The height change of 500mb isobaric surface in a barotropic atmosphere is calculated by making use of the coefficients of one-dimensional Fourier series along latitude circles with one-dimensional relaxation with respect to latitude. In this paper, the tendency equations concerning Fourier coefficients along latitude circles are derived as a function of latitude from a vorticity equation, and their finite difference expressions are given in order to simplify the calculation. The subjects as to the number of component-waves to be considered and the choice of their interactions were the most important. The problem of error in this method was also considered.
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.
An integrating actinometer for ultraviolet radiation with a photo-tube and a filter was constructed which is operated by a 100V A. C. power supply. The principle of operation is charging up the photo-electric current due to incident radiant energy in a condenser and then discharging and forming an impulse to operate a relay counter. Experiments on the linearity of the response, errors due to power supply fluctuations, temperature effects of the instrument and the absolute sensitivity were carried out. The general performance has been very satisfactory. Above all, the stability against the fluctuations of power supply is the essential merit of this instrument. Using these instruments ultraviolet solar and sky radiation falling on a horizontal plane were measured in two different ranges of wave-length, the one about 3, 700A and the other about 3, 400A. The observed results are compared with those of Robitzsch pyrheliometer. According to this result, the extinction of ultraviolet solar and sky radiation due to cloudy weather is stronger in the shorter range of wave-length than in the longer, and moreover, the extinction of total, that is, including visible and infrared radiation is by far the strongest, naturally because of the strong absorption of infrared radiation due to water vapour.
Following Inoue's (1951) results concerning the pressure fluctuation spectra, the authors present an interpolation formula as which gives rise to a 3 power region for small frequency N and a -7/3 power region for large frequency. By means of Fourier transform the Eulerian correlation function is calculated which is reduced to the 4/3 power formula for small process-time t as R(t/T0)=1-3.386(t/T0)4/3 Comparisons of these results to Ogura-Miyakoda's (1954) theoretical ones and also to Schumann-Hofmeyer's (1942) observational ones in the atmosphere are carried out. Making use of the observational knowledge as to T0 corresponding to the passage-time of atmospheric predominant turbulon, several remarks on the desirable instrumentation and process for the observation of atmospheric pressure fluctuations are stated.