TROPOSPHERIC PROPAGATION AND RADIO METEOROLOGY 145 
gradient is small, interest is mainly centered in the 
dependence of the modified refractive index M on the 
temperature and humidity distributions. Methods, 
useful in the field, have been developed for obtaining 
rapid determinations of temperature and humidity in 
the lowest levels of the atmosphere. The ordinary 
radiosonde (radiometeorograph) is not well adapted 
for this purpose since it is usually designed to give 
data at levels about 100 m apart, which often is not 
close enough to reveal the significant details of the 
M curve. Consequently it has proved to be necessary 
to develop new instruments for this purpose. 
Several types of instruments have been designed 
which can be placed on towers, or carried by slow- 
flying airplanes or dirigibles or carried aloft by captive 
balloons or kites with wires connecting the tempera- 
ture and humidity elements to measuring or record- 
ing equipment located on ground or aboard ship. 
Some such measurements have been made with 
instruments using electrical methods in which dry 
and wet electrical resistance elements are connected 
into a circuit to givé-“dry bulb” and “wet bulb” 
temperatures. Another electrical method uses the 
same “dry” temperature element but, in place of 
the wet bulb, obtains a relative humidity measure- 
ment by using an electrolytic humidity element of 
the type employed in the U. S. Weather Bureau 
radiosonde. Hair hygrometers; are definitely not 
suitable for this type of work on account of their 
lag in adjusting themselves to changes in relative 
humidity (of the order of 3 to 5 min for appreciable 
changes in humidity). 
Measurements made from airplanes have the 
advantage that it is possible to survey a compara- 
tively large area within a short time. This can be of 
great importance along coasts where conditions in 
the lowest levels of the atmosphere sometimes change 
rather rapidly with increasing distance from the 
shore. In the absence of suitable special equipment 
an ordinary psychrometer held out of the window of 
a plane will give quite satisfactory results in slow- 
flying planes, providing care is taken to keep the 
wet bulb sufficiently moist. When measurements are 
made from an airplane the height above the. ground 
is determined for each measurement by mez 1s of 
the plane’s altimeter. Unless carefully done this 
introduces the possibility of considerable error. 
In another method captive balloons, kites, ordi- 
nary radiosonde balloons, and, occasionally, barrage 
balloons have been used to carry the measuring 
elements aloft. Ordinary captive balloons will work 
in wind. speeds up to about 8 miles per hour; in 
higher winds kites or, occasionally, barrage balloons 
are used. Kites can be flown from boats even at low 
wind speeds or in calm weather. With this type of 
equipment the electrical measuring elements aloft 
are connected to an indicatiag or recording instru- 
ment at the ground or aboard ship by means of fine 
insulated wires wound around the balloon cable. 
Types of Modified Index Curves 
A large number of meteorological soundings of 
the lower atmosphere have been carried out by 
several laboratories and Service units. From these 
measurements the modified index curves have been 
calculated as a function of height, and it has been 
shown that practically all these curves fall into one 
of the six types illustrated in Figure 20. 
STANDARD TRANSITIONAL SUBSTANDARD 
I ng) Ip 
hfe h h 
M M M 
SIMPLE SURFACE 
TRAPPING ELZVATED S SHAPE  GROUND-BASED S SHAPE 
I IL, II, 
Seu Sa hae 
INVERSION ee h] INVERSION LAYER 
~ odct 
1\\NVERSION Laver 
Ficure 20. Types of M curves. 
For the standard atmosphere the M curve increases 
with height as shown in curve I. For nonstandard 
atmospheres, the M curves will take one or another 
of the forms. illustrated in curves Ia, Ib, II, Illa, 
and IIIb. Of particular interest are those curves in 
which M decreases with height for a range of alti- 
tudes. (This deorease is the result of a sufficiently 
sharp decrease in n with height as illustrated in 
Figure 15.) In this event an inversion layer is formed 
in the atmosphere. 
Throughout the range of altitudes of decreasing 
M the curvature of the rays exceeds the curvature 
of the earth. Nearly horizontal rays which either 
originate in, or penetrate into, this layer are trapped, 
and, if the layer extends far enough, energy may be 
carried to distances far beyond the geometrical 
horizon. However, the region in which the-waves or 
rays are trapped may have a thickness or depth 
exceeding that of the inversion layer. This region is 
known as a duct. Its precise definition may be taken 
from Figure 20. It is the strip between an upper 
minimum of the M curve and either the ground or 
the point where the vertical projection from the 
upper minimum intersects the M curve. There are 
two main types of ducts, the ground-based duct, 
illustrated by curves II and IIIb, and the elevated 
duct, illustrated by curve IIIa. 
The height in the atmosphere at which the varia- 
tions in refractive index occur may vary from a few 
feet to several hundred or even a few thousand : 
feet. These variations are likely to be found at fairly 
low elevations in cold climates and at the higher: 
elevations in warm climates. The meteorological con- 
