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The 2-port parameters of 4-terminal networks are often known. It is then simpler to supplement them rather than carry out a renewed complete analysis. A method is described for the analysis of linear reciprocal timeinvariant networks in terms of three parameters characterizing their behavior with respect to two disjoint ports and three further "balance" parameters, which are essentially open-circuit admittance parameters, thereby giving a complete description of 3-port 4-terminal networks. In the transmission line case the balance parameters are obtained as solutions of two-point boundary value problems, which in most common applications have simple solutions. The effects of parallel, series, and cascade connections of such networks are also investigated and the results can be regarded as generalizations of the cases satisfying the Brune conditions.