The paper describes a method of solution of synchronous-machine transient-stability problems by a more exact electronic analogue representation of the system equations than has hitherto been employed. In the machine analysis emphasis is placed on the variation of field flux linkage during transient disturbances, and reasons are given why this is necessary. The equations of performance are derived in the most convenient form for analogue computing.The equivalent analogue interconnections are given both for time-varying and for constant field flux linkage. The components required for these analogues are considered briefly.The section on computer control deals with the control of integrators with reference to the introduction of ‘initial conditions’, ‘hold’ and ‘compute’ states. A delay unit is described which enables the switching out of a faulted transmission line to be simulated.The results of various problems solved by the computer are presented in graphical form as boundaries between stable and unstable states. It is shown how instability subsequent to the first rotor oscillation may occur, and an explanation is proposed to account for this phenomenon.Synchronous-machine and transmission-line analysis are excluded from the main text for clarity and are presented in detail in the Appendices.