Eavttts Nonadiabatic Atmosphere. 519 



Now by passing to the limits the equation (18) can be readily 

 transformed into 



(23) g (z - z t ) = - 1> i— ^ - (Cp. - Cp l0 ) (T a - T.), 



and hence it is found by (22) and (23) that 



(24) - i (q\ - ql) - (Q, ~Q.) = - (Cp A - CpJ (T a - T.) f 



so that the departure of the specific heat from the adiabatic 

 value {Gp & — Gp 10 ) and the departure of the temperature from 

 the adiabatic rate (T a — T ) depend upon the circulation and the 

 radiation. Hence in the adiabatic atmosphere there is no 

 circulation and no radiation, and these occur only in the non- 

 adiabatic atmosphere. The one invariable term is the gravity 

 g(z—z ), and it may be broken up into three parts; one for 

 pressure g(z x —z ), one for circulation giz^ — z^), and one for 

 radiation g{z % — z^). The purpose is to compensate by mutual 

 adjustments such variations as occur so that the sum on a given 

 level shall always be the same g(z — z ). We have, therefore, 

 a large number of expressions which can be briefly summarized 

 in equivalent vertical columns. 



Adiabatic. Nonadiabatic. 



Gravity Pressure Circulation and Radiation 



(25) g(z-z ) ff-fa-K) + gt*-*,) +*7( 2 ,-zJ- 



— I qdq — I dQ. 



+ CCp T log Tdn. 



(28) g(z-z ) - *(rf_ri)_(Q_Q B ). 



rio 



(29) - Cp.(T.-T„)-= - Gp 10 (T.-T.) - (Cp-C P J (T a -T ). 



(30) - n.Cp.fT, - T ) = - n x CpJT, - T ) 



- Wl (C A - CpJ (T, - T ). 



1 T 1 T 



( 31 ) - m PP» T »« }o S Y = ~ M n ' C P" T ™ lo S "t 



- (Cp^-CpJ (T„-T ). 



It has been found by experience with the observed data in 

 the free atmosphere that the terms in (26), (27), (28) do not 

 balance, if one omits the radiation term (Q, — Q ). The grav- 

 ity, pressure, and circulation as computed from the observations 

 in cyclones, anticyclones, and in the general circulation, do not 

 conform, and all the efforts of meteorologists to make them do 

 so have been failures, or fictitious and improper solutions. The 



