302 THK MECHANICS OF THE EARTH's ATMOSPEERE. 



the secoud degree, in ?< ; dQ = the hear iiiiparted to the unit mass of 

 air during' the time dt ; 6',, = specific heat of air under constant vol- 

 ume; Cp = specific heat under constant pressure 



T = JK — 4- (} = '^ 4- S. 



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



li-RTj.^i=^-lR m 



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

 temperature variations of the air for rapid acoustic vibrations produced 

 by adiabatic compressions and expansions are considered, and the 

 velocity of propagation is therefore 





c = 



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

 variations as a consequence of the temperature variations not as a con- 

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

 (4a). 



III. WAVE OF TEMPERATURE. 



A progressive wave of temperature 



T = A sin {nt + mx) =A sin 2;r /^-^+^^ .... (5) 

 causes ;i wave of pressure 



€ = Bsin [nt + mx) ] 



U \ (^> 



advancing in the same direction. 



y—y is the velocity of the progress of both of these waves. The 



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

 or smaller than c. But V=c 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 



' P _1 0333x0.806 _^g- Q 

 273x1.293 " ' ' 



I 



