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The Differential Analyzer at the Massachusetts Institute of Technology has made possible the rapid and accurate solution of the idealized non-linear differential equations of motion of synchronous motors which describe the pulling-into-step transients. The purpose of this paper is to present the results of these solutions in a useable form. These results give a rather complete analysis of the phenomena, and thus enable the determination of the performance of practically any machine. One of the factors which is considered in this paper is the time constant of the field circuit with the armature short-circuited. Curves are given showing the additional load which may be synchronized when the field switching is angularly controlled to the best angle. The influence of salient poles has been considered as well as non-uniformity of the amortisseur winding. The practical application of the study is indicated by a numerical example.