178 



DYNAMICAL THEORY OF SOUND 



figure takes after a time some such form as B*. The wave 

 becomes, so to speak, continually steeper in front, and slopes 

 more gradually in the rear, until a time arrives at which the 

 gradient at some point becomes infinite. After this stage the 

 analysis ceases to have any real meaning. 



Fig. 62. 



The adiabatic hypothesis leads to results of the same 

 general character. The reader will find no difficulty in verifying 

 the following statement. The formula (16) is replaced by 



and the velocity of propagation of a particular value of s is 



Tc(l+*)* (7 + 1) .................. (22) 



relative to the undisturbed medium, or 



in space. In the latter formula the particle-velocity is added 

 to the velocity of sound proper to the actual density, which is 

 on the adiabatic hypothesis dependent on the degree of con- 

 densation and consequent change of temperature. The general 

 conclusions are as before. 



* It is not very important here whether the coordinate x be supposed (as in 

 the previous part of this investigation) to refer to the undisturbed medium, or 

 to be an ordinary space-coordinate. In either case the tendency is the same. 



