26 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



The gas constant R of dry atmospheric air is 2153 when the pressure is expressed 

 in millimeters of mercury, and 2870 when it is measured in m-bars. 



If the air be more or less moist, an equation of the form () can still be used, 

 only with a new value R' of the gas constant 



fa = R'd 



If the unit-mass of moist air contains in parts of water-vapor, and consequently 

 1 m parts of dry air, the laws for the mixtures of gases give for the constant R' 

 the expression 



R' = (1 - m)R + mR" 



R being the gas constant of dry atmospheric air, and R" that of water-vapor. 

 Now the constants of two gases are in proportion to their specific volumes. For 

 the case of water-vapor and dry atmospheric air this proportion has the well-known 

 approximate value 8/5, which will give sufficient accuracy for our purposes. Con- 

 sequently R' R(i -\- 0.6m). 



21. Virtual Temperature. The gas constant R' of moist air is thus a variable 

 quantity, changing with the variable mass m of water present. The second member 

 of the equation for moist air will therefore contain two variable quantities, R' and d. 

 The first of these will be, however, variable only between narrow limits. We can 

 therefore advantageously use a well-known artifice, considering the slightly variable 

 quantity R' constant and equal to R, while we for compensation add a small 

 correction to the widely variable quantity &. Thus, introducing 



(a) & = d(i + 0.6m) 



we can write the equation for moist air in the form 



(b) fa = R& r 



R being the gas constant for dry air, and d r a somewhat increased temperature, 

 namely, the temperature which dry air ought to have in order to get the same spe- 

 cific volume as the assumed mass of moist air of temperature d. With Guldberg 

 and Mohn, who first introduced this useful auxiliary quantity, we shall call #. the 

 virtual temperature. 



As may prove most convenient, we shall count this virtual temperature either 

 from the freezing-point of water or from the absolute zero, and denote it by r r and 

 # r respectively, thus 

 {c) r r = t + e r $ r =&+ e r 



where, according to (a), the correction e r has the value 

 d) e r = o.6md 



m being the mass of water-vapor per unit-mass of atmospheric air. 



22. Tables for the Virtual-Temperature Correction. The tormula (d) above 

 can be used to calculate the virtual temperature when the mass m of water-vapor 



