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The conditions for equilibrium in an elastically stressed hexagonal aeolotropic medium (transversely isotropic) are formulated, and solutions are found in terms of two ‘harmonic’ functions ø1, ø2, which are solutions ofν1, ν2 being the roots of a certain quadratic equation.It is also shown that in the case of axially symmetrical stress systems the solution may be expressed in terms of the third-order differential coefficients of a single stress function Φ.The solutions for an isotropic medium may be deduced as a special case.The problems of nuclei of strain in such a hexagonal solid are solved, and the results for zinc and magnesium contrasted with those for an isotropic solid.

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The method of transforms (7), (2) is shown to be directly applicable to the case of axial symmetric stress distributions in hexagonal crystals. It is shown that solutions for problems of indentation of the hexagonal plane by rigid punches can be found for punches of arbitrary axial symmetric shape. Solutions are given in full for the cases of spherical, conical and circularly cylindrical punches.The same method is used to find the solutions for a material containing disk-shaped cracks between hexagonal planes and the results for the isotropic case deduced from the general solution.