ERRORS IN USE OF EQUATION FOR A^ 



Table 1.4. Refractivities of water vapor and dry gases 

 (Dry gases at °C, 760 mm Hg; water vapor at 20 °C, 10 mm Hg) 



and Weintraub. With the exception of oxygen the same is true up to 

 72 Gc/s. This conclusion is somewhat strengthened by the resuUs of 

 Hughs and Armstrong [18] at 3000 Mc/s which agree within 1.5 percent 

 of those of Essen and Froome. It is important to note that the differ- 

 ences in formulas are greater than the frequency variation and, further, 

 as shall be seen in the next section, the errors of determining P, T, and e 

 are sufficiently large to mask even the differences in formulas. 



1.4. Errors in the Practical Use of the Equation for N 



A high degree of accuracy of temperature, pressure, and water vapor 

 pressure measurements is necessary for precise determinations of the 

 refractive index from (1.20). If one assumes that the formula for A^ is 

 exact, then a relation between small changes in N and small changes in 

 temperature, pressure, and vapor pressure may be evaluated from 



,,, dN -.^ . dN . . dN .j^ 



(1.21) 



assuming that the errors in P, T, and e are unrelated. 



The partial derivatives may be evaluated by reference to some standard 

 atmosphere to yield the approximate expression 



AN' = aAT + bAe + cAP. 



(1.22) 



The root-mean-square (rms) error is then 



AN = {(aATY + (bAeY + (cAPy\ 



2i 1/2 



(1.22) 



Typical values of the constants a, b, and c, based upon the International 

 Civil Aviation Organization (ICAO) standard atmosphere and assuming 

 60 percent relative humidity, are given in table 1.5 for various altitudes. 



