Three characteristic numbers h, k and l, which are related with the elastic behaviour of the earth, have recently been obtained by tidal observations at various regions of the world. Value of the characteristic numbers must in principle be equal at any point on the earth's surface. But their values obtained at many stations, are not always identical and a regional difference is clearly recognized in the values of the characteristic numbers. The most reliable value of diminishing factor D ≡ 1 + k - h derived from tidal observations with horizontal pendulums is 0.68 in Asia and 0.72 in Europe and that of gravimetrrc factor G ≡ 1-3k/2+h obtained from tidal observations with gravimeters is 1.14 in Asia and 1.19 in Europe. Combining the value of D with that of G, the values of Love's numbers h and k are calculated as follows: h = 0.68 and k = 0.36 in Asia, and h = 0.46 and k = 0.18 in Europe. Tidal observations with extensometers show that the value of Shida's number t is very closed to 0.05 in Japan and is 0.07 at Freiburg, West Germany. By using the value of k above obtained and assuming that the value of t, obtained at Freiburg, is applicable for other stations in Europe, the value of L ≡ + k - l is calculated to be 1.31 in Asia and 1.11 in Europe. On the other hand, the most reliable value of L derived from observations of latitude variations is 1.30 in Asia and 1.11 in Europe which is almost exactly agreement with that of L above derived. These value is one for M2-constituent with a speed of 12.421 mean solar hours. The M2-constituent has the wave length of about 20, 000 kilometres. It seems natural, therefore, that a value of the characteristic numbers depends on the elastic behaviour of materils under a fairly wide region such as Asia or Europe.

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In succession to the preceding paper in which the secular variation in the physical height of the datum was clarified, heights of the bench marks along the leveling loop in the southern part of the Kanto District are calculated in this paper. This loop is adjacent to the Tokyo loop, and 5 epochs of leveling, i. e., 1884. 7, 1896.4, 1925. 3, 1931. 2, and 1950.7, are selected. Moreover, the leveling loop in Izu Peninsula (epochs: 1904. 1, 1926. 9, and 1931.0), the leveling route along the western coast of Miura Peninsula (epochs: 1898. 9, 1925. 2, 1930.4, add 1952. 8), and the route between Hachioji and Totsuka (epochs 1926.0, 1930.4, and 1952.8) are added. These leveling loop and routes are shown in Fig. 1. Collecting all these heights of bench marks, the crustal movements during the respective epochs are calculated, and the results are shown as the contour maps of equal movement in Figs. 3, 4, 5, and 6. In the duration concerned, the Great Kanto Earthquake (Sep. 1, 1923) and the Izu Earthquakes (March, May and November in 1930) are involved. Accordingly, it can be considered that Fig. 3 shows the pre-seismic movements before a group of such great earthquakes, Fig. 4 shows mostly the abrupt movements due to the Great Kanto Earthquake, Fig. 5 shows the resultant of the movements due to the Izu Earthquakes and the recovery movements of the preceding earthquake, and Fig. 6 shows the post-seismic movements. For the sake of comparison, the movements of Figs. 3 and 6 are reduced to the annual movements in Figs. 7 and 8. It is clearly seen that the general tendencies of pre- and postseismic movements are reversed on the whole.

