140 TECHNICAL SURVEY 
In the general case, when k is not equal to %, 
equation (11) must be modified to the form: 
M — M, = — 105, 
a 
ll 
S 
ia 
rn 
nh 
h in meters , 
ll 
S 
j=) 
res 
wa 
h in feet , (12) 
to account for a linear moisture gradient correspond- 
ing to a different value of k. 
Since the change of the earth’s radius takes care of 
the variation of refractive index and substitutes a 
homogeneous atmosphere for the actual atmosphere, 
it follows that in a diagram in which the earth is 
given a radius ka, the radiation propagates along 
TRANSMITTER 
Ficure 10. Ray curvature over earth of radius a in an 
actual atmosphere. 
straight lines. The difference is illustrated in Figures 
10 and 11. In Figure 10, which shows the true geo- 
metrical conditions, the radio horizon appears ex- 
tended as compared to the geometrical horizon, be- 
1.2 
=25C -20C 
iN 
SSN 
= 
cause of the curvature of the rays. In Figure 11 the 
rays have been straightened out, but a line that was 
straight in Figure 10 appears curved in Figure 11. 
The value of % for k is a good average for the at- 
mosphere in the middle latitudes. For particular 
fas | 
Ma MMMM, 
Ficur£ 11. Rays in a homogeneous atmosphere. Equiv- 
alent radius ka. 
atmospheric conditions the value of k may be con- 
siderably different. The moisture content of the at- 
mosphere is small at the low temperatures of the 
arctic regions and increases considerably with the 
higher temperatures of the tropics. However, the 
value of k depends more particularly on the manner 
in which the moisture content varies with height 
above the surface of the earth, and to a lesser extent 
on the distribution of temperature with height. 
Figure 12 has therefore been constructed to show the 
dependence.of k& on the gradient of relative humidity, 
measured in per cent per 100 m, for a series of surface 
temperatures varying between 7)>=—30C and 
T, = +40C. It has been found convenient to plot 
1/k rather than k itself. The lines drawn correspond 
to the assumption of saturation humidity at the 
REL HUMIDITY GRADIENT 
% PER 100 METERS ———® 
Epanrar 
(e) er . 1 
45 +4 +3 +2 +) to -! =a) -3 
-S -6 o1/ -8 -9 -10 “ll -l2 -13 
Ficure 12. Graph: 1/k versus RH gradient and temperature for 100 per cent RH at ground. 
