On the dynamical formula for the formation of eyes of Typhoons and the deflecting angle of winds in case of circular isobars. It is well known that many authors have theoretically treated the famous Manila Typhoons, which was observed at noon, Octobar 20th, 1882, and believed as providing a suitable example of the eye that is warmer and drier than the outer part as if caused by the suosiding air. We obtained some important data by an autographic recorder of temperature when the centre of a Typhoon passed the weather station at Giran Situated at the middle part of Giran plain near the Seashore at 23th, September 11th, 1942. By this data as shown in fig.2 we realized the existence of a circular surface of discontinuity on the earth's surface. Such a surface of discontinuity has already been suggested by Haurwitz, Brunt, and Bjerknes, who derived the formulae for the inclination of a circular surface of discontin_??_ty. From the results as shown in table (1), we could find the fact that the central part of Typhoonis generally of a air mass warmer than the outer part, but not so dry as that of the famous Manila Typhoon. It may therefore be suggestea that the warmer eye is causea by the Sun's radiation passing through the thin cloud layers, and the transition of the air mass from the warmer region. By this reason, we may assume that the motion of the air referred to the centre within the boundary of the eye is nearly tangential to the circular isobars, and the vertical motlon is negligible. Now we have derived a formula for the deflecting, angle of winds in the case of circular isobars, as follows; where P is pressure, ρ density, R friction, l is written for 2ω sinφ, β the angle between R and V, V is the wind velocity, ω is vertical component of the wind, ψ is the deflecting angle of the winds. We may consider that the deflecting angle ψ tends to zero at the boundary of an eye at a distance _??_0 from the centre, then we get However it is difficult to solve the equation (1) including, such unknown quantities on the right hand side as Cosβ, and W which are not easily obtained from the results of observations. Therefore we try to determine the angle ψ from the empirical formula in the following manner. and by differentiating where β is the wind direction and α is determined from the track of the Typhoon, in many cases, β is almost constant until the centre comes close to the station, Δ is the minimum distance from the tack. Furthermore, we can determine the angle ψ, when the path of the Typhoon curves.
The amount of direct solar radiation upon four vertical planes oriented to N, S, E, W, also upon vertical cylinder and sphere during any period at any place on earth can be computed by mathematical formula expanded into series, the atmosphere being neglected. In case of vertical planes, somewhat similar to Milankovitch's method concerning a horizontal plane, but in other cases the computation was carried out in an original method. In considering the atmospheric absorption the amount was obtained by numerical integral from every day's value which was similarly obtained from every hour's value, in cases of atmospheric trans. coeff. P=0.6, 0.7, 0.8, 0.9, and 1.0. The author, has given all the necessary coefficients for expansion and the synoptical charts illustrating the summer and winter half years and of total year periods amount as well as of the annual variation of one day's amount for every 10 degrees of latitude from 0° to 90°, and for P=0.6, 0.7, 0.8, 0.9 and 1.0.
Model experiment of Tsunami or seismic sea wave requires to satisfy the law of similitude. However it is generally im_??_ossible when the effect of viscosity is taken into consideration and it has been considered that this effect is a serious problem to the model experiment of Tsunami. This erroneous idea comes from the fact that we have been concerned only with the molecular viscosity of water of which coefficient of viscosity is considered to be equal in both cases of molecular and turbulent viscosity. In these cases, however, turbulent viscosity predominates the molecular viscosity and its coerficient for sea water is considerably larger than that of water in the model. Thus even when the viscosity is taken into consideration we can satisfy the law of similitude by adjusting the size of model adequately. Furthermore the author obtained a formula expressing the height of wave in a bay in the case of viscous fluid and compared it with that of ideal fluid. Details of the research will be found in English in the “Science Report of Tohoku University”, series 5, Vol. 2.
A new formula for the rate of evaporation of small water dróps was derived theoretically by M. Tsuji under the assumption that the surface of water is not saturated. When the radius of a water drop is very small the rate of evaporation derived from his formula is far slower than that derived from the known formula, for instance, of Ogiwara. It is interesting to decide experimentally whether M. Tsuji's theory is correct or not, because it is not only the problem of evaporation but also concerned with the formation and disappearance of cloud-and fog-drops. In the present investigation we measured under the microscopic field the rate of evaporation of water drops whose radii are smaller than 25 μ. The obt_??_ined results agreed with the theory of Tsuji approximately