Many attempts have been made on the atmospheric oscillation but, because the vertical current are neglected in them, they have a failure that a maximum fo the pressure occurs at the time of the highest temperature and the amplitude calculated does not fit to the observations satisfactorily. In former papers the author treated this problem with respect to cartessian coordinates taking into account the vertical current. In the present paper the author solved the problem regarding the earth as a rotating sphere.
In the diurnal case, from a physical point of view, the solutions of the equation of oscillation are separately treated, one of which is the forced oscillation caused directly by the temperature change and the other is a free oscillation. Then it is explained that, if the temperature changes as to the height making a logarithmic spiral in the amplitude and phase-diagram as W. Schmidt or D. Brunt shows, the forced change of the pressure also makes a logarithmic spiral but its phase delays 15 hours, and the free oscillation has the phase which is constant to the height though 3 hours later than that of the temperature and the amplitude which is almost constant to the height but a little smaller than that of the forced at the ground. Thus the resultant of this forced and free oscillations may well agree with the observed diurnal pressure change.
As for the semi-diurnal oscillations, there is of course the forced one as the result of the temperature change of the half day period, though the main part is the free oscillation which has a cause in the diurnal case, and its phase and amplitude almost do not vary vertically.
Nextly the author calculates the pressure changes using only the temperature observations at Lin lenberg and compares them with the pressure observations of Potsdam.
Lastly the formula which shows the amplitudes of the free oscillations has some inadequateness for the lower latitudes but this defect can be removed if the surface resistance of the earth be taken into account, but it can not be assured numerically because the coefficient of resistance is an uncertained constant.
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