Several important properties of two or multi-dimensional Gamma-type distribution are investigated for application to the actual rainfall data. First, from a two-dimensional Gamma-type distribution introd u ced with the use of the modified Bessel function, the regression function, the distributions of the statistics such as the sum, the product and the ratio of two correlated veriables will be obtained. A χ2-distribution and an F-distribution in the two-dimensional random variables will be also discussed. Second, multi-dimensional Gamma-type distribution will be defined by the reverse transformation of the characteristic function which is obtained from the application of the sampling theory or as the special case of multi-dimensional WISFIART'S distribution. From the result thus obtained, the Gamma-type process will be also introduced, which differs from the so-called normal process. Finally, from the theore t ical consideration and the actual analysis of the change of correlation coefficient by the so-called normalizing transformations, it will be shown that the actual rainfall data are not normalized by these transformations and the frequency curve of the rainfall amounts thus transformed can be expressed by a Gamma-type distribution.
Assuming a photochemical equilibrium with regard to the concentration of NO2 in the polluted air, the following equation is obtained; where k1 and k2 are the rates of reactions of ozone respectively with NO2 and NO; ka, the rate of absorption of ultraviolet solar radiation by NO2; φ, the quantum yield of NO2 photolysis. To examine the validity of this equa t i on, simultaneous measurements of ozone, NO2, NO and the spectral intensity of the solar radiation (wave-length,370-395mμ) were done in April and May,1964, at the western suburb of Tokyo. The results showed that the concentrations of these constituents mostly ranged from 1 to 3 pphm. Although the observed ozone concentration on most of the days was about twice as high as the calculated value, there was a good parallelism between the diurnal variations of observed and calculated values. The discrepancy between observed and calculated ozone concentrations may be due to some uncertainties in the estimated values of constants in the above equation. If this discrepancy is disregarded, one can say that the concentration of ozone during most of daylight hours is controlled by the presence of oxides of nitrogen.
It is proposed that the term“preformed”nutrient matters which was given by REDFIELD et al (1963) should be replaced by the term“reserved”nutrient matters. Distribution of reserved phosphate in the surface waters of the Subarctic Pacific Region is shown, where the reserved phosphate concentration is probably highest in all the oceans. The mechanism by which such a high concentration is maintained in this region is illustrated.