44° SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



different quantities of moistures table 3 has been computed progress- 

 ing from o to 30 gram by gram with x as the argument giving in 

 column 4 the value m l for the different mixing ratios, for instance, 

 for x = 12.5 grams the humidity factor is m l = 3.459. The limits 

 of this table are for x = o grams or dry air m x = 3.44 and for x = 30 

 grams m 1 = 3.48. 



Equation 4 holds good for the adiabats of the dry stage only up 

 to the point when the air attains a condition of saturation. Any 

 further diminution of temperature then causes a condensation of the 

 aqueous vapor. This saturation point is therefore the bginning 

 of the rain stage and its determination is therefore necessary 

 before proceeding to any further computation. The expansion 

 proceeds not only by reason of the diminution of air pressure but 

 also by reason of the diminution of vapor pressure. But since so 

 long as the air is not saturated the weight of the vapor that is 

 present, or x, remains constant, therefore during the dry stage 



e elp 



x = e — e — — 



p — e 1 — elp 



is to be considered constant, hence also the ratio e/p is unchanged. 

 Further in equation 4 in place of the total pressure (p) the vapor 

 pressure (e) can be substituted (or the dry air pressure is zero) 

 whence 



log e/e = m 1 log T/ T 

 or 



log e — m x log T = constant (5) 



= log e - m 1 log T 



The fundamental condition for the existence of the dry stage 

 consists in the fact that the actual pressure of the aqueous vapor e 

 is smaller than the pressure e m that belongs to air 14 of the same tem- 

 perature saturated with aqueous vapor. This last equation (5) 

 therefore holds good up to the point when e = e m . At the moment 

 of saturation we have equation 



!°g e m ~ m i lo g T s = lo g e o - m i lo g T o - constant = 5. . (6) 

 where the subscript index designates the initial condition and T 8 



14 So in the original but possibly it would be more exact to say "that be- 

 longs to it when in air, etc." — C. A. 



