No research has not yet been attempted on the polarization angle on the secondary scattering of the sun's ray in the earth's atmosphere. The author has developed its mathematical characteristics and has given useful evaluation. In Fig. 2, P and Q are two points in the earth's atmosphere. Define any rectangular coordinate system X1Y1Z1 with its centre at Q, X1 being directed to the sun. The direct insolation at Q can be resolved into two plane polarized lights, the one travelling to - X1 and oscillating in Z1 direction, the other to -X1 and in Y1.ω and ω' are the angles of Z1 and Y1 suspended by QP. Define a rectangular coordinate system X2Y2Z2, choosing P to the origin, X2 to PQ, and Z2 to the direction of oscillation when the former polarized light proceeds from Q to P. Define another system X2' Y2'Z2', choosing P to the origin, X2' to PQ, and Z2' to the direction of oscillation when the latter polarized light proceeds from Q to P. Ω and Ω' are the angles of Z2 and Z2' suspended by PO', O' being a point on the earth's surface. Then the intensity of secondary scattering at O' generated by air particles at P and Q is proportional to sin2ωsin2Ω+sin2ω'sin2Ω'. For brevity let us write D=sin2ωsin2Ω, D'=sin2ω'sin2Ω'. The author calls D+D'as the polarization angle. This is naturally a function of the sun's altitude h and the positions of P and Q. Define a system of rectangular coordinates X'Y'Z' with its centre at O', Z' being directed normally upwards, X'lying in the vertical plane passing the sun and towards the sun-side. A is the angle between two planes O'Z'P and Z'X', θ is between O'P line and X'Y' plane. (see Fig. 4). XYZ system is produced by the parallel translation of X'Y'Z' system from the origin O' to the earth's centre O. Let the new system x1y1z1 be produced by rotating XY plane by the angle A around Z axis, then rotating the new XZ plane by the angle ∠POZ around the new axis Y. (see Fig. 5). ∠POZ is denoted by a. Let θ1 be the angle ∠OPQ, and A1 be the angle between two planes OPQ and x1z1. The author has had the next conclusions. D' is always independent to h, and D and D' are always indifferent to the substitution θ1, A1→π-θ1, π+A1. A). When A=0. D and D' are indifferent to the substitution θ1, A1→π-θ1, π-A1→π-θ1, π+A1. WhenA=π/2 D'is equal to D for A=0, The substitutionθ1, A1→π-θ1, .π-A1 is possible to D'for any h and D for h=0 and 90°. When.A=π. D' is equal to that for A=0. The substitution for .D and D' is the same as that for A=0. B) When h=O. D(A+π/2)=D(A) D'(A=π)=D'(A=0) D+D'is identical A=0, π, and D for A=0, π/2, π. When h=90. D(A+π/2)=D'(A), D'(A+π/2)=D(A) D+D' is identical for A=0, π/2, π, and D for A=0, π. C). When α=0. 1) When θ=0. Representing D, D' by D(A, A'), D'(A, A1), then D (π, π-A1)=D (0, A1) D'(π, π-A1)=D'(0, A1) . and D+D' is equal for both cases. Further D'(0, A1)=D'(0, π-A1) D(π, A1) =D'(π, π-1) . Especially for h=0 and 90°, the following four are each equal: D(0, A1), D(0, π-A1), D (π, A1) and D (π, π-A1). 2) When θ=90°. In this case there exists the same conclusion as for θ=0, and moreover, especially for A=0, h=0, D is independent to A1. 3) For any values of h. D(π/2, A1)=D(0, A1+π/2) D'(π/2, A1)=D'(0, A1+π/2).
A synoptic example is here presented in the vicinity of Japan in terms of the analysis based on the theory of isentropic upgliding motion described by J. Bjerknes (1). It is clearly seen that the upgliding motion on the warm side and the downgliding motion on the cold side of the cold front advectively generated by the Siberian High progressively develop, leading to the intensification of the front. It is also revealed how the incipient frontal wave has been characterized by the inception that the eastern portion of the cold front has changed into the warm one.
In this paper are presented the results of analysis and discussion about a series of showers. Character of showers under consideration is as follows: (a) this series of showers consists of at least 25 separated cells of rain regions (the writer calls these cells“Rregions”in this paper);(b) five narrow parallel much-precipitated stripes appeared in the precipitated area as a result of passage of showers;(c) every showers moved in the same direction at a speed of 70km/hr during the period under consideration;(d) no abrupt change of surface meteorological elements was observed at the time of passage of R-regions. The existence of low-level jet stream above the precipitated area was found and the relation between the low-level jet and the mechanical properties of Rregions are discussed.It is shown that the upper disturbances, which caused the precipitation, had wave nature and it is suggested that this wave was produced in the vicinity of frontal layer by a strong wind shear near jet stream.
A cold-box of the diffusion cloud chamber type has been constructed, and about 115 substances, inorganic as well as organic, after dispersed either by condensation method to smokes of particles ranging from 0.1μ to 0.8μ in diameter or by dispersion method to those of 0.5μ to 2.0μ diameter, have been put to test of the nucleating ability; the temperature of nucleation at which ice-crystals make their hasty appearance, and the vividness of the phenomenon have been observed by naked eye. The results show that, among others tested, NiO, CdCl2, BiI3, MgO, HgI2; etc., all of which are not of hexagonal type of crystal systems, behave as active ice-nuclei, though silver iodide is found, in fact, to be most effective. The runs of experiment on the particle size dependence of the ice-nucleating activity have been, next, carried out using iodides of silver, mercury and lead, oxides of nickel, magnesium, aluminium and zinc and besides, urea, each of them being of the particle size smaller than several microns in diameter. It was found in all these cases that the temperature of nucleation falls down rapidly as the particle size goes finer over 0.2μ or thereabout in diameter. A thermodynamical consideration on the relation between the nucleation temperature Tc (°K) and the particle radius γ(μ) leads to the following equation 1/(γ+Δ)=a-bTc, a=b(T0-x) wherein Δ, b, x are empirical constants and T0=273; Δ denotes the thickness of a quasi-ice structure formed by water molecules adsorbed from the vapor onto the nucleating particle, b is comprehensive of the surface tension of the outermost layer of the structure and x refers to a measure of the magnitude depending upon the accuracy of the determination of Tc. The equation has proved to agree with the experimental results.
In the previous paper(2), the author treated the motion of a typhoon by using a barotropic vorticity equation. The present short note is contributed to supplement some problems left to discuss. First, the physical meaning of β-effect on a circular vortex is made clear. Second, integrating primitive equations of motion, the relation between pressure and velocity is obtained. Third, the balance equation by Charney is obtained from the pressure function. Fourth, ageostrophic pressure is estimated.