ACTINOMETRIC MEASUREMENTS ol 
pheric gases, especially by water vapor and carbon 
dioxide. This absorption is not a simple function of the 
wave leneth, but is concentrated in certain spectral 
regions. The conditions are, however, simplified by the 
fact that the selective absorption by the variable gases 
is almost entirely confined to the far red and the infra- 
red, where the principal water-vapor and carbon dioxide 
bands occur. Only a small part, about 1-2 per cent of 
Qm +F 
(0) 2 3 4 5 6 
AIR MASS, m 
Fre. 1.—Atmospherie turbidity 6 according to Angstrém- 
Hoelper. Ordinate: total radiation measured (Q,,), with addition 
of water vapor absorption (/). Abscissa: air mass (unit vertical 
air mass at sea level and 760 mm). Actinometric scale: Smith- 
sonian. 
the total energy is subject to a variable absorption 
within the visible and the ultraviolet. 
Consequently, the total incoming solar radiation 
Qm, as measured for instance with a pyrheliometer, may 
be expressed as 
Qn = [ Inq” exp (—Bm/d"*) dd — F. (2) 
In this equation we may assume Q,, to be known from 
measurements; Jo,, the radiation outside the atmos- 
phere at the wave length X, is known from the elaborate 
investigations by the Smithsonian Institution (Abbot 
and collaborators) ;! q, the transmitted fraction of the 
incident energy for unit air mass (if only molecular 
scattering is considered), is computed from the theory 
of Rayleigh,? the air mass m is computed from the 
observed elevation of the sun (m is unity for zenith 
position of the sun). If we assume a to have a given 
value, the only unknown quantities are 6 and F. The 
total selective absorption Ff’ has been expressed by 
Fowle through the linear equation 
F = 0.10 + 0.0054e0m, (3) 
where é is the water-vapor pressure (mm Hg) at the 
surface of the earth, and m is the air mass. It is evident 
from several considerations that Fowle’s equation must 
include rather rough approximations. However, if we 
accept it as a first approach, it is evident that the 
quantity 6, which is a measure of the dust content, may 
be determined from equation (2) and a single pyrhelio- 
metric observation. In practice this determination is 
made by a graphical evaluation of the integral for 
various values of e) and m—made once and for all. The 
value of 6 which makes the value of the integral equal 
to the measured value of the radiation increased by 
F is then obtained from a diagram or from tables. We 
may effect the computation most simply by plotting 
the observed radiation, increased by F’, on the diagram 
shown in Fig. 1 and interpolating the value of 6. 
We can, however, derive a similar result more ac- 
curately if we add another pyrheliometric measure- 
ment to the one covering the total solar spectrum. By 
using a colored glass filter—RG 2 or OG 1 for instance— 
we can examine separately a part of the spectrum cover- 
ing all wave lengths longer than a given limiting value. 
The filter RG 2, for instance, lets through all radiation 
of wave lengths longer than about 0.6 ». With due 
regard to the nearly constant reflection (1 — y) by the 
filter (where y is the fraction of incident radiation trans- 
mitted by the filter, that is, its transmission coefficient), 
we obtain for the observed filter radiation Q,, in per- 
fect analogy with equation (2), 
Q.= 7 | Inv0n, 6,» dr — oF, (4) 
where 
y = q™ exp (—Bm/d"). 
The value of F may here be assumed with good ap- 
proximation to be the same as in (2). Hence, from equa- 
tions (2) and (4), we obtain 
Qm-2Q=[ Tova-f[ inva ©) 
or 
0.6 
OL oe [ Tou an. (6) 
Vi 0 
1. Given for instance in F. Linke, Meteorologisches Ta 2- 
buch, IV, Table 109, p. 238 (Akad. Verlagsges.) Leipzig, on, / 
2. See F. Linke, Meteorologisches Taschenbuch, IV, Lable 
113, p. 240. 
