76 METEOROLOGICAL OPTICS 
be relatively large. These particles may diffract the 
light dominantly at the angle g, toward the observer O, 
whose horizon is HH’, and for whom the sun’s depres- 
sion is 6. At the higher points P2 and P3, the prevailing 
sizes of the dust particles become successively smaller 
and the diffraction angles g, and ¢3 correspondingly 
larger. Since the incident beam is reddish, the dif- 
fracted rays converging toward O will outline a reddish 
area in the sky. The observer sees only those diffracted 
rays that fall in his cone of vision (and are sufficiently 
intense); for example, a particle at P,’ of the same size 
as that at P; and one at P,’ of the same size as the one 
at Po, will also diffract light toward O. It may be noted 
that an observer, for whom the sun is still above the 
horizon, may see Bishop’s ring around the sun. Also, 
the light scattered and diffracted by the dust layer in 
the region of the purple light is sometimes sufficiently 
intense to cause a secondary purple light for an ob- 
server located farther on the night side of the earth 
(z.e., to the right of observer O in Fig. 14). The red light 
diffracted by the dust layer and augmented by blue 
light scattered by the air in the region S,S2S3; above 
gives rise to a purplish tone. 
Fie. 14.—Schematic diagram for the purple light. 
From the geometric aspects we can see that the areal 
extent of the purple light depends on the particle size 
distribution, the thickness of the layer, and absorption. 
The latter generally prevents the purple light from 
appearing as a circular arc. The theory does not predict 
the exact color and intensity of the phenomenon; these 
depend on the modification of the incident beam by its 
first passage through the dust layer, its further fate in 
the air below this layer, the specific effect of the dust on 
the beam after re-entrance into the layer, and, finally, 
the modification of the diffracted light on the way to 
the observer, in conjunction with the sky light from 
above. For a homogeneous dust layer, an optimum 
particle concentration and size distribution must exist, 
whereby the red component of the incident sunlight 
experiences a minimum depletion on its first passage 
through the dust layer and produces maximum in- 
tensity of diffracted light when again penetrating the 
layer. 
In general, there are too many unknown variables, m 
particular the scattering function of the dust particles 
and attenuation of the direct rays, to render the problem 
as a whole accessible to an analytical solution, especially 
when multiple dust layers are involved. For the present, 
it appears most expedient to provide reliable observa- 
tional material by means of which the available theories 
may be checked more adequately. In order to eliminate 
from such material all the subjective variables that are 
involved in visual observations, only objective methods 
of observation should be employed. The design of the 
spectrophotometric equipment should incorporate the 
features of very high sensitivity, to enable the use of 
filters with narrow transmission bands, and of rapid 
response, so that the major portions of the sky area 
could be scanned within a few minutes. By means of a 
wide station network, the question regarding the cause 
of asymmetric twilight phenomena that have been var- 
iously attributed to the shape of the atmosphere as a 
whole or the slope of the tropopause [14] could be an- 
swered. The problem of the height of the effective layers 
of the atmosphere and of the shape of the ray envelope 
could be approached by means of airborne photometric 
instruments to furnish vertical cross sections of the light 
flux at various altitudes along a latitudinal line to repre- 
sent various sun’s depressions. Spectrophotometry of 
clouds of known height may furnish information on the 
geometrical and optical properties of the sun’s rays 
tangent to the earth’s surface. 
As regards determination of the terrestrial or possibly 
cosmic origin of dust layers [11, 14] that periodically 
produce striking twilight phenomena, only a long-range 
observational project on an international basis will lead 
to success. 
SCATTERING OF LIGHT IN THE ATMOSPHERE 
Scattering is the deflection of light quanta m a trans- 
parent medium such as the atmosphere. The atoms and 
molecules of the gaseous constituents cause the quanta 
of the incident light beam to be scattered more or less 
in all directions. In addition, there is scattermg by 
minute particulate suspensions such as condensation 
nuclei. When a beam of this scattered light encounters 
further matter, it is again subject to (multiple) scat- 
tering; however, the contribution of multiple scattering 
to the total intensity of scattered light is small, except 
in very turbid air or in the absence of primarily scat- 
tered light, (e.g., in the case of the dark segment). 
The classical theory by Rayleigh [e. 21] was found to 
be only in approximate agreement with pertinent ob- 
servations [c. 42]. The later theory by Mie and Debye 
[c. 29], which contains Rayleigh’s theory as a limiting 
case, is more general, but difficult to apply to atmos- 
pheric scattering because it requires a knowledge of 
specific constants, the distribution, and concentration 
of the scattering substances. For a thorough summary 
of the theories of scattering as well as of methods and 
results of observations, the reader is referred to the work 
by Linke [29]. 
It was shown that the scattering process was involved 
in some of the previously discussed optical phenomena, 
its more immediate manifestations are much less spec- 
tacular, but nevertheless of great practical importance. 
The essential consequences of scattering are: The restric- 
9. See also Chap. 7 on ‘‘Die kurzwellige Himmelsstrahlung”’ 
in the same volume, pp. 339-415. 
