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A polyphase induction motor provided with balanced windings on both stator and rotor can operate as a synchronous motor at a certain specified speed if each of these windings is connected to a balanced polyphase supply. Under the conditions of such double supply it can maintain this specified speed over a range of mechanical power output, thus exhibiting a synchronizing torque similar to that associated with the conventional synchronous machine. In addition to this synchronizing torque, there are present also torques which, being proportional to the speed of rotation, may be regarded as damping torques and which under certain circumstancesmay be negative, i.e. they may act in such a direction that a deviation from synchronous speed, though initially very small, will increase exponentially, thus making synchronous operation impossible. It is to the investigation of these damping torques that the discussion in this paper is directed, and they are considered in relation to the case which seems to present the greatest practical interestÂ¿that in which the stator and rotor are connected to the same busbars and in such sense as to give a synchronous speed which is twice that corresponding to the busbar frequency. Operating in this way the machine exhibits a negative damping torque which, in general, decreases with increase in rotor or stator leakage reactance but becomes positive over a small range of values of the coupling coefficient. It appears from the investigation that it is possible to design a motor for operation at the double synchronous speed which shall have a large positive damping torque and which will therefore be stable in operation.