PAPER BY PROF. BEZOLD. 231 



value and because of the minus sign before the integral it therefore 

 always exerts its influence in the same direction as the term AR K log 



Vz . Therefore for the same starting point and for equal values of T 2 , 



we must have v 2 in the case of the pseudo-adiabatic smaller than if we 

 had gone along on the adiabatic. 



C. THE HAIL STAGE. 



The above given equations hold good for the value T> 273° ; as soon 

 as the temperature 0° C. or the absolute temperature T= 273 has been 

 attained, then very different equations replace these but only when 

 liquid water is present. In this last case the following equation of mix- 

 ture holds good, namely : 



M=l-\-x+x / -{-x", 



an equation that can only be true for the temperature 0° C. since only at 

 this temperature can water and ice occur together. The equation of 

 elasticity therefore then acquires the simple form 



aR K , 



while the equation a?=— _ becomes x=—- iJ . . . (18) 



Jxs J- alls 



wherein a=273, e =62.56. But the one possible change of condition 

 in i Ins stage consists in an isothermic expansion. For this case there- 

 lore, the (IT also falls out of the equation for the transfer of heat and 

 this takes the form, 



d Q=r dx-ldx"+AEKa- (19) 



fr =latent heat of evaporation at 0° O. ; /^latent heat of liquefaction 

 of ice.] 



In this equation the first term on the right-hand side must be pos- 

 itive, the second must have a negative sigu when dx and dx" are con- 

 sidered as positive, since an increase in the quantity of vapor x makes 

 an addition of heat necessary, but an increase in the formation of ice 

 demands a withdrawal of heat. 



If we put dQ=0 then we have the differential equation of the adia- 

 batic which in this case coincides with the isotherm and is moreover 

 always a pseudo adiabat, since the ice that is formed falls away under 

 all circumstances. 



If we consider that 



aR& 



then the differential equation of the adiabat takes the form 



A R K J v + r ^dv-ldx"=0 (20) 



v uRs 



