DIELECTRIC CONSTANT, ABSORPTION AND SCATTERING 277 
As might have been expected, the dielectric absorp- 
tion « increases with decreasing: temperature. 
With the above values of ¢, and « the computation 
of the amplitudes a, and 5, is straightforward. The 
amplitudes a, and b, have the form 
a= Dd (a + ja) pl, (45) 
l=2n+3 
b= D>, (6° +58) ol. (46) 
l= 2n+1 
Thus we let «,*) denote the real part of the coeffi- 
cient of p° in a, and a, its imaginary part. Similarly, 
B, ©), B,@) are the real and imaginary parts of the co- 
efficient of p* in b,, etc. 
As equation (43) shows «,() anda,‘ are directly 
proportional to (—«) and (¢,—1) respectively. As 
the wavelength increases, a,‘°) changes approximately 
from —0.9 to —0.03 after passing through a shallow 
minimum on account of the variation of «. In the 
same interval a, 5) increases from about 0.5 to 1.8. 
£,©) turns out to be practically negligible, in com- 
parison with B®, which is almost constant in this 
wavelength range. 8,(°) and B,©) behave similarly. 
With £,© and B,©) the roles are inverted. 
Finally 8, and 8, both vary in the range under 
consideration. 
As a Tule, those coefficients of the powers of p ( = 
mD/) (DP = diameter of the sphere) which do not 
contain terms in ¢, and powers of ¢, separately in the 
numerator, but only the products «, «, and powers 
of «, are considerably smaller than those which do 
contain ¢, and its powers separately. 
The Attenuation of Radio Waves 
by Spherical Raindrops* 
The knowledge of the coefficients a, and b, allows 
finally the computation of the absorption cross section 
for any spherical water drops of given diameter D at 
those temperatures where the amplitudes can be 
computed. 
The absorption coefficient becomes, with the cross 
section found above, [equations (33) and (43) ], 
2 —s 
a = 0.4843 x 10° (Cre Donner) 
n=1 
db per kilometer. (47) 
In our approximation for the amplitudes, we may 
write 
a= 0.4343 x 108 S7NV 
(c1 + cop? + cap? + + ++) 
db per kilometer (48) 
*The attenuation values given in this report refer always 
to one-way transmission and are additive to the free space 
attenuation. 
where N is the number of spherical drops, each of 
volume V per cubic centimeter, \ is the wavelength in 
centimeters of the incident radiation. The parameter 
p is, as above, rD/d, D being the diameter in centi- 
meters of a drop, and the coefficients c,, c,, cs, --+ are 
the following functions of the wavelength, the tem- 
perature of the drops being taken as a constant (t~ 
18 C), 
ey 6e; 
ss (6-2)? + €?’ 
€; 5 € 
@= 357 3 @c43)*44e2 
6 €:[(é- +2) (Ze, — 10) +77] 
5 [(e--+2)?+e:7]? 
oe 4 (e— 1)?(e,+2)?+€,7[2 (6-— 1) (e,-+2)—9] +e;4 Es 
“PS [(é-+2)?+e,7] (49) 
It is possible to give the attenuation formula another 
simple form by noticing that NV is the total volume 
of water per cubic centimeter in the form of drops or 
10° NV is the total volume of water per cubic meter. 
Since the density of water is 1 g per cubic centimeter, 
numerically, the quantity 10° NV is the mass m of 
liquid water per cubic meter, in air. The transformed 
attenuation formula becomes finally 
a= 4.092 (c:+ cp?+ csp? +++) db per kilometer. 
(50) 
Tt is seen that when p= zD/d <1 so that all the 
terms in the expansion in equation (50) are small in 
comparison with c;, the attenuation factor reduces to 
4,092 me, 24.55 mes 
ints a eOue) mu Ana GD Eres 
db per kilometer. (51) 
Hence, when the diameter of the water drops is very 
small in comparison with the wavelength of the inci- 
dent radiation, the attenuation does not depend on the 
size of the drops but only on the total mass of liquid 
water per unit volume contained in the air. It is in- 
teresting to find, for a given wavelength, the largest 
diameter for which the approximation (51) can still 
be used in practice. If it is practical to use (51), (as 
in reference 12), for 
CO 
<< 2 
Cop) S55’ (52) 
then in order that (51) shall represent the attenuation 
factor within 10 per cent, the diameter of the spheres 
must (for given A), be equal to or less than D, with 
a 
ID), = aM ei cm. (53) 
; (2) 
In Table 3 appear the values of c,, c,, and D, in the 
