300 RADIO WAVE PROPAGATION EXPERIMENTS 
TasLE 17. Temperature variation of the dielectric 
properties of water. A = 1.24 cm.%8,89 
°C n ke er « @ mhos/m 
0 4.68 2.73 14.4 25.5 34.3 
3 oo 80 0058 27* 27* 36.0* 
5 5.24 2.89 19.1 30.3 40.7 
10 5.74 2.92 24.4 33.5 45.0 
15 6.17 2.88 29.8 35.5 47.8 
18 poco 2000 32.1 39.2 51.8 
20 6.53 2.77 34.9 36.2 48.6 
25 6.84 2.63 35* 23* 30.6* 
oc pote 2000 39.8 36.0 51.1 
30 7.10 2.48 44.2 35.2 50.0 
35 7.30 2.30 48.0 33.6 45.1 
40 TAT 2.11 51.3 31.5 42.4 
60 pecs 200 44* 14* 18.6* 
*Data from reference 22, at A = 1.25 cm. 
tData from reference 44, at \ = 1.26 cm. 
Taste 18. Temperature variation of the dielectric 
properties of water.38,39 ) = 1.58 cm. 
tC, n k & & o mhos/m 
0 5.24 2.90 19.0 30.4 32.0 
5 5.84 2.97 25.3 34.7 36.6 
10 6.36 2.91 32.0 37.1 39.2 
15 6.77 2.78 38.1 37.6 39.7 
20 7.13 2.61 44.0 37.2 39.2 
25 7.40 2.41 49.0 35.7 37.6 
30 7.59 2.21 52.7 33.5 35.4 
35 7.72 2.01 55.5 31.0 32.7 
40 7.81 1.80 BY te 28.1 29.7 
TaBLE 19. Relaxation times of water at different tem- 
peratures. 8,39 
°C 7 X 10!2 sec °C 7 X 10! sec 
0 19.0 25 6.8 
5 14.6 30 5.9 
10 11.85 35 5.2 
15 9.6 40 4.5 
20 8.1 
counted for with simple theoretical formulas. At any 
given temperature one single characteristic constant, 
the “relaxation time,” was sufficient to account for the 
frequency dependence of the complex dielectric con- 
stant of water. The formulas in question are the 
following: 
mies e+ én? 7 of, Soe 
14+2? 1l+2?’ 
O12 = (ey) ee 
1+2? 
(105) 
€s + €or? 
142?’ 
or 
« = n’?— k?, 
Gar €,0? (106) 
~ tae? 
and 
€5 = 2nk. 
Here 
L= or = Qnfr, 
with + denoting the relaxation time, ¢, is the static 
dielectric constant, «, the optical dielectric constant 
due to the sum of the electronic and atomic polariza- 
tions. 
Considering 7 as a parameter to be derived from 
the experimental data, one finds in Table 19 the re- 
laxation times in the 0 to 40 C temperature range. 
Table 20 refers to 10-em waves for which measure- 
ments were made in the temperature range 0 to 
40 C.*>48 In one series of measurements the wave- 
length was 9.72 cm, but this is considered close 
enough to have the corresponding data included with 
the 10-cm waves. 
The preceding table indicates that the agreement 
between calculated and measured values of n and & 
is satisfactory. It is to be noted here that the experi- 
mental results on S band were obtained by the stand- 
ing wave ratio method, those at K band with the reflec- 
tion-transmission method. 
Using equations (105) and (106), the temperature 
variation of the refractive and absorption index, or 
real and imaginary parts of the complex dielectric con- 
stant, can be tomputed at any wavelength provided 
that the relaxation time at the temperature in ques- 
tion is known. 
In tables on page 301 the temperature variation of 
the indices n and & are given. These results were com- 
puted with the aid of formulas (105) and (106). 
It is thought**** that until more extensive experi- 
mental results become available the computed values 
can be regarded as representing the best information 
available on the dielectric constant of water in the 
millimeter and centimeter range. Figure 25 represents 
the best available information on water at 20 C. 
Icr 
A certain number of measurements on the dielectric 
TasBLE 20. Temperature variation of the dielectric properties of water.45,46 2 = 10 cm. 
Refractive index n 
Absorption index k 
Experimental Experimental 
°C Cale 2X=9.72cm A= 10 cm Cale X=9.72em A = 10cm ercale «calc o mhos/m 
0 8.99 8.95 5000 1.47 1.35 p00 78.66 26.43 4.40 
5 9.04 20s S056 1.14 coo 3 nog 80.42 20.61 3.44 
10 9.02 9.00 cos 0.90 1.10 cooc 80.55 16.23 2.70 
15 8.96 pos 2090 0.76 oobe pose 79.7 13.61 2.27 
20 8.88 8.88 8.84 0.63 0.90 0.66 78.46 11.20 1.84 
25 8.80 noe Son6 0.50 coo 2006 77.20 8.80 1.46 
30 8.71 8.75 8.69 0.45 0.73 0.54 75.66 7.84 1.30 
35 8.62 soot 2009 0.40 boos one's 74,14 6.89 1.16 
40 8.53 8.60 8.56 0.36 0.60 0.40 72.63 6.15 1.02 
