ADDITIONS TO THE THIRD EDITION. 



BOOK VIII. 



ACOUSTICS. 



CHAPTER III. 

 SOUND. 



The Velocity of Sound in Water. 



THE Science of which the history is narrated in this Book has for 

 its objects, the minute Vibrations of the parts of bodies such as 

 those by which Sounds are produced, and the properties of Sounds. 

 The Vibrations of bodies are the result of a certain tension of their 

 structure which we term Elasticity. The Elasticity determines the rate 

 of Vibration : the rate of Vibration determines the audible note : the 

 Elasticity determines also the velocity with which the vibration travels 

 through the substance. These points of the subject, Elasticity, Rate 

 of Vibration, Velocity of Propagation, Audible Note, are connected in 

 each substance, and are different in different substances. 



In the history of this Science, considered as tending to a satisfactory 

 general theory, the Problems which have obviously offered themselves 

 were, to explain the properties of Sounds by the relations of their 

 constituent vibrations ; and to explain the existence of vibrations by 

 the elasticity of the substances in which they occurred : as in Optics, 

 philosophers have explained the phenomenon of light and colors by 

 the Undulatory Theory, and are still engaged in explaining the requi- 

 site modulations by means of the elasticity of the Ether. But the 

 Undulatory Theory of Sound was seen to be true at an early period 

 of the Science : and the explanation, in a general way at least, of all 

 kinds of such undulations by means of the elasticity of the vibrating 

 substances has been performed by a series of mathematicians of whom 

 I have given an account in this Book. Hence the points of the sub- 

 ject already mentioned (Elasticity, Vibrations and their Propagations, 



