258 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



liquid and partly vapor, contained in a kilogram of the mixture, 

 but of which y\ is vapor; then the quantity of dry air in a kilogram 

 of the mixture is 



1 - 0.001 y v 



If now the liquid water suddenly becomes ice then a rise of tempera- 

 ture must occur because 01 the setting free of the latent heat of 

 melting, but the freezing point cannot thereby be exceeded, since 

 no further freezing of the remaining liquid masses would be possible 

 above this temperature. 



In the case of very slight subcooling the dew-point is simply 

 attained, whereas for greater subcooling and not too great a quantity 

 of subcooled water, i.e., formoderate degrees of mechanical subcool- 

 ing, the temperatures remain below the freezing point. 



But no equilibrium can be thus attained by the simple conver- 

 sion of water into ice, for in consideration of the higher final tem- 

 perature and since the air is to remain saturated, a part of the 

 existing water must be converted into vapor and hence the final 

 temperature will not be so high as if this evaporation did not take 

 place. 



It seems to me probable that these processes take place not 

 exactly simultaneously and not with the same rapidity, but rather 

 that the freezing takes place suddenly, whereas the evaporation 

 takes place subsequently and gradually. 



Indeed, it is possible that at the first instant the particles of 

 water all attain the freezing point, but that so long as the sub- 

 cooling is not extraordinarily large, only a part of the water can 

 freeze and that afterwards the surrounding air, as well as the 

 evaporation, have a further cooling influence. 



However this may be, it is certainly advantageous analytically 

 to assume that first there is established a temperature equilibrium 

 t 2 between the frozen water particles and the air and that then the 

 temperature is reduced to t 3 by evaporation. 



The following consideration serves for this determination of the 

 temperature t 2 depending on the simple conversion of subcooled 

 water into ice and the corresponding warming of the air. 



In the freezing of y l = y t — y x ' grams of water 80 y v units of 

 heat (in small calories) are set free. 



This quantity of heat serves first to warm 1000 — y x grams 

 of moist air from t x up to t 2 , that is to say, by t 2 — t x = t degrees, and 

 furthermore to warm y t grams of ice from t x to t 2 degrees. 



