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A study is made of the free and forced oscillations of the earth. The natural periods are determined for radial, torsional and spheroidal types of oscillation. Several models of the earth are used: a homogeneous model, such as was assumed originally by Love, a model con­sisting of a homogeneous solid mantle enclosing a homogeneous liquid core, Bullen’s model B, and Bullard’s models I and II. It is found that the spheroidal oscillation of order 2 has a period of about 53·5 min in all models, except the homogeneous one, for which this period is only 44·3 min. The common period of 53·5 min agrees to within the observational error with the period of 57 min observed by Benioff on the seismograms of the Kamchatka earthquake of 1952. In contrast to all the other models, Bullen’s model B possesses an additional spheroidal oscillation of order 2 of a period of 101 min. The latter oscillation is confined mainly to the core, its amplitude in the mantle being relatively very small. Benioff’s observation of a second oscillation of a 100 min period in the Kamchatka earthquake record might be considered as evidence favouring Bullen’s model B. The latter differs from Bullard’s models mainly by having a central density of around 18 instead of about 12 g/cm 3 . However, a theoretical investigation of the relative excitation of the various free modes by an impulsive compressional point-source situated at a shallow focal depth, shows that the amplitude of the 100 min oscillation should be more than 1000 times weaker than that of the 53·5 min oscillation. It is thus not clear how a near-surface earthquake could have excited the core­-oscillation. The spectrum of the free modes of oscillation has also been determined for n = 3 and 4, including the fundamental and the first two overtones for each case. The computed free periods of spheroidal oscillation range from 53·5 min down to a period of 8 min for the fourth overtone in the case n = 2. We have also treated the bodily tides for Bullen’s and Bullard’s models. Love’s numbers were determined in the case n = 2 for tidal periods of 6, 6√2, 12 h and ∞. The dependence of the Love numbers on the period is small, a maximum range of variation of 13% occurring in the k -values between the periods of 6 h and ∞.

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The complete motion of an elastic quarter plane and of a three-quarter plane with free boundaries caused by an explosive point source, is obtained by finite difference methods.Varying ratio /?/a of the shear to compressional wave velocity shows that in the quarter plane the amplitude of motion at the corner increases with increasing /?/a, in the three-quarter plane it decreases. The motion in the quarter plane differs from the sum of reflections at perpendicular half planes. The amplitude of diffracted P waves varies mainly with distance from the corner. The amplitude of diffracted S waves varies mainly in angular direction. Comer-generated surface waves and elliptical particle motion in the waves are analysed. At the corner of a quarter plane, the amplitude of the Rayleigh wave is three to five times as large as on a half plane, the particle motion is elliptic and the major axes of the ellipses are inclined at 45" to the free surface.

ABSTRACT:A theory is developed for the effect of the earth's rotation on its spectrum. Each line is resolved *by rotation into a multiplet of (2n+1) lines, as in the Zeeman effect. A theory is also given of the intensity distribution in the lines of the multiplet for the case of a point-source.Good agreement is obtained between this theory and the doublets observed seismically and gravimetrically.