In Chapter I of this paper, the steady flow of air subjected to the isothermal and adiabatic changes along a mountain of Pockels' form was firstly treated by the aid of the stream function. As simple examples of vortical motion we take the case of two vortices lying wind-and leeward of a mountain which are caused by the effect of the profile itself. The configulations of the stream-lines are shown in Fig. I and Fig. II according as the upper boundary is a plane or a curved surface.In Chapter II, we take firstly two problems for a current flowing with the general velocity past a fixed cylindrical obstacle when the slight variations of densities of fluid follow the laws ρ=ρ0(1-mrcosθ) and ρ=ρ0(1+ma2/r2cosθ), the solutions being obtained by the method of successive approximation derived by Airy. The forms of the stream-lines are shown in Fig. III and Fig IV. The same method stated above is also applicable to the case of vortical motion in a cylindrical vessel, the density of fluid varying at very slow rate with ρ=ρ0(1+mrcosθ) Fig. V shews, with, of course, exaggerated magnitude in m, the stream-lines of the motion which is symmetrical with a certain radius.The problem for the motion in a cyclone relating to the case of symmetry about the axis was discussed. It can be solved from the hydrodynamical equations by separating into two parts, one the gradient wind system and the other vortical system. The solution for the latter was found to be expressed in terms of hypergeometric functions.In Chapter III, the flow of air past a fixed spherical obstacle was discussed as the density of fluid varies according to the law ρ=ρ0(1+ma3/r3sinφ), the solution being obtained by the same method as Chapter II. The forms of the stream-lines were shewn in Fig. IV.The circulation of the atmosphere with constant density in a spherical shell were then treated as a three-dimensional problem. The solution for a simpler case where f(x)=ax, F(x)=0 as shewn in equation (33) was easily obtained in terms of the associated Legendre functions, while in the case where f(x)=ax, F(x)=-b2/s2x the solution for the equation such as (43) was expressed by the terms of the continued fractions as derived by Kelvin and Darwin used for integrating the dynamical equations of the tides. Fig. VII and Fig. VIII corresponds to the former, the degree of the function being 2, 4, 6 and 8, and Fig. IX refers to the latter. The latter is the case in which the close coincidence of the observed and theoretical values shews the existence of this mode of circulation in the actual atmosphere.