SECT. XVI. REFLECTION OF SOUND ECHOES. 137 



the case, there would be no sound, because the inertia of the 

 receding waves of air would destroy the equal and opposite 

 inertia of those advancing ; whence it may be concluded that the 

 intensity of sound diminishes inversely as the square of the dis- 

 tance from its origin. In a tube, however, the force of sound 

 does not decay as in open air, unless perhaps by friction against 

 the sides. M. Biot found, from a number of highly-interesting 

 experiments made on the pipes of the aqueducts in Paris, that a 

 continued conversation could be carried on in the lowest possible 

 whisper through a cylindrical tube about 3120 feet long, the 

 time of transmission through that space being 2'79 seconds. In 

 most cases sound diverges in all directions so as to occupy at 

 any one time a spherical surface ; but Dr. Young has shown 

 that there are exceptions, as, for example, when a flat surface 

 vibrates only in one direction. The sound is then most intense 

 when the ear is at right angles to the surface, whereas it is 

 scarcely audible in a direction precisely perpendicular to its edge. 

 In this case it is impossible that the whole of the surrounding 

 air can be affected in the same manner, since the particles behind 

 the sounding surface must be moving towards it whenever the 

 particles before it are retreating. Hence in one half of the sur- 

 rounding sphere of air its motions are retrograde, while in the 

 other half they are direct ; consequently, at the edges where 

 these two portions meet, the motions of the air will neither be 

 retrograde nor direct, and therefore it must be at rest. 



It appears, from theory as well as daily experience, that sound 

 is capable of reflection from surfaces (N. 179) according to the 

 same laws as light. Indeed any one who has observed the re- 

 flection of the waves from a wall on the side of a river, after the 

 passage of a steam-boat, will have a perfect idea of the reflection 

 of sound and of light. As every substance in nature is more or 

 less elastic, it may be agitated according to its own law by the 

 impulse of a mass of undulating air ; and reciprocally the surface 

 by its reaction will communicate its undulations back again 

 into the air. Such reflections produce echoes ; and as a series of 

 them may take place between two or more obstacles, each will 

 cause an echo of the original sound, growing fainter and fainter 

 till it dies away ; because sound, like light, is weakened by re- 

 flection. Should the reflecting surface be concave towards a 

 person, the sound will converge towards him with increased in- 



