166 



DIELECTRIC CONSTANT. ABSORPTION AND SCATTERING 



For values of p<^ 1 aud when the terms in p- and 

 hi,i>her powers can be neglected in the braces, tlie 

 total cross section for scattering reduces, nsing the ex- 

 plicit expressions of /S/^' and /S/^'. to 



Q. , 



128 J 



■S\' 



(e.-l)-Ur + 2)^ + 6,-[2(€,-l)(6, + 2)+9] + e, 



cm-. 

 (60) 



When the dielectric absorption vanishes, i.e., e;- 

 this reduces further to 



>0. 



Qs. 



12S7rV 

 3X^ 



n' + 2 



(61) 



wliich is the well-known Eayleigh scattering cross 

 section, since t,- = ir in this case. 



In Table 1.2 aie given the seattcring cross sections 

 computed within the range of p, 0.00157 to 0..5T6, or 

 in the drojJ diameter range 0.05 to 0.55 cm and wave- 

 length range 3 to 100 cm. Needless to say, the actual 

 cross sections for scattering at the larger p ^■alues are 

 always larger than the Eayleigh cross sections [equa- 

 tion (60)]. For p < 0.10 the scattering cross sections 

 are, within a few per cent, given by the first Eayleigh 

 term ((iO) of equation (59). However, in the present 

 case of absorbing spherical drops, the parametric 

 representati(.)n (59) of the cross section is not of 

 much practical interest since some of the coefficients 



005 aiO 0.15 0.20 025 a30 0135 0.40 0.45 QSO ClSS 

 IN CM 



Figure 1.5. Scattering cross section, Q,„ of splierical 

 water drops as a function of the drop diameter. The 

 abscissa gives the drop diameter, Z), in centimeters. 

 The ordinate scale gives logio <?s, the scattering cross 

 section Q,, being expressed in square centimeters. The 

 numbers on the carves indicate the wavelength, X, of 

 the incident radiation in centimeters. 



of the powers of p are strongly dependent on the wave- 

 length. The cross section is not a unique function of -D of the raindrops at constant wavelength and as a 

 p = (ttD/X) but is a complicated function of A and function of the wavelength at constant diameter, 

 I), and the scries representation is valid only in de- respectively. 



scribing the dependence on the diameter D of the The knowledge of the total scattering cross section 

 drops, the wavelength being kept constant. In Fig- Qs and the total cross section Qt allows at once the 

 nres 15 and 16 two families of curves have been computation of the absolute probabilities cOj, for electro- 

 plotted representing (>s as a fimction of the diameter magnetic waves falling on spherical water drops to be 



Table 12. Total scattering cross section Q, (cm^) of spherical water drops of D cm diameter. 



