36 TECHNICAL SURVEY 
distinguished from ray bending, from the elevated 
layer of M inversion. The principle of this reflection 
phenomenon has previously been outlined at the end 
of Chapter 2, on page17. Further study shows that 
the rate of change of the field intensity and its varia- 
tion with frequency are just of the magnitude re- 
quired by the theory. Figure 15 shows a ray-tracing 
\diagram on which the paths of the reflected rays are 
indicated. Summarizing the results of this experi- 
ment, it may be said that the phenomenon of reflec- 
tion from an elevated layer has been well established 
qualitatively and, in some respects, quantitatively. 
The meteorological conditions at San Diego are rather 
singular, and so far such reflection occurring in a 
systematic fashion has not been described elsewhere 
though indications of similar effects have occasional- 
ly been reported. 
Another transmission experiment was made by 
the Navy Radio and Sound Laboratory in the 
‘Arizona desert in December 1944.!8* The path was 
nonoptical, 47 miles long, and the frequency used 
was 3,200 mc. The desert air is extremely dry so that 
the contribution of water vapor to the refractive 
index is small and the change in M owing to changes 
in humidity with height is nearly negligible. During 
the clear nights a pronounced temperature inversion 
develops from radiative cooling of the ground, a 
ground-based duct thus being formed. The received 
field strength varied in close correlation with the 
formation and disappearance of the duct, with a 
pronounced diurnal period. The overall results of 
this experiment are again in excellent qualitative 
agreement with the predictions of the duct theory. 
At the same time the experiment also furnished an 
opportunity for studying the development over land 
of low temperature inversions which are valuable 
for radiometeorological forecasting. 
EXPERIMENTS AT ANTIGUA 
Operational experience in the Pacific Ocean led to 
the conclusion that low ducts are very common over 
the ocean surface in subtropical and tropical climates. 
In order to study these ducts, an experiment was un- 
dertaken by the Naval Research Laboratory in the 
spring of 1945.94 The island of Antigua, one of the 
Leeward Islands of the Lesser Antilles in the British 
West Indies, was chosen as the site. The prevailing 
winds there are northeasterly and the air has an over- 
water trajectory of several thousand miles before 
arriving at the island and is therefore considered 
characteristic of large portions of the central Atlantic 
and Pacific oceans. There is almost no diurnal and 
only a limited seasonal variation in the air at the 
lowest levels. 
Equipment for the transmission experiments was 
comprised of S-band and X-band sets provided by 
the Radiation Laboratory, MIT. The transmitters 
with parabolic antennas were mounted on a ship at 
heights of 16 and 46 ft. There were two parabolas for 
each height and each frequency, one set pointing to 
the stern and one to the bow, so that measurements 
could be made on both the outward and inward runs 
of the vessel. Receivers were located at heights of 14, 
24, 54, and 94 ft on a tower at the edge of the water. 
Monitoring and automatic recording were similar to 
those used in the transmission experiments pre- 
viously described. Records were obtained while the 
ship was traveling away from the receiving station- 
and again on its return. Signals could usually be de- 
tected up to 190 miles for some combination of 
transmitter and receiver heights. Direction finding 
equipment was used for keeping the ship on its course, 
and fading of the signal caused by the ship’s being 
off course could be readily detected and rectified. 
An extensive program for measuring low-level 
M curves paralleled the transmission measurements. 
Since the weather conditions at Antigua are quite 
steady there is little variation in these curves, as 
shown by two typical ones illustrated in Figure 11 of 
Chapter 3. The low-level duct indicated by these 
graphs has been found present at all times in this 
location. 
Typical field strength records for the S band and 
the X band are shown in Figures 16 and 17, respec- 
tively, the most outstanding feature being the varia- 
tion of field strength with antenna heights. For the 
S-band transmission, the field strength increases 
slightly with increasing antenna height but not nearly 
so fast as it would under standard conditions. For 
the X band, on the other hand, the field strength, as 
a rule, is increased by lowering the antennas. This 
behavior can be explained on the basis of the mode 
theory of duct propagation as outlined in Chapter 2 
For the shorter wavelength X band, we have genuine 
trapping, so that the field strength is greatest when 
the transmitter or receiver or both are in the duct. 
In terms of the height-gain functions of equation 
(27), Chapter 1, it appears that these functions of the 
lowest mode or modes have a pronounced maximum 
in the duct and decrease rapidly above it. For S-band 
_transmission there is a transition between the com- 
plete cutoff, indicated by a highly simplified wave- 
guide theory, and complete trapping. This inter- 
mediate effect is caused by some leakage of this wave 
train from the duct and the retention by the duct of a 
portion of its wave-guiding properties. The height- 
gain functions, vhile still much larger in the duct 
than in the case of standard propagation, no longer 
have distinct maxima but show a gradual increase 
with height from the ground. This case is particu- 
larly interesting because it clearly exemplifies the 
possible variety of conditions intermediate between 
trapping, as described by the ray tracing of geo- 
metrical optics, and the diffraction around the earth’s 
surface characteristic of standard propagation. 
Figure 16 shows two regions with distinctly 
