556 RESEARCHES IN SOUND. 



noinenon. Indeed, it is difficult to conceive liow tlie results can be pro- 

 duced, even in a single instance, from a liocculent portion of atmosphere 

 in the prolongation of the axis of the trumpet, since a series of patches 

 of clouds of diiferent temperature and densities would tend to absorb or 

 stifle by repeated reflections a sound coming from their interior rather 

 than to transmit it to the ear of the observer. 



The question, therefore, remains to be answered : what is the cause 

 of the aerial echo ? As I have stated, it must in some way be connected 

 with the plane of the horizon. The only explanation which suggests 

 itself to me at present is that the spread of the sound which fills the 

 whole atmosphere from the zenith to the horizon with sound-waves 

 may continue their curvilinear direction until they strike the surface 

 of the water at such an angle and direction as to be reflected back to 

 the ear of the observer. In this case the echo would be heard from a 

 perfectly flat surface of water, and as different sound-rays would reach 

 the water at different distances and from different azimuths, they would 

 produce the prolonged character of the echo and its angular extent along 

 the horizon. 



While we do not advance this hypothesis as a final solution of the 

 question, we shall provisionally adopt it as a means of suggesting further 

 experiments in regard to this perplexing question at another season. 



Geneeal Conclusions. 



From all the experiments which have been made by the Light-House 

 Board in regard to the transmission of sound in free air and those de- 

 rived from other observations which can be fully relied upon, the follow- 

 ing conclusions may be considered established, subject however to such 

 further modification and extension as subsequent investigation may 

 seem to indicate: 



1. The audibility of sound at a distance (the state of the atmosphere 

 being constant) depends upon the character of the sound. The distance 

 through which a sound may be heard is governed by the pitch, the loud- 

 ness, and the quantity of sound. The pitch or frequency of the impulses 

 in a given time must not be too high, otherwise the amplitude of vibra- 

 tion will be too small to allow a sufficient quantity of air to.be put into 

 motion ; neither must the pitch be too low, for in this case the motion of 

 the atoms of air in the sound-wave will not be sufficiently rapid to con- 

 vey the impulse to a great distance. Again, the greater the loudness 

 of the sound, which depends upon the amplitude of the vibrations of the 

 sounding-body, the greater will be the distiince at which it will be heard. 

 And finally, the greater the quantity of sound, which depends upon the 

 magnitude of the vibrating surface, the greater will be the distance to 

 which it is audibly transmitted. • These results are derived from observa- 

 tions on the siren, the reed-trumpet, and the automatic buoy. The effect 

 of quantity of sound is shown in the fact that in sounding different in- 



