24 RADIATION 
findings are valid only for particles larger than 0.2 in 
diameter because their microscope could not detect 
smaller particles. Recently Crozier and Seely [22], mak- 
ing measurements from airplanes, found the greatest 
frequency of particle diameter in the free air to be 3-6 p; 
their instruments could not catch the smaller particles 
efficiently. Linke and von dem Borne [55] showed that 
y varied with the altitude of the observing station and 
from place to place. In general, for higher altitude and 
less smoky areas, y was larger than elsewhere, and 
hence the average particle size was smaller. 
All these are average values, and both 6 and y vary 
with time even at one observing station, for the num- 
ber, size, and shape of the scattermg particles vary con- 
tinually. Also, at any time the whole spectrum of par- 
ticle sizes ranging from below 0.2 u to 1 w and larger are 
to be expected. 
This complex scattermg by particles which are larger 
than molecules is a serious problem in spectral measure- 
ments. In particular, dust is troublesome in ozone 
measurements which ordinarily utilize light at 3000- 
4000 A where differential spectral scattering usually be- 
comes an important problem. Ramanathan and Kar- 
andikar [70] found that peculiar ozone effects can easily 
be produced by improper assumptions regarding dust. 
They also found, as might be expected, that y is not 
really constant and that in India it lies on the average 
between 0 and 1.3 in the region 3000-4450 A. 
Another measure of the dust parameter, the “tur- 
bidity factor,” was designed by Linke. He defines the 
turbidity factor 7 from 
IT, = In exp(—kaxt,m), (19) 
where 
Kan = Kax + KwxwW + kad, 
Kay, kw, and ka, are the extinction coefficients of air, 
water vapor, and dust, respectively, and d represents 
the “quantity” of dust [55, p. 266]. He uses an ‘“‘appro- 
priate” average value and integrates equation (19), so 
that 
I = I) exp(—karm), (20) 
where k,, and t now represent mean values over wave 
length. Such averages cannot really be obtained, so 
that the discussion which follows represents an ap- 
proximation. 
Let J;, designate the intensity of light transmitted 
through a pure dry atmosphere; then e*" = [),/Ih. 
Equation (20) can now be written 
In Jo — In I 
T lima (1) 
2 
By means of equation (21), 7 can readily be computed 
from a single measurement of J, for Jp is a constant 
(generally taken as 1.94) and J;, can be obtained from 
graphs such as Fig. 6. 
In equation (20), 7 can be interpreted as the number 
of pure, dry air masses which would produce the ex- 
tinction observed in the moist, dusty atmosphere. It 
was found, however, [42, 55] that 7 was a function of m 
and thus was not a reliable measure of turbidity. To 
overcome this defect, Linke [55] decided to relate 7, not 
to a dry air mass, but to a dustless air mass containing 
1 cm of precipitable water vapor. Instead of J,, in 
equation (21), we therefore introduce J;,,..1. The 
new turbidity factor becomes 
@ = ©, In (1/D) (22) 
where 
pi Lig walle cae 
BS Nn Tig = Von Tomei’ 
Linke’s values of ©,, are given in Table III. 
TaB.LeE III. VaLuns oF ®,, IN HQuaTIon (22) 
(Afler Linke [55)) 
m | 0.5 1 Be Fae | a | sw 
Py, P3)81) |} 113}.f597/ '9.607.97/6.04.5.02 3.80 | 3.10 | 2.63 
With the aid of a single pyrheliometric measurement, 
© can be computed. According to Linke, it will vary 
relatively little with air mass; any observed diurnal 
variation of © will be a real variation in turbidity. 
Turbidity factors for portions of the spectrum have also 
been designed and can be measured with filters [55]. 
Neither Angstrém nor Linke attempted to separate 
scattering by water vapor from scatterimg by dust, and 
indeed, as Angstrém pointed out, it may not be valid 
to do so. However, Kimball [52] assumed that scatter- 
ing by dust could be separated. He estimated w from 
either surface vapor pressure or radiosonde data. He 
measured 7 and computed the transmission a = I/Ip. 
From Fig. 6, he found a@»,., the transmission through 
a dustless atmosphere containing w em of precipitable 
water vapor. Then a,,. — @ = dg, the fraction of Ip 
which is depleted by the dust. The value of da, of course, . 
varies with m. Klein [53] gives some values of da which 
vary from 0 to 0.09 for m = 1, and from 0 to 0.13 for 
m = 2. 
Wexler [78] and Haurwitz [42] have discussed the 
turbidity factors of Angstrém and Linke and conclude 
that neither is wholly satisfactory. These factors are, 
however, among the best simple methods available at 
present for determining the atmospheric turbidity quan- 
titatively. Although expressions of the total turbidity 
such as 8 may have some specialized uses, for spectral 
measurements such as those involved in ozone and solar- 
constant measurements we shall have to know more 
about the way dust affects light of various wave lengths. 
This will probably involve determination of the size 
and number of dust particles above an observer, which 
in turn may be helpful in studies of condensation nuclei. 
Scattering by Liquid Water Droplets. Scattering of 
light by spherical particles which are not very small in 
comparison with the wave length is given by the well- 
known Stratton-Houghton curve. Recently Houghton 
and Chalker [46] have extended the earlier computa- 
tion; their results appear in Fig. 7. The extinction by 
spherical water particles (refractive index 1.33) is re- 
