In spite of many experimental researches, no surfaces which strictly obey _??_ambert's cosine law have been found. On the other hand, no theory for the explanation of the diffuse reflexion phenomena, seems to have been successful. In such circumstances, Pokrowski(5), (6) proposed a theory and deduced a formula for the total reflecting power of a diffuse surface, where R means the amount of energy reflected back to the former space by the surface when the initial incident light of unit intensity hits the surface for the first time; and R1, the rate of reflexion of the surface for individual rays of light coming back outwards from the inner portion of a medium. After some analysis of his theory, we come to a conclusion that the procedure he took, is similar to that of computation for the reflexion of pile of plates which is sometimes used in order to obtain the polarized light in optics. Therefore, his computation should be able to be compared to the well-known formula for pile of transparent plates, when we assume the case of no absorption of energy in the scattering medium. Here, we can point out his calculation may need some revise; for, he took only the reflected rays I, II, ...... shown in the figure in our article, into consideration; but he did not consider those as i, that is reflected back inwards by any planes inside the medium. In fact, we can show that, under the assumption of no absorption, the procedure he took, gives a smaller value than that for pile of plates. The diffence between both is negligible when the medium is very thin. However, when the medium is sufficiently thick the value, obtained by his method, gives only half of the true value. In another article by the present author (Decrease of Radiation Intensity in the Diffusely Reflecting Medium) we showed Dietzius' relation for the scattering medium, which was obtained by solving Schuster's equation. In the present work, we have shown how Dietzius' relation corresponds to the pile of plates, and also have shown, it is much easier to solve the differential equation than to make calculations basing upon individual reflexion and transmission at each face within the medium. In the article cited above, through solving differential equations, we got already relations which hold for radiation in the medium, that has property of scattering as well as absorption. Applying those results, we get for the total reflective power of the medium, K=R+(1-R)(1-R1)β0/1-R1β0 where and R. R' have same meaning as Pokrowski's. when _??_ is large enough, we have The present author also suggests that, in treating the present problem, we have to consider in particular, not a surface, but a surface layer of some thickness, in which brightness is not expressed by scalar quantity, unless the initial incident rays are uniform for all directions. Backreturning rays, which arrive at the base of the surface layer from inside after they have travelled through the medium, may be considered perfectly diffuse, and may obey Lambert's law. Deviations from that law may be attributed to the nature of reflexion R o_??_ the surface layer. In other words, we may consider, as long as (1) the distribution of the particles in the surface layer, (2) the nature of incident light and (3) the reflective property of the particles, are quite unfavourable to give rise to regular reflexion in the surface layer, any reflected light from the substance, whose constituents are minute particles, obeys Lambert's law in approximate degree. On the other hand, according to this opinion by the author, there may be no surface in nature, which obeys Lambert's law strictly; and any effort to explain the law strictly theoretical way, by the irregular distribution of small mirror facets, will be unsuccessful.
(1) Introduction. In considering the heat balance in the atmosphere, it is very important to know the exact value of the reflecting power of the atmospheric radiation by the sea surface, which covers about three fourthes of the area of the whole surface of the earth. Thus, in this preliminary paper, we shall report the method and the result of the measurement, though it is as yet rough. The measurement was done at the seashore of Tôkyô Bay in the last spring. (2) Method of observation. As a matter of course, it is desirable to measure the reflection of the atmospheric radiation directly, but it being so difficult, owing to the change of the state of the sky, that some artificial heat source was provisionally used in this observation. In the figure*, H is this heat source. It is warm water contained in a chemical flask, the diameter of which is 13.3cm. The surface of the flask was blackened with lamp-black so as to emit black body radiation corresponding to the temperature of the warm water. It is apparent that the energy _??_stribution with respect to the wave length of the radiation emitted from this artificial heat source is different from that of the actual atmospheric radiation, but as the temperature of the water is in the interval between 50°-100°C, it is supposed that the result obtained by the artificial heat source holds for the atmospheric radiation also. In the same figure, M is a parabolic mirror which was spattered by alluminium in order to reflect the heat radiation almost perfectly. Diameter of the mirror is 30cm. and the focal length is 15cm. J is a thermojunction of the compensation type, the surface of which is blackened with lamp-black, and G is a galvanometer, inner resistance of which is 11.4 ohm, critical damping resistance 13 ohm, period 4.8 second, and sensitivity 4×10-9 A and 1.0×10-7 V. The thermojunction and the mirror were installed in a wooden box. The aperture of this box was so designed that it is somewhat smaller than the solid angle which subtends the ice-box I, explained below, at the thermojunction as vertex at 25 meter distance from this ice-box, and hence the radiation of the sky around this ice-box was perfectly shaded when the heat source was screened by this ice-box. The glass, as is well known, is not transparent to the heat radiation, so that the window of the bulb of the thermojunction facing the mirror was made of rock-salt which is known to be transparent to heat radiation in the wave length interval of the atmospheric radiation under consideration. Unfortunately, the rock-salt is apt to deliquesce and looks dim by the vapour in the atmosphere, so that the surface of this rock-salt window was coated by a thin film of polystirol which is very transparent to heat radiation also. As the zero point of the deflection of the galvanometer, the reading of the scale when the ice-box I was set just in front of the heat source was used. The heat source was thus perfectly screened. This ice-box I was made of tin-plate, the size of which is about 75×75cm., and it was filled with smashed ice. The outer surface of it was painted with zinc-black so as to emit the black radiation corresponding to the temperature 273°C.
