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The operation of the single-phase induction motor is presented according to the cross-field theory as distinguished from the theory of oppositely rotating fields. The mathematics used require only a knowledge of algebra and trigonometry and no factors, such as cross-field iron loss and cross-field magnetizing current, are neglected. In addition to the derivation of the vector diagram, its transformation into an accurate circle diagram, which requires no assumption except sine wave voltage and primary field distribution, is shown. The result is a circle diagram practically identical with that derived by Branson (A. I. E. E. PROCEEDINGS, June, 1912) from comparison of the two-phase and single-phase induction motors, except that the derivation should be more easily followed and the result is a simpler diagram to construct and use.