SINGLE-PHASE INDUCTION MOTOR 97 as shunt motor, sparking is still more severe. Thus this method is used to a limited extent only. (c) By shifting the axis of armature or secondary polarization against the axis of inducing magnetism. This requires a secondary system, which is electrically un- symmetrical with regards to the primary system, and thus, since the secondary is movable with regards to the primary, requires means of changing the secondary circuit, that is, commutator brushes short-circuiting secondary coils in the position of effective torque, and open-circuiting them in the position of opposing torque. Thus this method leads to the various forms of repulsion motors, of series and of shunt characteristic. It has the serious objection of requiring a commutator and a corresponding armature winding; though the limitation is not quite as great as with the series or shunt motor, since in the re- pulsion motors the armature current is an induced secondary current, and the armature thus independent of the primary system regards current, voltage and number of turns. (d) By shifting the axis of magnetism, that is producing a magnetic flux displaced in phase and in position from that in- ducing the armature currents, in other words, a quadrature magnetic flux, such as at speed is being produced by the rotation. This method does not impose any limitation on stator and rotor design, requires no commutator and thus is the method almost universally employed. It thus may be considered somewhat more in detail. The infinite variety of arrangements proposed for producing a quadrature or starting flux can be grouped into three classes: A. Phase-splitting Devices.—The primary system of the single- phase induction motor is composed of two or more circuits displaced from each - other in position around the armature circumference, and combined with impedances of different in- ductance factors so as to produce a phase displacement between them. The motor circuits may be connected in series, and shunted by the impedance, or they may be connected in shunt with each other, but in series with their respective impedance, or they may be connected with each other by transformation, etc. B. Inductive Devices.—The motor is excited by two or more circuits which are in inductive relation with each other so as to produce a phase displacement. 7