Suppose a geometrical space and draw the surfaces z=p(x, y, t). We take the axes of x and y in the two principal directions at the pressure centre, then the velocity C(Cx, Cy) of the pressure cerrtre is given by Cx=-p101/p200 and Cy=-p011/p020, and the axes of x and y are at right angles to one another. Next we consider the well-known formula by S. Petterssen on the displacements (x and y) of the pressure centre: Eliminating t from the above equations we get the following expression as the equation representing the track of the pressure centre: This represents a parabola when AxCy-CxAy≠0. Its vertex is located at and the pressure-centre would reach there at the time t=-(CxAx+CyAy)/(Ax2+Ay2). The time rate of change of the resultant velocity V is given by so the resultant velocity of the pressure centre becomes minimum at the vertex. If(AxCx+AyCy)>0, then V increases as t increases and a pressure centre has no tendency to recurve. If(AxCx+CyAy)<0, then V decreases as t increases and a pressure centre will recurve in future. If the tendency profiles are curved cyclonically, i.e., p201>0 and p021>0, then (after S. Petterssen) a cyclonic centre increases in strength and it is retarded. Under the same condition, it is also concluded that the cyclonic centre tends to recurve in future. If the tendency profiles are curved anticyclonically, i.e., p201<0 and p021<0 than (after S. Petterssen) a cyclonic centre decreases in strength and it is accelerated. Under the same condition, it is also concluded that the cyclonic centre has no tendency to recurve. As for example, typhoons first travel westward and away from the Equator. In the vicinity of the tropic or a little beyond it, they sometimes recurve. They gradually slacken in their progressive movement and increases in their strength until they reach the point of recuvature. After recurvature, they travel to the northeastward and pass into middle latitudes, travelling at a great rate and decaying rapidly. It is also discussed on the low type and the high type of a cyclonic centre. And it is concluded that the estimated field of pressure at the level 3 Km of height is often useful to prognosticate the sudden deepening of a cyclonic centre.
Consider the equation of long wave in one dimensional form: Here ζ is elevation from free surface and h the depth. We put then we readily see that in case of no stable wave motion occurs, but in case of there exists stable oscillation. This is hydrodynamically interpretted such that the steep inclination of bottom form makes relatively slow oscillation unstable. In the above equation σ is the frequency of wave. Applying the present derivation some actual numerical examples are discussed here. The same consideration has been applied to the problem of free oscillation of surface layer, viz to that of elastic vibration. The similar characteristic condition has been derived and numerical examples are given.
It is well known as an observational fact that every locality has a proper surface wind direction of the maximum frequency on account of the peculiar topographic effect. Hence the angle between the directions of surface and gradient wind is always subject to a considerable fluctuation accompanied by the change of gradient wind direction. As an extreme case of such a procedure we can imagine an oblate Ekman's spiral. In this case the fundamental equations of motion based on the principle of vorticity transport are, in customary notation, We put here then we readily see that the eddy motion is stable or unstable according as Thus the critical state is characterized by the relation 2a2=1. Adopting Dobson's observation numerical computation has been performed and we see that the result once published by the present author obeys this stability condition. Next the thermal stability of atmosphere is discussed. According to the usual conception the stability of atmospheric stratification is determined by the lapse-rate of temperature and it is stable or unstable according as the lapse-rate is lower or higher than the adiabatic lapse-rate. But this is not always the case with the recent aerological observation so far as it concerns the lower atmosphere of 1 kilometer level, even if the atmosphere is considerably stable as revealed out by the observation of cloud form in the lower stratum. Namely we often find the case of super-adiabatic lapse-rate in which the stratification is comparatively stable. As one plausible explanation of this fact the theory of the thermal stability of viscous fluid has been applied and the recent study of A. L. Hales also supports this view.
During the June of 1935, studies were made regarding the light intensity and the photosynthesis of Chara in Lake Asinoko, Hakone. Light intensity was determined by the amount of decomposition of K I under acid medium. The amount of photosynthesis was determined by oxygen production as measured by a WINKLER method being corraborated by pH determinations. The optimum depth for photosynthesis was between 1 and 6 meters on bright day and was at the surface at the evening. Exposure under too much light proved that the photosynthesis was almost ceased. The lower limit of Chara growth of this lake found to be 20 meters below the surface, which was roughly correlated to the compensation depth of it on the bright day (18 meters).
This paper contains the following results: (1) The position of nodal-line and the distribution of amplitude of initial motion for some earthquakes were treated by means of the next relation: initial motion at the surface ∞P2(cosθ)/γ The path of seismic rays was considered in two cases assuming that the mechanism of earthquake is the “Nodal-cone type”. The one denied the exiteuce of the surface of discontinuity near the earth surface and the other assumed it. Comparing with the actual seismic observations, the author has ascertained that they are in good ag eement with the former case. (2) There appears the azimuthal distribution of maximum amplitudes in vertical component at the actual ea lhquakes of shallow origin and their greater part is in very good agreement with theoretical results of Rayleigh wave due to the dilatational wave issued from an internal source of multiple-type in a semi-infinite elastic body.
Ibukisan (1377m above the sea level) is an isolated mount in Central Japan and is one of the important places of the air way. Hence the measurement of visibility from Mt. Ibukisan is very important. Visibility on the high mountain is naturally better than those at the lower places and the former has special character. We investigated the visibility on Mt. Ibukisan from 1925 to 1934 at 10h, and 14h every day. We chose 9 objects, Mt. Hakusan, Ontake, Kinkasan, Hirasan, River Ibi, Island Oki and Bay of Tsuruga, locating at different distances and in different directions. Generally the visibility is best in November and worst in August. But as to the high mountain, it is best in November and worst in June. Generally speaking, visibility is better in the morning than in the afte noon. Visibility is the best in NE wards (mountainous districts), the next is in S wards (lower mountainous lands) and the worst is in NW wards (Bay of Tsuruga). The most cases of the best visibility were occured when the movable high pressure is over Central Japan, and those of the worst visibility were also occured when the stationary high pressure is over Central Japan.