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Until somewhat recently, synchronous machine theory has been satisfied with a relatively few characteristic constants, or reactances, in terms of which the behavior of machines has been calculated. Present theory, however, requires many more coefficients. There are now generally recognized two values each of leakage, synchronous, and transient reactance which correspond to the two symmetrical axes of magnetization of the armature current and which refer to balanced operation. Negative and zero phase-sequence reactances are also employed to determine operation under unbalanced conditions, and it is possible and desirable to distinguish other reactances. In view of the increasing complexity of the subject it is felt that a critical survey of it is in order and the object of the paper has been to provide that survey. The paper has been divided into two parts. Part I is descriptive, and treats the subject with regard to those factors which are important to application or operating engineers, and to designers. In particular, the major types of reactances which include the synchronous, transient, and phase-sequence reactances, are discussed. These quantities are defined and their methods of test outlined. It appears necessary to consider a second type of transient reactance, namely sub-transient reactance. Both reactances may be determined from short-circuit oscillograms as illustrated in the paper. A table is included which gives the numerical range of reactances for the various types of synchronous machines. Part II discusses the theoretical considerations, with a view to broadening and classifying existing conceptions of reactance.