considered lies in the fact, that, as the spherical shells of condensation and rarefaction spread, it is necessary, in order to keep up the wave-motion, to throw larger and larger surfaces of air into vibration; whereas within the tube the transverse section remained the same throughout. Hence, as the same amount of original disturbing force has to set a constantly increasing number of air-particles into motion, it can only do so by correspondingly shortening the distances through which the individual particles move, i.e. by diminishing their extent of vibration. Accordingly, when Sound-waves spread out freely in all directions, the further any given air-particle is from the point at which the sound originated, the smaller will be the extent of the vibration into which it will be thrown when the waves reach it.

23. Sounds are either musical or non-musical. The vast majority of those ordinarily heard-the roaring of the wind, the din of traffic in a crowded thoroughfare-belong to the second class. Musical sounds are, for the most part, to be heard only from instruments constructed to produce them. The difference between the sensations caused in our ears by these two classes of sounds is extremely well marked, and its nature admits of easy analysis. Let a note be struck and held down on the harmonium, or on any instrument capable of producing a sustained

tone. However attentively we may listen, we perceive no change or variation in the sound heard. A perfectly continuous and uniform sensation is experienced as long as the note is held down. If instead of the harmonium we employ the pianoforte, where the sound is loudest directly after the moment of percussion, and then gradually dies away, diminution of loudness is the only change which occurs.

In the case of non-musical sounds variations of a different kind can be easily detected. In the howling of the wind the sound rises to a considerable degree of shrillness, then falls, then rises again, and so on. On parts of the coast where a shingly beach of considerable extent slopes down to the sea, a sound is heard in stormy weather which varies from the deep thundering roar of the great breakers, to the shrill tearing scream of the shingle dragged along by the retreating surf. Similar variations may be noticed in sounds of small intensity such as the rustling of leaves, the chirping of insects, and the like. The difference, then, between musical and non-musical sounds seems to lie in this, that the former are constant, while the latter are continually varying. The human voice can produce sounds of both classes. In singing a sustained note it remains quite steady, neither rising nor falling. Its conversational tone, on the other hand, is perpetually varying in height

even within a single syllable; if it ceases so to vary, it assumes a musical character, witness the epithet 'sing-song' then commonly applied to it.

We may then define a musical sound as a steady sound, a non-musical sound as an unsteady sound. It is true we may often be puzzled to say whether a particular sound is musical or not: this arises, however, from no defect in our definition, but from the fact that such sounds consist of two elements, musical and non-musical, of which the latter may be the more powerful, and therefore absorb our attention until it is specially directed to the former. For instance, a beginner on the violin often produces a sound in which the irregular scratching of the bow predominates over the regular tone of the string. In bad flute-playing an unsteady hissing sound accompanies the naturally sweet tone of the instrument, and may easily surpass it in intensity. In the tones of the more imperfect musical instruments, such as drums and cymbals, the non-musical element is very prominent, while in such sounds as the hammering of metals, or the roar of a water-fall, we may be able to recognise only a trace of the musical element, all but extinguished by its boisterous companion.

We have seen that Sound reaches our ears by means of vibrations executed by the particles of the

atmosphere. It has also been shown that steadiness is the characteristic feature of musical, as distinguished from non-musical, sounds. We We may infer hence that the motion of the air corresponding to a single musical sound will be itself steady, i.e. that equal numbers of equal vibrations will be executed in precisely equal times. This conception of the physical conditions under which musical sounds are produced will suffice for the present. We proceed to consider in detail the various ways in which such sounds may differ from each other, and to investigate the mechanical cause to which each such difference is to be referred. In what follows, by the word 'sound' will always be meant 'musical sound,' unless the contrary be expressly stated.

CHAPTER II.

ON LOUDNESS AND PITCH.

24. A musical sound may vary in three different respects. Let a note be played, first by a single violin, then, by two, by three, and so on, until we have all the violins of an orchestra in unison upon it. This is a variation of loudness only. Next let a succession of notes be played on any instrument of uniform power, such as the harmonium without the expression-stop, or on the principal manual of an organ, only one combination of stops being in either case used. Here we have a variation of pitch only. Lastly, let one and the same note be successively struck on a number of pianofortes of the same size, but by different makers. The sounds heard will all have exactly the same pitch, and about the same degree of loudness; nevertheless they will exhibit decided differences of character. The tone of one instrument will be rich and full, of another ringing and metallic, that of a third will be described as 'wiry,' of a fourth as 'tinkling,' and so on.

Sounds thus related to each other are said to vary in quality only. The instances just considered