444 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



The value of the humidity factor m n of the rain stage is given in 

 table 4, column 5, for quantities of moisture between o and 30 grams. 

 [M is the modulus of the system of logarithms.] 



For example, we find for £ = ogr., 11 gr. and 30 grams respect- 

 ively, the following values m u = 3.44; 3 .60 and 3 .88. In conse- 

 quence of the high specific heat of water the differences are con- 

 siderably larger than those of m x for the dry stage. 



For the variable quantity of vapor (x) we may again also substi- 

 tute the partial pressure by introducing the relations 



P" *m 



P' P 



and 



R 

 Vp"= x-T 



where e m = / (t) is to be taken from the table of vapor tension for 

 saturated aqueous vapor as given in column 2, table 1. We have 

 here assumed that the volume of the saturated aqueous vapor fol- 

 lows the law of the equation for elastic gases; this assumption, for 

 the low temperatures we have to deal with, is far more correct than 

 if we should put V = xu in strict accordance with the law of thermo- 

 dynamics where u is the specific volume of aqueous vapor, which 

 must first be obtained for specific temperatures from the equa- 

 tion given by Clapeyron, 15 



r dp 



- = AT -£ 

 u at 



The volume of any water that may be present is negligible and is 

 indeed so slight relative to that of the vapor that numerically 

 speaking it cannot come into consideration. 



According to the above reasoning equation (7) now becomes (8), 

 where the small quantities r and e depend on temperature only. 



P' T * M (* m r e r \ 



lo g/V = m a log To + -- [ p , T - - Y J. . . (8) 



18 Vergl. Zeuner: Technische Thermodynamik., Bd. II, 1890, p. 333. 



