363-366] Propagation of Sound 307 



from which we find that 



2 K /,. 27-7T 



25/3 V 800 1*) ' 



so that the apparent viscosity would be equal to the true viscosity increased 

 in the ratio 



800 



Molecules of more general type. 



365. This completes the actual calculation for loaded spheres. Clearly 

 the result for. any other type of molecule would be similar. To illustrate, 

 let us consider an ideal diatomic molecule formed by placing two homo- 

 geneous spheres each of radius b, in contact. The value of k 2 , the square of 

 the radius of gyration, is now ^b 2 , while r 2 , the square of the distance from 

 the centre of gravity to the point at which a normal to the surface meets the 

 axis, is b 2 . Substituting these values, expression (742) becomes 



727^ 

 ^ 5 800 ' 



27-7T 



We ought, however, to correct the multiplying factor , this correction 



800 



being necessitated by the considerations explained in 109. To obtain an 

 estimate of the order of magnitude of the effect under discussion, we may 

 neglect this correction altogether, so that expression (742) must simply be 

 replaced by the quantity already found, of which the value is 1*146. 



The damping of sound due to the "lag" in the adjustment of sound is 

 therefore about one-seventh as great as that caused by viscosity. 



366. There is less difficulty in forming an estimate of the effect of this 

 " lag " upon the velocity of propagation of sound. 



flfY\ 



As far as squares of - , equation (738) gives the value 



= P A _ JL fo 48 p 2 



9 V\ 35/Sz/VK 1225 /9V* " 



so that the exponential e i(pt ~ qx} becomes 



2ff 2 . r x / 48 p* ~ 



The velocity of propagation, corrected as far as squares of the small 

 quantity, is therefore 



/ 48 p* \ 



I h T225/3V(J' 



202 



