In their first paper under the present title, the authors computed the “Trübungsfaktor” τd due to the impurities suspending in the atmosphere (excluding water vapor), from the results of observations of solar radiation carried out during the three years 1934-6 with the silver-disc pyrheliometer of various stations in Japan. But τd thus obtained had often a large negative value, for instance -1.00, especially in the summer time of southern districts of Japan. This can not happen in reality, and it was shown in the second paper that these negative values might have arisen from the defect of Kimball's graphical table for practical use and that the authors'graphical tables drawn over again directly from the experimental results of Fowle were more suitable. In the present paper, using our table and with the addition of the observed results in several, other stations of Japan and Manchukuo, we computed τd over again for 78 stations in all. From the distribution of the absolute values of τd and the state of its annual variation, it seems that τd of all stations situated within a certain area are closely similar to one another and proper for the locality, and so τd can be divided into 14 groups as to the type of their variation. Generally speaking, τd are very large in great cities, such as Tokyo, Osaka, Kyoto, etc., and are larger in the inland district than on the coast. These circumstances convince us that τd are closely connected with the climate of each district, especially with the vertical distribution of temperature in fair weather. τd reaches its maximum in Spring and its minimum in Summer. This variation might be'explained by the fact that in the former season the continental air mass, and in the latter the subtropical maritime air mass, prevail over the Far East, and the former is more turbid than the latter. The relation between this variation of τd and the seasonal change of the prevailing air mass is clearly shown in Fig. 4, in which points of equal values of τd are connected with a continuous line for every month. The vertical distribution of τd was also studied, for each of the three districts neighbouring respectively Mt. Tukuba, Ibuki, and Unzen.
If the sample variance tensor be Φ for a normal 2-dimensional vector population (the mean is unspecified), we can test the null hypothesis H0: the population variance tensor is isotropic, by a statistic G, which is equal to_??_. The sampling distribution of G is given by or where N means the size of the sample.