on a vibrating string; and pieces of paper placed at the half, third, fourth, or other aliquot points of its length, will remain on it during its vibration, but will instantly fly off from any intermediate points. They are points of equilibrium between two adjacent oppositely vibrating parts. Indeed all vibrating bodies have a tendency to divide themselves into a certain number of parts which perform their vibrations independently of each other.

§ 55. The amount of force which may be accumulated from the frequent and regular repetition of minute impulses to the particles of elastic solids is very great, just as momentum may be accumulated in a pendulum by frequent small impulses (§ 29); and the cohesion of glass itself has been known

(14) If a plate of glass, a b c d, be held horizontally at its centre, E, between the finger and a thumb, and sand be scattered over its upper surface, upon causing it to emit a musical note, by drawing a violin-bow along its edge, the sand will arrange itself in lines constituting regular figures, the form of which will depend upon the pitch of the note. The lines a E, b E, c E, d E, in the figure, repre· sent a common arrangement of these nodal lines; the point, E, by which it is held, will be, of course, quiescent.

6

ין

to yield under the intense vibrations of a musical note. If we pass our moistened fingers lightly along a glass tube, two or three yards in length, and from three-fourths of an inch to an inch in diameter, we may generate a force which will be sufficient to move a leaden ball placed within it, and even to draw it up against the action of gravity, when the tube is inclined several degrees to the horizon. Or if we fix a small glass tube into a beam of wood, and cause it to vibrate longitudinally, in the same way, the successive and periodic impulses will be sufficient to agitate the beam throughout its mass, and to produce vibrations of such an extent that whole handfuls of sand thrown upon it will be projected upon the lines of rest, which will thus be accurately defined.

$56. These vibrations alter the molecular arrangement and strength of bodies while they last, so that if a weight of 90 pounds be suspended from a copper band of three yards in length, 0.4 inch wide, and 0.04 inch thick, it will remain unchanged for any length of time; but if made to vibrate, it will become lengthened six or seven inches. M. Savart measured the lengthening of rods of glass and brass by the act of vibration, under the friction of a damp cloth, and ascertained the amount of mechanical force which would be required to be directly applied to produce the same effect, and found it to be in the first case, (the diameter of the cylinder being 1.14 inches,) equal to a weight of 2000 pounds; and in the second, (the diameter being 1.38 inches,) 3800 pounds. The facts are of the utmost practical consequence with regard to structures in metal which are destined to support great weights, and are at the same time exposed to regular oscillations and vibrations.

We will now direct our attention to the forces of homogeneous attraction and repulsion.

IV. HOMOGENEOUS ATTRACTION AND

REPULSION.

§ 57. THE force of COHESION in bodies is measured by the amount of any force which may be required to separate their particles, or break them, and may be ascertained by experiment. The opposing force may be applied in various ways. (1) It may tend to tear the body asunder, in the direction of its fibres; (2) it may tend to break the body across; (3) it may tend to

crush the body; (4) it may tend to separate the particles by means of torsion or twisting. The investigation of the strength of materials, and the different degress in which they resist the action of force, so variously applied, belongs to mechanical science. The following table shows the force of cohesion from experiment of a few solids, as indicated by the weights required to tear them asunder, and to crush them.

TABLE II. Of Strength of Materials.

§ 58. The force of cohesion is opposed to mechanical force in the case of the surfaces of two solids of the same substance moving upon each other, and is estimated by the resistance to the motion, which is denominated friction.

Friction is greatest between rough surfaces, and diminishes with the degree of polish given to them.

All other circumstances being equal, it is directly proportioned to the pressure of the two bodies. Friction also arises from a similar opposition of the force of adhesion, in the case of the two surfaces in motion being of dissimilar matter; but it is greater between homogeneous substances than between heterogeneous ones.

$59. The subject of FRICTION, again, is purely mechanical; but we re-enter within the strictest limits of our department in considering next, those adjustments of the two antagonist powers of homogeneous attraction and repulsion, which constitute the physical states of solid, liquid, and aëriform. The best, because the most familiar, illustration of these three different states may be derived from our every day observation of the changes which water undergoes. Every one knows that by abstracting heat from water, or cooling it to a certain point, we