As shown in Fig. 2 (A) and (B), the cold season temperature of Japan in some periods changed year by year parallel to the pressure difference between Milano and Haparanda (denoted by ΔPM_H hereafter). The January-February temperature of Irkutsk has a synchronous relation to ΔPM_H, the correlation coefficient being R=0.73, n=53 (1851_??_1936). In order to find a physical base for the relation between the climates of Europe and Asia, the distribution of the correlation coefficients of ΔPM_H and air temperatures and pressures at various places is investigated, as will be seen in Fig. 8, from which the following facts can be confirmed: (1) A close and stable correlation is found between the zonal index ΔPM_H and the Jan.-Feb. pressure of high-latitude zone. (2) A fairly large correlation of ΔPM_H with midwinter temperature can be found between 50°N and 60°N, and in the latitudes higher or lower than that zone, the correlation coefficients tend to rapidly decrease. The longitudinal distribution of the correlation coefficients of ΔPM_H and the temperature is shown in Fig. 6, the part of larger coefficients being in 10°W_??_30°E in West Europe, in 80°E_??_130°E in Central Asia, and the part of smaller coefficients being at about 55°E in North-European Plain. (3) The line of equi-correlation coefficient (R=-0.8 or R=-0.6) of ΔPM_H and the high-latitude pressure projects exceedingly southward in North-European Plain, where the correlation coefficient of ΔPM_H and the temperature is small. (See Fig. 8.) From the above mentioned facts the following conclusions can be derived: (a) Though the south-westerly warm air currents, whose mean strength is represented by ΔPM_H, invade into the Arctic air-mass, ascending along the Arctic frontal surface, and weaken the strength of the air-mass as a whole, little or no effects can be exerted upon the air temperature at the earth's surface in the region occupied by the Arctic air-mass. (b) At the boundary surface between the winds of the Arctic and equatorial air-masses with long wave length of about 90°, warm air intrudes northward between 10°W_??_30°E and 80°E_??_130°E, and cold air projects southward in the vicinity of 55°E. The air temperature in the region of the tongue of warm air correlates with ΔPM_H through two processes, one being the heat quantity transported directly by the prevailing westerlies and the other the strength of cold air currents from the Arctic air-mass whose intensity is controlled by ΔPM_H. The correlation coefficient of the Jan. -Feb. temperature at Upsala is R=+0.73 (1878_??_1926) when C=ΔPM_H, and is R=0.85 (1878_??_1926) when C=σ ΔPM_H-σPsty (Psty....pressure at Stykkisholm). In the circulation index C=σΔPM_H-σPsty, it seems that σΔPM_H represents the heat quantity transported from lower latitudes and σΔPsty indicates the strength of cold air currents from higher latitudes.
Owing to the circumstances that the atmospheric turbulence consists of eddies of various scales, scale of eddies detected by observations usually increases, as the time duration of the observations increases. Therefore, statistical quantities of the atmospheric turbulence obtained by observations within a finite time interval depend considerably on the time interval. In the present paper, the relations between the length of time under analysis and the quantities of turbulence, i.e. the Eulerian correlation coefficient, the scale of turbulence and the eddy diffusion confficient, were investigated. Comparison of these theoretical results with observed data confirmed their validity. Furthermore, it is an important problem to study how to compare the records of fluctuations obtained with various anemometers with each other. In the latter part of this paper, this subject is discussed from the view point of the over-lapping-mean procedure.
Many years ago a method convenient for photographing the whole sky with the aid of a convex mirror was advocated by Dr. S. Suzuki and J. Georgi independently. In the present paper some properties bearing on the geometrical optics of the mirror are discussed with a special reference to a new mirror of distortionless projection. Here the optical axis of a camera is taken vertically downwards passing through the center of mirror, and the angles between the axis, and rays before and after the reflection at the surface of the mirror are denoted by z and θ respectively. Then z is the zenith distance. If the solid angle subtended by any of clouds can be measured directly by the area of its image on the photographic plate in a camera, the following relation must hold: or This is the condition for solid angle projection. On the other hand when a convex spherical mirror is used instead of the above nonspherical, the corresponding relation is In (1) and (2) c and k are positive constants. If c and k are equal and large enough, then (1) and (2) express the same relation between z and θ, that is, when the photographing distance is great, a spherical mirror is the limiting one of solid ang_??_e projection. Fig. 1 explains this graphically and shows that the length of the diameter equal to the distance of the camera to the mirror meets any practical purpose of estimating the amount of clouds in solid angle. Therefore a spherical mirror may be used for solid angle projection with a good accuracy. Now, in order to get a good focus, it is desirable for us to know the location of image by the mirror and its astigmatic difference. In case of spherical mirror the location of image in quenstion can be inferend from the intersecting point of the rays which are parallel befor the reflection. In order to obtain the astigmatic difference, let us calculate the location of the primary image, which is made by the meridional rays, and the secondary by the sagittal rays (z=const.). Then the two images are distant from the center of camera lens by ρ+X and ρ+Y, respectively, where ρ is the distance from the lens to a point of mirror, then X and Y can be calculated easily to be R: radius of the spherical mirror. Of course these values are reduced to X=Y=R/2 in the limiting case when z_??_0. The form of the imaginary curved surface in which the primary image seems to lie depends on the camera distance as given in Fig. 2. From the above-mentioned the astigmatic difference is, From Fig. 1 can be seen an interesting fact that, on using a spherical mirror, several distances from a camera, that is respectively correspond to nearly (a) stereographic, (b) equidistant and (c) solid angle projections. In the second place, let us consider a distortionless projection of an apparently small object. After Robin Hill we call this a stereographic projection. If a small sphere lies afar, the ratio of its image contractions, vertical and horizontal, may be expressed in general as follows. When the above condition is satisfied, this value must be unity, that is, or This is the relation between z and θ in a stereographic projection. When a ray is reflected at the surface of a mirror, the law of reflection must be fulfilled, that is, Eliminating z from (7) and (8), we obtain easily an analytic expression of the stereographic mirror as follows: As an example, a sectional form of this mirror is given in Fig. 3 in case of c=4. Regarding the construction and photography of stereographic mirror, it will be stated in a later report. In conclusion, the author's best thanks aree due to Dr. Suzuki for his valuable suggestion and guidance and to Dr. Okada for his everlasting encouragement.