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The power loss of transformer cores can still be considerably reduced by improved joint design based on new knowledge of the localized flux distribution, both in the corners and in the limbs. Rotational flux has been measured in the T-joints of experimental cores, and it has been found to cause localized high loss regions dependent on the joint design. Circulating harmonic fluxes have been found in individual laminations in the limbs of three-phase cores. The path of the harmonics is independent of joint design although their magnitudes are dependent. Circulating 3rd harmonics as large as 0.3 T have been found in a core magnetized sinusoidally at 1.6 T. These cause additional losses calculated to be 20% of the nominal core loss, and great savings would be possible if the circulating harmonics could be reduced or eliminated.