medium requires time. That this is the case, we may satisfy ourselves by remarking the period that elapses between seeing the flash of a gun and hearing the report. It is greater as we are removed to a greater distance. In different media, the velocity of transmission depends on the density and specific elasticity. It has been found, by experiment, that in tranquil air the velocity of sound at 60°, and at an average state of moisture, is 1,120 feet in a second. The wind accelerates or retards sound, according to its direction, damp air transmits it more slowly than dry, and hot air more rapidly than cold, the velocity increasing about 1·1 foot for every Fahrenheit degree.

In a soniferous medium, all sounds move equally fast; it is wholly immaterial what may be their quality, or their intensity. Thus, we know that even the most intricate music executed at a distance is heard without any discord, and precisely as it would be close at hand. Nor does it matter whether it be by the human voice, a flute, a bugle, or, indeed, by many different instruments at once; the relation of the difference of sounds is accurately preserved. But this can only take place as a consequence of the equal velocity of transmission; for if some of these sounds moved faster than others, discord must inevitably ensue.

The experiments of Colladon and Sturm on the lake of Geneva show that the velocity in water is about four times that in air, being 4,708 feet in a second. With respect to solid substances, it is stated that the velocity in air being one, that in tin is 7, in copper 12, in glass 17.

Advantage is sometimes taken of these principles to determine distances. If we observe the time elapsing between the flash of a gun and hearing the sound, or between seeing lightning and hearing the thunder, every second answers to 1,120 feet.

Sounds are of different kinds: some are low or high, grave or acute, according as the vibrations are slower or faster. Again, the intensity of vibration, or the magnitudes of the excursions which the vibrating particles make, determine the force of sounds, an intense vibration giving a loud, and a less vibration a feeble sound.

The vibrations of a soniferous body may take place in three directions: they may be longitudinal, transverse, or rotatory vibrations; or, indeed,

they may all co-exist. A body may be divided into vibrating parts, separated from one another by nodal points or lines. Thus, if we take a glass or metal plate, and having strewed its surface with fine dry sand, and holding it firmly at one point between the thumb and finger, or in a clamp, as represented in Fig. 200, draw its edge, it yields a musical note, and the sand is thrown off those places which are in motion, and collects on the nodal points, which are at rest.

Fig. 200.

a violin bow across

The quantity, or strength, or intensity of a sound depends on the intensity of the vibrations and the mass of the sounding body. It also varies with the distance, being inversely proportional to its square.

Musical sounds are spoken of as notes, or as high and low. Of two notes, the higher is that which arises from more rapid, and the lower from slower vibration 3.

Besides this, sounds differ in their quality. The same note emitted by a flute, a violin, a piano, or the human voice, is wholly different, and in each

instance peculiar. In what this peculiarity consists we are not able to

say.

The several notes are distinguished by letters and names; we shall also see presently that they may be distinguished by numbers. They arcCDEFG ABC

or-Ut, re, mi, fa, sol, la, si, ut.

Such a series of sounds passes under the name of the diatonic scale.

CHAPTER XXXIII.

PHENOMENA OF SOUND.

Notes in unison-Concords and Discords-Octave-Interval of SoundsMelody-Harmony-The Monochord-Length of Cord and Number of Vibrations required for each Note-Laws of Vibrations in Cords, Rods, Planes-Acoustic Figures on Plates-Vibration of Columns of AirInterference of Sounds-Whispering Galleries-Echoes-Speaking and Hearing Trumpet.

Two notes are said to be in unison when the vibrations which cause them are performed in equal times. If the one makes twice as many vibrations as the other, it is said to be its octave, and the relation or interval there is between two sounds is the proportion between their respective numbers of vibrations.

[When two strings are vibrating together in different times, or not in unison, the ear can distinctly perceive the note of both; but, besides those two separate notes, there will be an impression from the two jointly, very different from that which it receives from either of them separately, and which leads to some curious considerations. This impression is sometimes most agreeable, at others harsh and grating, and according to these sensations the sounds are said to be in accordance or discordance. But the remarkable fact is, that this impression of concord will be experienced whenever the number of vibrations of the individual notes are in some near relation to each other, as 1 to 2, 1 to 3, 2 to 3, &c.; that is, where one string makes two, three, or four vibrations while the other makes one, or accomplishes three while the other accomplishes two or four; and the concord is the more perfect and pleasing the lower the terms of these ratios are. if, on the contrary, the times of vibration, or number of vibrations in a given time, have not a loud, numerical ratio to each other, but one in which the terms are considerable, as 8 to 15, that is, one string executing fifteen vibrations while the other executes only eight, then there is a discord: the impression on the ear is harsh and disagreeable. The whole harmony consists in following out these laws; any combination of sounds which violate them cannot be agreeable. The pleasure of these harmonious sounds depends, according to Dr. Young, on a love of order and a predilection for a regular recurrence of sensations, primitively implanted in the human mind. Hence,

But

when two sounds occur together, those proportions are most satisfactory to the ear which exhibit a recurrence of a more or less perfect coincidence at the shortest intervals. This same constitution of the human mind, which fits it for the perception of harmony, appears also to be the cause of the love of rhythm, or of a regular succession of any impressions whatever, at equal intervals of time." The Elements of Physics," by Thomas Webster, M.A., page 208.]

A combination of harmonious sounds is a chord, a succession of harmonious notes a melody, and a succession of chords harmony.

