By treating the horizontal and vertical stabilities three-dimensionally, it is shown that the criteria for stability are controlled by the value of the Richardson number, and that the ratio of the horizontal scale of atmospheric disturbances to the vertical scale plays an important rôle for the stability. In connection with this Richardson number the relation between the parcel method and the perturbation method is also investigated.
This paper deals with the secular variation and periodicity of the summer temperature in the Tohoku district of Japan. In the first chapter is stated the investigation on the secular variation and periodicity of the summer droughts and cold bad harvests described in the records of agricultural harvest for the period of 1610_??_1949. The obtained abstract results are as follows: (1) A remarkable durability of one year is recognized for the summer droughts and cold bad harvests in the Tohoku district. (2) The droughts have the periodicity of about 23-year period. (3) The droughts in northern parts of the Tohoku district have the periodicity of 26-year period. (4) The cold bad harvests have a remarkable secular variation. In the second chapter, first, as a result of the investigation on the similarity of the mean August temperatures in Japan proper, we find that the mean August temperature at Miyako exactly represents that in the Tohoku district. Next, we apply the periodgram and correlogram analysis to the mean August temperature series by means of meteorological observations for the period of 1883_??_1949. It is evident that the period of about 23 years suggested in the first chapter is composed of three periods of remarkable 7.4 year, 13 year and 11.4 year. These periods are verified by the significance test of Fourier's constants. Consequently, it is seen that the 7.4 year and 13 year periods are both significant on the level of significance 1%, and the period of 11.4 years is significant on the level of significance 5%.