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Recent advances in the theory of synchronous machines have introduced a large number of new constants. The method of symmetrical components requires sequence reactances, and an accurate theory of transients requires transient and subtransient reactances and time constants. Most of the published discussion on the constants has been concerned with the application, rather than the calculation of values. In this paper, all of the most significant constants are calculated, except the subtransient time constant. A general method of calculation is discussed in which the reactances are accurately resolved into components. Comparisons of test and calculated values are given. The formulas for salient-pole machines and turbine generators are given in Appendixes A and B. The principle of superposition is applied to resolve accurately the reactances into components which can be readily calculated. The induced currents in the field and additional damping circuits are accounted for simply by applying the constant interlinkage theorem.