228 THE MECHANICS OF THE EaRTH'S ATMOSPHERE. 



From these two equations we see, first of all, that the pseudo-adia- 

 bat descends more rapidly than the adiabat. Since for o*v>0 we always 

 have dTKO and since moreover x < x ai therefore the absolute value of 

 dT in the case of pseudo-adiabatic expansion must be larger than for 

 adiabatic; that is to say, the temperature must sink more rapidly when 

 all the condensed water is immediately discharged than when it re- 

 mains still suspended. 



Furthermore, both curves must sink more rapidly than the dew-point 

 curve, or, in other words, for dv>0 we must always have dx<fi. This 

 follows directly from the circumstance that in expansion along the dew- 

 point curve heat is to be added as also is shown from the manner in 

 which the adiabatics of the dry stage intersect this curve. On the 

 other hand, changes of condition with increase of heat are always 

 represented by curves that descend less rapidly toward the axis of 

 abscissas than do the adiabatics. 



Therefore in the expansion of air the adiabatics depart from the dew- 

 point curve toward the axis of abscissas and therefore x diminishes. 



The equation (8) is easily integrated and thus gives the following 

 equation of condition for the adiabat : 



AR,log^+(c v +x a )logT?+ x f 2 - x p=() . . . .(10) 



or if v is expressed in terms of p, e, and T with the help of the equation 

 of elasticity ; 



AR K log^+(c*+* a ) 16g5+5?-^=0 . • • (11) 



i>2 — C2 J-l -Li -Ll 



or finally by consideration of equation (7) and by the substitution of 

 the corresponding values of X\ and x 2 ; 



A^log^+K+^log^+|^-|^) 2 =0 . . (12) 

 or 



^■o g ^ +( o, + .^,o^; ;+ |[^^ r2Y ^ ) ].o . (1 3) 



If we consider the final condition as variable and corresponding to this 

 drop the subscript index 2 then the equations become the following : 



00 f 



AR K logv^(c v +x a )\ogT+^=C - (10a) 



ICY 



— AR, K \og (])-e) + (c p +x a )\og T+- T = G .... (11a) 



AB A log«+(c 1( +* a )logT+-g^2=C (12a) 



-ARJog (p-e)+(c p +x a ) log T+H ■ T **- e ) = G ' ' (13rt) 



