The diurnal barometric oscillation in free air over Lindenberg was calculated using the surface hourly barometric values and hourly temperature values in the free air observed at the aerological Observatoire, Lindenberg and compiled by Hergesell. The result was compared with the hourly barometric readings obtained at mountain observatories such as Obir, Säntis, Sonnblick and Mont Blanc and found very good similitude between the calculated free air values and observed summit values, while those observed values at mountain slope such as Zell a. S, Bad Fusch etc. are different with the free air values of similar altitudes. Thus it proves the creditability of the calculated values. Hence further steps are taken by applying the method of harmonic analysis and found the dependency of the amplitude and phase difference of diurnal, and semidiurnal pressure waves on the height above sea level.
Hitherto little is known on the vertical change of the diurnal variation of pressure. Recently, H. R. Kubota and S. Miyake have undertaken an investigation based on the data at Lindenberg computed by Fujiwhara and Takeda, but it ended in unsatisfactory result. In the present note, the same problem is attacked by solving the differential equation given by Max Margules, in which the vertical lapse rate of temperature is newly taken into consideration, so that the pressure variations at several heights are calculated. The obtained values coincide well with those calculated by Fujiwhara and Takeda, applying Laplace's formula, layer by layer, in the free air and these also agree in order and character with the results of mountain observations. By introducing a boundary condition that at the earth's surface, the vertical motion is zero, another solution is obtained, which after numerical calculation is'proved to coincide well with the above result.
S. Chapman and T. T. Whitehead calculated, first, the earth potential gradients induced by the magnetic variations, considering the earth core enveloped by the non-conducting layer, but the calculated gradients differed from the observed ones, much in amplitude (the latter was 5 or 6 times larger) and little in phase. Latley, H. Ertel made the amplitude-difference clear, due to non-uniform conductivity of the earth crust varying rapidly with depth. The author extends Ertel's idea to the anisotropic earth crust which is regarded as the isotropic when it is averaged over the sufficiently wide regions and generalises the Chapman's and Ertel's solutions. We see that the solution answers the existence of the vertical potential gradient and the phase-difference between the calculated and observed potential gradients.
In this paper it is treated on the case that a spherical pendulum is forced to vibrate from repose by plane waves. The authors give the solution for the vibration of the pendulum, when the motion of the air particle is cxpressed by the following formula It is proved that there is an oscillation which occurs in an instant of the arrival of sound waves at the pendulum and vanishes rapidly, besides the forced and self oscillations.