approaches, and closes it. Lastly, a curved wire, br, presses against the tongue, and can be moved up and down.

The vibrating part of the tongue can thereby be shortened or lengthened at will, and the number of vibrations thus regulated. By means of this wire, reed pipes are tuned.

The reed is fitted to the top of a rectangular pipe KN, called the wind channel. This is closed everywhere except at the bottom,

where it can be fitted on a bellows. In models of reed pipes used in illustrating lectures, the sides of the upper part of the tube are made of glass, so as to show the construction of the reed. This arrangement is represented in fig. 150.

When air arrives in the wind channel, it first passes between the tongue and the groove, and escapes by the pipe T; but as the velocity increases, the tongue strikes against the edge of the groove, and closing it completely, the current is stopped. But, in virtue of its elasticity, the tongue reverts to its original position, and thus by a

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Bellows.

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series of alternate openings and closings, the same series of pulsations are produced as in mouth instruments; hence is formed a sound which is higher the more rapid the current of air.

Free reed. Grenié invented in 1810 a kind of reed called a free reed, because the tongue, instead of striking against the edges of the groove, like the reed described above, grazes them so as to oscillate backwards and forwards. The groove consists, in this case, of a small wooden box, ac, the front of which is of brass plate. In the middle of this is a longitudinal slit, in which is applied the tongue, which can oscillate freely backwards and forwards so as to allow air to pass, which it closes each time it grazes the edges of the slit. In this case also a wire, r, regulates the length of the vibrating part of the tongue.

Between the four legs of a table there is a pair of bellows, S (fig. 153), which is worked by means of a pedal, P. D is a reservoir of flexible leather, in which is stored the air forced in by the bellows. If this reservoir is pressed by means of weights on a rod, T, moved by the hand, the air is driven through a pipe, A, into a wind chest, mn, fixed on the table. In this chest there are small holes closed by leather valves, s (fig. 154). These can be opened by pressing on keys, a, in front of the box. Below the valve is a spring, r, which raises the valve when the key is not depressed. syren or sounding pipe is placed in one of these holes.

The

182. Nodes and loops.-Experiment shows, that when a pipe is sounded, the column of air is subdivided into equal parts, vibrating in unison, and separated by surfaces where the velocity of air is null. These fixed parts are called nodes; and the parts between the nodes where the column of air is in a state of vibration is called a loop, or a ventral segment.

It will be seen afterwards, that one and the same pipe may be made to yield several sounds, and that the nodes and ventral segments are then displaced. When a pipe closed at one end, a stopped pipe, is made to yield its fundamental sound, that is, the deepest one, the bottom is always a node, and the mouthpieces a ventral segment. An open pipe when sounded has a ventral segment at each end; and if it yields the fundamental sound, there is a single Inode in the middle.

When an aperture is opened in the side of a sounding pipe, the sound does not change if the aperture corresponds to a loop; but if it corresponds to a node, the sound is altered, for this node then becomes a loop. This property is used in wind instruments like the flute, the clarionet, along which holes are made which can be closed by the fingers, or by the aid of keys.

The formation of nodes and loops is far from being restricted to sounding tubes. On strings, plates and membranes, when they vibrate, exhibit parts which are fixed, and parts which are very mobile, that is to say, nodes and loops.

182a. Laws of the vibration of air in pipes.-The vibrations of air in pipes present two cases according as they are open or stopped. Laws of stopped pipes. When having placed a stopped pipe on the bellows, air is slowly passed, the deepest note, the fundamental sound, is produced. If, then, we denote by 1 the corresponding number of vibrations, when the current of air is forced, we suddenly get the sound corresponding to 3; and if the wind be still more

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Wind Instruments.

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forced, we have successively the sounds 5, 7, etc.; that is to say, sounds which by their pitch correspond to vibrations 3, 5, 7, etc. times as numerous as those of the fundamental sound. Hence closed pipes, when the air is forced, give successively sounds represented by the series of odd numbers.

The sounds 3, 5, 7, etc., are called the harmonics of the fundamental note I.

2. With pipes of different lengths, the number of vibrations corresponding to the fundamental note are inversely as the lengths; that is to say, that a pipe, which is half as long as another, will yield a sound which is the octave of that yielded by this pipe.

Laws of open pipes.

The fundamental note being still represented by unity, the harmonics obtained by forcing the wind are successively represented by 2, 3, 4, 5, 6, etc., that is, by the natural series of numbers.

The fundamental note of an open pipe is always an octave higher than the fundamental note of a closed pipe of the same length.

These laws are known as Bernouilli's laws from the name of their discoverer, Daniel Bernouilli.

183. Wind instruments.—Wind instruments are straight or curved tubes, which are sounded by means of a current of air forced into them. They have all an aperture by which air is forced into them, and, according to the form of this aperture, they are divided into mouth instruments and reed instruments; in some, such as the organ, the notes are fixed, and require a separate pipe for each note; in others the notes are variable, and are produced by only one tube: the flute, horn, etc., are of this class.

The Pandaan pipe, the flageolet, and the German flute are mouth instruments. The principal reed instruments are the clarionet, the oboe, the cornopean, and the bassoon.

The Pandaan pipe consists of tubes of different sizes corresponding to the different notes of the gamut.

In the organ the pipes are of various kinds, namely, mouth pipes, open and stopped, and reed pipes with apertures of various shapes. The air is furnished by means of bellows, from which it passes into the wind chest, and thence into any pipe which is desired; this is effected by means of valves which are opened by depressing keys like those of the piano. In the larger and richer organs there are several rows of key-boards arranged at different heights.

In the flute, the mouthpiece consists of a simple lateral circular aperture; the current of air is directed by means of the lips, so

N

that it grazes the edge of the aperture. The holes at different distances are closed either by the fingers or by keys; when one of the holes is opened, a loop is produced in the corresponding layer of air, which modifies the distribution of nodes and loops in the interior, and thus alters the note. The whistling of a key is similarly produced.

Mouth instruments. In the trumpet, the horn, the trombone, cornet-à-piston, and ophicleide, the lips form the reed, and vibrate

in the mouthpiece (fig. 155), which terminates in a smaller tube by which it can be affixed to the instrument. In the horn, different notes are produced by altering the distance of the lips. In the trombone, one part of the tube slides within the other, and the performer can alter at will the length of the tube, and thus produce higher or lower notes. In the cornet-à-piston, the tube forms several convolutions; pistons placed at different distances can, when played, cut off communications with other parts of the tube, and thus alter the length of the vibrating column of air.

Fig. 155. The tuning-fork, the triangle, and musical boxes are examples of the transverse vibrations of rods. In musical boxes small plates of steel of different dimensions are fixed on a rod, like the teeth of a comb. A cylinder, whose axis is parallel to this rod, and whose surface is studded with steel teeth, arranged in a certain order, is placed near the plates. By means of a clockwork motion the cylinder rotates, and the teeth striking the steel plates set them in vibration, producing a tune, which depends on the arrangement of the teeth on the cylinder.