It can be shown easily that the Cross method of structural analysis may be applied to a given structure in such a manner that the process does not converge. In this paper the author gives necessary and sufficient conditions for the convergence of the Cross method, and exhibits a convergent process of balancing any given structure. In particular he shows that a balancing process can be described by real linear transformation, that is, by a matrix of real numbers, and that the process converges in the sense of this paper if and only if the infinite power of this matrix exists and is zero. The study is restricted to the case of a continuous beam.

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