I have already given an account of the ordinary stereoscopic photographs and sometimes of the stereoscopic cinematographs which I used for my study of cloud, but detailed explanation of the latter has not yet been given. For the convenience of my readers, I explain here the arrangements employed for my study which was carried out by means of stereoscopic cinematograph.
In this paper an approximate formula is introduced, which describes the change of the lapse-rate. Coordinates: x. y in horizontal, z in vertical plane. Velocity components: u in x axis, in y axis and w in z. Temperature. Pressure: T, P. Assumptions: Geostrophic wind is blowing. Two equations of horizontal motion (geostrophic wind), Laplace's equation, the first Iaw of thermodynamics and the following equation are used: This equation describes the change of the lapse-rate (∂T/∂z) of a fluid element with time (t). (The physical meaning of this equation needs to be examined. d/dt refers to one fluid particle, but ∂/∂z must be calculated from (at least) two particles. And so, it is necessary to consider the physical meaning of the notation d/dt (∂T/∂z)•. As regards this, see also my paper in the previous number of this journal.) If ∂/∂z (dQ/dt) is negligible, we get after some ealculations- where Q is the heat added from outside of the air particle. ρ the density A is a constant of an individual particle, and not a universal one. The formula states:- As regards one individual air element, the lapse-rate is proportional to its density. Particle of geostrophic wind has const. density and const. ∂T/∂z. It must be understood that the change of ∂T/∂z is caused by non-adiabatic changes.
Equations of steady motion are as usual:- where k is a coefficient of friction. V denotes the absolute velocity of wind, and then u=Vcosδcosα, v=Vcosδsinα, w=Vsinδ where δ is the slope angle of the earth. Pressure gradient is in direction n, and Notations α, β, δ, n, … are shown in fig. 1. After some simple transformations, we get (β-α) is an angle between pressure gradient and wind. (If the motion is only horizontal, the equation becomes This is Gull berg and Mohn's formula.) The equation shows that the angle (β-α) is a function of variables α, δ and φ. For example, of the wind is southerly, we get tg (β-α) 0 and so (β-α) 0 as δ tends to φ, also the slope angle δ equals to latitude φ In such a case, the wind blows perpendicularly to isobars. Thus, we know that (β-α) varies widely with δ, the slope angle of the earth. Numerical example: k is 7.6×10-5. Two cases (uortherly and westerly winds) are calculated on the latitudes 20°, 30° and 40°. Fig. 2 is the graph. From these discussions, we know that slope effect is not smaller than the other effec_??_s (∂/∂t, w∂/∂_??_ and so on), and we may say:- The angle between pressure gra_??_ient and wind fluctuates greatly as the result of slope effect, and not of acceleration or other factors. If we use Naver-Stokes' equations, we get almost the same results in free air, and it may be said:- Whem there is some vertical current, wind direction fluctuates greatly. The so-called “Ablenkungs Winkel” from geostrophic wind is not always the result of acceleration in the meaning of Ertel, Brunt-Douglas and others.
With the instrument which was made by Dr. Nukiyama, we observed the relation of the polarization and the formation of clouds on clear days. In the daily veriations of the polarization at the zenith, the plane of polarization changed with the variation of the azimuth of the sun, in accordance with Rayleigh's theory. The variations of the polarization were closely connected with the weather conditions. On really clear days the polarization indicated great values and on less-clear and somewhat cloudy days it gave moderate values. The abovementioned facts seem to indicate that when the moisture content in the air rises, it begins to condense on some particles and forms some water droplets before becoming visible clouds of droplets. Accordingly the droplets cause small variations of the polarization. On hazy days the polarization was observed to have smaller values. This, of course, means that the polarization produced by hazy particles is very slight.