568 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5I 



meters this quantity is 102 and the difference between the true 

 average temperature T* and the barometric average temperature 

 can only attain 2 Centigrade in extreme cases. For smaller values 

 of h the T* — is also smaller. We can therefore here substitute 

 r* for the corresponding O and obtain 



r / \ r 2 * 2 /v : 



2 g B h \ Rj \2T 



C p j(T 2 



Finally by writing 



(T*) 2 = T* T*, 

 T* - T? 



<p* 



= T, 



B ?h Jk,. = Z M (approximately) 

 Rl * 



we obtain the following expression for the available kinetic energy, 



P J 2 2 B 2 



V is independent of the constants R and C p that characterize the 

 physical properties of the gas. For a given value of B this expression 

 for the available kinetic energy is greatest when B t = B 2 = IB/where- 

 fore when the chambers 1 and 2 have equal volumes then the velocity 

 is 



V-\V^r (I) 



This approximate method suffices completely for the cases above 

 given as examples of our first method of computation (see section 

 24). Since in the limiting case neutral equilibrium becomes stable 

 equilibrium we may also apply this method of computation to 

 those examples also. In the computation of T we may substitute 

 \ (T + T h ) for the average temperature. The values of V com- 

 puted by the approximate formula for those four examples now 

 become respectively 



Example Velocity 



m. p. s. 



(0 12.3 



(2) 17-4 



(3) 18.6 



(4) 26.3 



