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A basic equation of dynamical diffraction for an imperfect crystal is derived based on a general dynamical theory of diffraction. This equation is given in the form of a differential equation, and therefore can be considered to describe the diffraction processes locally inside a crystal. A phenomenological interpretation of this equation helps to fill in the gap between modern quantum mechanical treatments and ordinary treatments by dynamical theory of diffraction for a perfect crystal. In the approximation of poor resolution the more exact equation reduces to Takagi's equation. A necessary condition which makes Takagi's equation valid leads to the concept of local reciprocal lattice vectors.