On the surface of water such as an ocean, waves are produced by winds or a sudden change of atmospheric pressure, but they decay immediately after proceeding into a place where no such agencies are working. In such cases, besides these forced waves, there exist free surface wavcs which have generally the very long wave length and progress far from the disturbing centre. In this paper the author intends to discuss these surface waves approximately, considering the effect of viscosity and the dcflecting force of the earth's rotation which are assumed to be constant everywhere and obtained the results: (i) the period of waves becomes little longer than that of perfect fluid on account of viscosity, (ii) the amplitude diminishes exponentially for time and is proportional to the inverse square root of the distance from the disturbing centre, (iii) each particle of water surface describes a space curve whose projections on the horizontal and vertical plane are both ellipese, (iv) the phase velovity V and the group velocity U are both the functions of the distance from the centre and have the relation 2U=V at γ=∞.
The observational data of the mountain cluds, fog and haze at Mt. Tukuba described in this report were mostly carried out between July, 1929 to. June, 1931 during two years. The outline of these investigations is as follows; (1) the annual or daily variation of the frequency of the appearance of mountain clouds and haze; (2) the diurnal or annual change of the height of mountain clouds and the frequency of their appearance for the height of the every stratum of mountain; (3) the variation of the vertical temperature distribution and relation to the mountai nclouds'change; (4) the classification of the forms of the mountain clouds; (5) the estimation of the size of the mountain clouds or fog particles; (6) the change of their formation with reference to the upper clouds-sheet; (7) the comparative study of the forms between the mountain clouds and the model clouds. The following results noticed in this report may be of special interest. The frequency of the appearance of the mountain clouds is very large in summer and small in winter. (See Fig. 1). The frequency of the mountain haze is large in summer and winter, and the smallest in early spring and autumn; it is large in the forenoon and small in the afternoon. The frequency of the fair weather on the mountain is generally large in winter arid small in summer, large in the afternoon and small in the forenoon. The mean height of the mountain clouds or the frequency of their appearance in every layer shows the daily remarkable variation, in which the highest elevation in the middle of the day and the lowest elevation occurred in the morning and evening, and also shows a high elevation in summer and a low in winter. The distribution of the vertical temperature in the layer of the mountain clouds is shown in Fig. 4. The dense clouds appear at the beginning of the elevation of temperature inversion; and with 100 meters up or down from the inversion height, clouds disappear. The lapse late of the temperature is smaller than about 1°/100m decrease below the stratum of the inversion layer, while the lapse late is larger than about 1°/100m increase in it. The thickness of the mountain clouds is nearly the same order of width of the inversion layer. The classification of the mountain clouds is as follows; (i) Mountain lenticular cloud. (ii) Crest cloud. (iii) Banner cloud. (iv) Mountain cumulus or Mountain cumulo-nimbus. (v) Mountain stratus. (vi) Summit or valley cloud. (See Plate 1 and Plate 2). These types of the mountain clouds noticed in this report, may be of special interest. When the crest cloud changes its form from the stratus into the cumulus fine weather will come; but when its form changes from the cumulus into the stratus, we may expect bad weather will come in the night or the following day. The forms of the mountain cumulus and mountain cumulo-nimbus are maintained the character of the summit type. The formation of the upper cloud-sheet of stratus shows long wave form at dawn and after gradually changes into cumuli form. (See Plate 2). The observed size of the mountain clouds or fog particles is about 30 microns for the mean radius; in which 31.8 microns by the direct observation with the microscope the magnification being from 60 to 1000, and 27.4 microns by the observing rings of the colored light with the Broken-bow or Mountainspectre and the coronas of the lamp. The extreme values of these observed radii of the particles are about 5-150 microns with the microscopic observation and about 10-70 microns with the corona. In the Plate 3, the photographic pictures of the Broken-bow and Mountain-spectre are shown. In the last paragraph, we described concerning the following experiment. By the use of the model of the Mt. Tukuba district (scale 1-50, 000), which installed in the rectangular glass-case, we send a smoke of tabacco from one side to another by a pipe. The result of the experiment is shown in the Plate 3 and Plate 4.
It has been shown by G. I. Taylor that the daily variation in wind velocity is due to that in turbulence in the lower atmosphere. Recently Iswelkow, in order to explain it fully theoretically, solved the equation of motion by an assumption that k=k0+k1 sinσt, where k is eddy diffusion, σ=2π/86400, but the equation obtaioned between the eddy diffusion and the heifht of the reversal does not agree with Hellmann's observations. In the present praper, therefore, I solved the equation by the assumption that V=e_??_(l-μ)l_??_(z), where l-μ=2π/86400, and that the eddy diffusion is a function of heights, and the equation obtained agrees well with the results of aetual observations.
In this paper the effects of topography on the direction and velocity of wind are studied hydrodynamically. For the sake of simplicity, the mountain is assumed to be a semi-circular cylinder. Then we can prove that; when a mass of air passes near the top of mountain, the velocity component transverse to the ridge of mountain increases and the directions of wind transverse to the ridge are much more observable than those parallel to the ridge; and such tendencies decrease as the height increases. These are in accordance with the statistical results.
I have communicated to the Journal Vol VIII. No.9 on the correlation between pressure and temperaure of winter in 1930 at the summit of Mt. Huzi. Continuing previous study I have made the same observations in the following year and have found that the correlation coefficient is 0.83 which is larger than 0.69 for the preceding year. In addition I have obtained the following curve by the individual observations for pressure (P) and temperature (t) in summers 1927-1931 and in winters 1930-1931 at the same place: P=487.5+0.568t-0.0111t2. The relation between the pressure and temperature is very intimate at the level 5 or 6km. as obtained from the hypsometric formula where the change of 1 m. m. mercury in pressure corresponds to that of one degree centigrade in temperature; but the relation between them is not so intimate at the summit of Mt. Huzi where the height is about 3.8km.