Table 72 (continued) 297 



VIRTUAL TEMPERATURE INCREMENT OF SATURATED AIR 



where r = actual mixing ratio of the air and r«, = saturation mixing ratio at the same 

 pressure p and temperature T (see Table 73). Equation (4) may be rewritten in terms of 

 the virtual temperature increment AT V 



AT.= (T v - T)=TUr„ (i - l) ( 1 _J__) (17) 



The saturation virtual temperature increment (T v — T) w , corresponding to the virtual 

 temperature increment , under saturated conditions, i.e., with U = 1 (100 percent rela- 

 tive humidity), is therefore given by 



(T '- T) -=M4- , )(rk) (18) 



Making use of equation (18), equation (17) may be rewritten 



(T.— T) = U(T V -T)„ + U(\-U) ( t +" Ur ) (T,-T)„ (19) 



where U is expressed decimally. 



Table 72 contains values of (T v — T) w as a function of pressure and temperature. 



Comparing the two terms of the right-hand member of equation (19) it will be seen that 

 the first term is the dominant one and that the second term does not contribute more than 

 0.1 °C. to (T v — T) so long as (T v — T) K does not exceed 8 C C. The second term may 

 therefore be ignored in rough calculations, so that 



(T v - T) = U(T. - 7%, approximately (20) 



where U is expressed decimally, or 



( 7% - T) = ( T v - T) • -^ , approximately (21 ) 



where U is expressed in percent. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



