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The paper discusses the measurement of simple and central moments of a one-dimensional density function. It is found that, if the incident function is multiplied by a scaling function which varies exponentially with time, these moments may be evaluated by the use of a circuit having repeated eigenvalues. A measuring system to evaluate the simple moments is synthetised, and it is indicated how this may be modified to find the central moments. The system obtained may be readily realised on an analogue computer. The relevance of these measurements to the problem of pattern recognition is discussed.