In the present paper, an exact formulation of the problem of the motion of a rotating solid cylinder on a rotating earth is attempted by means of the Hamiltonian equations of motion. The theorems of the conservation of angular momenta, about the polar axis and about the vertical axis of the cylinder, and of the total energy are obtained as the results of three intermediate integrals. From these integrals, the equations of motion of the cylinder are examined. In addition to the force acting upon the cylinder endowed with given amounts of relative vorticity, first noticed by Rossby, the inertia force acting upon the cylinder is separated, and the importance of this force is emphasized. Such results are in accord with those obtained by Syono in another way.
Some studies on the pressure distribution and its changes in typhoons revealed that the minima of the center pressures of typhoons are divided into four groups. This seems to come from the difference in the mechanism of development of typhoons. Following each life stage of a typhoon, the isobar profiles show very interesting deformations which are almost the same with the changes of appearance shown by the water spout trunk in its life stages. From those pressure profiles the author pointed out the importance of the eye wall on the mechanism of typhoon development in its immature stage.
The droplets of cloud on mountains and those of fog in urban area were captured, and the form, nature and size of their nuclei were studied by using an electron-microscope and a chamber of constant humidity. These nuclei are of the same form and nature as the hygroscopic particles in haze and the combustion products artificially produced. No sea-salt nuclei were found in our observations, and therefore the sea-spray appears to be insignificant as the source of condensation nucleus. It is supposed that cloud and fog nuclei are composed of combustion products, which are the mixture of hygroscopic and nonhygroscopic substances. It was also found that the hygroscopic substance is not pure sulphuric acid.
The effect of stability on the mixing length near the earth's surface is considered upon the basis of Deacon's newly proposed wind velocity formula and a relation l=0.4hzβ is obtained, where h is a parameter, the variation of which with stability being determined from Pasquill's experiments. It is shown that the parameter h is contained in wind velocity distribution, eddy viscosity and in the evaporation formula, and that the Thornthwaite's method of obtaining evaporation from large areas, i.e., from observations of wind and moisture concentration alone, is inapplicable without knowing h.