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A Generalization of a Theorem of Dimensional Analysis

Any function relating several variables for which admissible scale transformations are specified is assumed to satisfy a functional equation that requires admissible transformations of the independent variables to effect only admissible transformations of the dependent variable. When there are not any dimensional constants that, in effect, cancel out the admissible transformations of the independent variables, this equation severely limits the possible functions relating the variables. The equation is solved for any finite number of variables that are either ratio or interval scales.