Dynamic properties of marble and granite have been investigated at room temperatures, using bars of these rocks vibrating transversely at audio frequencies in free-free modes. The results are as follows;
1. Up to a critical strain amplitude, the internal friction and resonant frequency are almost independent of strain amplitude. When the strain amplitude exceeds this critical value, the internal friction increases and resonant frequency decreases.
2. The break point, i. e., the strain at which the internal friction becomes dependent of amplitude shifts to lower strain amplitudes as the relative humidity increases.
3. Previous thermal and static stress (cold work) histories experienced by test samples are found to have a large effect on the internal friction.
4. The internal friction and the longitudinal wave velocity are both almost independent of frequency with a range between 300 and 5, 000cps.

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The vertical distribution of amplitudes is studied for the M11 type dispersive Rayleigh wave which is propagated along the surface of a superficial layer overlying a semi-infinite elastic medium.
Among others, the case in which the velocity of the distortional wave in the substratum is lower than that in the superficial layer, that is to say, the case that the substratum is a low velocity layer, is especially investigated.
The results obtained are as follow.
(1) The amplitude distribution and the particle orbits of the M₁₁ waves are analogous to those of the nondispersive Rayleigh wave which is propagated along the surface of a semi-infinite elastic solid. This is true even if the substratum is a low velocity layer.
(2) If the substratum is rigid, the particle orbit for the waves of which the wave lengths are longer than about 4.6H (H: thickness of the superficial layer), is of an opposit sense in contrast with that for other waves in the existence domain.

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The variational calculus method is applied to the problem of surface waves propagating along a free surface of a semi-infinite elastic medium of variable density and elasticity.
Numerical examples are worked out for Love (§ 3) and Rayleigh waves (§ 5) in a medium of constant density and elasticity increasing linearly with the depth from the free surface-

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The essence of the dynamo theory of the earth's main magnetic field is that we have groups of magnetic fields which can be maintained stationarily by some fluid motions of a certain magnitude. The problem considered here is what the time characteristics of these groups of magnetic fields are when driven by motions of larger or smaller magnitude than those required just to keep the fields stationary. As expected, when driven by motions of larger or smaller magnitude, the fields develop or decay exponentially. In the second half of this paper, we have simplified the mathematics of induction of T₂⁰ field from S₁⁰ field by T₁⁰ motion, which is the most important process in the dynamo theory of the earth's magnetic field.

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A narrow canal is sometimes used in order to shield the platform on which a delicate instrument is placed from the disturbing vibrations caused by ground noises. The shielding effect of the canal was examined in a model experiment using an ultrasonic technique. Whenthe canal is as deep as 3/4 of the wave-length, the maximum amplitude of an elastic pulse decreases to 1/3 of that in the case without a canal. Several other types of canals were also examined. Even when the canal width is enlarged up to half of the wave-length, the shielding effect is not so. much improved in comparison with the case of a narrow canal. The increase in the number of narrow canals is also found to be not effective. When two narrow canals are dug at an interval of half of the wave-length, the maximum amplitude is about 70% of that in the case of a single canal. In actual cases, therefore, canals of any type scarcely serve the purpose of shielding.

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