224 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



as in the case of the dew-point curve) one can by a simple method of 

 construction cover the plane of coordinates with a series of such adi- 

 abatics, each of which, with reference to its neighbor, shows a constant 

 difference in the entropy by the amount AS. 



B. THE RAIN STAGE. 



For the rain stage, as already stated, there obtains the equation of 

 mixture 



M=l + x + x', 



where x' is in general very small, but x, except in exceptional cases, 

 can only diminish. The equatiou of elasticity, on the other hand, is 



P = — + e (0) 



where e is the vapor pressure, which in this stage, that is to say in the 

 condition of saturation, depends simply and alone on the temperature 

 T. Moreover, there obtains also the equation developed as a limiting 

 condition in Art. 3 above, viz : 



e= (7) 



This last formula shows at once the above suggested fact, that here we 

 have in general to do with changes that are reversible to only a very 

 limited extent. If, for instance, T is put constant while v increases, 

 then the equation can only be fulfilled when # increases. This same 

 holds good (because c increases rapidly with increasing T) when v is 

 kept constant and T increases, or, as expressed still more generally, 

 it holds good for all changes in condition that are represented in the 

 diagram by a movement toward the concave side of the dew-point curve. 



But an increase of a? is only to a very limited extent possible in gen- 

 eral in the free atmosphere, namely, only when liquid water, in addi- 

 tion to the vapor, is suspended in the air, and only so long as this 

 store of liquid holds out. The latter in most cases is soon exhausted, 

 since it is precisely the liquid drops of water that fail as rain as soon 

 as their mass becomes considerable. 



Therefore in the rain-stage, changes of condition toward the concave 

 side of the dew-point curve are possible only to a very limited extent 

 and only until the condition of supersaturation comes to its end and 



the quantity of heat communicated to the air. Therefore au increase of the quotient 



Q 



-j corresponds to a diminution of the entropy according to the definition of entropy 



as given hy Clausius (see Clausius's Collected Memoirs, Brunswick, 1884) Memoir 

 IV > P a S° 140, and Memoir vi, page 276. 



