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Assuming zero divergence, the equations of forced long waves in a uniformly rotating, homogeneous ocean are reduced to a single partial differential equation for the stream function. A shelf of exponential slope between a rigid continent and a sea of uniform depth is taken as a model, and certain other assumptions are made which appear physically reasonable. Calculations made on the basis of this simplified theory are in good qualitative agreement with observations of shelf waves, indicating that these waves are generated by the stress of the longshore component of the geostrophic wind.

The displacements due to a radiating point source in an infinite anisotropic elastic medium are found in terms of Fourier integrals. The integrals are evaluated asymptotically, yielding explicit expressions for displacements at points far from the source. The relative amplitudes of waves from a point source are thus determined, and it is found that although in general the decay of wave amplitudes is proportional to the distance from the source, it is possible that in certain directions the decay is less than this. The method used in this paper is also shown to be an alternative way of deriving known results concerning the geometry of the propagation of disturbances. As an example, the radiation in a transversely isotropic medium from an isolated force varying harmonically with time is discussed.

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A Green's function for a semi-infinite rotating ocean of uniform depth is obtained, and the resulting near and far fields are estimated asymptotically.Given a tide of uniform height at the mouth of a narrow channel on a semiinfinite ocean, the Green's function is used to calculate the diffracted Kelvin and Poincaré waves propagating up the channel and into the ocean.