The propagation of an electron through a crystal is conceived as involving two qualitatively different mechanisms, a quasifree motion as in empty space and a jumping from one localized state attached to an atom to another. A Hamiltonian containing two terms corresponding to these mechanisms is examined, and its behavior in the presence of a dislocation is studied. In particular, the case of a screw dislocation is investigated, and all the eigenfunctions are found under the assumption that there is no screening. The electron density in the neighborhood of the screw dislocation is computed. It is shown that there is a net repulsion of the electrons from the dislocation axis which results in a well denned positive effective charge per unit length, even though there is no volume change. © 1966.