Usual method for studying earthquake phenomena as statistical time series is to investigate the variation of number of earthquake occurrences in a prescribed time interval, say hour; month etc.. Anotherr method, i. e. of investing the mode of distribution of the time intervals of consecutive earthquakes has been adopted by a few writers. Which method of these is more adapted for the study of earthquake occurrence is a problem which depends on the nature of earthquakes, and at present neither can be neglected.In this paper, the frequency distribution of the time interval between consecutive earthquakes and its relation to the distribution of maximum trace amplitudes of earthquake motions has been statistically investigated.The results obtained are as follows.(1) Time interval (τ) distribution of consecutive earthquakes is empirically expressed by the formula f(τ)=kτ-p for the earthquakes which occured in sarms as volcanic earthquakes or as after shocks. This means that the occurrence of these earthquakes are not at random unlike in the case of usual conspicuous shocks which occur at interval of more than 1 or 3 days.(2) The formula on the time interval distribution mentioned above is quite similar to what is called Ishimoto-Iida's formula; i. e. the distribution of maximum trace amplitude of earthquake motions at an observation position is expressed by the formula φ(a)=ka-m. This is quite a remarkable fact worh noticing.(3) The rektion between two quantities p and m is empirically described as p=m+1/2 This means that the time interval distribution and the distribution of “square of maxium amplitude” obey the same distribution law. This relationship is verified for earthquakes which occured in swarms at volcano Asama and for after shocks of destructive earthquakes which occured in Tango and Fukui districts.(4) It is also verified that the formula for the time interval and for the maximum amplitudes holds well even in the case when the period consideed is rather short as 1 day or so, provided that the number of occurrence of shocks is large enough, say more than 200 or more. In this case, however, the relation, between p and n (or m) is no more so evident as that is obtained by the data covering long period of about one year.(5) It is perhaps plausible to think that, after a long time interval, the shock having large energy propotional to the time interval is expected, or that after a shock having large energy, a long time interval propotional to it is expected. If this is actually the case, a good correlation between the time interval and the maximum amplitude must be expected. In order to verify this, correlations between τ and a were investigated. It is found that things are not so simple, no correlation being found between these quantities. It is found that these two quantities are statistically independent.(6) As it is reasonably conceivable that the time interval and maximum amplitude are subjected to various sorts of distorsions, when observations are carried out at a position far distant from the origin region. Therefore, the correlation between these two quantities may become more and more obscure according to the distance from the origin region, even if a good correlation does actually exsist there. Can we then expect a good correlation to exsist at the origin region? In order to investigate this, the relation has been investigated regarding the volcanic outbursts of Volcano Mihara, observations being carried out at the nearest approachable point from the crater. But the results obtained are obscure and we can hardly say anything definite about this problem, leaving much to be investigated in the future.