after any blow, as of a hammer, the pitch of which (see Art. 496) depends upon the number of pulses or repetitions of a sound produced there in a given time by the returns from its walls. The velocity of sound being uniform, this number must depend on the size of the apartment.

500. There is a curious effect of echo which both illustrates the nature of the phenomenon, and proves that a tone or musical sound is merely a repetition of pulses following each other very quickly and at regular intervals. A sharp sound, such as the blow of a hammer, occurring near the end of an iron railing, formed of square bars, is echoed to a corresponding place on the other side by every bar in it; and as the echoes do not return all at once, but in regular succession according to the increasing distances of the bars, the consequent regular succession of slight pulses, with uniform and small intervals, affects the ear, not as the echo of a single blow, but as a continued musical tone, the pitch of which depends on the distance of the bars from each other. The writer of this had observed, in passing on horseback along a particular portion of road, where there were first a length of plane wall and then two lengths of wooden paling with rails or bars overlapping at the edges, and the rails of one length being narrower than those of the other-that as he neared the palings there was a clear echo of the horse's cantering feet, and also a ringing sound for every step of the horse. He at first concluded that the road there was singularly hard, although that did not appear, and he slackened the horse's pace, until observing one day that the ringing sound was of a different pitch near the two pieces of paling, and such as to correspond with the different width of the rails, the true explanation occurred to him that the sound was an echo of the nature above described.

501. That an echo may be perfect, the reflecting surface must be smooth, and of a regular form; for a sound-wave rebounds according to the same law as an elastic ball, such as a billiard ball rebounding from any surface on which it impinges. When a billiard ball strikes a side of the billiard-table directly, or perpendicularly, it returns or rebounds exactly along the line of its approach; but when it strikes obliquely, it goes off on the other side, the line of its rebound making the same angle with the side of the table as the line of its approach. This law of impact, which holds equally for liquid waves, for aërial waves, and for rays or waves of light, is expressed shortly in these words: "the angle of reflection is equal to the angle of incidence," -and the velocity of the reflected sound is equal to that of the

Concentration of Sound by Reflection.

331

waves which impinge on the reflecting surface (Art. 495). A little consideration of this law and of the annexed figure (137), will show that a regular concave surface, such as

eg, may concentrate sound, and bring all the rays which fall upon it, as from a b c d, to a common centre or focus, f, and so produce there a very powerful effect.

If a watch is placed within the focus, f, the ticking will be plainly heard in the space within which the rays, a b c d, are reflected, but not at

a

f

Fig. 137.

a little distance on either side. A similar reflector placed at some distance in front of this, will receive the parallel rays of sound and cause them to converge to a focus. The ticking of the watch may be heard at this focus by the ear, or by means of an ear trumpet, as distinctly as at the focus, f.

On the other hand, an irregular surface will reflect impinging airpulses in different directions, causing a mutual interference in place of mutual concentration. We thus see the reason why an echo is much less perfect from the front of a house which has windows and doors, than from the plane gable, or any plane wall of the same magnitude—and why the resonance of a room is so irregular and indistinct, when the room contains curtains, carpets, and other furniture, presenting numerous irregular surfaces, or when there is a crowded assembly. Halls for music have generally plane walls. Theatres for the drama, again, have boundaries broken in all directions by rows of boxes, and various ornaments, in order that distinct echoes may not mix with a speaker's words.

The concentration of sound by concave or hollow surfaces produces curious effects both in nature and in art.

There are remarkable situations, as at the Falls of Niagara, where the sound from a cascade is concentrated by the surfaces of a neighbouring cave so completely, that a person accidentally bringing his ear into the focus, is suddenly astounded, as if all nature were crashing around him. A chair placed in the cave, so that a person sitting down in it has his ear in the focus, insures the success of the intended surprise.

502. The centre of a circle is the focus in which sound issuing from it is again collected after reflection: hence the powerful echo near the centre of a round apartment. An oval has two centres or

332

b

Laws regulating the Reflection of Sound.

C

foci-one towards each end, as at a and b (fig. 138)—and the nature of the curve is such, that sound, or light, or heat, spreading around from either of the foci, as a, by obeying the law of reflection above stated, is all directed from the various points, as at c, d, e, &c., to the other focus, b. Hence a person whispering at one focus of an oval room d may be heard quite distinctly at the other focus, although he may not be heard by persons placed anywhere else. Such a room might be called a whispering gallery, as whispers would be thus conveyed and heard. Concave surfaces facing each other, as two alcoves in a garden, or covered recesses on opposite sides of a street or bridge, will enable persons seated in their foci, to converse by whispers across louder noises in the space between, and without being themselves overheard in that space.

e

Fig. 138.

