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 thau the adiabat. Since for rfr>0 we always 

 have dT<. and since moreover x < .r„, therefore the absolute value of 

 dT in the case of pseudoadiabatic 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 susi)ended. 



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

 curve, or, in other words, for dv'^Q we must always have dx<.0. This 

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

 l^oint 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 (S) is easily integrated and thus gives the following 

 equation of condition for the adiabat : 



AR^\og':'Mc,-V-r,)\og^'+%'-''p=^^ . • . .(10) 



Vx ±1 ±2 J^l 



or if V is expressed in terms of 2h e, and T with the help of the equation 

 of elasticity ; 



AE.logff-;^ + (.V+^'JlogJ^+^^-'P=0 . . . (11) 



pi — €2 ±1 -L2 -LI 



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

 the corresponding values of j^i and X2', 



^z.,iog;;^+(,+.jiog|4^-|f^=o . . 



(12) 



or 



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

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



TV 



AR,\ogv + {c,.+x„)\ogT+rp=C - (lOrt) 



XV 



.-AR^\og {2y-e) + {c,.+x,)\og T+^=C .... (Ua) 



AR,]ogv + {c,-^x,)logT+-£'j,2=C (12«) 



-AR,\og{p-e)-^{c^,^x^,) \og T J^^IJ^ ' y^^j^^ = C . . (13rO 



