The intensities of sky radiation from varying zenith angles in the sun's vertical plane were calculated using the two methods, that is, the method of integro-differential equation developed by Chandrasekhar and the method of direct integration developed by Chapman, Hammad and the present author. The theoretical distributions were compared with those observed of ultraviolet sky radiation of two kinds of wave-length, the longer one about 3500-3700Å and the shorter one about 3100-3300Å. As to the distribution between θ=0° and 60°(θ: zenith angle) in the sun's opposite side at the sun's altitude of 30° the theoretical values obtained by Chandresekhar's method showed satisfactory agreement with observed data whereas those obtained by the process of direct integration did not, because the scattered light higher than the second which amounted to as much as 30-40% in the shorter wave-length region played an essential role in the distribution.
The distribution observed at the sun's altitude of 60° showed a marked deviation from both of the theoretical ones presumably because a non-Rayleigh scattering due to large particles in the air would be an indispensable factor.
An approximate method of calculation of the scattered light higher than the second where we assumed the linear extrapolation to the decrease of the subsequent scattered light intensity was examined, using the primary and secondary scattered light on Rayleigh's law which were previously computed by this author. In the visible region these results showed a good agreement with correct ones within a error of few percent in contrast with Bernhardt's results which gave a marked deviation because the scattering law was incorrect. However, in the ultraviolet region our results also gave errors greater than 10% especially in the direction of large zenith angles.
According to the results of calculation in the visible range the scattered light higher than the second does not exceed at most several percent. And consequently, regarding the polarization of the sunlit sky, the better result of Hammad than that of Chandrasekhar, which was obtained neglecting the scattered light higher than the second and taking into account the molecular anisot_??_opy of air molecules was justified to some extent in the visible range of wave-length.
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