97* LECTURE XXXI. 



as to occupy at any one time nearly the whole of a spherical surface. But it 

 is impossible that the whole of this surface should be affected in a similar man- 

 ner by any sound, originating from a vibration confined to a certain direc- 

 tion, since the particles behind the sounding body must be moving towards 

 the centre, whenever the particles before it are retreating from the centre; so 

 that in one half of the surface, the motions may be called retrograde or nega- 

 tive, while in the other they are direct or positive; consequently at the sides, 

 where these portions join, the motions can be neither positive nor negative, 

 and the particles must remain at rest; the motions must also become gra- 

 dually less and less sensible as they approach to the limit between the two 

 hemispheres. And this statement may be confirmed by an experiment on 

 the vibration of a body of which the motion is limited to a certain direction, 

 the sound being scarcely audible when the ear is in a direction precisely per^ 

 pendicular to that of the vibration. 



The sound thus diverging must always be spread through a part of a 

 spherical surface, because its velocity must be equal in every direction, so 

 that the impulse will always move forwards in a straight line passing through 

 the centre of the sphere, or the vibrating body. But when a hemispherical 

 pulse arrives at the surface of a plane solid obstacle, it is reflected, precisely 

 in the same manner as we have already seen that a wave of water is reflected, 

 and assumes the form of a pulse proceeding from a centre at an equal dis- 

 tance on the opposite side of the surface. This reflection, when it returns 

 back perpendicularly, constitutes what is commonly called an echo : but in 

 order that the echo may be heard distinctly, it is necessary that the reflect- 

 ing object be at a distance moderately great, otherwise the returnii^- sound 

 will be confused with the original one; and it must either have a smooth 

 surface, or consist of a number. of surfaces arranged in a suitable form ; thus 

 there is an echo not only from a distant wall or rock, but frequently from 

 , the trees in a wood, and sometimes, as it is said, even from a cloud. 



B (xmam^ h4^^' If ^ sound or a wave be reflected from a curved surface, the new direction 



' which it will assume may be determined, either from the condition that the 



velocity with which the impulse is transmitted must remain unaltered, or 



from the law of reflection, which requires that the direction of the reflected 



pulse or wave be such as to form an angle with the surface, equal to tliat 



