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The predetermination of the performance of a polyphase a-c. machine is greatly facilitated by the fact that at constant voltage and frequency its magnetic field is of constant intensity and rotating with uniform velocity. It is easy to form a mental picture of lines of ferce moving in space and being cut by conductors, which may be moving or stationary. Furthermore, the rate of cutting, and therefore the generated voltages, which form the basis for quantitative analysis, are readily determined by the relative motion of the flux and the conductors. Because of the ease with which a physical conception can be formed of a rotating magnetic field, the idea of considering a single-phase alternating field as made up of two oppositely rotating fields has been found very useful. In a paper entitled “A Physical Conception of the Operation of the Single-phase Induction Motor” Transactions A. I. E. E., Vol. XXXVII), Mr. B. G. Lamme has given an excellent description of single-phase induction motor operation based on a conception of two oppositely rotating magnetic fields. From the discussion of Mr. Lamme's paper, it appears to be the concensus of opinion that the method he uses furnishes the simplest and clearest physical conception of the single-phase motor. However, this is not the method usually employed in the quantitative analysis. Reference to text books will show that the mathematical treatment is usually based on the so called “cross field” theory. In this method the secondary induced voltage is considered made up of two components, one the voltage induced by transformer action of the alternating field and the other the voltage generated by rotation of the secondary conductors in the magnetic field. It has been argued against the method based on two oppositely rotating fields, also known as the “Rotating Field” theory, that it is more apt to lead to erroneous results, requires more expert handling and that it is an indir- ct method, being based on the previously determined performance of the polyphase motor. However, the main argument against it seems to be its limitation to induction motors only, and that it must be abandoned when we come to motors of the commutator type. Even those who otherwise favor the method appear to agree that it is not applicable to commutator motors as we are then no longer dealing with induction machines, but with shunt or series motors, as the case may be. The objection to the rotating field theory, that it is applicable to induction motors only, would be a serious one if it were valid. However, it will be shown in this paper that the theory can be readily applied to commutator machines also, and that so far from being more apt than other methods to lead to erroneous results, it undoubtedly furnishes the simplest and most direct means for mathematical deductions in the more complicated problems where three or more circuits are inductively related and moving with respect to one another.