230 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



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

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



of abscissas, therefore the adiabatics must 

 experience a bend at the dew-point curve 

 in the manner shown in the figure 30. 

 In this 8 # 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 pos- 

 sible even when the connection of the independent variables was not 

 explicitly 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: 



A£ A log + c v log ,., + / T + T - - T =0, 



Fig. 30. 



or, preferably, 



v T 



A R x log - 2 + {c v +x a ) log ; 



I 



W (x a —x)AT x 2 r 2 x-jYi 



=0 



(15) 



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

 then will x x = # a ; and if then we consider the point (2) alone as vari- 

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



r-'i 

 A 22 A log- + (o, + x a ) log T - J 



(i) 



or after further modifications 



(X a — X) AT XT X a Y\ 



T ^T Ti ~ 



(16) 



AR K \ogv + (c v + x a )\ogT+ 



xr 

 T 



(2) 



(1) 



x) AT 



= C 



. (17) 



We omit the development of formula} entirely analogous to equations 

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

 correcting term. Happily its value remains always within very moderate 

 limits, so that iu the computation 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 (16) that the pseudo-adiabatic curve de- 

 scends more rapidly than the adiabatic as was already pointed out 

 above. For since when v 2 >.«?i we always have AT < therefore the 

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



