572 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



whence the available energy 



C p J (T - V) dm = C p { dx f (T - T) y.dz 



= M v = ip h gh -h. x 



2 h RT* VI 



\ ■ .(C) 



Using the approximate value 



"-'A* jr. 



we obtain 



v- V g - r m 



In this case the available kinetic energy for the unit of mass is 

 smaller in the ratio of 2 to 3 than in the system previously con- 

 sidered, if we substitute T * and 7\* therein instead of 7\* and 

 7\*. In this first approximation, this energy depends only on 

 the altitude and on the maximum horizontal difference of tempera- 

 ture and is independent of the length of the trough and therefore 

 also of the horizontal temperature gradient. 



The result is principally determined by the assumption that the 

 vertical diminution of temperature is that corresponding to neutral 

 equilibrium, as is shown in the following section. 



§(28) To find the location of the surfaces of equal entropy in a mass 

 of air when the pressure is constant throughout any level surface and 

 the temperature is a function of the length and a linear function of 

 the altitude. 



In the expression for the entropy 



5 = Constant + C p log T — R log />, 

 we put 





i ( T 



T = T- h '+^ (*-*) and p = p h [j 



where T h is a function of x only and p h is constant. The system 

 of curves of equal entropy in the xz plane is determined by the equa- 

 tion 



F (x, z) = n\og T h — (w — 1) log T = Constant 



