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The gibbsian model for surfaces is reformulated in order to account for stress and strain within quasi-ideal crystals and on their surface. Tensor calculus, extensively used, leads to an invariant formalism. The symbols appearing therein are given a physical interpretation. The Second Principle, applied to the crystal-crystalline surface-vapour system, yields necessary equilibrium conditions. Herring's formula for the chemical potential is derived as a special case. The validity of the usual assumptions relating to shape equilibria are investigated.