If a periodic phenomena y shown by a function is observed at six equidistant points throughout the period, the coefficients A0, A1, B1, A2 and B2 can be determined by the method of harmonic analysis. But, when one of the observed values, y1, for example, is unknown, the usual method can not be used. The author proposes a method of harmonic analysis for such a case. In this case' we may estimate graphically the unknown value, namely y1", and with this estimated value togather with the observed values, we can determine the coefficients provisionally. From these coefficients we can calculate the value of y1, and call it y1". Then the true value of y1, is given by the following equation, Generally, when the periodic phenomena is shown by the function, above method is applied repeatedly, and the most probable value of y1, may be determined. Similarly, when one of the observed values at 2m equidistant points throughout the period of the function is unknown, the same method may be applied, and the most probable value of the unknown one is given by the equation
Part I. Thermodynamical and Colloid-Meteorological Problems. Fig. 2 in Pl. III shows cumulus-like clouds produced by the exhaust vapour issuing from the piston “A” of the pile driving hammer shown if fig. 1. Its formation is completed in the following three processes:- In the first of these processes a mass of the vapour which is pushed out into the air at a pressure of 6.9 atmospheres, makes adiabatic expansion, till the pressure reduces to one atmospheric pressure. By cooling the vapour condenses to water-droplets which are large enough to form drizzle. In the second process the cooling and expansion of the vapour is continued by mixing with the surrounding air, until it attains a certain temperature somewhat higher than that of air. By the condensation in this process minute cloud particles are produced. In the second process the mixing of air into vapour is based upon thermodynamical unstability, but in the third process it is forced by mechanical or hydrodynamical action and gives rise to the evaporation of the vater particles in the cloud. Part II. On the “Surface Evaporation” of clouds. Cloud particles evaporate in de_??_cending air. We call the phenomena the “volume evaporation”; on the boundary of cloud with unsatuiated air there takes place also the evaporation of the cloud We call the phenomena “surface evaporation”. Surface evaporation of clouds might be considered analogous to that of liquids from their surface, when the diffusion of cloud particles caused by turbulence of the air is very slow compared with the rate of the evaporation. As an example of it we calculated as for the exhaust clouds the time of their disappearance under the assumption where V is the volume of the cloud, S its surface area, p the saturation difference of the surrounding air, and k a constant. The stronger the wind, the more the cloud is prolonged, and if its velocity be taken into consideration, a solution of the above equation is obtained in the form where r is the time of disappearance of the cloud, v wind velocity, A and B are constants. Our observations agree well with the calculations. Part III. On the Size Distribution of the Water-drops. In absorption method we made photographic magnification (×5) of the spots of water-droplets on filter paper to read accurately their diameters up to decimal fractions of a millimeter, and at the same time to measure such a small spot as 0.2mm in diameter. In the size distribution of the drizzle from “A” cloud, we found a group of drops which lacks the second term, that is, the water-droplets which have the ratio of 1:4:8:16:32 in weight predominate. This might be explained from the view-point of coagulation by the consideration of the effect of the wind upon the falling paths of waterdroplets. They are driven leeward by the wind, and the droplets of different sizes go down in different paths. Let it be assumed, that a group of uniform water-droplets starts together to fall down to the ground, and that on the way they coagulate once, twice, and more. And if the exposure of the receiving filter paper is short, the droplets which have coagulated twice (correspond to the second term in the group distribution) are observed not at the same time with the others.
