320 RADIO WAVE PROPAGATION EXPERIMENTS 
be explained by, and predicted from, meteorological 
data and whether observed extreme deviations can be 
realized from plausible meteorological stratification. 
The Bell Laboratories’ experimental angle-of-arrival 
measurements made during the summer of 1944 have 
been compared with deviations evaluated from mete- 
orological data obtained concurrently by the Signal 
Corps though not coordinated at the time with these 
experiments. The current paper is intended to report 
the results of this study and the procedure utilized in 
the analysis and, in turn, to establish a framework 
for interpreting further propagation experiments of 
this type. 
Theory 
The equations of propagation can be written in a 
form such that the angle of departure of the radiation 
at the transmitter (the direction of the normal to the 
wave front) and the angle of arrival at the receiver 
can be written as functions of the meteorological 
stratification and the constants of the installation (dis- 
tance between and heights of transmitter and re- 
ceiver). The solution of the equations of motion is 
given below by the use of an electromagnetic wave 
velocity profile obeying a radial power law. The re- 
lation of the exponent m in this power law to the 
excess modified refractive index M is then deduced. 
The power m in the velocity profile equation is as- 
signed the definition of “meteorological stratification 
parameter,” since it determines the change of modi- 
fied index of refraction with height. 
From Figure 4, 
dr ds 
rtanB Tb 
() 
Introduce the electromagnetic wave velocity profile 
(2) 
Hence, 
(3) 
Fiaure 4. Geometry of a ray in the atmosphere. 
where 
cos 8B = Gi as COs a. (4) 
Snell’s law states that 
Vo Og. 
beosa rcosp (5) 
Then, 
(1 — m)dr = r tan BdB (6) 
and 
ds dg 
b 1l—m @) 
Now r=b+h, 
8 
where h<b (8) 
The excess modified refractive index M is given by 
nr 
M-10-* =—-—1 
b 
nN 
[HQ senha 
If now the relation for the distance s is solved simul- 
taneously with the equation stating Snell’s law of 
refraction, we have the angle of arrival « as a function 
of the excess modified refractive index M, uniquely 
relating the angular deviation from true bearing to 
the distribution of modified refractive index required 
to produce that deviation. 
Analysis of the BTL New York- 
to-Beer’s Hill Circuit 
The results obtained by Bell Telephone Laboratories, 
Ine., on measurements of the angle of arrival of micro- 
waves in the X band are contained in two BTL -re- 
ports." The New York-to-Beer’s Hill propagation 
circuit proved to be the more suitable for the meteor- 
ological analysis of angle of arrival. On this path the 
transmitter was located on the New York Telephone 
building at an elevation of 492 ft above mean sea level ; 
the receiver was erected on top of Beer’s Hill at an 
elevation of 353 ft. The propagation path had a length 
of 24.08 miles and ran several degrees east of north 
from Beer’s Hill to New York. The bearing from re- 
ceiver to transmitter on this circuit on the basis of 
true earth geometry is 0.11 degree below zero eleva- 
tion angle of Beer’s Hill. 
During the summer of 1944 a limited number of 
vertical temperature and humidity soundings were 
secured by personnel of Wave Propagation Studies, 
Evans Signal Laboratory, at a 400-ft radar tower in 
Oakhurst, New Jersey. The location of the tower is 
shown on the map in Figure 5. The tower stands on a 
hill 128 ft above mean sea level. The limit of observa- 
tion is 875 ft above the base of the tower; hence the 
absolute elevation was 503 ft. It follows that soundings 
over the height of the tower sample the atmosphere 
