The travel time curve of shallow earthquake gives information about the structure of the earth's crust. But, in usual the observed travel times are plotted against epicentral distances without any consideration on azimuthal differences of observatories with respect to the epicentre. Therefore, by the analysis of the travel time curve made by the above procedure, only vertical irregularities of structure of the earth are obtained in assumption of no lateral irregular structures of the crust. Plots of the observed travel time have some deviations from mean curve in Japan. These deviations seem to contain systematic tendencies which exceed the amount of observation errors. The systematic deviations may be caused by the lateral ununiformness of crustal structure. From this view point, the author attempted a new method of analysis of travel time curves. That is, vertical sections are taken in Japan as in Fig. 1 and the travel time curves of the sections are made from the date of earthquakes and observatories in the belt near the sections. Thus we can easily determined the local characteristics of the structure which derived from analysis of several travel time curves of another section at intersection.
Epicenters of the earthquakes and sections are illustrated in Fig. 1. The crustal structure derived by this method are illustrated in Fig. 2, Fig. 3 and Fig. 4. The present report is a preliminary one satisfying the observed travel times of shallow earthquakes. The more accurate data from the observations of artificial explosions and local earthquakes will give some modification to this structures.

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The problem on the propagation of tremors over the plane surface of a semi-infinite homogeneous isotropic elastic solid, generated by a three dimensional point source, was studied at first by T. Sakai in 1934. He assumed three kinds of sources which admit simple interpretation and treated three cases as corresponding to three kinds of sources independently with one another by utilizing the method of steepest descent on the complex plane to evaluate the integrals. After that, some authors studied the same problem more in detail by assuming the various boundary conditions.
In stratified mediums, however, only a few approximate calculations concerning the generation of Love have been treated, because such a problem in a general case is very complicated mathematically. One of this difficulty is to obtain poles on the complex plane. To avoid this difficulty, in this paper, we take water as one medium and the other as solid in which the same point source as assumed by Sakai exists. Futhermore, for simplicity, we assume that both water and solid are homogeneous, isotropic and perfectly elastic, and that the effect of gravity is negligible and rigidity, μ=0 in water and Poisson's ratio σ=1/4 in solid. Since, if the depth of the water is finite, the problem becomes very complicate (we will state this in a later paper), so we assume it is infinite, namely no reflected wave at the free surface of water exists.
In this paper, as the first stage for solving our subject we study the branch points and poles of D(γ) or E(γ) (see (3.2) or (4.2)) which is the similar function as defined by Sakai.

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Earthquake waves recorded on the seismograph have been considered to depend chiefly on the mechanism of earthquake, path of the wave and local ground structure of the observatory. Deepseated earthquakes are comparatively free from anomalous groundstructure of the surface, and so the author tried to characterize the wave-froms in case of deepseated earthquakes and found vibrating character especially damping of the oscillator which is assumed to emitt seismic waves depends on its region of origin of the earthquke.

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Square wave of 1c/s. generated from the electrical contact of a chronometer contains various higher harmonics. One of these heigher harmonics is picked up by a “mechanical tuned filter”. Revolutions of a phonic motor which is driven by this filterd harmonic is as precise as the chronometer.
An instrument on this principle has been constructed. It has been proved that this is one of the most dependable methods for obtainning precise revolutions of the accuracy 10^-5-10^-6.

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The frequency of M_K (magnitude defined by Kawasumi) can be expressed by the following formula,
N(M_K)dM_K=const.10^-bM_KdM_K,
where, N(M_K) is the number of shocks whose M_K is between M_K and M_K+dM_K. However, a problem on the limit of applicability of this formula still remains to be solved. In the present paper, the seismicity of minor earthquakes in the Kanto District, Japan, is statistically investigated. The above-mentioned formula is also found to hold good, if the statistics are made on the whole earthquakes occurring there and whose M_K is from 4 to 1. However, if the Kanto District is divided into five domains, it is statistically proved that the formula does not hold good for the shocks occurring within each domain. This leads to the conclusion that the applicability of the formula is dependent upon the range of magnitude of shocks and the area where they occur.
The present author proposed a hypothesis on the limit of the applicability of the formula.

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If numbers of near earthquakes are recorded at a certain station during a certain period, the frequency curve of their P-S intervals can be obtained. As the P-S interval of a near earthquake is approximately proportional to its hypocentral distance, it is apt to be considered that the P-S interval frequency distribution stands for the geographical distribution of hypocenters. Of course, it is wrong. In the present paper, the writer pointed out that it is dependent not only on the geographical distribution of the foci, but also on N(M)dM or the magnitude frequency distribution, the decay of the seismic waves, and the response of the seismograph. It is noteworthy that the value of the absorption-coefficient of the earth's crust can be estimated from the data on the P-S interval frequency distribution.

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The relation of M_K and M (Richter's Instrumental Magnitude) was discussed. The both systems are not consistent, for the reason that the predominant period T is assumed independent of the magnitude in M_K-system. This discrepancy is beyond the range of the observational errors in seismometry.

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In this paper it is shown that the distribution of density in the earth's crust the author adopted in the previous paper (II) is not inconsistent with the elastic property of the crust.
If the subterranean matter was in a hydrostatic equilibrium and if its compressibility and the gravity are assumed to be constant being independent of the depth z, the density of subterranean matter increases indefinitely great as the depth does so. This is evidently absurd. Should the density remain finite at the infinitely great depth, the compressibility should change with depth. Thus the author obtains the compressibility as a function of depth and from this result are deduced values of Young's modulus E and velocity of longitudinal wave v.

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