This investigation is concerned with the foundations of the geometry of a continuum approximation to the deformation of a crystalline solid.nA method of formulating the infinitesimal deformation of a system of particles based on an averaging process is developed. This formulation is based on the construction of a "polyhedral mesh" valid for any system of particles whether or not they lie in a lattice configuration. However, when the particles lie in a perfect lattice, the mesh will be shown to yield the familiar definition of dislocation motion. The averaging process is then extended to include deformations at grain boundaries.
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