advanced to permit drawing definite conclusions, As 
for surface phenomena, an excellent qualitative agree- 
ment has been obtained between theoretical and ob- 
served results. There has been no indication of a need 
to revise the formula used for computing the modified 
index of refraction. 
Following presentation of this paper the following 
data were presented on a similar experiment* made on 
an over-water path between San Pedro and San Diego, 
California. Transmitting and receiving antennas were 
at 100-ft elevation, with continuous wave transmission 
conducted from the San Pedro end of the link simul- 
taneously on 52, 100, and 550 me. The typical non- 
standard condition in this area is produced by dry air 
aloft subsiding over moist air near the sea surface. 
This gives rise to a sharp discontinuity in the index 
of refraction distribution with altitude at some eleva- 
tion above the earth. 
In analyzing the data from this experiment, the 
index of refraction modified for 4a/3, instead of the 
modified index M, was used. The new modified refrac- 
tive index, B, thus obtained is shown in Figure 15. 
The pertinent factors for reflection considerations are 
as follows: h, the height of the layer above the earth; 
AB, the total change in index through the layer; and 
D, the thickness of the layer. For moderately high 
layers, D is much less than h. 
Maximum field strength measured during the hour 
in which a meteorological sounding was taken is 
plotted against height of the layer above the ocean. 
The data are segregated into groups for different 
ranges of change in index of refraction through the 
layer. Figure 16 shows the data for changes in AB 
between 30 and 40 by means of crosses; for AB of 40 
to 50 with dots; and for AB of 50 to 60 with circles. 
Tf reflections are assumed to take place midway 
between the transmitters and receivers, the field 
strength may vary roughly as shown in Figure 16. 
The height-gain function holds the lower frequency 
fields down when the layer is low, whereas the added 
advantage in the reflection coefficient produces rela- 
tively stronger fields for the lower frequencies when 
the layer is high. A complete report will be made soon 
yon the experimental data and its relationship with 
this consideration. 
It was further pointed out.that maximum observed 
field strength need not always coincide with complete 
trapping. The experimental evidence that for a given 
frequency the signal strength over a low fixed path 
first increases as the height of the base of the M in- 
version increases and then decreases does not neces- 
sarily contradict the wave guide theory. When the base 
is low, transmission is by means of well-excited modes 
with low attenuation. As the base height increases, the 
attenuation of some of the modes decreases and the 
‘field strength therefore increases. Further increase 
in base height results in well-locked modes which are 
more and more difficult to excite. It is then that the 
most effective mode is one which leaks sufficiently to 
be excited by a transmitter outside the duct and yet 
does not leak sufficiently to be strongly attenuated 
before reaching the receiver. As the height continues 
to increase, modes which can be excited are all strongly 
attenuated, and the ones which are only slightly at- 
tenuated cannot be excited. Thus signal strength ul- 
timately decreases with increasing height. 
NEAR SAN DIEGO 
ONE-WAY TRANSMISSION EXPERI- 
MENTS OVER THE SEA BETWEEN 
LOS ANGELES AND SAN DIEGO? 
NE-WAY TRANSMISSION tests have been made by 
two methods: over a fixed path and by means of 
an airplane to sample vertical distribution of field 
strength. The fixed path is a nonoptical over-water 
*By L. G. Trolese, U. S. Navy Radio and Sound Labo- 
ratory, San Diego, California. 
APPENDIX 
path, 80 nautical miles in length 1rom San Diego to 
San Pedro near Los Angeles Harbor. No intervening 
landscape is present at either end of the path. The c-w 
transmitters are located at the San Pedro end of the 
path at 100-ft elevation and operate on frequencies 
of 52, 100, 547, and 3,200 me. The latter frequency 
has just recently been added, and insufficient data 
have been obtained to include in this report. The trans- 
mitters are quite conventional, the 62 me being crystal 
controlled and the other two being self-excited units 
in which adequate frequency stability has been ob- 
tained by use of high-@Q circuits. Monitors, which are 
read periodically, are provided on each transmitter. 
The receiver location, at 100-ft elevation, is located 
on Point Loma, San Diego, near the laboratory. The 
receivers are of standard construction incorporating 
a balanced d-c amplifier md Esterline-Angus recorder 
in the output circuit. Filament and plate voltages are 
regulated. Detuning effects due to temperature changes 
are minimized by temperature regulation in the re- 
ceiver house. Receivers are calibrated at least once 
each week. 
Four receivers have been installed in a PBY-5A 
plane which is used to sample vertical sections of field 
strength distribution at various distances up to 130 
miles from the transmitters at 100-ft elevation. The 
frequencies used are 63, 170, 524, and 3,250 me. 
Certain precautions were found necessary to insure 
correct orientation of transmitting antennas on the 
ground and receiving antennas on the plane. Receiving 
antennas on the plane are fixed in position, and meas- 
urements are taken only with the plane flying toward 
the transmitters. The plane’s orientation is controlled, 
and the distance from transmitters determined, by 
utilizing the plane’s Type ASE (Admiralty Signal Es- 
tablishment) radar to home on a beacon located near 
the transmitters. All four transmitters and transmit- 
ting antennas are installed on a single rotating mount. 
