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DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 285 
TABLE 12. Total scattering cross section Q, (cm?) of spherical water drops of D em diameter. 
D, em 
A,em =: 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 
3 3.621078 2.3510-§ 2.7410-5 1.5810-4 6.061074 1.981078 5.3610-$ 1.311072 2.9610-? 6.36107? 1.31 10-1 
5 4.7010-9 3.041077 3.5110-§ 1.9710-5 7.5610-5 2.3210-4 5.971074 1.3610-3 2.8610-3 5.6110-8 1.04102 
8 7.23107! 4.641078 5.351077 2.9810-§ 1.141075 3.4410-5 8.7210-5 1.9610-4 4.0110-4 7.651074 1.37 10-3 
10 2.93107! 1.8810-8 2.151077 1.211076 4.6210-§ 1.381075 3.50105 7.851075 1.59104 3.0110-4 5.41 10-4 
15 5.8010" 3.7510-9 4.331078 2.431077 9.0310-7 2.7010-§ 6.8010-§ 1.5210-5 3.10105 5.871Q-5 1.0410-4 
20 =1.8310-! 1.171078 1.351078 7.5110-8 2.861077 8.531077 2.16106 4.8110-§ 9.7410-§ 1.8310-5 3.25 10-5 
30 3.6210-! 2.321079 2.6610- 1.491078 5.6610-§ 1.691077 4.111077 9.5110-7 1.92106 3.6210-6 6.43 10-6 
50 4.6510-!8 2.991071! 3.4410-19 1.911079 7.291079 2.181078 5.5110°8 1.221077 2.481077 4.651077 8.271077 
75 9.2210-“ 5.91107! 6.7910! 3.7810-!9 1.441079 4.3110-9 1.08108 2.42108 4.9110-§ 9.221078 1.63 10-7 
100 §=2.9310-M 1.881071? 2.15107! 1.201079 4.561071 1.371079 3.4510-9 7.641079 1.5610-§ 2.931078 5.20 10-8 
representation (59) of the cross section is not of computation of the absolute probabilities @, for electro- 
much practical interest since some of the coefficients 
of the powers of p are strongly dependent on the wave- 
length. The cross section is not a unique function of 
p = (rD/d) but is a complicated function of A and 
D, and the series representation is valid only in de- 
scribing the dependence on the diameter D of the 
drops, the wavelength being kept constant. In Fig- 
ures 15 and 16 two families of curves have been 
plotted representing Q, as a function of the diameter 
D of the raindrops at constant wavelength and as a 
function of the wavelength at constant diameter, 
respectively. 
The knowledge of the total scattering cross section 
Q, and the total cross section Q; allows at once the 
DIN CM 
FicureE 15. Scattering cross section, Q;, of spherical 
water drops as a function of the drop diameter. The 
abscissa gives the drop diameter, D, in centimeters. 
The ordinate scale gives logio Qs, the scattering cross 
section Q, being expressed in square centimeters. The 
numbers on the curves indicate the wavelength, X, of 
the incident radiation in centimeters. 
magnetic waves falling on spherical water drops to be 
scattered in any direction and the absolute probabil- 
ities @,,,, for being absorbed by the drops, the absorbed 
energy being then transformed into heat in the drops 
(true absorption). Indeed, this probability w, of the 
waves being scattered in any direction is equal to the 
ratio of the scattering cross section Q, to the cross sec- 
tion Q+ which is associated with all the possible even- 
tualities, here only two, namely, scattering and true 
absorption. Heuce, 
an 
®, = — (62 
Q : 
and, consequently, the probability of true absorption is 
Wabs = 1 a Qs. 
(63) 
-14! 
o 10 20 30 40 80 60 70 
D INCH 
60 90 100 
FicureE 16. Scattering cross section, Q;, of spherical 
water drops as a function of the wavelength. The 
abscissa gives the wavelength, A, of the incident radia- 
tion in centimeters. The ordinate scale gives logic Qs, 
the cross section Q; being expressed in square centi- 
meters. The numbers of the curves indicate the drop 
diameter, D, in centimeters. 
