The general equations of a synchronous machine, with continuous regulation and connected by tieline to a large system, are reduced by small-departure methods to linear relationships from which is derived the characteristic equation for a particular situation.An examination of the coefficients of this equation over a range of operating levels shows that the results obtained for one operating point would be valid over a considerable range.Stability and dynamic response depend on the roots of the equation, and root-locus diagrams are introduced to demonstrate their value in displaying variations in performance of several parameters of the regulator circuit, such as gain, exciter time constant and the constants of certain derivative circuits used for stabilising.