The Climate of Japan has been studied from the view of the air-mass calendar. In the cold season (September to June), Japan is decidedly under the influence of the Siberian Air Mass. In the mid-summer (July to August), the North Pacific tropical air controlls the weather of Japan. Sometimes in the early summer, the North Pacific polar air comes from the northeast and results the gloomy weather. Monthly percentage frequencies for each air mass type were tabulated in the Table for 4 representative stations (Fukuoka and Takamatsu for W-Japan, Tokyo for E-Japan and Sapporo for N-Japan.)
Let equations of an air be Where U east component, V north component of velocity, _??_ density of the air, P pressure, l Coriolis factor. By putting and averaging on cirtain time interval and space, (1) becomes where U, V are velocity components of mean motion. The third and fourth term of the rlant. hand side of the above equation are so called Reynold's stresses force, which the author proposed here. Driving equation (2), the Coriolis fäctor l is thought generally independent of y, but exactly it is the function of latltude and hence l is dependent of y Following analogous consideration for the eddy viscosity, the magnitude of the fifth term is estimated to be Where _??_y is mixing length, and _??_ eddy kinematic viscosity. Thus the equations of atmospheric motion are Next, the equation of general circulation of atmosphere are deduced as follows by assuming consevation of angular momentum and following analogous ideas as above. Where U westerly winds, _??_ latitude, R radiu_??_ of the earth, ω angular velocity of earths rotation, _??_ cirtain constant. approximately, except at the immediafe neighbourhood of the pole where the equation becomes Numerical example which calculated by equation (6) and (7) is shown in Figure. Easterlies at tropics are about 10m/sec, Position of middle latitude high is 35.2°, westerlies of high latitude are 16m/sec, easterlies at the pole and discontinuity must exist between easterlies of pole and the westerlies. These natures agree with actual circulation at least qualitatively.
The results of 8-hourly observations of radio sonde at Tokyo in one winter are used. By the characteristics of 8-hourly pressure variation in winter, the following facts are found. The troposphere is divided into three layers which are the 1 st layer from surface to 4km, the 2nd layer from 4km to 10km and the 3rd layer higher than 10km. The axis of pressure wave moving eastwards in winter, extends upwards with some inclination to rear side in 1 st layer, while the axis upwards vertically in 2nd layer. The height of 7km is the representative height of the 2nd layer for the pressure variation.
In a medium which consists of numerous small particles of transparent substance, like snow, fog and cloud, the intensity of radiation, passing through it, decreases. However, there is a question, if the rate of decrease obeys an exponential law, as was expected by many investigators. In this regard, Dietzius, in 1922, obtained equations: solving Schuster's equations and tried to discuss the decrease of brightness in fog. In the above equation, A0 means intensity of incident radiation at x=0 and A intensity of radiation advancing to x direction at the point x and B that of radiation returning backwards by the effect of diffuse reflexion of the part of the medium ahead. And, 2_??_ means a coefficient of diffuse reflexion of the medium, h its thickness, and μ the albedo at the base (x=h). The present writer investigated the value of γ and β, when the medium is not homogeneous, that is, (1) when (2) when the medium consists of two layers, whose coefficients are _??_ and _??_ respectively. In the case (1), the decrease of the radiation is no more linear, but parabolic. In the case (2), we can show that the relations hold, where A', B' are the proceeding and backing radiation in the second medium, whose coefficient is _??_; A'h'_??_ advancing radiation at the boundary of two layers; h' the thickness of the first medium; and the other notations are same as before. The above equations contain only _??_, and independent of _??_, so they fit _??_or computation of _??_ from experimental data. After we have got _??_ by use of _??_e above relation, then we can use the following relations for the first medium, where μ* means The relations (4) may enable us to calculate the value of _??_ This method will be also applied to the medium which consists of more than two layers and will be extended further to the medium whose coefficient changes continuously, if we divide the whole layer into many thin strata and carry out the above procedure for each stratum. Returning to the case of the uniform medium, the radiation, which reaches the base, is obtained, put ng x=hin the equation (1), viz. This means, _??_h depends on μ extraordinarily, and in the extreme case, μ=1, _??_h becomes 1. In the other words, if we place a mirror at the base of a fog stratum, the incident ray at the top, after passing through it, reaches the mirror without any drop in its strength. This is far beyond our imagination based upon experience. Such a misleading conclusions may come from the unnatural assumption of no absorptive power in the medium. Let us take absorption into account, and put From this equation we get, under the same boundary condition for the uniform medium, where At x=0, we have and at x=h, we have When _??_ is large enough, we have for smaller value of x, that is, at the portion near the surface; for the value of x not considerably different from h that is, at the portion near the base plane. These equations (11), (12) teach us the-following facts in the case of fog, for example. If the fog layer is sufficiently thick, the decrease at the top portion obeys exponential law, while at the base (that is at the ground), the intensity changes linearly. From the equation (11), we get We must take special care in treating with the surface condition, as will be shown in another article. However, we may think that β0 is an approximate value of albedo of the fog (and also, of the cloud). As we see, β0 and accordingly the albedo does not depend on absolute values of k and _??_, but on, their ratio k/_??_ Also, we have to remark, that β0 has no dependence upon μ the albedo of the base, against Dietzius' solution (1). It is also interesting to consider about the condition at the base.
By setting the thermo-couple just above the earth's surface, letting the cylinders of ito passive junctions burried into the ground, we had 84 sheets of automatic graph of nocturnal radiation from late in April to Dec. in 1942. On the same sheet we gained the automatic graph representing the temperature difference between the ground and 5 meter height (both are in the free atmospnere). The correlation's factor betweem both. curves has in general very high positive value, and is small in warm reason and large in cold season. i. e. The nocturnal .radiation R (outgoing-incoming) amounts 0.01-0.15 Here, outgoing radiation is 6T4 (T: earth's surface temperature). Let e the water-vapour tension (m.m) and Method of least squares. Seeking the relation between R/6T4 and √e by plotting on a graph, we have R/6T4=0.670-0.110√e Accordingly, the incoming radiation G=6T4(0.328+0.110√e This represents very good identity with that gained formerly by others.
As an example of earthquake-proof structures, we studied on the free vibration of the simple structure which has pillars of different width and thickness. If both pillars have square sections and we fix the size of one pillar constant and vary that of another one, it will be supposed that the period of the free vibration increases with the decrease of the size, of the later pillar. According to our theoretical results, however, it should not increase monotonously but it reaches a maximum value once, and then decreases gradually to a minimum one and again increases as shown in Fig. (3). Thus between these maximum and minimum. values there are three combinations of pillars of a same period of free vibration. And in these three combinations, periods are equal but displacements, bending moments and shearing stres_??_ are different among each other. For example as shown in this paper, we can show that weak parts exist in the pillar with smaller section of one structure of the three one_??_. with _??_ _??__??_me periods, becaus_??_ the amplitude of its d_??__??_placement become_??_ much _??_reater th_??_ those _??_n the two other structures. But shearing st_??_e_??_ and bending moment do not differ so much that it will not happen that the smaller pillar breaks earlier than the other by backling or _??_hearing. In the case of rectanglar pillars, corresponding to the sectional size one pillar, maximum and minimum periods do not appear, but there exists a region with a nearly constant period. So we can say that, in this case again, structures have a similar nature as in the square sections.