FACTORS INFLUENCING TRANSMISSION 
367 
radius ka is introduced (Figure 5), this amount of humidity : 
upward curvature is just canceled and the rays eta 4,800 
appear as straight lines. (ies LO" = T\?P as ay ae (12) 
Alternate Method 
Instead of taking account of refraction by chang- 
ing the earth’s curvature, another method is some- 
times more convenient. It may be shown that the 
ratio of the field EZ to the free-space field Hy trans- 
forms in the same way, whether (1) radius a is 
replaced by ka, or (2) the horizontal distance z is 
replaced by xi" °/* and at the same time all elevations 
hare replaced by hk!/*. An anglea must then be 
replaced by ak~'/?. Method (2) is usually less con- 
venient than method (1) because it involves a change 
of horizontal distance which makes it necessary to 
transform the ratio H/E rather than the field itself. 
In method (1) where only curvatures are changed, 
this difficulty does not appear as the distance z 
and hence Zp remains unaltered. 
Method (2) may be used to advantage to account 
for deviations of k from the standard value of 
k = 4/3. Coverage diagrams are usually drawn 
for this value; the deviations owing to a change in 
k may then be estimated by multiplying distances, 
heights, or angles with the appropriate powers of 
k/(4/8). 
Computation of Refractive Index 
The following equation gives the dependence of 
the refractive index on temperature, pressure, and 
where 7’ is the absolute temperature, p is the total 
pressure, and e the water-vapor pressure, both the 
latter in millibars. 
Introducing M from equation (3), the modified 
refractive index, for use on a plane earth diagram, 
is equal to $ 
79/ . 4,8006 
u = 0.157h, 
T (° ir ) is 
where the height h is in meters. If A is in feet, the 
last term is 0.048h. 
Tables have been prepared by means of which M 
can be computed rapidly from meteorological data, 
namely temperature, humidity, and pressure given 
as a function of height. For this purpose M is the 
sum of three terms which are computed independ- 
ently: 
(13) 
M=M.+M,+M.,. (14) 
The dry term Mj is obtained from Table 1 as a 
function of temperature and height in meters above 
the ground. (If the pressure at the ground po is 
substantially different from 1,000 millibars all 
values of M, should be multiplied by po/1,000. In 
general this correction may safely be neglected un- 
less the difference between po and 1,000 is quite 
large, corresponding to an elevation of the ground 
level of several thousand feet above sea level.) 
The wet term M,, is obtained from Table 2 as a 
function of temperature and relative humidity. 
TaBLp 1 
M, 
h(ft) 
—16 -14 —12 —10 —8 —6 —4 —2 =E0 
307.4 305.0 302 7 300.4 298.1 295.9 293.7 291.5 289.4 0.0 
307.0 304.6 302.3 300.0 297.7 295.5 293.3 291.1 289.0 32.8 
306.6 304.2 301.9 299.6 297.3 295.1 292.9 290.8 288.7 65.6 
306.2 303.8 301.5 299.2 297.0 294.8 292.6 290.4 288.3 98.4 
305.8 303.4 301.1 298.8 296.6 294.4 292.2 290.1 288.0 131.2 
305.4 303.0 300.7 298.4 296.2 294.0 291.8 289.7 287.6 164.0_ 
304.4 302.1 299.8 297.5 295.2 293.0 290.8 288.7 286.6 248.1 
303.4 301.1 298.8 296.5 294.3 292.2 290.0 287.9 285.8 328.1 
3013 299.0 296.8 294.6 292.4 290.3 288.2 286.1 284.0 492.1 
299.3 297.1 294.9 292.7 290.5 288.4 286.3 284.2 282.2 656.2 
297.3 295.1 293.0 290.8 288.7 286.6 284.5 282.5 280.5 820.2 
295.4 293.2 291.1 288.9 286.8 284.7 282.7 280.7 278.7 984.3 
293.4 291.2 289.1 287.0 285.0 282.9 280.9 279.0 277.0 | 1,148.0 
291.5 289.4 287.3 285.2 283.2 281.1 279.1 277.2 275.3 1,312.0 
289.6 287.5 285.4 283.3 281.3 279.3 277.3 275.4 273.5 | 1,476.0 
287.7 285.6 283.5 281.5 279.5 277.6 275.6 273.7 271.8 1,640.0 
283.8 281.8 279.9 277.9 276.0 274.1 272.2 270.3 268.5 1,969.0 
280.1 278.1 276.2 . 274.3 272.4 270.5 268.7 266.9 265.1 | 2,297.0 
276.4 274.5 272.6 270.7 268.9 267.1 265.3 263.6 261.8 2,625.0 
272.7 270.9 269.0 267.2 265.4 263.7 262.0 260.3 258.6 | 2,953.0 
269.1 267.3 265.6 263.8 262.1 260.4 258.7 257.0 255.3 3,281.0 
251.8 250.2 248.7 247.2 245.7 244.2 242.8 241.3 239.9 4,921.0 
235.7 234.3 233.0 231.7 230.4 229.1 227.8 226.5 225.3 | 6,562.0 
+3.20 6.80 10.4 14.00 17.6 21.2 24.8 28.4 32.0 
h(ft) 
tC) 
