644 Mr. J. H. Jeans on the 



Equation (16) now becomes 



ip(t- xa ) - lafL 

 <p = Ae ^ "Vv'e «Vv (18) 



It appears from this that the value of 7 deduced from expe- 

 riments on the velocity of sound will not be the true 7, but. 

 will be «y /a 2 



This, however, only differs from 7 by terms depending on 

 the square of p/^(E). The effect of the first order terms is 

 the introduction of a real exponential term into the expression 

 for (/>, corresponding physically to a damping of the sound.. 

 The amount of the damping, as also of that due to viscosity, is 

 proportional to jo 2 ; so that the effect of the " lag " in the value 

 of F may be regarded as an apparent increase in the coefficient 

 of viscosity. 



Lord Rayleigh * shows that corresponding to a small 

 coefficient of viscosity /*, the coefficient of decay (measured 

 per unit length along the path of the wave) is 



2np 2 



•6 P ^ 



while the coefficient of decay due io the "lag" in F has been 

 shown to be 



pY(E) 



3yV X (E)((l+/(B)f 



Thus the apparent value of fx will be 



f ^(E) 1 



V + 2m % (E)(1+/(E))*J (19) 



Since a only differs from unity by terms depending on the 

 square of _p/%(E), we see that at first the apparent value of 7 

 remains unaltered, being equal to the true value. As soon as 

 squares of #>/%(E) become appreciable, the apparent value of 

 7 begins to increase, and ultimately, when jt>/%(E) becomes 

 infinite, the apparent value of 7 will be If. 



Hie Lag in Rotatory Energy in Air. 



§ 7. As an illustration of the foregoing theory, let us 

 examine the effect of the lag in the rotation of molecules of 

 air, the molecule being regarded for the purpose as a rigid 

 body of which the shape is that of a solid ot revolution. The 

 quantity F is now the energy of the rotation of the molecule. 



* < Theory of Sound,' § 346, equation (7). 



