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The characteristics of an anisotropic permanent magnetic when subjected to fields in the non-preferred direction, as well as the preferred one, is a subject which has not been explored in any depth except for some work on single crystals. An experiment is performed on a cylinder of anisotropic polymer-bonded rare-earth material, which can be subjected to relatively strong fields, either in the preferred or non-preferred direction, or in both. As a result of the observed interaction, a permeability tensor is proposed and evaluated for the particular material used in the experiment. The use of the tensor in a finite-element method of solution is explained and demonstrated.