6. When a sonorous wave strikes against an obstacle, it exhibits the same phenomena as an elastic body striking an elastic wall. The sonorous wave is reflected in such a way that the angle of incidence is equal to the angle of reflection. The angle formed by the ray of sound which impinges on the wall, with the perpendicular to the wall drawn from the point at which it impinges, is called the angle of incidence. The angle formed by this perpendicular with the reflected ray of sound is called the angle of reflection. By means of this law the direction taken by a ray of sound after its reflection can always be perfectly determined.

An innumerable quantity of phenomena of reflection exist. The two most distinct forms are resonance and echo. When a sound is produced in a closed chamber, the sonorous waves are propagated in every direction, strike against the walls of the chamber, and are sent back from them by reflection, and can be repeated several times from one wall to another. An observer within the chamber will hear not only the sound which comes direct from the sounding body, but will also receive the vibrations which come by reflection from all parts of the chamber.

The sound is thus remarkably strengthened, and this is the reason why it is easier to hear and to make one's self heard in a closed room than in an open space.

Evidently in such a case the sound will not only return strengthened, but even altered; because the reflections from the walls, on account of the low velocity of sound, require some time, and prolong the sound more or less considerably. If the chamber be small, this prolongation is not considerable and can be neglected; but when the chamber assumes large proportions—as, for example, in a theatre each note spoken, sung, or played, may be considerably prolonged: it is confounded with the next note, and this phenomenon of resonance may become extremely troublesome unless it be remedied. This happens in all large, enclosed, empty places, where reflection takes place freely. There is only one way to prevent it, which consists in breaking up the large walls. The seats of a theatre, the decorations between them, the galleries, even the

hangings, serve not merely for the accommodation of the spectators and for the internal beauty of the theatre, but also fill an even more important office-viz., that of preventing the disagreeable resonance of the place. It is one of the most difficult problems for an architect to construct a room on proper acoustic principles-that is to say, a room in which sound shall be considerably strengthened without degenerating into resonance, and it may be said that up to the present time this problem has been solved in very few theatres in a satisfactory way.

The reflection of sound has been utilised in various ways; nature and art have combined to solve some problems not deficient in interest. The celebrated "ear of Dionysius" is well known; it is a sort of hole excavated in the rocks near Syracuse, where the least sound is transformed into a deafening roar. The great dome of St Paul's Cathedral in London is so constructed that two persons at opposite points of the internal gallery, placed in the drum of the dome, can talk together in a mere whisper. The sound is transmitted from one to the other by successive reflections along the curve of the dome. Similar phenomena are often met with under the large arches of bridges, viaducts, &c.; and there was a period when problems of this nature were much sought after, and often solved, by architects. It is for this reason that whispering - galleries, speaking - pipes, &c., are so often met with in old houses.

An elegant mode of demonstrating the reflection of

sound is by the use of two parabolic reflectors MN M'N' (fig. 18), placed one opposite the other in such a way that their centres shall be on the straight line AA'. Placing a sounding body at a particular point F, called the focus of the reflector MN, the sound-wave strikes against the reflector, is driven back thence by reflection on to the second

reflector, and by it is concentrated on to its own focus F; that is to say, the ray FC is reflected in the direction CC, and by a second reflection along C'F'. Each of the remaining rays is reflected in the same way, and they all

concentrate at F. An ear placed at this point distinctly perceives a very slight sound made at F, by means of the reflectors and of the double reflection which they give, whilst without the mirrors it would only be possible to perceive the ray FF', which is much too feeble by itself to excite a sufficiently strong sensation.

Another case of multiple reflection is met with in the famous Baptistry at Pisa, a building surmounted by a narrow cupola of peculiar form. Placing one's self under the cupola inside the Baptistry and singing a note, the sound is prolonged for a very considerable time; therefore by singing three or four notes in cadence, by the effect of the reflections, a most beautiful chord is heard, as if from an organ, which is considerably prolonged.

7. The best understood of all the cases of reflection is that which is called echo. In order that an echo may be produced, it is necessary that there should be, at some distance from the observer, a large vertical wall, or some other object—as, for example, a rock-which roughly resembles a wall. A sound sent by the observer towards the wall returns from it by reflection, and if the distance passed over by the sound be sufficiently great, the reflected sound will be clearly separated from the sound uttered. The velocity of sound being, at our ordinary temperature, about 340 metres per second, the tenth of this is 34 metres. But experiment shows that about five syllables are pronounced in one second, therefore the time necessary to pronounce one syllable is one-fifth of a