The rain often begins in the southerly air; current without obvious depression or discontinuity. Such the rain are produced by the invasion of warm air mass, and the cloud is formed by the contraction of air column due to the latitude effect. It is shown that the cloud is formed firstly in the upper layer of the air mass and then it lowered with the northward motion of the air mass.
In the first part of the present inquiry, we calculated the, effective (outgoing) radiation in the free atmosphere at any level above the ground. confining ourselves to the case in which the sky is clear (Tab. 4). The result of this computation seems to be in accordyance with what is reached by the common sense; for example, the effective. radiation increases in proportion as the temperature grows or in approaching the ground from the higher level. At some level lower than 1km, it seems that there exists a layer of inversion with respect to the outgoing radiation, but the detail of which was not examined in this preliminary report. From the result of this computation, the geographical distribution of the outgoing radiation was calculated and shown in Fig. 3 and Fig. 4. In the second part of this paper, the foregoing theory was extended to the case of the overcast sky (Tab. 5 and Figs. 5-10). From these Tabs. and Figs.. we can draw the following evidences:- (i) In the atmosphere between the ground and the cloud sheets, the outgoing radiation diminishes as we go up from the ground toward the upper layer, regardless of the height of the cloud sheets. The ratio of this decrease incrases in proportion as the temperature at the ground grows. (ii) When the height of the cloud sheet is fixed, the radiation at any level is also nearly proportional to the temperature near the ground. (iii) At any fixed level above the ground, the radiation is nearly proportional to the height of the cloud sheet, the ratio of this increasing, and hence the difference of radiations at two different levels, is greater in proportion as the airtemperature grows coming nearer the ground. (iv) When temperature is fixed, the distance between the two sheets of cloud which corresponds to the constant difference of radiation is almost independent of the height of level under consideration. (v) The distance between the two levels in the atmosphere which corresponds to some constant difference of radiations generally diminishes with the temperature near the ground. Higher the temperature, the more remarkable is the variation of outgoing radiation with respect to the vertical distance, but when the temperature is fixed at a certain point, the ratio, of this variation is almost independent of the height of the cloud sheet. In the third part, the results of the investigations in the two preceeding cases-clear skies and overcast skies-are combined, and the general cases in which the sky is partly covered by the cloud, were investigated. The mean cloud amount for the respective zone of latitude was taken from Brook's Table, and assuming the mean height of the cloud over the whole earth to be 5km, the geographical distribution of the terrestrial radiation at the ground was computed and shown in Fig. 11. From this Tab. or Fig., we can see that the radiation (outgoing) equator moves from latitude 0° (in winter) to about 30°N (in summer), just the same as the seasonal movements of the thermal equator of the temperature of the air.
Virtual temperature of the second kind Tυυ is difined by Tυυ=Tg/g-2ωcosφu where, g, ω, φ, u are gravity acceleration, angular velocity of rotation of the earth, latitude and zonal velocity components taken positively to the east respectively. In Linke's Meteorologische Taschenbuch, the differences between Tυυ and T is tabulated but the formal definition is not given. The above definition is given by the auther taking accounts of various points of view. This may be probably identical with that given by Linke. Tυυ-Tυ, is very small quantity and negligible in many cases, but in the neighbourhood of the horizontal front, the gradient of Tυυ-T becomes important. If we introduce virtual polytropic potential temperature of the second kind of class k defined by the criterion of vertical stability obtained by the author becomes
As a natural extension of the standard error or, the confidence limits may be conveniently used in the case of small sample. For this purpose, R. A. Fisher's methods are not only somewhat laborious, but also attended by innegligible errors. Utilizing H. E. Soper's table, the auther has calculated two kinds of tables which give the confidence limits for the following values of n (size of sample) and r (observed correlation coefficient), n=5, 6, …25, 50, 100 r=0, 0.05, …, 0.95, and has prepared two diagrams corresponding to them. The confidence coefficient of the limits in one table is 1-2Φ (1), and in the other is 1-2Φ (2), where and the errors of calculated numbers are, on the whole, less than 0.005. These tables and diagrams can be used for the following problems: (1) To find the confidence-limits of observed correlation coefficient r. (2) The significance test of r. (3) To test the difference between observed r and its previously assumed value. (4) To test the difference between two observed values r1 and r2. (5) The composition of these r1 and r2.