The theory of variant fields, as set forth in R-392-PR, "The Structure of Field Space," is based upon a Lagrangian formulation in which the Lagrangian function is assumed to have no preassigned transformation properties. The implications of this assumption are examined in the context of the transformation properties and the structure of the variant field equations. The salient results of the previous exposition are given, as modified by the transformation-theoretic problems of geometrizable field theories. 36 pp
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