As an illustration of this, it may be stated that the stone recesses of old Westminster Bridge were semidomes exactly opposite to each other, and so accurately constructed that a person whispering in the focus, A, of one of these recesses (see fig. 139), could be distinctly heard by another placed in the focus, B, of the opposite recess. The lines drawn from a represent the directions in which the sonorous vibrations were reflected so as to be concentrated at B.

A

B

Sound is reflected from the earth. Persons who have ascended in balloons have been surprised at the distinctness with which voices and the sounds made by animals have been heard at a considerable elevation.

The plane surface of a smooth wall prevents the lateral spreading and dissipation of sound, although only on one side. Thus persons far apart may converse along a smooth wall. For a similar reason Fig. 139. the smooth surface of water powerfully reflects sound, The barking of dogs, or the clear voice of a street-crier, in a town situated on the border of a lake, may be heard across the water on a calm evening at a distance of several miles, as the writer one evening perceived near Southampton. The sound of bells, of course, is audible much farther, and in the stillness of night, even the splashing oars of a boat will announce by a reflection of the sound its approach to persons waiting at a great distance.

Whispering Galleries. Ear-trumpet.

E

B

333 503. If a wall be curved inwards, or concave, it not only prevents the spreading outwards of any sound which passes along it, but is constantly condensing the sound waves by driving them from the external part inwards. Hence, in a circular space, such as a gallery under a dome, as in St. Paul's Cathedral, persons close to the wall may whisper to each other and be heard at great distances, the sound being concentrated at a point exactly opposite to that at which it issues from the mouth of the speaker. Thus, in fig. 140, the interior of the dome or whispering gallery is re- C presented by the circle, but it is, in fact, a hollow hemisphere, adapted to reflect sound in all directions, and concentrate them on a single point. Thus a sound emitted at A reaches the concave surface at B, and is reflected to C. In the same manner the sonorous vibrations which go from A to D and F, are reflected respectively to E and G, and from these points by a second reflection to C. All intermediate rays which reach the interior of the dome are carried by reflection to C, and thus it happens that if a door at A be shut with violence, the sound at C resembles thunder in its impression on the ear. 504. The Ear-trumpet (fig. 141) is a tube wide at one end, A, where the sound enters, and narrow

at the other, B, where the ear is applied its sides are so curved that, according to the laws of reflection, any sound which enters is condensed towards the narrow end. Considering the sonorous vibrations to enter by the lines C; D, E, they are reflected from

BO

Fig. 140.

the points F, G, H, and are concentrated in the smaller end of the tube, B. By using such an instrument, persons who have had their sense of hearing impaired, may obtain from it such aid to the ear, as spectacles give to the eye.

The concave hand held behind the ear helps to concentrate the sound, as is illustrated by almost any ordinary assembly of listeners,

particularly if the speaker has a weak voice or is distant. A good substitute for the hand is a small cup of wood or other light material and two such cups-or ear-shells, as they may be calledjoined by an elastic wire, might be very advantageously worn by deaf persons. The writer of this once tested the value of the contrivance by experiment, and the result was very satisfactory.

The various forms of ear-trumpet act more powerfully than this combination, particularly the long flexible tube with a small trumpetopening to be held near the mouth of the speaker, while the hearer places the other end to his ear; but all these occupy inconveniently the hands of one or of both parties, while the ear-shells no more incommode a person using them than a pair of spectacles.

505. A notorious instance of a sound-collecting surface was the Ear of Dionysius, in the dungeons of Syracuse; the roof and walls of the prison are said to have been so formed as to collect the words and even whispers of the unhappy prisoners, and to direct them along a hidden conduit to where the tyrant sat listening. The wide-spread sail of a ship, rendered concave by the breeze, is also a good collector of sound. It happened on board a ship sailing south in the Atlantic, towards Rio de Janeiro, while out of sight of land, that one day, persons on the deck, when near a particular part of it, thought they heard distinctly the sound of bells. All were attracted to listen, and the phenomenon was mysterious. Weeks afterwards it was ascertained that, at the time of observation, the bells of the city of St. Salvador, on the Brazilian coast, had been ringing on the occasion of a festival; their sound, therefore, favoured by the wind at the time, had travelled over at least 100 miles of smooth water, and had been condensed by the concave sail to a focus on the deck of the vessel where it was listened to. It appears from this that a great concave might be constructed having a like relation to sound that a telescope has to light. A gentleman while sitting, on the 18th of June, 1815, by the wall of his garden, on the heights near Dover, believed that he heard distinctly the firing of the cannon at the great battle of Waterloo then raging in Belgium. The perception of sound may in this case have been partly aided by reflection. In remote country places there is reason to believe that the reflection of distant sounds from the walls of lonely and uninhabited houses has sometimes led to the report that they were haunted.

506. Apart from ary reflection of the sound-waves, sounds may be heard at considerable distances when the temperature and other atmospheric conditions are favourable. Peschel states that the