It is cleared by the recent research that the earth's crust is bulit up of blocks. but still it's sense on seismic waves is scarcely studied. Accordingly, the author tried some discussion on this problem and found that it plays a very important rôle especially in energetic problem of seismic waves, though it is small so long as we deal with the initial motion such as P and S waves. Some of the results obtained are as follows. 1. The so-called Omori's coefficient has never determined distinctly owing to the irregularity of the wave velocity in each block, and the scale of blocks and the irregularity of the wave velocity in each block can be calculated from this amount and they are about as follows, the scale of blocks 10-40km in shallow crust 400-1000km in deep crust the irregularity of the wave velocity 10% in shallow crust 2% in deep crust 2. The analysis of the proper oscillation of the ground was done. 3. The observation of seismic waves has done macroscopically in usual for example, and hence, the calculated values from such observation, the velocity of P or S waves have only the meaning of average, and the idea “macroscopic elastic constant” is introduced corresponding to the macroscopical observation. And it is shown that the macroscopic elastic constant is not always isotropic even it is isotropic microscopically. 4. The so-called anomalous propagation of seismic waves can be explained with this macroscopic elastic constant and the fact that seismic waves propagate earlier to the direction of earth layer than the other coincides with above thought. 5. The macroscopic equations of seismic waves in the medium which has very complexed block structure are deduced, and found following equations for sp_??_cal cases. The first is so-called telegraphic equation which used by Prof. H. Nagaoka to explain the formation of tail of distant earthquake, and the last is the equation of waves in viscoelastic medium which often applied for seismic waves. 6. The decay of the maximum amplitude of seismic waves which calculated from the stand point of the block agrees well with the observed value, and the relation between the absorption coefficient and the period discovered by Dr. K. Wadati can also be explained from this standpoint. 7. The total duration of seismic waves has following nature, (a) it depends a little on the epicentral distance, (b) it is proportional to the square of the period of the maximum amplitude, (c) the distribution of the region where it is smaller than normal coincides approximately with the abnormal distribution of seismic intensity. 8. The nature of (b) in 7. can be explained as the damped proper oscillation of seismic waves in visco-elastic medium which expected from the present point of view, and the coefficient of the visco-elastic constant of the crust has calculated and found that it is about 10R c. g. s. which agrees with the usual valuc. 9. The energy of seismic waves can propagated not as waves but something like heat in the medium which has very complexed block structure as in actual crust, and the equation of heat conduction is applied for propagation of the energy of seismic waves and the result is The equation of heat conduction is also applied for the propagation of the energy of the pulsatory oscillation, and it is given by approximately Both results agree well with the observation at least qualitatively. 10. Some notes on the pulsatory oscillation are also made.
Shiranui, which means literally an unknown fire, has been very famous from ancient times as a mysterious sea fire in Japan. It is usually said that on the Yatsushiro Sea (or the Shiranui Sea) in Kumamoto Prefecture, Kyushu, Japan, it appears most clearly at the time of lower low water on the night of the last day of the seventh month of the lunar calendar. It is also said that it is not seen from the sea, but only from heights of the coast of the Sea. At first, only one luminous point appears, and then it splits out into a great many starlike twinkling fires in the length about 4 kilometers in the horizontal direction of the Sea. Such fires as just above mentioned are seen almost continuously from midnight to dawn. On that night, many people flock to the coast together from the neighbouring villages to see these misterious fires, Shiranui; but it can not be seen well unless when it is very fine. Many investigators or explorers already tried to study “What Shiranui truely is.” But they were all in vain, for whenever they would try to draw near it going on board, it would suddenly disappear. Thus the true nature of Shiranui has remained unknown. Now, there are various opinions about it. Some people are of the opinion that Shiranui is a fishing fire, and the others that it is due to the luminescence of microbions in the Sea. But there are not so many fishing fires as those of Shiranui, nor so bright luminescence of microbions as that of it either. In last summer, we observed Shiranui with many co-workers by using large telescopes, a spectroscope and a falling camera, from a high place at Eino in Matusai, one of the towns in the coast of the Sea. Then we measured the temperatures of the sea water and of the air on the Sea. and also of the air on the beach of the vicinity where Shiranui would most frequently appear. The thermometers used by us were mercurial ones and thermographs. From the results of these observations and measurements, it is concluded that the light sources of Shiranui are acetylene lamps used in fishing. The light emitted from a lamp scintillates, flying in the direction of the horizon, splitting out into many lights, when it passes through the discontinuous air mediums produced near the surface of the sea as shown in Fig. 2. This, indeed, is the true cause of the phenomenon of Shiranui. Why these air mediums are formed discontinuously will be explained as follows. At a time of lower low water, many extremely wide beaches appear along the coast, which is, indeed, a characterestic of this vicinity. Now, the temperature of the air on the beaches is lower than that of the air on the sea at night. Thus when a breeze blows in the direction of light beams, the warmer air on the sea is mixed with the cooler one which comes from the beaches. Then it produces on the sea many discontinuous air layers, through which we can see Shiran_??_i. The phenomenon of Shiranui is very interest from the point of view of meteorolog'cal optics.