156 



DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 



Using eqiuitidu (40) in Uie amplitudes (38) one 

 gets 



ai = — [— ei — j (er — 1) ] p^ 

 45 



Re bi = 



2ei 



(e. + 2)- + e,= 5 



[(e. + 2)(7t.-10)+76,^] . _ 4 



(t,-l)2(e. + 2)2 + e,2[2(e.-l)(e, + 2)-9] + e,^^, 



. , 2 (.. - 1) (6. + 2) + er- 3 2 



Im Oi = — p^ — - ■ 



3 (.. + 2)2 + 6^2 5 



(£.-l)(«.-2)(e.+2)2 + e,= [2(e,+ l) = -(3e.+20)] + e,* 



[(€. + 2)2 + e,2]^ 



i£,[(6.-l)(e. + 2)+€,2] , 



+ 



[ (e. + 2)2 + 6,2]^ 



^ 1 -6.-(i/5) [dr- 1) (26. + 3) + 2e,2] , 



02 = — P • 



3 (2€. + 3)= + 4ei2 



(43) 

 These amplitudes are the same as those found by 

 Eyde.s They allow the computation of attenuation 

 and back scattering with a certain approximation. 

 The results thus obtained are the more accurate, the 

 smaller the parameter p = Zwa/K. 



In the computation of the amplitudes a„ and &„ 

 we have used the same values of the real and imag- 

 inary parts of the dielectric constant of water cr and 

 £j as the ones used by Kyde. These were obtained by 

 using the Clarendon Laboratory values for e. and a 

 for waves of 1.26-cm wavelength" and determining 

 with them the transition wavelength Xo in the Debye'' 

 formulas 



€r ~~ 6op -p 



1 + 



6i - 



(«r - eop), (44) 



e Ip = 1.33, t^ = SI, Xu= 1.59 cm. 



The values of t,. computed with these formulas happen 

 to be ill fair agreement with the experimental valuer 

 obtained by a large group of independent workers."'-- 

 There seems to be a regrettalile situation concerning 

 the values of £,-, and no serious studies have been made 



"In his first report. Rj'dei' gave incorrectly the coefficients 

 of p'" in both the real and imaginary parts of bi. The coefficient 

 of p5 in the real jiart was corrected in the second report. In 

 comparing the bi's witli the amplitudes given by Ryde, the 

 relations (38) have to be taken into account. 



Table 1. Values of the dielectric constant of water at 

 t --^ ISC, used in this work.* 



*The computations of the attenuation and scattering effects are all 

 based on this table and refer therefore always to temperatures of about 

 ISC, unless stated otherwise. 



Table 2. Temperature variation of the dielectric 

 constant of water (K band). 



Degrees C 



on the temperature and frequency variation of this 

 quantity, so fundamental for the microwave region. 

 A beginning in this direction has been undertaken by 

 the Eadiation Laboratory.-^ In Figure 4 we have 

 drawn the curves er{k) and £i(A) in the range 1 to 11 

 cm, and Table 1 gives the values of the dielectric con- 

 stant used in tliis work in the wavelength interval 1 

 to 100 cm. 



It is interesting to consider here the temperature 

 variation of e^ Eeceut measurements made in the 



80 



70 

 60 



«r 50 



40 

 30 

 20 





30 



20 



10 



1234 56789 10 H 



A IN CM 



Fkiuue 4. Dielectric constant of water (/^lSC)£c = 

 «r —jfi- 



