DIELECTRIC PROPERTIES OF WATER AND ATMOSPHERE 



183 



ured, this dielectric constant may be derived from the 

 relation 



27rO€r 



= 2.4048 



or 



= 0.1461-1 = 



C-.)' 



(102) 



No appreciable error will be committed in using the 

 preceding results for the ftractical case of dielectrics 

 with low but finite conductivity. 



The Q of the filled cylindrical resonator is shown 

 to be 



a 



Q = 



'0+^) 



+ a tan 5 



Here (/ is the wave-guide skin depth, ^z„ is the axial 

 length of the resonator and tan 8 = £,/c,- is the loss 

 factor of the dielectric. Consequently 



'""' = ^-^' 



(104) 



where (J^ is the (J of the air-filled resonator. 



It should be remembered in this connection that 

 the theoretical Q„ values, in general, are found to be 

 considerably different from the measured ones. This 

 tends to limit the reliability of the method. 



After having thus sketched the diff'ereut methods 

 used in the determination of the complex dielectric 

 constant of substances of importance in wave propaga- 

 tion, we turn now to the presentation of the data. 



Liquid "Watee 



Table 17 gives 

 liquid water, 



the 



38,39,44 



results obtained recently on 



Table 17. Temperature variation of the dielectric 

 properties of water. X = 1.24 cm.ss>39 



(°C 



(I a nihos/m 





 3 

 5 

 10 

 15 

 18 

 20 

 25 



30 

 35 

 40 

 60 



4.68 



5.24 

 5.74 

 6.17 



6.53 

 6.84 



7.10 

 7.30 



7.47 



2.73 



2.89 

 2.92 

 2.88 



2.77 

 2.63 



2.48 

 2.30 

 2.11 



14.4 



27* 



19.1 



24.4 



29.8 



32.lt 



34.9 



35* 



39.8 



44.2 



48.0 



51.3 



44* 



25.5 



27* 



30.3 



33.5 



35.5 



39.2* 



36.2 



23* 



36.0 



35.2 



33.6 



31.5 



14* 



34.3 



36.0* 



40.7 



45.0 



47.8 



51.8 



48.6 



30.6* 



51.1 



50.0 



45.1 



42.4 



18.6* 



]t has been found by Saxton and Lane that the 

 temperature variation of the dielectric constant in the 

 range to 40 C at 1.24 and 1.58 cm can be ac- 

 counted for with simple theoretical formulas. At any 

 given temperature one single characteristic constant, 

 the ''relaxation time,"' was suflficient to account for the 

 frequency dependence of the complex dielectric con- 

 stant of water. The formulas in question are the 

 following : 





+ 



1 + .r^ ■ 

 e, + f„.r- 



(105) 



(103) or 



= n'- - k' 



+ tsX- 



(106) 



1 + x'- 



and 



e, = 2nk. 

 Here 



X = COT = 2tJt, 



with T denoting the relaxation time, cj is the static 

 dielectric constant, «„ the optical dielectric constant 

 due to the sum of the electronic and atomic polariza- 

 tions. 



Table 18. Temperature variation of the dielectric 

 properties of water.'8,39 x = 1.58 cm. 



l°C 



6( a mhos/m 







5 



10 



15 

 20 

 25 

 30 

 35 

 40 



5.24 

 5.84 

 6.36 

 6.77 

 7.13 

 7.40 

 7.59 

 7.72 

 7.81 



2.90 

 2.97 

 2.91 

 2.7S 

 2.61 

 2.41 

 2.21 

 2.01 

 l.SO 



19.0 

 25.3 

 32.0 

 38.1 

 44.0 

 49.0 

 52.7 

 55.5 

 57.7 



30.4 

 34.7 

 37.1 

 37.6 

 37.2 

 35.7 

 33.5 

 31.0 

 28.1 



32.0 

 36.6 

 39.2 

 39.7 

 39.2 

 37.6 

 35.4 

 32.7 

 29.7 



Considering t as a parameter to be derived from 

 the experimental data, one finds in Table 19 the re- 

 laxation times in the to 40 C temperature range. 



Table 19. Relaxation times of water at different tem- 

 peratures.2'i39 



*Data from reference 22, at X = 1.25 cm. 

 ^Data from reference 44, at ^ = 1.26 cm. 