By theoretical calculations the author has obtained a formula which represents the rate of evaporation of fog particles. Let a fog particle whose initial radius is _??_1 fall a distance H, then both the final radius _??_2 and the time required to fall the distance T, are given by _??_1, H and the temperature and humidity of the air. Eliminating _??_1 from these two relations, one relation will be obtained between _??_2, H T and the temperature and humidity of the air. His present attempt was to test whether this relation holds or not and the result of experiment was satisfactory. The evaporation formula which we have obtained proved to be correct.
The author studied the air temperature and the drop size of cloud particles formed in the adiabatically ascending current which contains condensation nuclei of the same size. Results which were obtained are as follows. (1) Cloud particles grow very rapidly in the lower layer of the cloud, therefore the base of cloud must be sharp and well defined which is in accordance with the well-known fact. (2) Because of the rapid condensation near the base a temperature inversion is formed in this region. It is more predominent when the nucleus is small and the temperature of the upward current is high. (3) Above the inversion layer the temperature depends on the size of nucleus and is higher as the nucleus is smaller, but is independent on the number of the nucleus contained. The lapse-rate of the temperature is in this region independent not only on the number but also on the size of the nucleus and is equal to the wet adiabatic lapse-rate. (4) The temperature and the drop size of cloud particles are somewhat lower (smaller) as the upward velocity of the air is larger, but the effect is considerablly small.
The usual solution of equation of motion of lake water generated by wind is mathematically true under the boundary condition that the component current normal to the vertical lake wall is zero along the coast, only when the tractive force of wind is zero at the coast. When the tractive force of wind is uniform all over the lake surface, the solution is not correct under the given boundary condition. In the present paper, the author treats the problem of this latter case. He transforms the usual equation into a equation which contains the total flow S. In that case, the order of the differential equation coincides with the number of boundary conditions, so a solution of the equation can be obtained. The obtained result is as follows: where _??_= the surface elevation or depression from the mean water level T= the tractive force of the wind per unit area of the lake surface, and it is uniform forO<X<a t= time both coasts of the lake _??_= the depth of the lake f= constant number Lastly the author investigates the ca_??_ Resonance Effect.
The amount of chlorine was chemically analysed on the 17 samples of precipitation taken during August 5, 1947 and January 1, 1948 at the Nagano City, and it was found that the groyp distribution of chlorine does not exist, which H. Köhler and H. Israel published to be so in fog and rain, respectively. Besides this a new fact was found that the chlorine contained in rain has a close relation to the air-mass that occupies the area at the time of the precipitation. The amount of chlorine in each of the four kinds of air-masses, which the author has classified, are as listed below. These results can be summarized as follows: (1) The amount of chlorine in precipitation is fifty times larger when the air-mass of the Pacific Ocean origin occupies the area than when that from the Japan Sea side occupies: (2) The air-masses of Siberia or Japan Sea origin can still be classified into two kinds, that is, the air-mass generated in September and that generated in Winter. The former is accompanied by smaller amount of chlorine than the latter. The author suggests that the difference of the amount of chlorine accompanied with these air-masses is due to the causes, such as, the difference of the areas of the Japan Sea and of the Pacific Ocean, the concentration of chlorine content, etc.