second.

68 metres.

In this time sound passes over twice 34, or

It follows that, if the reflecting wall be at a distance of 34 metres from the observer, one syllable when pronounced would take one-tenth of a second to be transmitted to the wall, and another tenth of a second to return to the observer; in all, therefore, one-fifth of a second. Therefore the echo would reach the ear of the observer after the syllable had been pronounced, and therefore separate and distinct. In this case the echo is called monosyllabic; it is called dissyllabic when two syllables can reach the observer distinctly. This happens when the wall is at twice the distance—that is to say, at a distance of about 68 metres. At a triple distance an echo may be trisyllabic, and so on. An echo may also be multiple, when the sound is reflected from two parallel walls, placed at a sufficient distance from each other. The most interesting case of this sort is certainly that of Simonetta, near Milan, a villa with two lateral wings. The report of a pistol is repeated as often as thirty-two times.

Examples of echoes are found almost everywhere. Their explanation is always easy; it seems therefore useless to dwell longer on the point.

CHAPTER III.

1. CHARACTERISTICS OF SOUND, and DIFFERENCE BETWEEN MUSICAL SOUND AND NOISE-2. LOUDNESS OF SOUND, AND THE VARIOUS CAUSES ON WHICH IT DEPENDS-3. PRINCIPLE OF THE SUPERPOSITION OF SOUNDS -4. SOUNDING-BOARDS AND RESONATORS.

1. ALL the different musical sounds in nature, whatever may be their origin, and by whatever means they may be propagated, may be distinguished from each other by three different qualities.

Firstly, By the greater or less energy by which they are produced, or by their loudness.

Secondly, By their pitch.

Thirdly, By a certain characteristic difference, by which even an almost unpractised ear easily distinguishes the sound of the violin from that of the flute, that of the pianoforte from that of the human voice, &c., even though these sounds are all of the same loudness and the same pitch. This characteristic difference is called "quality," "tone," or "timbre."

We ought, then, to examine on what these three different characteristics of sound depend. But before entering into this important matter, it is necessary to explain what is really meant by sound, when its qualities are spoken of.

A distinction is generally made in physics between sound and noise. Sound is the result of very regular vibrations which follow a law, complicated perhaps, but still a law. When the vibrations assume the simplest possible form— viz., that offered by the oscillations of the pendulum—the resulting sound is called simple, or a simple note; if the law be more complex, the sound is called compound, or a compound note. Noise, on the contrary, is a mixture of sounds collected together under no law, or under some law so complicated that the ear neither understands nor feels it. It follows that in most cases it is easy to distinguish the one from the other, but the limit between sound and noise is not always so clearly drawn. That which is a sound to one, is a noise to another, and vice versa. The confused sound produced by the movement of the waves of the sea is generally considered to be a noise; but an attentive and practised ear distinguishes determinate musical sounds, and finds a musical meaning. Thus the poets speak often, and not without reason, of the harmony of the waves. An orchestra, when the individual instrumentalists are tuning their instruments and preparing to play, produces a noise which may perhaps be considered as the line of demarcation between musical sound and noise. In fact, there really is a considerable amount of music in it, although perhaps somewhat irregular, and the general impression produced is by no means disagreeable.

A fine or practised ear is able to pick out a determinate note from the midst of a confused noise. Often those who

have not the habit are not aware of the presence of a more marked note in the midst of so many others; but with very little attention it becomes easy to recognise it.

In order to demonstrate this fact, use is made of a series of eight small boards, which are all of the same length and breadth, and which differ only in thickness. If one of these boards be allowed to fall on bench, most people would be unable to distinguish any note in the noise of the blow. But a very marked note is there. To make it, however, perfectly evident, the eight boards may be allowed to fall one after another. They are tuned so as to produce the musical scale, which will be perceived very distinctly. It follows that in the confused noise, produced by the fall of each board, there is a note, which at first is not easily perceived, but which is nevertheless sufficiently clear and distinct.

In the study which we have now commenced, I shall always consider musical sounds, or notes, and not noises, because the attempt to determine the quality of a noise would be meaningless. It has no definite pitch, loudness, or timbre.

2. This being so, let us now investigate what may be the causes on which the modification of the loudness of musical sounds depends, or by which it is produced. The loudness depends, in the first place, on the greater or less energy by which the sound is produced. Now, all the experiments described in the earlier part of this work show that greater energy produces a more marked vibra

tory movement in the particles of the sonorous body, in the sense that each vibrating particle traverses a longer space. The law of isochronism of vibrations shows that the duration is independent of the space passed over, within a certain approximation, which is generally considered sufficient. We will call the greatest space passed over by each particle the amplitude of its vibration, therefore we may say that the greater or less energy by which a sound is produced only influences the amplitude of the vibrations, and not their duration. In other words, the loudness of a sound is represented by the amplitude of the vibrations causing it.

The loudness of a sound depends also on the nature and density of the body which is to transmit it. In fact, a sounding body is heard in different degrees of loudness, according as the sound is transmitted by air, some other gas, water, or some other liquid or solid body. As to the density, it is enough for me to refer to the experiment described in the second chapter, of a bell under a glass receiver. When the air is completely exhausted, the sound can scarcely be heard, and the sound becomes stronger and stronger as the air is gradually allowed to enter the receiver. The loudness depends, again, on the distance of the sounding body. It is a general law of nature, confirmed by numerous experiments and by theory, that all those phenomena, whatever they may be, which have the property of being transmitted equally in all directions, must follow the inverse ratio of the square of the distance.