Chemical structure of the earth's mantle is discussed under the assumptions that (1) chemical equilibrium and hydrostatic equilibrium are attained; (2) it is isothermal and incompressible. Based upon these assumptions, the distribution of chemical elements would be controlled by differences in their chemical affinities as well as by gravitational separation due to their density differences. Calculation of the equilibrium distribution of FeO-MgO-Fe-SiO₂ system, it is concluded that FeO would increase with depth, reach maximum at a depth of several hundred kilometers, and then would decrease toward the earth's center. This result suggests the origin and the physical property of Jeffrey's 20° discontinuous layer.

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C. Tsuboi has found that the following formula is useful for calculating the Gutenberg-Richter's magnitude of an earthquake occurring in and near Japan from seismological data;
M=αlogΔ+logA+γ
α can be regarded as the decay factor for each station of maximum amplitude of earthquake waves according to distance.
The present writer determined the constants α and γ for each seismological station which make seismological data at it fit the corresponding Gutenberg-Richter's magnitude as closely as possible.
The result is shown in Table I and Fig. 1. The value of α differs for different stations, and its distribution appears to have close relation to that of Bouguer Anomalies.

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The Ishimoto-Iida's statistical formula is described as follows:
na^m=k
where, a is a traced maximum amplitude; n is an annual average frequency of small shocks with a, while m or k is a constant at that place.
What interests us, the same statistical form holds good in the maximum amplitude distribution of cracks, occurring naturally in an earthen wall or in that of cracks in a glass sheet artificially produced by heat.

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Japanese seismologists succeeded in explaining the push-pull distribution of the initial motion of earthquakes by assuming two types stress distribution on the sphere which covers the hypocenter. Type A is the combination of hydrostatic pressure and pressure with distribution expressed in spherical harmonic P₂(cosθ). Type B is the distribution of pressure expressed in P₂¹(cosθ)cosφ. Generally the polar axis of these spherical harmonics does not coincide with vertical axis. On this point, Y. Sato obtained the formulae which express the transformation of the spherical harmonics by the rotation of coordinate system. According to his result,
P₂(cosθ₀)=P₂(cosθ)(1/4+3/4cos2χ)+P₂¹(cosθ)cos(φ-φ)(1/2sin2χ)+P₂²(cosθ)cos2(φ-φ)(1/8-1/8cos2χ)
P₂¹(cosθ₀)cosφ₀=[sinφA₂¹-cosφB₂¹]
where A₂¹=P₂¹(cosθ)sin(φ-φ)cosχ+P₂²(cosθ)sin2(φ-φ)(1/2sinχ)
B₂¹=P₂(cosθ)(3/2sin2χ)-P₂¹(cosθ)cos(φ-φ)cos2χ-P₂²(cosθ)cos2(φ-φ)(1/4sin2χ)
where (φ, φ, χ) is Euler angles which express the rotation of the coordinate.
In this paper, we calculated the strain produced in a semi-infinite elastic solid when hydrostatic pressure and pressure with distribution expressed in spherical harmonics P₂(cosθ), P₂¹(cosθ)cosφ, P₂²(cosθ)cos2φ were applied at the interior spherical cavity.
The deformations expressed in cylindrical coordinate (R, φ, z) at the surface of semiinfinite elastic solid are as follows:—
(1) The case in which hydrostatic pressure -P is applied
U_R=3a³P/4μR/(f²+R²)^3/2, Uφ=0, U_z=-3a³P/4μf/(f²+R²)^3/2
(2) The case of -PP₂(cosθ)
U_R=3a³P/46μ[-5P/(f+R^23/2)+18f²R/(f²+R²)^5/2], Uφ=0, U_z=-3a³P/46μ[-5f/(f²+R^23/2)+18f³/(f²+R²)^5/2]
(3) The case of -PP₂¹(cosθ)cosφ
U_R=54a³P/23μcosφ[-f((f²+R²)^3/2+f³(f²+R²)^5/2], Uφ45a⁵P/184μsinφf(R²+f²)^5/2, U_z=45a⁵P/184μsinφf(R²+f²)^5/2
(4) The case of -PP₂²(cosθ)cos2φ
U_R=9a³P/23μcos2φ[4f/R³-4f²/R³(R²+f²)^1/2+5R(f²+R²)^3/2-2f²/R(R²+f²)^3/2-6f²R

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Correlogram analysis of seismograms was done by means of a specially designed automatic relay computer. The correlogram was obtained for each section, into which seismograms were divided by an adequate time interval, of about sixty seismograms of shocks of various magnitudes and epicentral regions. Those seismograms were recorded at the Tokyo Central Meteorological Observatory by a Wiechert type seismometer. The predominant period for each section was estimated from the correlograms obtained, and its dependence on the magnitude and epicentral region were investigated.
The periods of seismic waves of the same magnitude show a marked difference by their epicentral regions, and these differences are conspicuous in the earlier sections of seismograms and seem to disappear later in the coda sections. The period of every section of seismic waves of the same epicentral region increases with their magnitude, but there are some differences between the situation in the cases of the initial section and that of the coda sections.

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Strain rate of rock near the explosion is measured by a instrument newly devised for for this experiment. The strain wave are calculated from the records. The tension wave produced at free surface as a reflexion of compression wave caused by the explosion is most remarkable near the surface. As a result, the fracture of rock is conceived chiefly done by this tension wave. Ths relation between stress and strain must be in the plastic region for this case.

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