Circular cones of internal and external refraction were shown to exist for light waves in optically biaxial crystals by Hamilton in 1833.Recently, a circular cone of internal refraction has been shown to exist for transverse elastic waves in a cubic crystal.An analysis is now presented which shows that an elliptic cone of internal refraction may exist for quasi-transverse waves of appropriate common normal propagated in a tetragonal crystal.Values of the elastic constants of zircon are used to illustrate the phenomenon.
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Michael Musgrave (1957) studied this question.