This paper deals with the motion of the earth s surface when a heavy body moves on it, on the assumption that the earth is a semi-infinite elastic solid. We assume further that the body is in uniform rectilinear motion, and exerts only normal pressure on the surface. Owing to mathematical difficulties and practical interest, we restrict ourselves to the motion of the surface.
To avoid the difficulties related to the convergence of integrals used in the text, we seek the solution assuming that the pressure is uniformly distributed in a circle of finite radios and let the radius tend to zero. We obtain the following results : (i) When the velocity of the body is larger thin those of propagation of both waves in the medium, the components of displacement are obtained in finite forms involving no integrals. (ii) When r lies between two wave-velocities, the solutions cannot be reduced to finite forms. (iii) When r is smaller than both wave-velocities, only the vertical component is expressible in a finite form. If r is very small, the horizontal components are obtained in series. In the case (i), the solutions take different forms for each region I, II, III in Fig. 12, 13, and vanish in I, as will be expected.
In the case (iii), if r is sufficiently small, the solutions ale symmetric in back and forth as in the static problem

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