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By using the result of the levelings which were carried out 15 times during 1898-1963 in the Miura Peninsula, and the record of the tidal observation during 1897-1963 at the Aburatsubo mareographic station, crustal movements in this peninsula are clarified con siderably. In this period the Great Kanto Earthquake, Sept. 1, 1923, is involved. In Section 2, the heights of the bench marks shown in Fig. 1 are calculated in all epoch of leveling surveys, according to the general principle of reduction which was explained in the serial paper (I). In Section 3, taking the heights of the bench marks in 1923.9 as the standard of reference, the accumulative variations in heights after 1923.9 at each bench mark along the western coast of the peninsula were calculated (Table II). The result is shown in Fig. 2 as the projective contour map with time dependence, and in Fig. 3 where the secular variations of 3 representative bench marks are plotted. From these two figures, it can be seen that all areas have been subsiding as a whole at the rate of about - 3.8 mm/yr in the period of 1923. 9-1963. 6. This subsidence is considered as the recovery motion of the crust after the abrupt upheaval due to the Great Kanto Earthquake. However, the disturbance of small amplitude began in 1946, and it continues up to the present showing somewhat regular oscillation. In Section 4, from the result of the levelings along the loop line in the peninsula which was completed in 1952, a contour map of equal crustal movements during 1952. 8-1963. 6 is made (Fig. 4). In Section 5, the yearly mean sea level at Aburatsubo during the period of 1923. 9-1963. 5 are analyzed after extracting the crustal movements of the fixed point. The secular variation of the corrected sea level can be dissolved into the eustatic uplift and the astronomical tide of 18.6 year period. Their numerical values are shown in the equation (3). The rate of the eustatic uplift is 2.13 mm/yr. In Section 6, the eustatic uplift and the long-period tide of 18.6 years are extracted from the yearly mean sea level during the period of 1897.5 N 1923. 9, and the secular variation of the crust at Aburatsubo is obtained. The abrupt upheaval of the crust at the instant of the earthquake is found to be 1.362 m. The featuae of the crustal movements in the pre-seismic period is very characteristic. As a whole, neither upheaval, nor subsidence could be seen. There existed, however, small disturbance of oscillation whose amplitude amounted to about 5 cm. The overall feature of the crustal movements during the period of 1897 1963 is illustrated in Fig.7

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Succeeding the previous report on the gravity survey in Torishima and Hachijojima, gravity survey in Niijima and Ooshima was carried out by the Geographical Survey Institute in November 1963. This work is also a part of the project for the geophysical study of Idzu-mariana arc islands. In Niijima 20 stations were observed and a general figure of the distribution of Bouguer anomalies was obtained. In Ooshima 33 stations were newly established and the Bouguer anomaly chart was drawn after combining the result with those of the gravity surveys by the Geological Survey of Japan and the Earthquake Research Institute. Reoccupation of some old gravity stations were made for detecting the secular change of gravity by the volcanic activity in Ooshima Island. From the comparison between the old and the new gravity values it may be concluded that after the great explosions of 1950-1951 change of gravity occured near Miharayama. Observed gravity difference is 0.8 mgal at most assuming unchangeableness of the gravity of the station at the Ooshima Meteorological Observatory.

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If g is the gravity value observed at point P at an elevation of H(m),
[g] + [corrections for topography] + [0.3086×H]-[normal gravity at point 0 on the geoid right under point P]
is usually taken to be the BOUGUER anomaly at point 0. This can be written as [g] + [corrections for topography] - [(normal gravity at point 0 ) - (0.3086 × H)]
Since the third term is the normal gravity at point P, this is equal to [g] + [corrections for topography] - [normal gravity at point P]
and is therefore more properly to be called the BOUGUER anomaly at point P, or the station BOUGUER anomaly, rather than the BOUGUER anomaly at point 0. The neglect of this differentiation between the BOUGUER anomaly at P and 0 in the customary procedures of reduction will sometimes cause no small errors in ravity interpretations.
In two-dimensional cases, if ΔG₀, ΔG₁, …BG₆ are station BOUGUER anomalies observed at horizontally equal intervals, 2π/6, but at various elevations, h₀, h₁, …h₆ (in radian), the real BOUGUER anomaly at χ=π on the geoid is given by the formula (8) in the text, where φ₀, φ₁, φ₂, φ₃, represent the respective coefficients of Δg3, Δg2, Δg1, Δg2 in the formula (6).
The formula (8) contains unknown Δg₈'s on its right hand side. The value of Δg₃ in various degrees of approximation can be obtained by replacing these Δg₈'s by their approximate values. In the formula (13), the innermost frame represents the zero-th approximation, the middle frame the first approximation, and the outermost frame the second approximation. Numerical values of 1/φ ₀, φ ₁ /φ ₀, φ₂ /φ₀, φ₃ /φ₀ are given in Table I.
Model calculations have shown that this method works satisfactorily, especially by the second apporoximation.

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