The problem of reduction of data, i.e., the derivation of the value of certain physically meaningful parameters which enter into the analytic description of the trend of the data, is solved by a generalization of the usual methods of fitting empirical curves. In taking a rather general point of view toward this method of trend analysis, the problem of “closeness of fit” is formulated in a new way and investigated briefly. Some applications of the method presented herein are to the problems of the analysis of radioactive samples, of the responses of electrical networks or electromechanical systems, of instrument records and vibrations including drift of the baseline of recording instruments, of variable illumination from stars, and of statistical distributions, and to the problem of differentiation of empirical data.

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