Tlieoretical Evaluation of y . 643 



In accordance with this we find, on putting p=yo in (14), 

 that we obtain V = If. 



The Propagation of Sound. 



§ 6. Independently of any assumptions about the internal 

 energy of the molecules, the equation of propagation of sound 

 is* 



di l 6p ~dx^ 



where cf> is the velocity-potential, and 5, as before, denotes 

 excess above mean value. 

 Assuming (f} = <j> 1 e i P t , we find 



(' + ?£)*-* 



•or, by equation (12), 



<>+££)*-« <w 



The solution for a wave travelling along the positive axis of 



.i: is 



^=A«*(*-?), (16) 



where l- r ^. 



This gives Y = a^T, 



where a U the Newtonian velocity of sound. 



The difference between this solution and that usually found 

 lies in the occurrence of terms in //)/;c(E). From equation 

 (14) we obtain 



r-*=y-*(«-»/3), (17) 



where 



--i r p vr /(E) . ( /(E))' i 



"~ lx(E)J L3r(l+/(E))»" 1 "67*(1+/(E))*J' 



/(E) 



/3= 



x (E)-iy(l+f(E)r 



as far as squares o£p/%(E). 



The functions x( E ), /( E ) will be positive (cf § 8), so 

 that as far as terms in p 2 , (3 will always be positive, and a less 

 than unity. 



* Rayleigh, ' Theory of Sound,' § 244. 