A direction finder system also installed on the rotat- 
ing assembly and operating on the plane’s radar fre- 
quency is used to check the plane’s bearing during 
flight and keep the transmitting antennas pointed at 
the plane. Bearing checks have been consistently ob- 
tained at ranges up to 130 miles. The d-f bearings 
agree quite well with those obtained by use of a type 
FC fire control radar. 
One-Way Fixed Link Data 
Ray THEORY — GEOMETRIC Oprics 
On the basis of ray theory, when it is assumed im- 
plicitly that the energy follows the rays, the modified 
index criterion for trapping should be expected to 
agree with experience. Ray tracing theory states that 
when the modified index at some elevation above a 
transmitter attains a value equal to or less than its 
value at the transmitter height trapping can occur. 
As a preliminary check on this criterion the maxi- 
num field strength observed during the hour in which 
the meteorological sounding was taken is plotted 
against AM in Figure 1. When the minimum value 
of M in the refracting stratum is less than its value 
at the transmitter elevation, AM is negative, and the 
trapping condition is fulfilled. The 52-, 100-, and 547- 
me links all show strong fields for large positive AM. 
These data are not compatible with the assumption 
that the energy follows the rays. The diffracted field is 
below detection for all the frequencies used on the 80- 
mile over-water link. This has been confirmed experi- 
mentally. On Novemher 5, 1944 a front passed accom- 
panied by heavy rain which dissipated all low-level 
inversions, and a standard condition resulted. During 
this period all the signals decreased below detection. 
Figure 2 shows the above field strength data plotted 
against the height of the base of the temperature in- 
version. (The curves appearing in this figure will be 
explained later.) Although both the thickness of the 
inversion layer and the strength of the inversion vary 
considerably, the correlation of signal strength with 
the height of the hase of the inversion is quite remark- 
485 
able. The 547-me signal decreases below detection as 
the layer heights increase above 3,000 ft; whereas the 
100- and 52-me signals are still relatively strong when 
the inversion base is above this altitude. These lower 
frequencies do show a decreasing trend as the layer 
continues to rise, going completely out, as stated above, 
when the low-level inversion is washed out. 
Figure 3 shows a condensed log of the field strength 
data taken on the one-way link. Maximum and mini- 
mum field strengths during successive 2-hour intervals 
are plotted, thus showing the general level and fading 
range for each frequency during a 6-week period. The 
corresponding elevation of the base of the tempera- 
ture inversion is shown by the discrete points in the 
upper part of Figure 3. It is at once apparent that the 
signal level is higher for all frequencies when the layer 
is low and also that tlie fading range is smaller under 
these conditions. For a given elevation of the layer the 
fading range is greater for the higher frequencies. 
Figure 4 shows the character of the signal received 
on the one-way link when the inversion was low and 
trapping was definitely indicated by the modified in- 
dex curve. Figure 5 shows the signals under the con- 
dition of a high inversion. The time scale is shown 
along the horizontal at the top of 547-me tape and at 
the bottom of the 52-me record. For the condition of 
a low layer and strong trapping the level of all the 
signals is high and the lower frequencies are quite 
steady. As the elevation of the layer increases the 547- 
me signal decreases below detection, the lower fre- 
quencies become less steady and the maximum level 
decreases. Figure 5 in contrast with Figure 4 clearlv 
demonstrates this situation. 
Wave Guipe THEORY 
According to the simple wave guide theory, using 
the modified index, trapping can occur only when 
AM=0; and then only when the wavelength is suffi- 
ciently small compared with the height of the reflect- 
ing layer above ihe earth. The degree of trapping 
depends upon the number of modes, or eigenvalues, 
allowed under the given boundary conditions. 
The San Pedro to San Diego continuous transmis- 
sion link yields data which can be compared with the 
simple wave guide theory. The 52-me data are of par- 
ticular interest, since for this frequency no meteoro- 
logical data have been taken which would indicate any 
modes allowed. Yet the field strength has varied over 
a range of some 30 db, the strongest fields occurring 
at times of high fields on the 547- and 100-mce links. 
Figure 6 shows the variation of the maximum field 
strength of the 547- and 100-mc frequencies versus 
the number of modes allowed as calculated from the 
meteorological data. There is no apparent correlation 
at either frequency. 
ReFLection THEORY 
It has been shown theoretically* that retlection from 
a nonhomogeneous stratum may occur, even when both 
the index of refraction and its gradient are continu- 
ous functions through the layer. The controlling fac- 
tor, for a given incident angle, is the ratio of the 
stratum thickness to wavelength, D/A. At normal 
incidence the reflection coefficient is small, even for 
D/A~0; however, such reflections have been ob- 
served experimentally.? At oblique incidence, for the 
cases where the index of refraction varies monotoni- 
cally through the layer, the reflection ratio increases 
as D/\~0. For the modified index type the reflection 
ratio increases as D/) decreases, passing through a 
maximum after which it again decreases.1 
Figure 7 shows the reflection ratio as a function of 
D/x for various angles of incidence, where here the 
index of refraction is a monotonically decreasing func- 
tion of height through the layer. The total change in 
n through the layer is taken to be 60 X 10“ which is 
the order of magnitude of the changes noted in this 
area during the summer season. For a given stratum 
thickness and height above the earth such that the 
radiation will be incident upon the layer at angles 
