This is an investigation of the field due to a general-point source of energy in an isotropic, elastic solid with a free surface. The paper is divided into three parts;nIn Part I .we are concerned with the development of new plane wave representations for the fundamental solutions of elastodynamics. There are two types of situation involved;we have the simpler type involved in the case of a steady point source which moves steadily with any constant velocity in an elastic medium, this type Involves superposition of plane waves with respect to a single parameter, and we have the more complicated transient problem in which a point source is set up at a given moment, and thereafter moves at constant velocity, without change of strength:nIn Part II we make use of the new representation for the field of a steadily moving source in the calculation of fields and displacements in the presence of a free surface and in Part in we do the same for the transient source. We discuss in some detail the application of the new approach to the case of a vertical load, to a horizontal load, and to a couple of arbitrary orientation, and we give a general discussion of the singularities to be expected for die general point source.
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