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A synchronous motor started as an induction motor must pass through an electro-mechanical transient after the field circuit is supplied with electrical excitation in order to change its action from that of an induction motor to that of a synchronous motor. The calculation of this problem has been difficult because the differential equation of motion is of a non-linear type of which no analytical solution has been made. The integraph at the Massachusetts Institute of Technology has given a new and direct method of solving equations of the type encountered in these pulling-into-step transients. In this paper are compiled the results of many integraph solutions which were made after combining the factors that influence the performance of such machines into ratios and relative factors so that the results will apply to all practical cases. From the solutions several generalizations are made which can be directly applied to determine whether or not any type of salient-pole synchronous motor will synchronize properly. These solutions take into account inertia, saliency, incompleteness of amortisseur windings, load, switching angle, and field current, and assume negligible armature resistance, negligible rotor leakage reactance, no saturation, constant load torque near synchronous speed, and negligible electrical transients. Oscillograph tests of a 160-hp. motor and a sample calculation are given.