296 Table 72 (continued) 



VIRTUAL TEMPERATURE INCREMENT OF SATURATED AIR 



Substitution of this expression in equation (5) yields 



Accordingly, the adjusted virtual temperature (T' v ) may be defined as the tempera- 

 ture which dry air would have when, behaving as a perfect gas, it would possess the same 

 density as the actual air at pressure p, temperature T, and mixing ratio r, the pressure 

 being the same in both cases. 



For precise calculations of air density, equation (5) or equations (6) and (7) are 

 necessary; but for rough calculations, equation (3), which omits the compressibility factor 

 C, will be satisfactory. 



In view of equations (5), (6), and (7), the differential form of the hydrostatic equation 

 for precise calculations is, in cgs units, 



dp = - pgdZ = - L -£- gdZ, (8) 



K L 1 v 



or 



and 



since 

 where 



d±_ 1_ 



p ' RT\ 



gdZ, (9) 



d\og.p = --±-d*; (10) 



Kl v 



d$ = gdZ (11) 



Z = geometric height, 



g = acceleration of gravity, 



§> = geopotential. 



Mean adjusted virtual temperature. — From equation (10), it follows that the hydro- 

 static equation, in cgs units for precise calculations is 



*»-*i = /?r»,log.^. (12) 



where $i is the geopotential at pressure pi, and *» the geopotential at pressure pi, and the 

 mean adjusted virtual temperature T'mv is defined by 



r Pa c p2 



T' v d loge p CTvd log e p 



^■=-5 = t£- (13) 



(ft i. ta 



d lOge p d lOge P 



Pi J Pi 



For most meteorological calculations, the hydrostatic equation may be closely approxi- 

 mated by 



#»-#» = K7*m.log.i!. (14) 



pa 



where the mean virtual temperature T m * is defined by 



Pa 



Tvd log 6 p 



T m , = -h (15) 



Pa 



d lOge P 

 Pi 



Virtual temperature increment. — Since the definition of the relative humidity U 

 adopted by the I. M. O. in 1947 is (see Table 93) : 



U = — , expressed decimally (16) 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