We have remarked in the last chapter that sounds may be expressed by numbers as well as by letters or names, and their relations to one another clearly exhibited. For this purpose we may take the monochord or sonometer, CC, Fig. 201, an instrument consisting of a wire or catgut stretched over two bridges, F F', which are fastened on a basis, S S'; one end of the cord passes over a pulley, M, and may be strained to any required degree of weights, P. The length of the string vibrating may be changed by pressing it with the finger upon a movable piece, H, which carries an edge, T, and the case beneath is divided into parts, which exhibit the length of the vibrating part of the wire. The upper part of Fig. 202 shows a horizontal view of the monochord, the lower a lateral view. The instrument here represented has two strings, one of catgut and one of wire.

Now, it is to be understood that the number of vibrations of such a cord is inversely as its length; that is, if the whole cord makes a given number of vibrations in one second, when you reduce its length to one-half it will make twice as many; if to one-third, thrice as many, &c.

Suppose the cord is stretched so as to give a clear sound, which we may designate as C, and the movable bridge is then advanced so as to obtain successively the other notes of the gamut, D, E, F, G, A, B, C, it will be found that these are given when the lengths of the cord, compared with its original length, are—

Name of note
Length of cord

CDEFG A B C
1, §, 4, 4, 3, 3, 15, 1.

But as the number of vibrations is in the inverse ratio of the lengths of the

vibrating cords, we shall have for the number of vibrations, if we represent by 1 the number that gives C, the following for the other notes:

Name of note

Number of vibrations

CDEFG A B C
1, 2, 4, †, 2, §, V,
15, 2.

From C to C is an octave; and from this we gather that, in the octave, the higher note makes twice as many vibrations as the fundamental note, and that between these there are other intervals, which, heard in succession, are harmonious; the eight, therefore, constitute a scale, commonly called the diatonic scale.

Musical instruments are of different kinds, depending on the vibrations of cords, rods, planes, or columns of air.

It has already been stated that the number of vibrations of a cord is inversely as its length; the number also increases as the square root of the force that stretches it; thus, the octave is given by the same string when stretched four times as strongly; the material of the string, whether it be catgut, iron, &c., also affects the note.

In rods, the height of the note is directly as the thickness, and inversely as the square of the length. The quality of the material also, in respect of elasticity, determines the note.

The foregoing observations apply to transverse vibrations of cords and rods; but they may be also made to execute longitudinal and torsion vibratiens, the conditions of which are different.

In planes held by one point, and a bow drawn across at another, or struck by a blow, sounds are emitted, and by the aid of sand, nodal lines may be traced. Thus, in Fig. 202, a is the point, in each instance, at which the plate is held, and 6 that at which the bow is applied; the sand arranges itself in the dotted lines.

The two large figures are formed by putting together four smaller plates,

in one instance bearing the nodal lines, represented at I, and, in the other, at II. They may, however, be directly generated on one large plate of glass by holding it at a, touching it at w, and drawing the bow across it at b.

Circular plates, a in III., may be made to bear a four-rayed star, by holding them in the centre, drawing the bow at any point at b, and touching the plate at a point 45° distant from the bow; but if the plate be touched 30°, 60°, or 90° off, it produces a six-rayed star, Fig. IV.

Columns of air may be made to emit sounds by being thrown into oscillation, as in horns, flutes, clarionets, &c. In these, the column of air, included. in the tube of the instrument, is made to vibrate longitudinally. The height of the note is inversely proportional to the length of the column, and therefore different notes may be obtained by having apertures, at suitable distances, in the side of the tube, as in the flute.

Two sounds may be so combined together that they shall mutually destroy each other's effect, and silence result. This arises from interference taking place in the aerial waves, the laws of which are those given in Chapter XXXI. The following instances will illustrate these facts:

When a tuning-fork is made to vibrate, and is turned round upon its axis near the ear, four periods may be discovered during every revolution in which the sound increases or declines. We may produce standing vibrations of the air within a closed tube, by bringing an oscillating body before the open mouth of the tube, so that it may produce such a tone, that the length of the tube is equal to 4, 4, 4, &c., of the wave-length of the tone.

α

If we take two tuning-forks of the same note, a d, Fig. 203, and fasten a circle of cardboard, half an inch in diameter, on one of the prongs of each, and make one of the forks a little heavier than the other, by putting on it a drop of wax, and then filling a jar, b, to such a height with water, that either of the forks, when held over it, will make it resound, so long as only one is held, there will be a conFig. 203. tinuous note, without pause or interruption; but if both are held together, there will be periods of silence and periods of sound, according as the longer waves, arising from one of the forks, overtake and interfere with the shorter waves, arising from the other.

[In order to throw the inclosed air into regular vibrations, or to make it resonant with the sounding body, it is not indispensably necessary to bring a sounding body before the opening of a tube. Thus, in organ pipes there is a current of air flowing past the open end of the tube, breaking against the edges, and creating, by its impulses, waves that are reflected on the bottom, and interfere with the newly incident waves. Although these impulses are at first not quite regular, they are soon regulated by the accession of reflected waves, provided the tube sounds well, so that regularly standing waves are formed, by means of which the air in the tube becomes resonant. The notes yielded in this manner by a tube are of the same kind as those which must be given forth by another sounding body brought to the opening of the tube, for the purpose of inducing spontaneous sound in the inclosed air.-Professor Müller's "Physics and Meteorology," Lecture XVII.] Sounds undergo reflection, and may therefore be directed by surfaces of suitable figure. If; in the focus of a concave mirror, a watch be placed, its ticking may be heard at a great distance in the focus of a second mirror, placed so as to receive the sound waves of the first.

On similar principles, also, whispering galleries depend. These are so constructed that a low whisper uttered at one point is reflected to a focus