360-363] Propagation of Sound 305 



This is simply Laplace's formula, since 7 = f for loaded spheres. In fact 

 iu supposing the left-hand member of equation (734) to be very great, we 

 assume that the ratio of the energies adjusts itself with a rapidity which is 

 great compared with the rate of wave motion an assumption which can be 

 fulfilled either by the greatness of /3i>\/K or the smallness of p. 



362. If the left-hand member of equation (734) is very small, the 

 equation reduces to 



p 

 q 



and this becomes identical with Laplace's formula if 7 = If. The smallness 



^QlJ \/K 



of the term - - can be effected either by the smallness of fSv VK or by 



the greatness of p. The energy here adjusts itself slowly in comparison with 

 the rate of passage of the sound, so that the variations in the translational 

 energy are too rapid to affect the rotational energy at all. Here, then, 

 we have a gas of which the molecules have five degrees of freedom, and yet 

 from experiments on the velocity of sound we should deduce the value 7= If. 

 This is the possibility to which it was necessary to refer in Chapter X., 

 although a brief calculation shewed that it was not likely to occur in nature. 



363. Let us write V for Laplace's value of the velocity of sound, so that 



then equation (734) becomes 



p 



so that 



1 , a 



If TS 7^ is small, we have as far as the first order of small quantities 

 pv VK 



so that the exponential 



e Hpt qx) 



may be replaced by 



20 



