makes twice as many vibrations as one of double the size. Other things being equal, the notes rendered differ by an octave.

3. The length and size being the same, the number of vibrations varies as the square root of the tension.

If a cord renders a given note, it will, if its tension be quadrupled, render a note an octave higher, and so on. This property is "utilized in stringed instruments by means of an apparatus for increasing or diminishing the tension at pleasure.

4. Other things being equal, the number of vibrations varies inversely as the square root of the density.

Dense cords render graver notes than those of less density. Small, light, and short cords, strongly stretched, yield acute notes. Large, dense, and long cords, not strongly stretched, yield grave notes.

169.

Verification of the Laws of Vibration.

The laws enunciated in the preceding article may be verified by means of an instrument called a Sonometer, shown in Fig. 115.

The sonometer is said to have been invented by PYTHAGORAS, about 600 years before our era. In its present form,

The third law? Illustrate. The fourth law? Illustrate. (169.) How may the preceding laws be verified? What is a Sonometer?

it consists of a wooden box about four feet in length, upon which are mounted two fixed bridges, A and B, and a movable one, D. On these bridges, two cords, CD and AB, fastened firmly at one end and passing over pulleys at the other end, are stretched by means of weights, P.

Let the cords be exactly alike and stretched by equal weights. If the bridge D, be moved so as to render CD equal to one half of AB, the notes of the two cords will differ by an octave; that is, CD will vibrate twice as fast as AB. If CD be made equal to one third of AB, by moving the bridge D, the former will vibrate three times as fast as the latter, and so on. This verifies the first law. To verify the second law, we remove the bridge D, and use two cords, one of which is twice as large as the other. It will be found that the notes yielded will differ by an octave. If one cord be taken three times as large as the other, the latter will be found to vibrate three times as fast as the former.

To verify the third law, let the two cords be alike, and stretch one by a weight four times as great as that employed to stretch the other. The notes will differ by an octave. If the stretching force in one, is nine times that in the other case, the former will vibrate three times as fast as the latter, and so on.

To verify the fourth law, we make use of cords equal in length, size, and equally stretched, but of different densities. It will be found that the law is verified in each case

Stringed Instruments.

170. All stringed instruments of music are constructed in accordance with the preceding laws. They are divided into instruments with fixed sounds, and instruments with variable sounds.

Describe it. How is the first law verified? The second? The third? The fourth? (170.) How are stringed instruments classed?

To the former class belong the piano, the harp, &c. They have a cord for each note, or else an arrangement is made so that by placing the finger at certain points, as in the guitar, the same cord may be made to render several notes in succession.

To the latter class belong the violin, the violoncello, &c. They are provided with cords of catgut, or sometimes of metal, put in vibration by a bow. Various arrangements are made for regulating the notes, such as increasing the tension, placing the finger upon the cords, and the like. These instruments are difficult to play upon, and require great nicety of ear, but in the hands of skillful players they possess great power. They are the soul of the orchestra, and it is for them that the finest pieces of music have been composed.

Sound from Pipes.

171. When the air in a pipe, or hollow tube, is put into vibration, it yields a sound. In this case, it is the air which is the sonorous body, the nature of the sound depending upon the form of the pipe and the manner in which the vibrations of its contained air are produced.

To produce a sound from a pipe, the contained air must be thrown into a succession of rapid condensations and rarefactions, which is effected by introducing a current of air through a suitable mouth-piece. Two principal forms are given to the mouth-piece, in one of which the parts remain fixed, and in the other there is a movable tongue, called a reed.

Pipes with fixed Mouth-pieces.

172. Pipes with fixed mouth-pieces are of wood or metal, rectangular or cylindrical, and always of considerable

Examples of each class. Which are most difficult to play upon? (171.) What is the sonorous body in the case of a pipe? How thrown into vibration ? What is a mouth-piece? How many forms? (172.) What are the characteristics of pipes with fixed mouth-pieces?

length compared with their cross section.

To this class

belong the flute, the organ pipe, and the like. Some of the forms given to pipes of this class are shown in Figs. 116, 117, 118, 119, and 120.

Fig. 116 represents a rectangular pipe of wood, and Fig. 117 shows the form of its longitudinal section. P represents the tube

through which air is forced into it. The air passes through a narrow opening, i, called the vent. Opposite the vent is an opening in the side of the pipe, called the mouth. The upper border, a, of the mouth, is bevelled, and is called the upper lip, the lower border is not bevelled, and is called the lower lip.

Describe the mouth-piece The vent. The mouth. The lips.

The current of air forced through the vent strikes against the upper lip, is compressed, and by its elasticity, reacts upon the eutering current, and for an instant arrests it. This stoppage is only for

an instant, for the compressed air finds an outlet through the mouth, again permitting the flow. No sooner has the flow commenced than it is a second time arrested as before, again to be resumed, and

so on.

This continued arrest and release of the current gives rise to a succession of vibrations, which are propagated through the tube, causing alternate and rapid condensations and rarefactions, which result in a continuous sound. The vibrations are the more rapid as the current introduced is stronger, and as the upper lip approaches nearer the vent

Fig. 118 represents a second form of organ pipe, which is shown in section in Fig. 119. This is but a modification of the pipe already explained. The letters indicate the same parts as in the preceding figures.

Fig. 120 represents the form of the mouth-piece of the flageolet, and it will be seen that it bears a close resemblance to the pipes already explained.

In the flute, an opening is made in the side of the pipe, and the arrest and flow of the current are effected by the arrangement of the lips of the player.

Reed Pipes.

173. In REED PIPES the mouth-piece is provided with a vibrating tongue, called a Reed, by means of which the air is put in vibration. To this class belong the clarionet, the hautboy, and the like. The reed may be so arranged as to beat against the sides of the opening, or it may play freely through the opening in the tube.

Figs. 121 and 122 show the arrangement of a reed of the first kind, A piece of metal, a. shaped like a spoon, is fitted with an elastic tongue, l, which can completely close the opening. A piece of

Explain the action in detail. How is the mouth-piece in the flute? (173) What is a reed? What are some of the reed instruments? Explain the arrange ment of a reed of the first kind.