336 
into two or more returned components, and the angle 
of arrival give information concerning the medium re- 
sponsible for return of the wave energy. 
In terms of the penetration frequency fo and the 
wave frequency f, the index of refraction for elementary 
purposes is given by 
(2) 
Clearly the index of refraction is a function of frequency 
and therefore the ionosphere is a dispersive medium. 
Usually, also, each successive wave packet emitted is 
of a radio frequency differing incrementally from that 
preceding. When this process is carried out over a large 
frequency range, the results can be recorded on a graph 
€ 
as In Fig. 2. 
2 
[e} 
= 
2 = 
8 E 
EB if) 
o = 
: E z 
z Ss = 
a = ira} 2 
5 = a ro) 
i < oO 
w Fe Zz Cc 
oe ft) ° iva 
Se z ro) 1 
in w a 
S o ina = 
5 1 
ial ee ae ee 
es cae 
uw 
x Ww a E- 
Sef oS 8 =— REGION 
WE > WwW re 
x= So ees 
a 2 
20 2 | R-Recion 
=) = a, 
a }E-REGION 
Su 
EMITTED PULSES 
WAVE FREQUENCY ——> 
TIME REQUIRED TO SWEEP OVER THE FREQUENCY RANGE ——> 
Fie. 2.—Typical data obtained by radio sounding of the 
ionosphere. 
This is the usual form taken by data embracing time 
of flight versus frequency in temperate latitudes during 
daylight. Splittimg of the original wave packet into two 
or more components is caused by the effect of the earth’s 
magnetic field. Transmission and reception are at verti- 
cal incidence. This technique is the most widely used 
and is an elegant development of the original Breit- 
Tuve experiment. Study of the ionosphere at vertical 
incidence immensely simplifies the general theory for a 
special case and, although involving some approxima- 
tions, has given the bulk of useful information about 
the ionosphere. This procedure fails at low frequencies 
and is usually replaced by the Appleton-Barnett phase- 
interference method. Polarization and angle-of-arrival 
measurements are quite important but have been little 
used systematically because of inherent interpretative 
and instrumental difficulties. More attention should be 
given to them because some uncertainties in the theory 
cannot be resolved otherwise. 
The amount of information to be derived from data 
represented in Fig. 2 has not been fully realized. For 
years it was known that the time of flight of a wave 
THE UPPER ATMOSPHERE 
packet to and from the ionosphere did not measure the 
height of the region returning the wave energy. It was 
not until about 1940, however, that the heights and 
reasonably sure distributions of ionization were possi- 
ble. The theoretical investigations of Booker and Seaton, 
and especially of Rydbeck, now permit distributions to 
be determined from data in the form of Fig. 2. Briefly, 
the Booker-Seaton relationship is as follows. 
Define a function 
ae eh 1+ 2 id 
ola) = Sin Ft?) 1, (3) 
and write 
h’ = hy +7 - O(f/fo), (4) 
where h’ is the virtual (or apparent) height at a wave 
frequency f, and fo is the penetration frequency. If 
heights at two convenient values of f are taken, 7 (the 
semithickness of the parabolic distribution) and hy, 
(the height of maximum electron density) may readily 
be determined. 
Because of the discontinuities evident in Fig. 2 it 
was believed at first that the ionosphere was divided 
into discrete layers. Application of Rydbeck’s equations 
gives a different viewpoint and indicates a general 
region wherein maxima and minima of ionization oc- 
cur, but probably no sharp separation into strata. 
The difference between penetration frequencies in a 
region is a measure of the strength of the earth’s mag- 
netic field at that height. The reason for this is given 
in the complicated magneto-ionic theory. 
Probable Distribution of Ionization 
Consider Fig. 3, in which the heavy curves represent 
oft-measured quantities, heavy broken lines infrequent 
400 
300 
200 
HEIGHT IN KILOMETERS 
100 
=== jy) 
Fic. 3.—Contemporary ideas of free-electron distribution in the 
ionosphere. 
determinations, and dashed lines estimates based upon 
what seem at present to be reasonable assumptions. 
Parabolic distributions are shown, but may be replaced 
