§ 5. Shape of the Discontinuous Surface. If the origin of coordinates is placed on the section of the discontinuous surface with the earth, the formula (17), which represents the, shape of discontinuous surface, is transformed to (19). (19) is again transformed to (22), if coordinates (x, y, z) are rotated by an angle δ given by (20), and then transformed to coordinates (ξ, η, ζ) given by (21). (22) is a fundamental type of parabola. Thus it is seen that the shape of the vertical section of discontinuous surface is approximately a parabola. Though the position of the vertex of parabola depends on the nature of the air on both sides of the surface, the angle δ and the parameter P are determined only by the situation and direction of the discontinuous surface. Therefore, the shape of the surface is easily drawn from these values, as is shown in Fig. 2.
In this paper convenient approximate expressions between saturation vapour and the size of a nucleus containing given amount of solute were derived. At first we assumed that saturation vapour pressure for plane surface of aqueous solution is given by where P is saturation vapour pressure of aqueous solution, Po that of pure water at the same temperature as the aqueous solution, θ mol concentration of solute, α, β, constants depending on the nature of solute. Then using (1) we derived approximate formulae of saturation vapour pressure for a condensation nucleus containing given amount of solute. They are as follows: where P' is saturation vapour pressure for the drop of solution of radius r, P0 that for plane surface of pure water at the same temperature as the drop, m the mass of solute in the drop, A, B, constants depending upon the nature of solute, r0 the radius of the drop when the solution is saturated with solute, r_??_, the radius of the final crystalline nucleus. Constants A, B were determined for NaCl-, MgCl2-, MgSO4-, K2SO4-, H2SO4-solution, and saturation vapour pressure versus drop size relations for several given amounts of solute were obtained for the above solution.
The remarkable diffusing power in the turbulent flow is supposed to be caused by the irregular motion of turbulons (ordinarily named eddies) in the flow. Representing the interaction between turbulons by means of the turbulent friction, the relationship between the scale _??_ and the velocity V of turbulon is obtained. From this result, the spectral function of turbulon energy with regard to its own period τ (or the life-time, given by _??_/V) is deduced as follows: F(τ)_??_const. The so-called Lagrangian correlation function R(ξ) (Taylor, 1922) is obtained in connection with F(τ), and finally deduced to R(ξ)=1-(ξ/τ0), where τ0 means the life-time of the largest turbulon. On the other hand, putting the limit of application for the theory of turbulent diffusion, the state of the smallest turbulon is given by ν=_??_∞V∞. The distinct differences between R(ξ) and R(t), the Eulerian correlation function, are made clear. And also the relations between the smallest turbulon in this paper and the smallest eddies in the meanings of Taylor are shown. The practical applications of the results are left for the following papers.
The disturbance of the atmospheric potential gradient, caused by the eruption smoke of the Volcano Aso and observed in the neighbourhood of the crater, was positive when the volcanic ashes were falling. The negative disturbance was observed in a short duration when the tip of the smoke reached the zenith of the observing spot. The electrification of ashes caused by the mutual collision was investigated in the laboratory and it was found that the larger particle got the positive electricity and the smaller particle the negative.