442 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



dition V = 0.869 cubic meters and v = 0.858 cubic meters. Under 

 diminishing pressure the air becomes specifically lighter, hence for 

 the same mass the volume becomes larger. 



If we wish to form an equation for the direct determination of 

 t t it is necessary to represent e m as a function of t. For this purpose 

 we can make use of the empirical formula of Magnus 



7.45/ 

 log* w - log 4.525 + 235+7 



Substitute this value of e m in the equation (6) and we obtain 

 for the variables t or T the relation 



7.45 t 

 235 + t 



= m log T — (m log T — log e Q -f log 4 . 525) 



but from this equation i can only be obtained in an indirect way 

 by successive trials. 



The upper limit of the first stage is determined by the saturation 

 point. When the expansion continues further, the values just 

 computed become the initial values for the second or rain stage. 



In the dry stage the behavior of moist air differs from the behavior 

 of dry air only by reason of the value of the factor m which can be 

 taken from table 4 as a function of the quantity of vapor {%) that 

 is present. The departures of the value m x from that for dry air 

 m = 3.44 are only slight. 



§4- THE RAIN STAGE 



After the attainment of the saturation point the condensation of 

 aqueous vapor begins and during the further expansion of the air 

 it continues to be saturated. In order to obtain the relation between 

 pressure and temperature in this stage we form the thermo-dynamic 

 equations. First we have 



dQ' =c p dT- ART 



dp' 



7 



in which dQ' expresses the quantity of heat that is necessary for 

 the expansion of 1 kilogram of air. 



The total quantity of moisture at the beginning of the condensa- 

 tion, consisting of vapor (x grams) and water (y grams) we will call 



