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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 1.

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 Pandæan 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

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.

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GENERAL EFFECTS OF HEAT. THERMOMETERS. 184. Heat, Hypothesis as to its nature. The sensations of heat and cold are familiar to all of us. In ordinary language the term heat is not only used to express a particular sensation, but also to describe that particular state or condition of matter which produces this sensation. Besides this effect, heat acts variously upon bodies; it melts ice, boils water, makes metals red-hot, and so forth.

Two theories as to the cause of heat are current at the present time; these are the theory of emission, and the theory of undulation.

On the first theory, heat is caused by a subtle imponderable fluid, which surrounds the molecules of bodies, and which can pass from one body to another. These heat atmospheres, which thus surround the molecules, exert a repelling influence on each other, in consequence of which heat acts in opposition to the force of cohesion. The entrance of this substance into our bodies produces the sensation of warmth, its egress the sensation of cold.

On the second hypothesis the heat of a body is caused by an oscillating or vibratory motion of its material particles, and the hottest bodies are those in which the vibrations have the greatest velocity and the greatest amplitude. Hence, on this view, heat is not a substance, but a condition of matter, and a condition which can be transferred from one body to another. It is also assumed that there is an imponderable elastic ether, which pervades all bodies and infinite space, and is capable of transmitting a vibratory motion with great velocity. A rapid vibratory motion of this ether produces heat, just as sound is produced by a vibratory motion of

atmospheric air, and the transference of heat from one body to another is effected by the intervention of this ether.

This hypothesis is now admitted by the most distinguished physicists ; it affords a better explanation of the phenomena of heat than any other theory, and it reveals an intimate connection between heat and light. In accordance with it, heat is a form of motion; and it will hereafter be shown that heat may be con. verted into motion, and, conversely, motion may be converted into heat.

Although the undulatory theory of heat is the correct one, the one, that is, which best explains and accounts for the greatest number of facts, yet it may be sometimes convenient to use language which is based on the older hypothesis. Thus, in speaking, of a body becoming heated or cooled, we say that it gains or loses heat; in reality, the motion of the particles is increased or diminished.

In what follows, however, the phenomena of heat will be considered, as far as possible, independently of either hypothesis.

185. General effects of heat.—The general action of heat upon bodies is to develope a repulsive force between their molecules which is continually struggling with molecular attraction. Under its influence, therefore, bodies tend to expandthat is, to assume a greater volume.

All bodies expand by the action of heat. As a general rule gases are the most expansible, then liquids, and, lastly, solids. The expansion of bodies by heat is thus a new general property to be added to those already studied.

The action of heat upon bodies is not merely to expand them; when accumulated in sufficient quantity, bodies first lose their solidity and become somewhat softer; then, as the heat still increases, the force of repulsion balances molecular attraction, and then bodies liquefy. Wax, resin, sulphur thus pass readily from the solid to the liquid state ; heat thus produces in solids a change of state of aggregation. But in liquids it produces a similar change. When bodies are heated they first expand; heated still more their molecular attraction is again overcome by the force of repulsion, and bodies are then changed into aëriform fluids called vapours.

If, instead of becoming accumulated in bodies heat is given out, that is, if bodies are cooled instead of being heated, the opposite phenomena are produced: the molecules come nearer each other,

-186] Expansion.

181 the volume of the pores diminishes, and hence that of the body, which is expressed by saying that the body contracts. By cooling, vapours losing their elastic force revert to the liquid state ; and liquids themselves, by the same process, gradually revert to the solid state. Thus water changes into ice, and mercury becomes as hard as lead.

Thus, according as heat accumulates in, or is dissipated by, bodies, two physical effects may be produced : 1, changes in volume, consisting in expansions and contractions. 2. Changes of condition, that is, the change of solids into liquids, of liquids into vapours, and conversely. We shall first discuss the expansion of bodies, and afterwards their changes of state.

186. Expansion.—All bodies are expanded by heat, but to very different extents. Gases are most expansible, then liquids, and after them solids.

In solids which have definite figures, we can either consider the expansion in one dimension, or the linear expansion; in two dimensions, the superficial expansion, or in three dimensions, the cubical expansion or the expansion of volume, although one of these never takes place without the other. As liquids and gases have no definite figures, the expansions of volume have in them alone to be considered.

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Fig. 156. To show the linear expansion of solids, the apparatus represented in fig. 156 may be used. A metallic rod, A, is fixed at one end by

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