Using the theoretical results of the present author's preceding papers which appeared in the former numbers of this magazine, he has calculated the intensity of reflected light from the snow surface which is supposed to be consisted of numerous facets of ice. The chief results are as follows. Whether the normals of the facets are directed uniformly into space or the majority of them are directed vertically upwards, we have the theoretical result that the reflection is strongest in the horizontal direction of the side opposite to the incident light, not in the direction expected from the regular reflection of a plane surface. As a next problem, the author has discussed the unevenness of the surface. If we separate the total reflection into two parts, one the surface reflection, the other the multiple reflection inside the medium, it will be the projections of the uneven surface that take part in the surface reflection, the hollows having little effect on it. Therefore, the amount of surface reflection will be reduced in some proportion, say 30%, than the value expected from the above theory. These facts have been confirmed also in the photometric experiment taken by H. Oura. In conclusion, the author has suggested the possibility to classify the surface conditions of snow from the intensity distribution of the reflected light.
There are many theories and hypotheses on the structure of typhoons. Especially the classical theories of F. H. Bigelow W. Wien and Lord Rayleigh are well known. But since the theory of the eddy viscosity had been published, it was difficult to obtain an exact solution referred to the eddy viscosity. While we succeed for the first time, to obtain an approximate solution in the year 1928. Afterward in the year 1935, B. Hauriwtz obtained an exact solution under the conditions that the wind velocity and the pressure gradient are proportional to the distance from the centre of the rotating fluid and that the isobars are circular. Here it will be shown that the new solution is more satisfactory than the previous ones. The equations of motion of a viscous fluid moving symmetrically round a stationary centre expressed in cylindrical coordinates, are where u, v, w are velocities reckoned positive in the directions in which r, θ z increase. Now we shall proceed to a solution of the equation when w=wo Sin 2 m_??_ where w0 and m are constants, puting U=U', v=V+v' and U=u'+iv' ξ=m_??_ and Neglecting the last term, in which A2 is a small quantity of higher order, the equation may be written Now we may assume as a particular solution where The value of c is the same as that which was obtained by Lord Rayleigh and it appears that c is real or complex according as (Ao-1)2 is greater or less than A21 The general possible solution subject to the condition that the ascending velocity can be represented as the same form used by Bigelow and Wien, is therefore given by where C=α+iβ, W is the wind velocity, V is the gradient wind U is the wind velocity induced by the turbulent motion of air, and the equation (7) is expressed in the form of vector. But this solution is not exactly applicable, because the pressure gradient was treated as constant for all heights. On the other hand the pressure gradient varied with height from the observation on high mountain. According to the results of an observation at Mt. Niitaka (3850m above mean sea level), the minimum pressure was 605mb and it was 95smb at Shinko (33m above mean sea level). From these results, we have estimated approximately the gradient winds as follows 25.0m/sec at the distance 28km from the centre and at the height 3850m, 40.0m/sec at the same distance and at the sea level. Thus further investigation is necessary in order to solve the equations of motion in which the gradient is introduced as a certain function of r and z determined by the results of the observation of typhoons.
At the weather station on Mt. Fuji the author investigated the various properties of rime deposits and the conditions controlling their types. Basing on the results of observation, he proposed a new theory about the mechanism of rime formation. The results are summarized as follows:_ (1) The densities of various types of rime were measured: the glazed frost and the almost transparent hard rime 0.9; hard rime with finny parts on both sides 0.7-0.9; white shelly rime 0.6-0.7; soft rime of finny structure <0.6. (2) The opacity of the hard rime increases with decreasing drop size and liquid water content in fog. It is also closely related to the temperature rise on the front surface of rime, as shown in fig. l. (3) The adhesiveness of rime is the greatest in hard rime with finny sides. The force of adhesion ranges 0-13kg/cm2 and increases with lowering temperature. (4) The shape of cross section of the rime can be classified into 7 types shown in fig. 2. A and B type are formed by flowing of water before freezing, C and Dl type occur when λ>2.5, (λ=2_??_r2/9_??_) D2 and E type when λ<2.5, and F type when λ<1.0. The type depends also upon the length grown. Fig. 3 shows this relation. (5) The finny structure of rime seems to occur to occur when the impinging angle of cloud drops with regard to the front surface is less than a certain velue. we may say, therefore, that the finny structure develops with decreasing λ. When λ is very small, the finny structure becomes isolated and a deep groove is formed on the central line of soft rime. (6) The angle of widening of breadth is also closely related to the value of λ. It is shown in fig. 4. (7) The mean surface temperature of the hard rime was measured with thermojunctuion. It was about 1_??_2°C higher than the air temperature. (8) If we write the mean effective icing time neglecting the heat conduction as τe, and the mean time interval of successive impingements as ε, the mean temperature rise upon the front is theoretically Δθ=τe/εθ, when the air temperature is -θ°C. Using the 1/4 of the Frössling's formula for the rate of evaporation of water drop and the similar one for the convective heat transfer, we obtain the following experession of Δθ:- Δθ=6.12×106M r012/1+2.62 v0.5 r00.6 (1) where M is the rate of icing in gr/cm2 sec, r0 the radius of cloud drop, and v the local wind velocity. Fig. 5 shows the relation between the observed value of Δ_??_/θ and the oaloulsted one, taking v_??_o in the expression (1). The difference is attributed to the neglected wind velocity and heat conduction. This result means that the hard rime is formed by independent freszing of individual water drop, hence the over-supply of water does not occur. (9) Ifτe_??_ε, since the surface temperature must be always 0°C, the impinged dropos unite together before freezing, and the surplus water must flow away. This is the case of glazed frost. Using the formulae of the cooling of s circular cylinder, we obtain the following expression of icing rate for glazed frost: where V0 means the general wind velocity, R the radius of cylinder. The relation between the observed value and the calculated one is shown in Fig. 6. (10) The microscopic structure of rime was studied with polarized light. The isolated finny soft rime is usually a monocrystal, whose oriedtation of optic axis is rather random. In massive soft rime, although each piece of finny sturcture is also composed of a few monocrystal, whose orientation of their optic axes are almost parallel to the direction of growth.
Calculating the maximum amplitudes of dispersive waves propagated in absorptive media, it is proved that the wave groups of the maximum amplitudes are propagated with constant velocities which differ from those in non-dispersive media, and their amplitudes are O(1/γ) (r being distance), while in non-dispersive media, they are O (_??_) as the author has proved in his previous papers.
Rain drops grow by capture of cloud particles which encountered during their fall in the cloud sheet. The author made some calculations to evaluate rate of capture and found that it depends on the drop size of cloud and rain and is about 0.8-1 in usual case. Using this rate of capture and he obtained a formula expressing the rate of growth of rain drops by capture of cloud particles and then made some considerations on the formation of rain from the water cloud aheet. Details of the investigation will be found in the “Sciance Report of Tohoku University”, series 5, Vol. 2.
We discussed the motion of air in the neighbourhood of frontal zone as the motion of a laminar boundary layer, and we treated the frontal zone as a jumped phenomena of the boundary layer, thus we gain the equation of motion in cylindrical co-ordinates of follows; and also the equation of continuity is thus, from these relations, we induced the formula of dh/dr, where h is the depth of laminar boundary layer. Therefore, dh/dt is defferent for each case of the assumption of velocity distribution in the boundary layer. Then the formula of dh/dt will be as follows: from this relation, we trace the stream line of the laminar flow, by the method of isoclination line. Moreover, in case of the velocity distribution whose gradient of the stream line is linear, we can solve the motion of air by means of the Weieretras's elliptic function _??_(z), and the total mass of flow is