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Knowledge of the internal magnetization distributions of polarizable media allows straightforward calculation of fields for any configuration which includes these media. Although useful calculations have been made using an assumed , little work directed at calculating has been done. This paper includes assumptions that, in addition to Maxwell's equations, are sufficient for determining the resultant integral equation. A method for the solution of this equation for is also presented. As an example, the nonuniform demagnetizing fields and magnetization distributions are calculated for cylinders of isotropic magnetic material. The results for these samples are compared with experimentally determined values and show average errors less than 9 percent for .