Computation of the unbalance factor of a three-phase triangle when lengths of three sides are given

In an important paper read before the June 1918 Convention of the A. I. E. E., it was shown by Mr. C. L. Fortescue, that any dissymmetrical system of three-phase voltages or currents could be resolved, by vector methods, into a pair of symmetrical systems, one forward and the other backward. The numerical ratio of the latter to the former is called the unbalance factor of the system. Although several vector methods were developed in the paper and its discussion, for evaluating the forward and backward components when the dissymmetrical triangle is given, so far as is known to the writer, no scalar and purely numerical method of developing them has been published. As it is useful sometimes to compute the two components without recourse to vector methods or to the drawing board, a numerical method is here offered.