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A vertical electric dipole over an electrically homogeneous sphere generates waves that propagate through the sphere, in addition to those that propagate around the sphere. Results of a quantitative analysis of the former are reported for the case where both the dipole and the point of observation lie on the spherical interface. The results are valid for a sphere whose radius is much larger than the wavelengths inside and outside the sphere. It is verified that the waves propagating through the sphere can be visualized in terms of ray optics. © 1999 American Institute of Physics.