322 ; RADIO WAVE PROPAGATION EXPERIMENTS 
TABLE 2 
Deviation 
Type of a at B at of a and B 
atmospheric receiver transmitter from true 
stratification (degrees) (degrees) bearing m 
“Standard” 
atmosphere — 0.069 — 0.194 + 0.042 2.44 
Adiabatic 
equilibrium — 0.083  — 0.208 + 0.028 0.16 
Rectilinear 
propagation on 
a true earth — 0.111 — 0.236 0 0 
a = —0.11°, which is the true bearing from receiver 
to transmitter. From the data of Table 1 it follows 
that a “standard” atmosphere and an atmosphere 
vertically mixed so as to be in adiabatic equilibrium 
both provide a variation of modified refractive index 
with height of a magnitude such that the angle of 
arrival measured at the Beer’s Hill receiver under 
these conditions is within 0.04° of true geometric 
bearing. In view of the fact that the instrumental ac- 
curacy of the Beer’s Hill antenna system is +0.04°, 
it follows further that the differences among. these 
three meteorological stratifications will not be evident 
in the measurements. 
Consider now a case in which the radiation path 
penetrates the layer above the transmitter. The oc- 
currence of an angle of arrival at the Beer’s Hill re- 
ceiver in excess of 0.236° above true bearing will re- 
quire a path of propagation rising to some level above 
the New York City transmitter. The variation of M 
with height within the layer immediately above the 
transmitter will be critical in determining the magni- 
tude of the signal received and its angle of arrival. 
The analysis following is limited to one particular 
case of this category producing an extreme deviation 
from true bearing in the angle of arrival. 
For the paths shown in Figure 6C, the M distribu- 
tion between 353 and 492 ft above mean sea level is 
that computed from the observed meteorological data 
on the 400-ft tower at 0800 on July 7, 1944. Using 
only this portion of the actual sounding, the variation 
of modified index of refraction in the layer immedi- 
ately above the transmitter has been computed as a 
Function of the angle @ at the receiver. In the case of 
the angle % = 0.355° (deviation from true bearing 
equal to +-0.466°), the calculated index at the level 
of total refraction, which computes as 505 ft, is very 
closely that observed at the uppermost level of mete- 
orological sounding (503 ft). Thus an angle of ar- 
rival deviating by as much as 0.47° from true geo- 
metric bearing is entirely possible for the meteoro- 
logical situation of 0800, July 7, 1944 and for the 
positions of the New York transmitter and Beer’s 
Hill receiver and could have been predicted from the 
observed meteorological sounding. 
A second significant conclusion can be readily de- 
duced by considering the modified refractive index 
distributions required in the layer immediately above 
the transmitter for different values of a. It is ap- 
parent that the lapse of modified index required for 
any of the angles considered in this example is not 
substantially different among all four angles; the 
primary requisite for the larger a’s is that the lapse 
continue to greater heights. Thus relatively small 
fluctuations in the meteorological elements can cause 
a time change of 0.1° in the angle of arrival measured 
at the Beer’s Hill receiver. Furthermore, a particu- 
larly unfavorable combination of small changes in the 
meteorological elements in this layer may cause the 
signal at the receiver to fall to a very low level. A 
similar conclusion is not valid for the case of propaga- 
tion confined to the layer between transmitter and re- 
ceiver and the case of path penetration below the re- 
ceiver, since another slightly different path can al- 
ways be found along which energy can reach the re- 
ceiver directly. 
A third significant conclusion can be deduced by 
inspecting the computed deviations from true bear- 
ing of the angles at the receiver and the transmitter, 
as given in Table 3. It will be noted that the devia- 
tion from true bearing of thé angle of arrival at the 
receiver is not the same as the deviation from true 
bearing of the angle of departure at the transmitter. 
Tm fact the data of Table 3 indicate that, under the 
meteorological situation of 0800 on July 7, 1944, the 
angle of arrival at the receiver would have been 
TABLE 3 
a at B at Deviation from 
receiver transmitter true bearing 
(degrees) (degrees) a B ™ 
+ 0.355 + 0.038 + 0.466 + 0.274 1.366 
+ 0.372 + 0.119 + 0.483 + 0.354 1.972 
+ 0.401 + 0.190 + 0.512 + 0.426 2.436 
+ 0.458 + 0.292 + 0.569 + 0.528 3.052 
MULTIPLE PATHS 
(EXAMPLE OF TABLE 4) 
PATH PENETRATING LAYER ABOVE 
XMTR SS 
i <= = To aS a 
XMTR AND RGVR 
DEVIATION OF OC AT RCVR FROM TRUE BEARING 
o Ol a2 03 04 0.5 06 O7 
DEVIATION OF B AT XMTR FROM TRUE BEARING 
Ficure 7. Correlation of deviations. 
