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Graphical methods of solving linear circuits in the steady state have been reviewed at various times  and recently it was suggested by Boehne  that "simpler straight line methods for Â¿-Y transformations might be sought." The present paper describes some novel constructions resulting from this search. The constructions are very simple for transforming any polyphase star or mesh, whatever the degree of unbalance, if the impedances are all of equal power factor. A star-connected circuit of any impedance and any number of phases may also be transformed graphically into a mesh circuit. The star-equivalent to a mesh circuit of four or more phases does not necessarily exist. If, however, the conditions for convertibility are satisfied, then the mesh circuit may also be transformed into its star-equivalent by means of a construction. The constructions are related to each other and similar to those for determining parallel impedances, which recently have become well known through repeated references in the technical press.