302 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



the second degree, in u ; dQ= the heat imparted to the unit mass of 

 air during the time dt ; C, = specific heat of air under constant vol- 

 ume; C p = specific heat under constant pressure 



C P =C V +R 



Q v T G v G„ T G p 



By combining this last equation with (4a) we obtain 



*l-BT.°*.*=-±-™ («) 



Jt> C v dx 2 G V T dt 2 



which converts into the Laplacian equation when Q = 0. In this the 

 temperature variations of the air for rapid acoustic vibrations produced 

 by adiabatic compressions and expansions are considered, and the 

 velocity of propagation is therefore 



'-JbT.% 



For our purpose it will be more convenient to consider the pressure 

 variations as a consequence of the temperature variation snot as aeon- 

 sequence of the variable flow of heat. We therefore return to equation 

 (4a). 



III. WAVE OF TEMPERATURE. 



A progressive wave of temperature 



t — A sin (nt + nix) =A sin 2tt (*+?£\ .... (5) 

 causes a wave of pressure 



s = B sin (nt -f mx) ~) 



p- if ± I- (6) 



advancing in the same direction. 



= V is the velocity of the progress of both of these waves. The 

 vy 



phases of the waves are the same or opposite according as V is larger 

 or smaller than c. But V=e leads to an infinitely large value of B, a 

 result to which we must always come when in a frictionless medium 

 the period of the forced vibrations agrees with those of the free. 

 For the atmosphere we have 



l? __10333x9.80C 9Q7n 

 jK -T73xh29r =287 -°' 



