124 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



The law of Mariotte and Gay-Lussac as applied to a kilogram of 

 gas is written 



p = ap (273°*+ t) (1) 



where 273 -f x is the absolute temperature. 



Here a designates a constant which depends on the nature of the 

 gas; for dry air we have 



a = 287.09 



In applying this law to a mixture containing 1 — q kilograms of 

 dry air and q kilograms of the vapor of water, expressing the tension 

 of the vapor of water by / and its relative density by i/e we find 



p - f - a (1 - q) p (273 + r). 

 f =eaqp (273 + r). 

 p = a (1 + (e - 1) q) p (273 + t) (2) 



t _ 11 (3) 



P~ 1 + (t - 1) q k > 



1 / 

 q = e ' P (4) 



1 - £-1 f 



T~ ' p 



By substituting this value of q in equation (2) and putting 



273 + t 



t = nr73T-7 (5) 



e ' P 

 we have for moist air 



p = apT % (6) 



We call the quantity T the virtual temperature; for dry air the 

 virtual temperature is the same as the absolute temperature. 



If we consider a mixture which contains 1 kilogram of dry air 

 and x kilograms of vapor of water, we shall have 



'-rr q -i j=} • • - (7) 



i = r x* (8) 



p I + £ x 



