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 alone. 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

have the advantage of simplicity, since they allow of changes in loudness, pitch, and quality being exhibited separately. They are, however, less striking than other cases where sounds vary in two, or in all three, of these respects at the same time. A practised ear may be requisite to detect the difference between the tone of two pianofortes, but no one is in danger of mistaking, for instance, a flute for a trumpet. There is here, no doubt, considerable difference of loudness as well as of quality, but let the more powerful instrument be placed at such a distance that it sounds no louder than the weaker one, and the distinction between the two kinds of tone will be still quite decisive.

Two assigned musical sounds thus may differ from each other in loudness or pitch or quality, and agree in the other two or they may differ in any two of these, and agree in the third-or they may differ in all three. There is, however, no other respect in which they can differ, and accordingly we know all about a musical sound as soon as we know its loudness, its pitch, and its quality. These three elements determine the sound, just as the lengths of the three sides of a triangle determine the triangle.

25. The loudness of a musical sound depends entirely, as we shall easily see, on the extent of oscillatory movement performed by the individual

particles composing the medium through which the sound is conveyed to our ears. A sound-producing instrument can be readily observed to be in a state of rapid vibratory motion. The vibrations of a tuning-fork are perceptible to the eye in the fuzzy, half-transparent, rim which surrounds its prongs when it is struck; and to the touch, if, after striking the fork, we place a finger gently against one of the prongs. The harder we hit the fork the louder is its sound, and the larger, estimated by both the above modes of observation, are its vibrations. The experiment may be tried equally well on any pianoforte whose construction allows the wires to be uncovered. It is natural to infer that a vibration on the part of a sound-producing instrument communicates to the particles of the air in contact with it a corresponding movement. Thus a sound of given loudness is conveyed by vibrations of given extent, and, if the sound increases or diminishes in intensity, the extent of the vibrations will increase or diminish with it.

We conclude, then, that the loudness of a musical sound depends solely on the extent of excursion of the particles which constitute the conveying medium in the neighbourhood of our ears. This last condition is clearly essential, since a sound grows more and more feeble, the greater our distance from the point

where it is produced. This diminution of intensity with the increase of distance from the origin of sound is a direct consequence of the connection between loudness and extent of vibration. We have seen [§ 22] that the further an air particle is from the point where a sound is produced, the smaller will be the extent of the vibration into which it is thrown by the sonorous wave. Hence, as the sound advances, it will necessarily become feebler, provided always that the waves are permitted to spread out in all directions. If they are confined, say, in a tube, the intensity of the sound will not diminish with anything like the same rapidity. We have here the theory of message-pipes, which are used in large establishments to enable a conversation to be carried on between distant parts of a building. A whisper, inaudible to a person close to the speaker, may, by their means, be perfectly well heard by a listener at the other end of the tube.

26. We have next to enquire to what mechanical causes differences in the pitch of musical sounds are to be referred. Rough observation at once indicates the direction in which we must look. If we draw the point of a pencil along a rough surface, first slowly and then more quickly, the sound heard will be distinctly shriller the more rapid the movement of the pencil. As its point passes over the