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The paper reviews the conditions under which triple harmonic voltages and currents are produced in Y-and delta-connected transformers. These voltages are produced by hysteresis in the core. In a single-phase transformer, increase of series resistance tends to suppress the current harmonic and produce the voltage harmonic. In three-phase transformers, a Y connection suppresses the current harmonic and allows the full flux and voltage harmonics to appear. Delta connection provides a closed path for the current harmonic, and suppresses the triple voltage. A case is cited where a Y-connected auto-transformer was used to step up from 6600 to 12,000 volts at a substation. The neutral was not grounded, and trouble resulted due to partial resonance at triple frequency between line capacity and transformer reactance. The paper shows that, although not generally recognized, a triple component can exist in the line-to-line e.m.f. wave of a three-phase system. This is possible in a case where a two-to-three-phase transformation is used, and when the e.m.f. wave of the two-phase generator contains a triple harmonic. Vector diagrams and curves are given illustrating this possible effect.