206 RADIO WAVE PROPAGATION EXPERIMENTS 
LABORATORY 10 20 30 
1500 
OCTOBER 24,'44 
SAN PEDRO 
Ficure 9. Curves of constant refractive index along the San Diego to San Pedro path. 
TABLES FOR COMPUTING THE 
MODIFIED INDEX OF REFRACTION, Mt 
Introduction 
The index of refraction of the atmosphere, modi- 
fied for use on a plane-earth diagram, is a quantity of 
great importance in the study of radio wave propaga- 
tion. It is defined by 
M= [ hry ‘| 10%, (1) 
where n = ordinary index ot refraction, 
h = height above sea level (not ground level), 
a = radius of the earth. 
The equation for n is obtained from Debye’s theory 
of the dielectric constant of gases. In terms of atmos- 
pheric quantities, equation (1) assumes the form 
Ap De . Be 3 
TS ee han ar Oley (2) 
where p = barometric pressure (in millibars) 
(1 mm Hg = 1.333 mb), 
e = water vapor pressure (mb) 
(e is of order of 1% of p), 
T= temperature in degrees Kelvin, 
A= 19, B = 3.8 X 10°, C = 0.1570, D = 11, 
where h, the height above sea level, is measured in 
meters. 
The constants A, B, and D have been selected to get 
‘By E. R. Wicher, Columbia University Wave Propagation 
Group. 
the best agreement with experimentally determined 
values of n. The constant C is 10° times the reciprocal 
of the earth’s radius in meters. A more detailed ex- 
planation of this formula is given under “Constants 
of the Index of Refraction Formula” found on p. 219. 
The formula (2) may be used to calculate M when 
p, T, and e are known functions of height. Nomo- 
grams have been prepared to facilitate such calcula- 
tions. In this paper tables are presented which permit 
these calculations to be carried out quickly and accur- 
ately. M is a number of the order of 300 to 500. 
Physically, the important quantity is the slope of M, 
i.e., dM/dh. This often calls for calculating M at fairly 
close height intervals, 15 m or even less. The values of 
M at such heights may differ by only two or three M 
units. Hence, to obtain even two significant figures 
for this quantity, the M’s must be computed to four 
significant figures, that is, to tenths of an M unit. 
It is with a view to this situation that tables were 
computed. 
These tables fall into two groups, depending upon 
how the moisture in the atmosphere is evaluated. In 
the first group (Tables 3 to 7) the moisture is given 
in terms of relative humidity or vapor pressure ; in the 
second (Tables 8 to 11) the mixing ratio is used. 
Use of Tables 
The following examples explain the mechanics of 
using these tables. The first two examples use the first 
group of tables: Tables 3 to 7 inclusive. The quantities 
H and G which appear in these examples are auxiliary 
functions which are fully explained in the appendix. 
Examples III and IV use Tables 8 to 11. 
