40 RADIATION 
caused by smoke or combustion gases from the chim- 
neys of London. Quite similarly, Falckenberg [16] tried 
to explain the deviations he found for different air 
masses not by temperature gradients, but by the haze 
content which is not indicated by the water vapor. 
Volz [49] attempted to measure the emissivity of various 
substances in the laboratory. 
Robitzsch [45] pointed out another as yet unex- 
plained relationship. He established the formula 
R = oT) (0.135p + 6.0e) 
which includes not only the vapor pressure €o but also 
the air pressure p. This formula permits, in particular, 
the use in the interpolation equations of measurements 
on mountains or in the free atmosphere. Whether the 
term containing the air pressure can be attributed to 
an effect of the CO, content or to a diminution of ground 
inversion with decreasing values of p (anticyclonic and 
cyclonic conditions) would have to be determined by 
future research. 
F. A. Brooks [7] and Robinson [43] developed radia- 
tion diagrams based upon observational data exclu- 
sively. The above-mentioned law for monochromatic 
radiation, according to which the radiation of an at- 
mospheric layer is equal to that of a cylindrical column 
of air with °8 times the water-vapor content, applies 
also to the “chromatic” radiation of the natural CO», 
plus H,O atmosphere. Therefore, a radiation diagram 
for diffuse radiation can be used also for the investiga- 
tion of linear or parallel radiation arriving from a 
definite zenith distance if we multiply the vapor scale 
by 1.66. The authors cited above proceeded conversely 
and developed from the measurements of a zonal sky 
radiation a grapb that was then adapted to the use of 
hemispheric radiation.’ 
Atmospheric radiation finds an important applica- 
tion in the theoretical investigation of the nocturnal 
cooling process and in the prediction of frost. It has 
been shown by various authors that the nocturnal 
cooling cannot be traced essentially to a heat emission 
of the air by radiation (see the objections raised to this 
on page 45). The decisive factor is the heat loss from 
2. (Note added July, 1950.) Robinson [44] recently published 
a detailed test of his diagram and of the Elsasser chart, for 
which he used numerous radiation measurements made at 
Kew. He found considerable differences which, to a great ex- 
tent, are caused by the change in the emissivity of a vapor 
layer with temperature. According to his measurements, the 
emissivity increases with increasing temperature, whereas 
according to calculations by means of the Elsasser chart, it 
decreases by an amount half that of the measured increase 
(see numerical data on page 39). The prerequisites for the 
explanation of this discrepancy are as follows: (1) new experi- 
mental investigations are needed which would furnish the 
variation of absorption by vapor layers of finite thickness; (2) 
the theoretical computations must be checked; the change in 
radiation with temperature is derived (a) from the displace- 
ment according to Planck’s radiation law, (b) from the change 
in the width 6 of a spectral line with./7, and (c) from the 
change in the line intensity S with temperature. It appears 
that the last two influences have, to date, not been sufficiently 
considered. 
the ground by its effective radiation, and the distribu- 
tion of this heat loss through conduction into the 
ground and through convection into the air. In the 
theoretical treatment of this problem the effective ter- 
restrial radiation H = oT)'-— R was often assumed to 
be constant. However, o7'o* decreases with progressive 
cooling, and R decreases with the development of a 
ground inversion, but somewhat more slowly. Groen 
[21, 22] pointed out the necessity as well as the possi- 
bility of considering the change of # with 7) by means 
of the radiation diagram in such a way that the equa- 
tions for the nocturnal cooling continue soluble. His 
final equation represents an important step forward 
in the theory of nocturnal cooling, especially since he 
can include in his equation the different disturbing 
influences such as initial temperature distribution, con- 
densation, and the influence of the wind on turbulent 
heat exchange. 
The Absorption Coefficient as a Function of Pressure 
So far we assumed the absorption coefficient k, to 
be independent of pressure and temperature. However, 
that is not exactly the case. True, the variation is so 
small that the downcoming atmospheric radiation at 
the ground is not materially changed, because 88 per 
cent of it originates in the lower 500 m of the atmos- 
phere where the pressure differs little from that at 
ground level. At higher altitudes, however, the varia- 
tion is more effective. The individual absorption line in 
a band spectrum increases its half-value width with 
increasing air pressure and temperature. Yet the ‘‘total 
intensity” of the line, that is, i) k,dv, is not changed. 
Only the shape of the line is altered. With increasing 
pressure it becomes wider and less intensive, with de- 
creasing pressure 1t becomes narrower and more in- 
tensive. This means that, as the pressure decreases, 
the absorption increases even more in the narrow center 
of the line with a large value of k,, whereas k, becomes 
even smaller on the wings of the line [14]. As to the 
absorption by a line, it is found that, im thin layers, 
the radiation is absorbed almost completely in the core, 
whereas only in the case of thicker layers is the radia- 
tion also absorbed in the wings. With decreased pressure, 
the absorption in the core is increased and is very effec- 
tive over the first part of the optical path length. How- 
ever, subsequent absorption over the remainder of the 
path is diminished because of the small amount of 
radiant energy left to be absorbed. Since the initial 
segment can hardly be observed, the measurements 
indicate only that the mean absorption coefficient is re- 
duced [46] in proportion to 1/p/po. In the absorption 
formulas k appears only in the product k-m. Therefore, 
it is customary to apply the factor » = +/p/po not to 
k, but to the radiating mass m or to the densities of 
water vapor and CQ». This correction is very important 
for all investigations into the radiation phenomena of 
the free atmosphere. 
The intensity S ofaline, S = / k,dy, remains un- 
changed with a change of the line width 6 because of 
