MOVEMENTS OF ATMOSPHERE GULDBERG AND MOHN 133 



Having determined x, we shall rind p by equation (7). 



When all the water is transformed into ice and vapor, we have 

 a mixture of vapor of water and of ice and from this moment on- 

 ward the vapor of water is transformed directly into ice by the 

 lowering of the temperature. 



(5) The aqueous vapor is partially transformed into ice. 



For this stage we will apply the formulas given in case (3) sub- 

 stituting / + L for I and the specific heat of ice (c" = 0.5) for the 

 specific heat of water. 



'og(^) =3.441 (1 + 2 ..05Olo g (f|^) 



fx (l + L) x(l + L) \ 



We have supposed that the water and the ice remain suspended 

 in the air and take part in the thermal phenomena during the three 

 periods in which the vapors of water are condensed. If we wish to 

 consider the case in which the water and the ice after their formation 

 separate from the mass of air, it will be necessary to consider the 

 term c + £ c' or c + £ c" as variable, We can in this case give to 

 £ a mean value and consider it as constant, since its value is very 

 small. In this case the period of freezing at o° disappears. 



M. Peslin 1 has developed similar formulae, but he has not considered 

 the variation with temperature of the latent heat of vaporization. 

 This causes the difference between his formulae and ours. 



We shall apply our formulas to the case in which a mass of air rises 

 in the atmosphere with a velocity so small that it can be neglected. 

 Designating the height by h we can write the equation of equilib- 

 rium from §4, 



V d p = - (1 + $) dh 



Combining this equation with equation (1) we find 



= d U + A d (p V) + A(i + £) dh . . . . (11) 



Applying this formula to moist air we find the formulas of section 4. 

 When we consider the cases in which the vapor is condensed, we 

 distinguish the following: 



x The bulletin hebdomadaire de l'association scientifique de France, No. 

 67. 



