SOLAR RADIANT ENERGY 23 
is in excellent agreement with Linke’s results [55, p. 
248]. 
Spectral Scattering by Water Vapor. The perenne 
is, however, never pure nor dry; both dust and water 
yapor are ever present in varying degree. Fowle [28] 
examined the transmission of the atmosphere at wave 
lengths where water vapor does not absorb. At those 
wave lengths, if dust is neglected, 
Th = Ip exp(—saym) exp(—suxwm) au 
= To, ardor)” = Ipnax. 
Here the transmission coefficient through one dry at- 
mosphere at vertical meidence is given by aa = 
exp(—Sa) and through one centimeter of precipitable 
water vapor by a», = exp(—s.a). From equation (14) 
(15) 
G = Acar Ay, 
or 
In a = In aa + w In ay. (16) 
A plot of In a against w should yield a straight line 
whose slope is In @,,, and whose intercept at w = 0 is 
In ay. Hence, @,,, and aa, can be determined. 
As might be expected, for a given \ the observed cor- 
responding values of In a and w do not fall exactly on 
a straight line. In order to remove random fluctuations 
Fowle compiled average values, but it is not clear 
whether he averaged values of a, or of In ay. At any 
rate, Fowle plotted his average In a, against w. The 
points still scatter quite a bit, but the “best” straight 
lme was drawn through the data, and the correspond- 
Mg ao, and a,, were determined. His values of ay, are 
given by List [56]. 
Fowle [28] assumed that the \~* law (equation (11)) 
applied also for scattering by water vapor and found 
that his transmission coefficients a,, were such that 
the scattering is greater than might be expected from 
the number of water-vapor molecules. He concluded 
from this that the water vapor existed as aggregates of 
water-vapor molecules (see also [76]). Moon, however, 
using Fowle’s data, plotted the logarithm of the average 
@» against In \, and found that 
(17) 
Ay & Nes 
Any relation between a,, and » (such as equation 
(17)) should apply for a single set of measurements of 
Gy. It seems necessary therefore to plot In \ against 
In a@,, and not against In a,,. Differences in their pro- 
cedure perhaps account for the difference in the wave- 
length laws obtained by Moon and by Fowle. 
It should be pointed out that Angstrém [11] ques- 
tioned the validity of assuming that the water vapor 
was the actual scattering agent. If dust and water- 
vapor advection usually occur together so that an in- 
crease im one accompanies an increase in the other, it 
may be the dust which is actually performing the scat- 
tering. However, Fowle evaluated the effect of dust in 
his data, and found it to be only about one-half of 1 per 
cent for a and 2 per cent for a», [28]. As these con- 
flicting views indicate, the wave-length dependency of 
water-vapor scattering 1s not very well known. 
Total Water-Vapor Scattering. Here again the total 
transmission is often desired in lieu of the spectral 
transmission. With the aid of Fowle’s data for a, and 
Gx, Kimball [52] computed the fractional transmission 
of solar energy at normal incidence through a dustless 
atmosphere for various values of w. The computations, 
which include scattermg but exclude absorption, are 
shown in Fig. 6 by the dashed curves (1) through (8) 
for values of w up to 6.0 cm. By adding the depletion 
due to water-vapor absorption, Kimball computed the 
transmissions shown in curves (9) through (15); the 
latter curves include the effect of both scattering and 
absorption. 
AIR MASS, m ( PRESSURE-76,0 cm.) 
wm 
Fig. 6.—Fractional transmission of solar energy through 
the earth’s atmosphere. Curves (1)-(8), scattering only; 
curves (9)—(15), scattering plus absorption by precipitable 
water vapor (w) amounts shown on curves; curve (16), frac- 
tional absorption by water vapor as a function of wm. (After 
Kimball [52).) 
Dust. There remains the scattermg from the direct 
solar beam by dust. Angstrom [11] has derived a law 
for dust extinction,’ 
San = Beer (18) 
where @ is a constant representing the number of scat- 
tering particles, and y another constant representing 
the size of the scattering particles. Angstrém describes 
graphical methods for obtaining # either from a total 
radiation measurement or by filter measurement. By 
analyzing the spectral measurements of the Smith- 
sonian Institution, he found y = 1.3 on the average. 
From laboratory measurements of the relation between 
y and the size of scattering particles, he showed that 
the average size of the scattering particles was 1 yw. Ives 
and his co-workers [48], however, have found from ac- 
tual particle measurements near the ground in cities 
that the most frequent diameter size is near 0.5 uw. Their 
2 . . . . 
7. Angstrém’s extinction coefficient, here designated by say, 
includes seattering by water vapor, but not absorption. 
