PAPER BY PROF. BEZOLD. 231 



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

 always exerts its intiuence in the same direction as the term AR^ log 



'^^. Therefore for the same starting point and for equal values of T2, 



■we must have Vo 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 i;emperatureT=273 has been 

 attaineil, 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 : 



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 tben acquires the simple form 



while the equation .r=^*' becomes .r=^^ . . . (18) 

 R& 1 (iRs 



wlieiein rt=273, «?o=()2.5G. But the one possible change of condition 

 ill I Ills stage consists in an isothermic expansion. For this case there- 

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

 tills takes the form, 



dQ=rodx-l(U" + ARKa^ (19) 



I »„= latent heat of evaporation at 0° C; / = latent heat of liquefaction 

 of ice.J 



In this equation the first term on the right-hand side must be ])os- 

 itive, the second must have a negative sign 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 



then the differential equation of the adiabat takes the form 



AR^a—-^^dv-ldx"=0 (20) 



V aRi ^ ' 



