522 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



We choose an appropriate altitude for the column of air such 

 that the horizontal motion of the upper layer takes place in the 

 direction of the gradient — though this is not really important. 



The potential energy would diminish by the amount of work 

 done by the pressural forces, if there were no addition of heat. 

 The quantity of heat converted into work supplies that potential 

 energy which is converted into kinetic energy by motion in the 

 direction of the gradient. This increase of kinetic energy is con- 

 sumed by friction. 



For each kilogram of air that makes this complete circulation, 

 and during the interval of time occupied in so doing, we have the 

 quantity of heat added at P 2 , or below 



(T[-T 2 ) Q = C p 



The quantity of heat abstracted at p t or above 



(t - r 2 ) Q' - C p 



The quantity of heat converted into work 



Q-Q> = q=C p [T 2 - T[ - (r' 2 - rj ] 



Now we have 



Whence 



or 



and 



r 2 =T 2 -^h 



T i - T t 



g 



h 



T — - = T — r 



1 2 *2 x 1 ''l 



T 2 + *1 = T l + ^2 



q = C p (T, - 77 + r 2 - x[) 



C p T t 



I -Its 



Pi 



p 2 



l P 1 \ R / C P 



J 



(IV) 



As stated in §6 the work done on 1 kilogram of air by the pres- 

 sural forces in the stationary field along the path P t P 2 is C p (T t — 

 T{) and C p (z 2 — r! 2 ) along the path p 2 p v According to the assumed 

 conditions of <mr problem there is no active effective force and 



