SPECIFIC VOLUME AND DENSITY OF ATMOSPHERIC AIR AND SEA-WATER. 27 



per unit-mass of the air is known. But this quantity m is never observed directly. 

 What is generally determined is the relative humidity, i. e., the proportion of the 

 quantity of water-vapor really present to that which would be present if, at the 

 same pressure and temperature, the air were saturated with moisture. 



If f be the pressure of the saturated vapor at the temperature considered,/) 

 the total pressure, and r the relative humidity, rf will represent the pressure of the 

 vapor and p rf that of the dry air in the mixture. The partial pressures of each 

 constituent in a mixture are in the same ratio as their volumes were before mixing. 

 The specific volumes of air and water-vapor being in the ratio 5 : 8 the volumes of 

 1 m parts of air and m parts of water-vapor are in the ratio 5(1 m):8m and 

 consequently 



U> - r f) rf- 5(i - ) : Sm 



If the value of m found from this equation be substituted in the equation (d), sec- 

 tion 21, we find the temperature correction 



It appears as a function of four variable quantities. But only three of these pres- 

 sure p, temperature &, and humidity r are independent, while the vapor pressure 

 _/"is a known function of temperature. 



To conveniently calculate e, we can first put r= 1, and calculate the tempera- 

 ture correction 



(*) * 10 . = 8^17* 



corresponding to 100 per cent humidity. This s m being calculated, the value of e 

 corresponding to any relative humidity is easily found. Division of (a) by (d) gives 



8 "3 Z 



where the temperature # has dropped out. Numerical calculation easily shows 

 that, even under unfavorable circumstances, the coefficient of r can be set equal to 

 unity without producing any error in the tenths of the centigrade degree. Thus 

 the equation is reduced to 

 ( c ) r = re m 



As an immediate result of equations (&) and (c) we get the following rule for 

 the calculation of the virtual-temperature correction s r for air of r per cent relative 

 humidity: First calculate the correction e 100 for saturated air of the given tempera- 

 ture and pressure; then r per cent, of s 100 gives the required correction e r . 



The virtual-temperature correction e m for saturated air is given in table 7 M of 

 the Meteorological Tables as function of the pressure in m-bars and degrees of the 



