MOVEMENTS OF ATMOSPHERE— GULDBERG AND MOHN 131 



Substituting the values of d U and of p d V in equation (i)and 

 introducing the values given by the equations mentioned, we shall 

 find 



= Cj d x 4- £ c' d x + (273 + x) d I 2? * + y ) 

 .4 a rf (p - f) 



-T^^H (5) 



Expressing the initial values by the subscript index o, we shall 

 by integration and introducing numerical values find 



/ Po-fo\ f 273 + r ] 



log ( f^f) = 3.341 [1 + 4210 £] log [ —- \ 



1 + r ~ 273 + x J ' * • 



+ 6.291 



*0 



273 



(6) 



From equation (7) of §1 we have 



* - ; ■ r^i (7) 



£ p-f 



Equations (5) and (6) apply in general, so long as the tempera 

 ture remains above zero. The temperature being at zero the water 

 is changed into ice. However, we can imagine the possibility of the 

 vapor of water being changed into water at temperatures above 

 zero. We know this phenomenon in physics; it is not water only, 

 but several salts which present the phenomenon of super-saturation. 

 This passage from the state of vapor to the liquid state at tempera- 

 tures above the point of congealing involves a state of unstable 

 equilibrium and the introduction of a crystal of ice makes the whole 

 mass pass suddenly into a solid state. It is probable that this state 

 of unstable equilibrium is intimately connected with the formation 

 of hail. In ordinary cases congelation commences at the tempera- 

 ture zero and we will now consider the passage from the liquid state 

 to the solid state at zero. 



(4) Congelation at o°. 



During this stage the temperature remains constant, the water is 

 transformed for the most part into ice, but a part of the water is 

 vaporized because according to equation (7), section (1), any dimi- 

 nution of the pressure produced by dilatation demands a greater 

 quantity of vapor of water for the same vapor tension. 



