230 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



Since, however, on the other hand, the dew-point cnrves descend 

 more rapidly than the isotherms toward the positive side of the axis 



of abscissas, therefore theadiabatics must 

 experience a bend at the dew-point curve 

 in the manner shown in the ligure 30. 

 In this S /S presents a part of a dew-point 

 curve; A A, A' A', etc., adiabatics; T T, 

 T T', etc., isotherms. 



The differential equation of the pseudo- 

 adiabatic can be treated in a similar man- 

 ner to that of the adiabatic, but whereas 

 in the adiabatic the integration was p08- 

 &iblc even when the connection of the independent variables was not 

 ■exidicitly given, on the other hand this is not the case for the pseudo- 

 adiabatic. That is to say, instead of equation (10) we have for the 

 pseudo-adiabatic the following: 



^i^.log ; -f c, log :+ / - +-i J- ' '=0, 



or, i)referably, 



Fig. 30. 



AR,\osJ+{c„+x, 



loi 



Ty j, 



1) 



T 



' T, 



=0 



(15) 



If therefore the point (1) is at once located in the dew point curve 

 then will Xi = Xg,; and if then we consider the point (2) alone as vari- 

 able, that is to say, omit the subscript index 2 entirely, we obtain 



(2) 



AEAlog^^+ ic + .r„) log ^-P'- 



— x) dT ,rr x^ri 



= 



(i) 



or after farther modifications 



(IG) 



AR^logv + (e,, + a-J log T+ 



(2) 



xr_ n 

 T J 



{x,-x) dT 



= C 



(1) 



(1-) 



We omit the development of formula? entirely analogous to equations 

 (11) etc., and it suffices to say that in them all the integral occurs as a 

 correcting term. Happily its value remains always within very moderate 

 limits, so that in the c()m])utation one can be satisfied with more or less 

 perfect approximations. One can therefore omit the further considera- 

 tion of the pseudo-adiabatic process and only call attention to the fact 

 that it follows from equation (IG) that the pseudo-adiabatic curve de- 

 scends more rapidly than the adiabatic as was already pointed out 

 above. For since when rj > ^i we always have dT <. therefore the 

 definite integral that still occurs in the equation has always a negative 



